166300. (VERSION 2020.05) total number of lines in file (including this line) 2 4. number of sections below 3 100. P first line number of P section 422400. Q first line number of Q section 525500. R first line number of R section 642500. S first line number of S section 7 8---------------------------------------------------------- 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100------------------------- *P* ZZZZZ-------------------- 101 102-----PAGE TEST----------------------------------------- 103 104PAGE TEST 105 106Name: 107 PAGE TEST 108 109Type: 110 Analysis Command 111 112Purpose: 113 Perform a Page test that k treatments have identical effects 114 against the alternative of ordered treatment effects. 115 116Description: 117 The Page test is a non-parametric test for analyzing randomized 118 complete block designs. It is derived from a Spearman's rho 119 rank correlation of the Friedman within block rankings and the 120 specified ordering of the treatments. The Page test statistic 121 is actually a monotonic function of Spearman's rho when there is 122 no ties in the data. 123 124 The distinction between the Friedman test and the Page test 125 is that the Page test is used when you want to test for ordered 126 effects. By ordered effects, we mean that treatment 1 is 127 less than or equal to treatment 2 which is less than or equal to 128 treatment 3 and so on (and at least one of these should be 129 strictly less than). 130 131 As with the Friedman test, assumes that there are k experimental 132 treatments (k >= 2). The observations are arranged in p blocks, 133 that is 134 135 Treatment 136 Block 1 2 ... k 137 1 X11 X12 ... X1k 138 2 X21 X22 ... X2k 139 3 X31 X32 ... X3k 140 ... ... ... ... ... 141 b Xb1 Xb2 ... Xbk 142 143 Let R(Xij) be the rank assigned to Xij within block i (i.e., 144 ranks within a given row). Average ranks are used in the case 145 of ties. The ranks are summed to obtain 146 147 R(j) = SUM[i=1 to b]R(X(ij)) 148 149 Then the Page test is 150 151 H0: The treatment effects have identical effects 152 Ha: mu1 <= mu2 <= .... <= mu3 or 153 mu1 >= mu2 >= .... >= mu3 154 Test Statistic: 155 The Page test statistic is 156 157 T4 = SUM[j=1 to k][j*R(j)] 158 159 In order to compare this to a standard normal distribution, 160 this statistic is transformed to 161 162 T5 = {T4 - b*k*(k+1)**2/4}/SQRT{b*(k**3 - k)**2/(144*(k-1))} 163 Significance Level: ALPHA 164 Critical Region: 165 T5 > NORPPF(ALPHA) where NORPPF is the normal percent point 166 function 167 Conclusion: Reject the null hypothesis if the test 168 statistic is in the critical region. 169 170Syntax: 171 PAGE TEST <y> <block> <treat> 172 <SUBSET/EXCEPT/FOR qualification> 173 where <y> is the response variable; 174 <block> is a variable that identifies the block; 175 <treat> is a variable that identifies the treatment; 176 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 177 178Examples: 179 PAGE TEST Y BLOCK TREATMENT 180 PAGE TEST Y X1 X2 181 PAGE TEST Y BLOCK TREATMENT SUBSET BLOCK > 2 182 183Note: 184 Dataplot formulates the test as a "less than or equal to" 185 test. That is, the treatment that is hypothesized to be 186 the smallest should be coded as 1, the treatment that is 187 hypothesized to be the second smallest should be coded as 2, 188 and so on. If your treatments are coded in the opposite order, 189 you can reverse them with the command 190 191 LET TREAT2 = FLIP TREAT 192 193Note: 194 In Dataplot, the variables should be given as: 195 196 Y BLOCK TREAT 197 X11 1 1 198 X12 1 2 199 ... 1 ... 200 X1k 1 k 201 X21 2 1 202 X22 2 2 203 ... 2 ... 204 X2k 2 k 205 206 ... ... ... 207 208 209 Xb1 b 1 210 Xb2 b 2 211 ... b ... 212 Xb3 b k 213 214 If your data are in a format similar to that given in the 215 DESCRIPTION section (i.e., you have colums Y1 to Yk, each 216 with b rows), you can convert it to the format required by 217 Dataplot with the commands: 218 219 LET NBLOCK = SIZE Y1 220 LET BLOCKID = SEQUENCE 1 1 NBLOCK 221 LET Y BLOCK TREAT = REPLICATED STACK Y1 Y2 Y3 Y4 Y5 BLOCKID 222 PAGE TEST Y BLOCK TREAT 223 224Note: 225 The response, ranked response, block, and treatment are 226 written to the file dpst1f.dat in the current directory. 227 228Note: 229 The Page test is based on the following assumptions: 230 231 1) The b rows are mutually independent. That means that 232 the results within one block (row) do not affect 233 the results within other blocks. 234 235 2) The data can be meaningfully ranked. 236 237Note: 238 The following statistics are also supported: 239 240 LET A = PAGE TEST Y X1 X2 241 LET A = PAGE TEST NORMALIZED Y X1 X2 242 LET A = PAGE TEST CDF Y X1 X2 243 LET A = PAGE TEST PVALUE Y X1 X2 244 245 The PAGE TEST returns the T4 value described above and the 246 PAGE TEST NORMALIZED returns the T5 value described above. 247 248 Enter HELP STATISTICS to see what commands can use these 249 statistics. 250 251Default: 252 None 253 254Synonyms: 255 None 256 257Related Commands: 258 FRIEDMAN TEST = Perform a Friedman test. 259 QUADE TEST = Perform a Quade test. 260 ANOVA = Perform an analysis of variance. 261 DURBIN TEST = Perform a Durbin test for two-way 262 incomplete balanced block designs. 263 COCHRAN TEST = Perform a Cochran test for two-way 264 complete block designs (binary data). 265 KRUSKAL WALLIS = Perform a Kruskall Wallis test. 266 BLOCK PLOT = Generate a block plot. 267 DEX SCATTER PLOT = Generates a dex scatter plot. 268 DEX ... PLOT = Generates a dex plot for a statistic. 269 270Reference: 271 Conover, "Practical Nonparametric Statistics", Third Edition, Wiley, 272 1999, pp. 380-383. 273 274 275Applications: 276 Analysis of Variance 277 278Implementation Date: 279 2013/2 280 281Program: 282 . Test Page test as given in 283 . Conover (1999), "Practical Non-Parametric Statistics" 284 . Third Edition, pp. 380-381. 285 . 286 read y treat block 287 79 1 1 288 78 1 2 289 72 1 3 290 66 1 4 291 75 1 5 292 64 1 6 293 68 1 7 294 70 1 8 295 76 2 1 296 76 2 2 297 74 2 3 298 65 2 4 299 75 2 5 300 66 2 6 301 70 2 7 302 72 2 8 303 77 3 1 304 76 3 2 305 77 3 3 306 68 3 4 307 72 3 5 308 65 3 6 309 68 3 7 310 78 3 8 311 84 4 1 312 80 4 2 313 78 4 3 314 72 4 4 315 74 4 5 316 69 4 6 317 74 4 7 318 76 4 8 319 82 5 1 320 80 5 2 321 75 5 3 322 65 5 4 323 77 5 5 324 68 5 6 325 70 5 7 326 77 5 8 327 end of data 328 . 329 let statval = page test y block treat 330 let statva2 = page test normalized y block treat 331 let cdf = page test cdf y block treat 332 let pval = page test pvalue y block treat 333 . 334 set write decimals 4 335 page test y block treat 336 337-----P CHART----------------------------------------------------- 338 339P CHART 340 341Name: 342 P CHART 343 344Type: 345 Graphics Command 346 347Purpose: 348 Generates a (binomial) proportion control chart. 349 350Description: 351 A P chart is a data analysis analysis technique for determining if 352 a measurement process has gone out of statistical control. The p 353 chart is sensitive to changes in the proportion of defective items 354 in the measurement process. The "p" in P CHART stands for the p 355 (the proportion of successes) of a binomial distribution. The p 356 control chart consists of: 357 Vertical axis = the proportion defectives for each sub-group; 358 Horizontal axis = the sub-group designation. 359 A sub-group is typically a time sequence (e.g., the number of 360 defectives in a daily production run where each day is considered a 361 sub-group). If the times are equally spaced, the horizontal axis 362 variable can be generated as a sequence (e.g., 363 LET X = SEQUENCE 1 1 N where N is the number of sub-groups). 364 365 In addition, horizontal lines are drawn at the mean number of 366 defectives and at the upper and lower control limits. The control 367 limits are calculated as: 368 UCL = pbar + 3*sqrt(pbar(1-pbar)/N) 369 LCL = pbar - 3*sqrt(pbar(1-pbar)/N) 370 where pbar is the total number of defectives divided by the total 371 number of items and N is the number of items in a given sub-group. 372 Also, zero serves as a lower bound on the LCL value. 373 374Syntax: 375 P CHART <y1> <y2> <x> <SUBSET/EXCEPT/FOR qualification> 376 where <y1> is a variable containing the number of defective 377 items in each sub-group; 378 <y2> is a variable containing the total number of items 379 in each sub-group; and 380 <x> is a variable containing the sub-group identifier 381 (usually 1, 2, 3, ...); 382 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 383 384Examples: 385 P CHART Y1 Y2 X 386 P CHART D T X 387 388Note: 389 The distribution of defective items is assumed to be Binomial. 390 This assumption is the basis for calculating the upper and lower 391 control limits. 392 393Note: 394 The P chart and NP chart are related to one another. The 395 distinction is that the P chart is used when sub-groups have equal 396 size (so the number of defectives is plotted) while the NP chart is 397 used when the sub-groups have unequal sample sizes (so the 398 percentage of defectives is plotted). 399 400Note: 401 The attributes of the 4 traces that make up the NP control chart 402 are controlled by the standard LINES, CHARACTERS, SPIKES, and BAR 403 commands. Trace 1 is the response variable, trace 2 is the mean 404 line, and traces 3 and 4 are the upper and lower control limits. 405 Some analysts prefer to draw the response variable as a character 406 or spike rather than a connected line. 407 408Default: 409 None 410 411Synonyms: 412 PROPORTION CHART for P CHART 413 414Related Commands: 415 NP CHART = Generates a Np control chart. 416 U CHART = Generates a U control chart. 417 C CHART = Generates an C control chart. 418 XBAR CHART = Generates an xbar control chart. 419 R CHART = Generates a range control chart. 420 S CHART = Generates a standard deviation control chart. 421 422 CHARACTERS = Sets the types for plot characters. 423 LINES = Sets the types for plot lines. 424 SPIKES = Sets the on/off switches for plot spikes. 425 BARS = Sets the on/off switches for plot bars. 426 PLOT = Generates a data or function plot. 427 LAG PLOT = Generates a lag plot. 428 4-PLOT = Generates a 4-plot for univariate analysis. 429 ANOP PLOT = Generates an ANOP plot. 430 431Applications: 432 Quality Control 433 434Implementation Date: 435 88/2 436 437Program: 438 . DEFECTIVE MOTORS 439 . 1. X = SUBGROUP ID (1 TO 25) 440 . 2. NUMDEF = NUMBER OF DEFECTIVE ITEMS IN SUB-GROUP 441 . 3. SIZE = TOTAL NUMBER OF ITEMS IN SUB-GROUP 442 . 443 SERIAL READ NUMDEF 444 14 19 19 24 15 16 38 40 21 32 40 25 39 36 17 19 4 9 12 26 445 END OF DATA 446 SERIAL READ SIZE 447 125 200 188 200 200 250 390 360 250 250 395 300 310 200 300 185 55 448 90 130 300 449 END OF DATA 450 LET X = SEQUENCE 1 1 20 451 . 452 LINES SOLID SOLID DOT DOT 453 XLIMITS 0 20 454 XTIC OFFSET 0 1 455 . YLIMITS 0 15 456 . YTIC OFFSET 2 0 457 . 458 P CONTROL CHART NUMDEF SIZE X 459 460-----PAPCDF (LET)-------------------------------- 461 462PAPCDF 463 464Name: 465 PAPCDF (LET) 466 467Type: 468 Library Function 469 470Purpose: 471 Compute the Polya-Aeppli cumulative distribution function. 472 473Description: 474 The formula for the Polya-Aeppli probability mass function is 475 476 p(x;theta,p) = EXP(-theta) x = 0 477 = EXP(-theta)*p**x*SUM[j=1 to x] 478 [(x-1 j-1)*(theta*(1-p)/p)**j/j!] 479 x = 1, ...; 480 0 < p < 1; theta > 0 481 482 with theta and <i>p</i> denoting the shape parameters. 483 484 The cumulative distribution function is computed using the 485 following recurrence relation (from page 379 of Johnson, 486 Kemp, and Kotz) 487 488 p(X+1) = (THETA*(1-P)/(X+1))*SUM[J=0 TO X] 489 [(X+1-J)*P**(X-J)*p(X)] 490 491Syntax: 492 LET <y> = PAPCDF(<x>,<theta>,<p>) 493 <SUBSET/EXCEPT/FOR qualification> 494 where <x> is a non-negative integer variable, number, or 495 parameter; 496 <theta> is a positive number or parameter that specifies 497 the first shape parameter; 498 <p> is a positive number or parameter that specifies 499 the second shape parameter; 500 <y> is a variable or a parameter where the computed 501 Polya-Aeppli cdf value is stored; 502 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 503 504Examples: 505 LET A = PAPCDF(3,3,0.5) 506 LET Y = PAPCDF(X1,2,0.3) 507 PLOT PAPCDF(X,2,0.3) FOR X = 0 1 20 508 509Note: 510 Library functions are distinguished from let subcommands 511 in the following ways. 512 1) Functions enclose the input value in parenthesis. Let 513 subcommands use spaces. 514 2) Functions can accept (and return) either parameters 515 (i.e., single values) or variables (i.e., an array of 516 values) while let subcommands are specific in which they 517 accept as input and what they return as output. 518 3) Functions can accept expressions while let subcommands 519 do not. For example, the following is legal: 520 LET Y2 = ABS(Y1-INT(Y1)) 521 For let subcommands, you typically have to do something 522 like the following: 523 LET YTEMP = Y**2 + 8 524 LET A = SUM YTEMP 525 526Default: 527 None 528 529Synonyms: 530 None 531 532Related Commands: 533 PAPCDF = Compute the Polya-Aeppli cumulative 534 distribution function. 535 PAPPDF = Compute the Polya-Aeppli probability 536 mass function. 537 LPOPDF = Compute the Lagrange-Poisson 538 percent point function. 539 BTAPDF = Compute the Borel-Tanner probability 540 mass function. 541 LOSPDF = Compute the lost games probability 542 mass function. 543 POIPDF = Compute the Poisson probability 544 density function. 545 HERPDF = Compute the Hermite probability 546 density function. 547 BINPDF = Compute the binomial probability 548 density function. 549 NBPDF = Compute the negative binomial 550 probability density function. 551 GEOPDF = Compute the geometric probability 552 density function. 553 554References: 555 Douglas (1980), "Analysis with Standard Contagious 556 Distributions", International Co-operative Publishing House, 557 Fairland, MD. 558 559 Evans (1953), "Experimental Evidence Concerning Contagious 560 Distributions in Ecology", Biometrika, 40, pp. 186-211. 561 562 Johnson, Kotz, and Kemp (1992), "Univariate Discrete 563 Distributions", Second Edition, Wiley, pp. 378-382. 564 565Applications: 566 Distributional Modeling 567 568Implementation Date: 569 2006/6 570 571Program: 572 title size 3 573 tic label size 3 574 label size 3 575 legend size 3 576 height 3 577 multiplot scale factor 1.5 578 x1label displacement 12 579 y1label displacement 17 580 . 581 multiplot corner coordinates 0 0 100 95 582 multiplot scale factor 2 583 label case asis 584 title case asis 585 case asis 586 tic offset units screen 587 tic offset 3 3 588 title displacement 2 589 y1label Probability 590 x1label X 591 . 592 ylimits 0 1 593 major ytic mark number 6 594 minor ytic mark number 3 595 xlimits 0 20 596 line blank 597 spike on 598 . 599 multiplot 2 2 600 . 601 title Theta = 0.5, P = 0.5 602 plot papcdf(x,0.5,0.5) for x = 1 1 20 603 . 604 title Theta = 1, P = 0.5 605 plot papcdf(x,1,0.5) for x = 1 1 20 606 . 607 title Theta = 2.5, P = 0.5 608 plot papcdf(x,2.5,0.5) for x = 1 1 20 609 . 610 title Theta = 5, P = 0.5 611 plot papcdf(x,5,0.5) for x = 1 1 20 612 . 613 end of multiplot 614 . 615 justification center 616 move 50 97 617 text Cumulative Distribution for Polya-Aeppli 618 619-----PAPPDF (LET)-------------------------------- 620 621PAPPDF 622 623Name: 624 PAPPDF (LET) 625 626Type: 627 Library Function 628 629Purpose: 630 Compute the Polya-Aeppli probability mass function. 631 632Description: 633 The formula for the Polya-Aeppli probability mass function is 634 635 p(x;theta,p) = EXP(-theta) x = 0 636 = EXP(-theta)*p**x*SUM[j=1 to x] 637 [(x-1 j-1)*(theta*(1-p)/p)**j/j!] 638 x = 1, ...; 639 0 < p < 1; theta > 0 640 641 with theta and <i>p</i> denoting the shape parameters. 642 643 The Polya-Aeppli distribution can be derived as a model for 644 the number of objects where the objects occur in clusters, 645 the clusters follow a Poisson distribution with shape 646 parameter theta, and the number of objects within a cluster 647 follows a geometric distribution with shape parameter p. 648 For this reason, this distribution is sometimes referred to 649 as a geometric Poisson distribution 650 651 Note that there are a number of alternative parameterizations 652 of this distribution in the literature. The parameterization 653 used above is the one given in Johnson, Kotz, and Kemp. 654 655 The moments of this distribution are: 656 657 mean = theta/(1-p) 658 variance = theta*(1+p)/(1-p)**2 659 skewess = (1+4*p+p**2)**2/((1+p)**3*theta)"> 660 kurtosis = 3 + (1+11*p+11*p**2+p**3)/((1+p)**2*theta) 661 662Syntax: 663 LET <y> = PAPPDF(<x>,<theta>,<p>) 664 <SUBSET/EXCEPT/FOR qualification> 665 where <x> is a non-negative integer variable, number, or 666 parameter; 667 <theta> is a positive number or parameter that specifies 668 the first shape parameter; 669 <p> is a positive number or parameter that specifies 670 the second shape parameter; 671 <y> is a variable or a parameter where the computed 672 Polya-Aeppli pdf value is stored; 673 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 674 675Examples: 676 LET A = PAPPDF(3,3,0.5) 677 LET Y = PAPPDF(X1,2,0.3) 678 PLOT PAPPDF(X,2,0.3) FOR X = 0 1 20 679 680Note: 681 Library functions are distinguished from let subcommands 682 in the following ways. 683 1) Functions enclose the input value in parenthesis. Let 684 subcommands use spaces. 685 2) Functions can accept (and return) either parameters 686 (i.e., single values) or variables (i.e., an array of 687 values) while let subcommands are specific in which they 688 accept as input and what they return as output. 689 3) Functions can accept expressions while let subcommands 690 do not. For example, the following is legal: 691 LET Y2 = ABS(Y1-INT(Y1)) 692 For let subcommands, you typically have to do something 693 like the following: 694 LET YTEMP = Y**2 + 8 695 LET A = SUM YTEMP 696 697Note: 698 For a number of commands utilizing the Polya-Aeppli 699 distribution, it is convenient to bin the data. There 700 are two basic ways of binning the data. 701 702 1) For some commands (histograms, maximum likelihood 703 estimation), bins with equal size widths are 704 required. This can be accomplished with the 705 following commands: 706 707 LET AMIN = MINIMUM Y 708 LET AMAX = MAXIMUM Y 709 LET AMIN2 = AMIN - 0.5 710 LET AMAX2 = AMAX + 0.5 711 CLASS MINIMUM AMIN2 712 CLASS MAXIMUM AMAX2 713 CLASS WIDTH 1 714 LET Y2 X2 = BINNED 715 716 2) For some commands, unequal width bins may be 717 helpful. In particular, for the chi-square goodness 718 of fit, it is typically recommended that the minimum 719 class frequency be at least 5. In this case, it may 720 be helpful to combine small frequencies in the tails. 721 Unequal class width bins can be created with the 722 commands 723 724 LET MINSIZE = <value> 725 LET Y3 XLOW XHIGH = INTEGER FREQUENCY TABLE Y 726 727 If you already have equal width bins data, you can 728 use the commands 729 730 LET MINSIZE = <value> 731 LET Y3 XLOW XHIGH = COMBINE FREQUENCY TABLE Y2 X2 732 733 The MINSIZE parameter defines the minimum class 734 frequency. The default value is 5. 735 736Note: 737 You can generate Polya-Aeppli random numbers, probability 738 plots, and chi-square goodness of fit tests with the 739 following commands: 740 741 LET N = VALUE 742 LET THETA = <value> 743 LET LAMBDA = <value> 744 LET Y = POLYA AEPPLI RANDOM NUMBERS FOR I = 1 1 N 745 746 POLYA AEPPLI PROBABILITY PLOT Y 747 POLYA AEPPLI PROBABILITY PLOT Y2 X2 748 POLYA AEPPLI PROBABILITY PLOT Y3 XLOW XHIGH 749 750 POLYA AEPPLI CHI-SQUARE GOODNESS OF FIT Y2 X2 751 POLYA AEPPLI CHI-SQUARE GOODNESS OF FIT Y3 XLOW XHIGH 752 753 To obtain the method of moments, the method of zero frequency 754 and the mean, and the weighted discrepancies estimates of 755 lambda and theta, enter the command 756 757 POLYA AEPPLI MAXIMUM LIKELIHOOD Y 758 POLYA AEPPLI MAXIMUM LIKELIHOOD Y2 X2 759 760 The method of moments estimates are 761 762 thetahat = 2*xbar**2/(s**2 + xbar) 763 phat = (s**2 - xbar)/(s^2 + xbar) 764 765 with xbar and s**2 denoting the sample mean and sample 766 variance, respectively. 767 768 The mean and zero frequency estimates are 769 770 thetahat = -LOG(f0/N)) 771 phat = 1 - thetahat/xbar 772 773 with f0 denoting the sample frequency at x = 0. 774 775 The method of the first two sample frequencies estimates 776 are 777 778 thetahat = -LOG(f0/N)) 779 phat = -f1/(f0LOG(f0/N)) 780 781 with f0 and f1 denoting the sample frequencies at 782 x = 0 and x = 1, respectively. 783 784 The maximum likelihood estimates are the solution to the 785 following equations 786 787 xbar - thetahat/(1-phat) = 0 788 789 xbar - SUM[i=1 to N][(f(j)*(j-1)*Phat(j-1)/(N*Phat(j)) = 0 790 791 with f(x) and Phat(x) denoting the frequency at x and the 792 Polya-Aeppli probaility mass function value at x, respectively. 793 794 You can generate estimates of theta and p based on the 795 maximum ppcc value or the minimum chi-square goodness of fit 796 with the commands 797 798 LET THETA1 = <value> 799 LET THETA2 = <value> 800 LET P1 = <value> 801 LET P2 = <value> 802 POLYA AEPPLI KS PLOT Y 803 POLYA AEPPLI KS PLOT Y2 X2 804 POLYA AEPPLI KS PLOT Y3 XLOW XHIGH 805 POLYA AEPPLI PPCC PLOT Y 806 POLYA AEPPLI PPCC PLOT Y2 X2 807 POLYA AEPPLI PPCC PLOT Y3 XLOW XHIGH 808 809 The default values of p1 and p2 are 0.05 and 0.95, 810 respectively. The default values of theta1 and theta2 811 are 1 and 25, respectively. Due to the discrete nature of 812 the percent point function for discrete distributions, the 813 ppcc plot will not be smooth. For that reason, if there is 814 sufficient sample size the KS PLOT (i.e., the minimum 815 chi-square value) is typically preferred. However, it may 816 sometimes be useful to perform one iteration of the PPCC PLOT 817 to obtain a rough idea of an appropriate neighborhood for the 818 shape parameters since the minimum chi-square statistic can 819 generate extremely large values for non-optimal values of the 820 shape parameter. Also, since the data is integer values, one 821 of the binned forms is preferred for these commands. 822 823Default: 824 None 825 826Synonyms: 827 None 828 829Related Commands: 830 PAPCDF = Compute the Polya-Aeppli cumulative 831 distribution function. 832 PAPPPF = Compute the Polya-Aeppli percent point 833 function. 834 LPOPDF = Compute the Lagrange-Poisson 835 probability mass function. 836 BTAPDF = Compute the Borel-Tanner probability 837 mass function. 838 LOSPDF = Compute the lost games probability 839 mass function. 840 POIPDF = Compute the Poisson probability 841 mass function. 842 HERPDF = Compute the Hermite probability 843 mass function. 844 BINPDF = Compute the binomial probability 845 mass function. 846 NBPDF = Compute the negative binomial 847 probability mass function. 848 GEOPDF = Compute the geometric probability 849 mass function. 850 INTEGER FREQUENCY TABLE = Generate a frequency table at 851 integer values with unequal bins. 852 COMBINE FREQUENCY TABLE = Convert an equal width frequency 853 table to an unequal width frequency 854 table. 855 KS PLOT = Generate a minimum chi-square plot. 856 MAXIMUM LIKELIHOOD = Perform maximum likelihood 857 estimation for a distribution. 858 859References: 860 Douglas (1980), "Analysis with Standard Contagious 861 Distributions", International Co-operative Publishing House, 862 Fairland, MD. 863 864 Evans (1953), "Experimental Evidence Concerning Contagious 865 Distributions in Ecology", Biometrika, 40, pp. 186-211. 866 867 Johnson, Kotz, and Kemp (1992), "Univariate Discrete 868 Distributions", Second Edition, Wiley, pp. 378-382. 869 870Applications: 871 Distributional Modeling 872 873Implementation Date: 874 2006/6 875 876Program: 877 let theta = 1.7 878 let p = 0.7 879 let y = polya aeppli random numbers for i = 1 1 500 880 . 881 let y3 xlow xhigh = integer frequency table y 882 class lower 0.5 883 class width 1 884 let amax = maximum y 885 let amax2 = amax + 0.5 886 class upper amax2 887 let y2 x2 = binned y 888 . 889 set write decimals 5 890 polya aeppli mle y 891 relative histogram y2 x2 892 limits freeze 893 pre-erase off 894 line color blue 895 plot pappdf(x,thetaml,pml) for x = 0 1 amax 896 limits 897 pre-erase on 898 line color black 899 let p = pml 900 let theta = thetaml 901 polya aeppli chi-square goodness of fit y3 xlow xhigh 902 case asis 903 justification center 904 move 50 97 905 text Theta = ^thetaml, P = ^pml 906 move 50 93 907 text Minimum Chi-Square = ^minks, 95% CV = ^cutupp95 908 . 909 label case asis 910 x1label P 911 x2label Curves Represent Values of Theta 912 y1label Minimum Chi-Square 913 let theta1 = 0.5 914 let theta2 = 5 915 let p1 = 0.3 916 let p2 = 0.9 917 polya aeppli chi-square plot y3 xlow xhigh 918 let theta = shape1 919 let p = shape2 920 polya aeppli chi-square goodness of fit y3 xlow xhigh 921 case asis 922 justification center 923 move 50 97 924 text Theta = ^theta, P = ^p 925 move 50 93 926 text Minimum Chi-Square = ^minks, 95% CV = ^cutupp95 927 928-----PAPPPF (LET)-------------------------------- 929 930PAPPPF 931 932Name: 933 PAPPPF (LET) 934 935Type: 936 Library Function 937 938Purpose: 939 Compute the Polya-Aeppli percent point function. 940 941Description: 942 The formula for the Polya-Aeppli probability mass function is 943 944 p(x;theta,p) = EXP(-theta) x = 0 945 = EXP(-theta)*p**x*SUM[j=1 to x] 946 [(x-1 j-1)*(theta*(1-p)/p)**j/j!] 947 x = 1, ...; 948 0 < p < 1; theta > 0 949 950 with theta and <i>p</i> denoting the shape parameters. 951 952 The cumulative distribution function is computed using the 953 following recurrence relation (from page 379 of Johnson, 954 Kemp, and Kotz) 955 956 p(X+1) = (THETA*(1-P)/(X+1))*SUM[J=1 TO X] 957 [(X+1-J)*P**(X-J)*p(X)] 958 959 The percent point function is computed by computing the 960 cumulative distribution function until the appropriate 961 probability is obtained. 962 963Syntax: 964 LET <y> = PAPPPF(<x>,<theta>,<p>) 965 <SUBSET/EXCEPT/FOR qualification> 966 where <x> is a integer variable, number, or parameter in the 967 interval (0,1); 968 <theta> is a positive number or parameter that specifies 969 the first shape parameter; 970 <p> is a positive number or parameter that specifies 971 the second shape parameter; 972 <y> is a variable or a parameter where the computed 973 Polya-Aeppli ppf value is stored; 974 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 975 976Examples: 977 LET A = PAPPPF(0.95,3,0.5) 978 LET Y = PAPPPF(P,2,0.3) 979 PLOT PAPPPF(P,2,0.3) FOR P = 0 0.01 0.99 980 981Note: 982 Library functions are distinguished from let subcommands 983 in the following ways. 984 1) Functions enclose the input value in parenthesis. Let 985 subcommands use spaces. 986 2) Functions can accept (and return) either parameters 987 (i.e., single values) or variables (i.e., an array of 988 values) while let subcommands are specific in which they 989 accept as input and what they return as output. 990 3) Functions can accept expressions while let subcommands 991 do not. For example, the following is legal: 992 LET Y2 = ABS(Y1-INT(Y1)) 993 For let subcommands, you typically have to do something 994 like the following: 995 LET YTEMP = Y**2 + 8 996 LET A = SUM YTEMP 997 998Default: 999 None 1000 1001Synonyms: 1002 None 1003 1004Related Commands: 1005 PAPCDF = Compute the Polya-Aeppli cumulative 1006 distribution function. 1007 PAPPDF = Compute the Polya-Aeppli probability 1008 mass function. 1009 LPOPDF = Compute the Lagrange-Poisson 1010 percent point function. 1011 BTAPDF = Compute the Borel-Tanner probability 1012 mass function. 1013 LOSPDF = Compute the lost games probability 1014 mass function. 1015 POIPDF = Compute the Poisson probability 1016 density function. 1017 HERPDF = Compute the Hermite probability 1018 density function. 1019 BINPDF = Compute the binomial probability 1020 density function. 1021 NBPDF = Compute the negative binomial 1022 probability density function. 1023 GEOPDF = Compute the geometric probability 1024 density function. 1025 1026References: 1027 Douglas (1980), "Analysis with Standard Contagious 1028 Distributions", International Co-operative Publishing House, 1029 Fairland, MD. 1030 1031 Evans (1953), "Experimental Evidence Concerning Contagious 1032 Distributions in Ecology", Biometrika, 40, pp. 186-211. 1033 1034 Johnson, Kotz, and Kemp (1992), "Univariate Discrete 1035 Distributions", Second Edition, Wiley, pp. 378-382. 1036 1037Applications: 1038 Distributional Modeling 1039 1040Implementation Date: 1041 2006/6 1042 1043Program: 1044 title size 3 1045 tic label size 3 1046 label size 3 1047 legend size 3 1048 height 3 1049 multiplot scale factor 1.5 1050 x1label displacement 12 1051 y1label displacement 17 1052 . 1053 multiplot corner coordinates 0 0 100 95 1054 multiplot scale factor 2 1055 label case asis 1056 title case asis 1057 case asis 1058 tic offset units screen 1059 tic offset 3 3 1060 title displacement 2 1061 x1label Probability 1062 y1label X 1063 . 1064 xlimits 0 1 1065 major xtic mark number 6 1066 minor xtic mark number 3 1067 . 1068 multiplot 2 2 1069 . 1070 title Theta = 0.5, P = 0.5 1071 plot papppf(x,0.5,0.5) for x = 0 0.01 0.99 1072 . 1073 title Theta = 1, P = 0.5 1074 plot papppf(x,1,0.5) for x = 0 0.01 0.99 1075 . 1076 title Theta = 2.5, P = 0.5 1077 plot papppf(x,2.5,0.5) for x = 0 0.01 0.99 1078 . 1079 title Theta = 5, P = 0.5 1080 plot papppf(x,5,0.5) for x = 0 0.01 0.99 1081 . 1082 end of multiplot 1083 . 1084 justification center 1085 move 50 97 1086 text Percent Point for Polya-Aeppli 1087 1088-----PARALLEL LINES-------------------------------------------------- 1089 1090PARALLEL LINES 1091 1092Name: 1093 PARALLEL LINES 1094 1095Type: 1096 LET Subcommand 1097 1098Purpose: 1099 Given a line defined by two points and a third point, find the line 1100 parallel to the first line and containing the third point. 1101 1102Syntax: 1103 LET <yout> <xout>= PARALLEL LINES <x1> <y1> <x2> <y2> <x3> <y3> 1104 <SUBSET/EXPCEPT/FOR qualification> 1105 where <x1> is a variable or parameter containing the x-coordinates for the 1106 first point of line one; 1107 <y1> is a variable or parameter containing the y-coordinates for the 1108 first point of line one; 1109 <x2> is a variable or parameter containing the x-coordinates for the 1110 second point of line one; 1111 <y2> is a variable or parameter containing the y-coordinates for the 1112 second point of line one; 1113 <x3> is a variable or parameter containing the x-coordinates for the 1114 third point; 1115 <y3> is a variable or parameter containing the y-coordinates for the 1116 third point; 1117 <yout> is a variable containing the y-coordinates of the 1118 second point of the parallel line; 1119 <xout> is a variable containing the x-coordinates of the 1120 second point of the parallel line; 1121 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 1122 1123Examples: 1124 LET YOUT XOUT = PARALLEL LINES X1 Y1 X2 Y2 X3 Y3 X4 Y4 1125 1126Default: 1127 None 1128 1129Synonyms: 1130 None 1131 1132Related Commands: 1133 POINTS IN POLYGON = Determine whether points are in the interior 1134 of a convex polygon. 1135 CONVEX HULL = Determine the convex hull of a set of points. 1136 TRANSFORM POINTS = Perform location, scale, and rotation 1137 transformation for a set of points. 1138 EXTREME POINTS = Determine the extreme points of a set of points. 1139 LINE INTERSECTIONS = Determine the intersection points for a set of 1140 lines. 1141 PERPINDICULAR LINE = Determine the coordinates for a point that defines 1142 a perpindicular line determined by a point and a line 1143 defined by two points. 1144 1145Applications: 1146 Computational Geometry 1147 1148Implementation Date: 1149 2012/10 1150 1151Program: 1152 dimension 40 columns 1153 skip 25 1154 read convhull.dat x y 1155 . 1156 let y2 x2 = 2d convex hull y x 1157 let xtemp = x2(1) 1158 let ytemp = y2(1) 1159 let y2 = combine y2 ytemp 1160 let x2 = combine x2 xtemp 1161 let x3 = x2 1162 let y3 = y2 1163 let n = size y2 1164 let nm1 = n - 1 1165 retain x2 y2 for i = 1 1 nm1 1166 retain x3 y3 for i = 2 1 n 1167 let slope = slope(x2,y2,x3,y3) 1168 let pdist = dpntline(xtemp,ytemp,x3,y3,slope) 1169 let xtempv = xtemp for i = 1 1 nm1 1170 let ytempv = ytemp for i = 1 1 nm1 1171 let y5 x5 = parallel line x2 y2 x3 y3 xtempv ytempv 1172 . 1173 set write decimals 4 1174 print "Anchor Point: (^xtemp,^ytemp)" 1175 print " " 1176 print " " 1177 print x2 y2 x3 y3 x5 y5 1178 1179-----PARALLEL COORDINATES PLOT-------------------------------------- 1180 1181PARALLEL COORDINATES PLOT 1182 1183Name: 1184 PARALLEL COORDINATES PLOT 1185 1186Type: 1187 Graphics Command 1188 1189Purpose: 1190 Generates an parallel coordinates plot. 1191 1192Description: 1193 A parallel coordinates plot is a graphical data analysis 1194 technique for plotting multivariate data. 1195 1196 In the parallel coordinates plot, a set of parallel axes 1197 are drawn for each variable. Then a given row of data 1198 is represented by drawing a line that connects the value 1199 of that row on each corresponding axis. For example, 1200 given the row of data (0, 1, 0) for variables X1, X2, and 1201 X3: 1202 1203 X3 +---------------------- 1204 1205 X2 ----------------------+ 1206 1207 X1 +---------------------- 1208 1209 0 1 1210 1211 The "+" positions identify plot coordinates (these would be 1212 connected on a graphics device). 1213 1214 Paralled coordinate plots were first recoginized as a 1215 data analysis tool by Ed Wegman (see the Reference section 1216 below). 1217 1218 There have been a number of variants of the parallel 1219 coordinate plots recommended in the literature. 1220 1221Syntax 1: 1222 PARALLEL COORDINATES PLOT <y1> <y2> ... <yk> 1223 <SUBSET/EXCEPT/FOR qualification> 1224 where <y1> through <yk> are the response variables; 1225 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 1226 1227Syntax 2: 1228 GROUP PARALLEL COORDINATES PLOT <y1> <y2> ... <yk> <tag> 1229 <SUBSET/EXCEPT/FOR qualification> 1230 where <y1> through <yk> are the response variables; 1231 <tag> is a group-id variable; 1232 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 1233 1234 With this syntax, the last variable listed is interpreted as 1235 a group-id variable. All rows of the response variable 1236 with the same group-id are plotted with the same line and 1237 character attributes. See the Note section below for 1238 additional clarification. 1239 1240Examples: 1241 PARALLEL COORDINATES PLOT Y1 Y2 Y3 Y4 Y5 1242 PARALLEL COORDINATES PLOT Y1 TO Y5 1243 PARALLEL COORDINATES PLOT Y1 Y2 Y3 Y4 Y5 SUBSET TAG > 2 1244 1245Note: 1246 For the GROUP PARALLEL COORDINATES PLOT case, you can use 1247 whatever numerical grouping scheme you find convenient. 1248 For example, you can use a categorical response variable 1249 that already provides grouping or you can define your own 1250 groups based on whatever criterion you find relevant. 1251 1252 However you define the original grouping, Dataplot automatically 1253 recodes the group id's as the integers from 1 to NG where NG is 1254 the number of groups. The coding is from smallest value of 1255 the original group id's to the largest value of the original 1256 group id's. 1257 1258 When the parallel coordinates plot is generated, observations 1259 with a group value of 1 use the first settings of the 1260 line and character settings, observations with a group value 1261 of 2 use the second settings of the line and character settings, 1262 and so on. 1263 1264Note: 1265 The data are typically scaled for a parallel coordinates 1266 plot. In Dataplot, you can use the following command: 1267 1268 SET PARALLEL COORDINATES PLOT STANDARDIZE <NONE/USCORE/ZSCORE> 1269 1270 where 1271 1272 NONE - means no scaling is applied 1273 USCORE - scales the data between 0 and 1 (specifically 1274 xscale = (x - xmin)/(xmax - xmin) 1275 ZSCORE - scales the data by subtracting the mean and 1276 dividing by the standard deviation 1277 1278 The default is USCORE. The NONE option is useful if you 1279 want to apply your own scaling. For example, you may 1280 want to scale the data based on the full data set, but only 1281 generate the parallel coordinates plot for a subset of the 1282 data. 1283 1284Note: 1285 By default, Dataplot draws the parallel axes on the 1286 vertical axis and the data scale on the horizontal axis. 1287 To reverse this, enter the command 1288 1289 HORIZONTAL SWITCH ON 1290 1291Note: 1292 The order of the variables on the plot can affect the 1293 appearance of the parallel coordinates plot. At the 1294 current time, Dataplot simply draws the axes 1295 in the order they are given on PARALLEL COORDINATES PLOT 1296 command. 1297 1298Note: 1299 Dataplot currently allows up to 30 variables to be plotted. 1300 1301Note: 1302 The TO syntax is allowed on this command. For example 1303 1304 PARALLEL COORDINATES PLOT Y1 TO Y10 1305 1306Default: 1307 None 1308 1309Synonyms: 1310 None 1311 1312Related Commands: 1313 LINES = Sets the types for plot lines. 1314 PLOT = Generates a data or function plot. 1315 ANDREWS PLOT = generate an Andrews plot. 1316 STAR PLOT = Generate a star plot. 1317 PROFILE PLOT = Generate a profile plot. 1318 1319Reference: 1320 "Hyperdimensional Data Analysis Using Parallel Coordinates", 1321 Edward Wegman, Journal of the American Statistical Association, 1322 85, 664-675. 1323 1324Applications: 1325 Multivariate Analysis 1326 1327Implementation Date: 1328 2003/3 1329 2003/5: Added the GROUP PARALLEL COORDINATE PLOT case. 1330 1331Program: 1332 ROW LIMITS 26 50 1333 COLUMN LIMITS 20 132 1334 READ AUTO79.DAT Y1 TO Y9 1335 . 1336 YLIMITS 0 8 1337 MAJOR YTIC MARK NUMBER 9 1338 MINOR YTIC MARK NUMBER 0 1339 Y1TIC MARK LABEL FORMAT ALPHA 1340 Y1TIC MARK LABEL CONTENT PRICE MPG 1978SP()REPAIR 1977SP()REPAIR ... 1341 HEADSP()ROOM REARSP()SEATCR()ROOM TRUNKSP()SPACE WEIGHT LENGTH 1342 YGRID ON 1343 TIC OFFSET UNITS SCREEN 1344 TIC OFFSET 3 3 1345 . 1346 PRE-SORT OFF 1347 FRAME CORNER COORDINATES 20 20 90 90 1348 PARALLEL COORDINATES PLOT Y1 TO Y9 1349 1350-----PARAMETER EXPANSION (SET)--------------------------------------- 1351 1352PARAMETER EXPANSION 1353 1354Name: 1355 PARAMETER EXPANSION (SET) 1356 1357Type: 1358 Set Subcommand 1359 1360Purpose: 1361 Specify whether parameters substituted for by the "^" 1362 character are expanded into a numeric or exponential format. 1363 1364Description: 1365 The "^" is normally used to substitute parameters into text 1366 strings for various types of labels. For this reason, a 1367 limited amount of precision is maintained. 1368 1369 The "^" can also be used to define a constant in a fit. In 1370 this case, more precision may be necessary. Setting 1371 PARAMETER EXPANSION to EXPONENTIAL will substitute the 1372 number as 1373 (0.number*10**(exp)) 1374 where number and exp are the values for the number in 1375 scientific notation. 1376 1377 In brief, setting this parameter to EXPONENTIAL is 1378 sometimes needed for fits. For all other purposes, you 1379 typically want this parameter set to NUMERIC. 1380 1381Syntax: 1382 SET PARAMETER EXPANSION <value> 1383 where <value> is NUMERIC or EXPONENTIAL. 1384 1385Examples: 1386 SET PARAMETER EXPANSION EXPONENTIAL 1387 SET PARAMETER EXPANSION NUMERIC 1388 1389Default: 1390 The default is NUMERIC. 1391 1392Synonyms: 1393 None 1394 1395Related Commands: 1396 ^ = Substitution character. 1397 FIT = Perform linear and non-linear fits. 1398 1399Applications: 1400 Fitting 1401 1402Implementation Date: 1403 2000/1 1404 1405Program: 1406 read richter.nice1 x y 1407 . 1408 set parameter expansion exponential 1409 let pii = 3.141592654 1410 let ee = 1.602177*(10**(-19)) 1411 let h = 6.6260755*(10**(-34)) 1412 let hb = h/(2*pii) 1413 let sn = (ee*ee)/(pii*h) 1414 . 1415 . 1416 let me = 9.10939*(10**(-31)) 1417 let mstar = 0.067*me 1418 . 1419 let minsig = 0.0028308966 1420 let ns = 3.342*(10**(15)) 1421 let mobility = minsig/(ee*ns) 1422 let taue = mstar*mobility/ee 1423 let kfermi = sqrt(2*pii*ns) 1424 let vfermi = kfermi*(hb/mstar) 1425 let d = (vfermi*vfermi*taue)/2.0 1426 . 1427 . 1428 let taup = 5 1429 let x0 = 9.36*(10**(-6)) 1430 . 1431 let function arg1 = (^hb)/(4*(^d)*(^ee)*(taup*(10**(-11)))*abs(x-x0)) 1432 let function arg2 = (^hb)/(4*(^d)*(^ee)*(^taue)*abs(x-x0)) 1433 let function arg3 = (taup*(10**(-11)))/(^taue) 1434 . 1435 let function f0 = (digamma(0.5+arg1)-digamma(0.5+arg2)+log(arg3)) 1436 let function f = (^sn)*(f0)+(^minsig) 1437 . 1438 fit y=f 1439 1440-----PARAMETER EXPAND DIGITS (SET)--------------------------------------- 1441 1442PARAMETER EXPAND DIGITS 1443 1444Name: 1445 PARAMETER EXPAND DIGITS (SET) 1446 1447Type: 1448 Set Subcommand 1449 1450Purpose: 1451 Specify the number of digits to the right of the decimal point 1452 when parameters are substituted by the "^" keyword. 1453 1454Description: 1455 The "^" is normally used to substitute parameters into text strings 1456 for various types of labels. For this reason, a limited amount of 1457 precision is maintained. The "^" can also be used to define a 1458 constant in a fit. In this case, more precision may be necessary. 1459 1460 The SET PARAMETER EXPAND DIGITS command can be used to specify 1461 exactly how many digits to use after the decimal point. Note that 1462 trailing digits will be included. 1463 1464Syntax: 1465 SET PARAMETER EXPAND DIGITS <value> 1466 where <value> is a numeric value. 1467 1468 If <value> is -1, then Dataplot will automatically determine the 1469 number of digits to use. If <value> is 0, the parameter will be 1470 expanded to an integer value. If <value> is a positive integer 1471 value, then the parameter will be expanded with <value> digits to 1472 the right of the decimal point. 1473 1474Examples: 1475 SET PARAMETER EXPAND DIGITS 8 1476 SET PARAMETER EXPAND DIGITS -1 1477 1478Note: 1479 The command SET PARAMETER EXPANSION EXPONENTIAL can be used to expand 1480 the parameter in exponential format. This can be useful when 1481 expanding the parameter in numerical computations (e.g., fitting). 1482 1483Note: 1484 The 2016/05 version of Dataplot expanded the default parameter 1485 expansion to handle up to 9 digits (prior to this, the limit was 1486 6 digits). 1487 1488 The 2016/05 version also increased the number of digits that can be 1489 used by the SET PARAMETER EXPAND DIGITS command from 9 to 15. 1490 1491 One distinction is that the default expansion does not include 1492 trailing zeros. If the SET PARAMETER EXPAND DIGITS command is used, 1493 trailing zeros will be included. 1494 1495Default: 1496 The default is -1 (i.e., Dataplot automatically determines the 1497 number of digits to use). 1498 1499Synonyms: 1500 None 1501 1502Related Commands: 1503 ^ = Substitution character. 1504 PARAMETER EXPANDSION (SET) = Specify whether parameter expansions 1505 are generated in real format or 1506 exponential format. 1507 1508Applications: 1509 Plot Labeling 1510 1511Implementation Date: 1512 2005/02<BR> 1513 2016/05: Increase maximum number of digits from 9 to 15.<BR> 1514 1515 1516Program: 1517 let a = .0001 1518 print "a = ^a" 1519 . 1520 let a = .00001 1521 print "a = ^a" 1522 . 1523 let a = .000001 1524 print "a = ^a" 1525 . 1526 let a = .0000001 1527 print "a = ^a" 1528 . 1529 let a = .00000001 1530 print "a = ^a" 1531 . 1532 let a = .000000001 1533 print "a = ^a" 1534 . 1535 let a = .0000000001 1536 print "a = ^a" 1537 . 1538 set parameter expand digits 9 1539 let a = .000000001 1540 print "a = ^a" 1541 . 1542 set parameter expand digits 10 1543 let a = .0000000001 1544 print "a = ^a" 1545 . 1546 set parameter expand digits 12 1547 let a = .000000000001 1548 print "a = ^a" 1549 1550-----PARCDF (LET)-------------------------------- 1551 1552PARCDF 1553 1554Name: 1555 PARCDF (LET) 1556 1557Type: 1558 Library Function 1559 1560Purpose: 1561 Compute the Pareto cumulative distribution function with 1562 shape parameters gamma and a. 1563 1564Description: 1565 The standard form of the Pareto cumulative distrubution 1566 function is: 1567 1568 F(x;gamma,a) = 1 - (a/x)**gamma x >= a; a, gamma > 0 1569 1570 with gamma and a denoting the tail length shape parameter 1571 and the lower bound parameter, respectively. 1572 1573 Note that although the a parameter is typically called a 1574 location parameter (and it is in the sense that it defines 1575 the lower bound), it is not a location parameter in the 1576 technical sense that the following relation does not hold: 1577 1578 f(x;gamma,a) = f((x-a);gamma,0) 1579 1580 with f denoting the probability density function. 1581 1582 For this reason, Dataplot treats a as a shape parameter. 1583 In Dataplot, the a shape parameter is optional with a 1584 default value of 1. 1585 1586Syntax: 1587 LET <y> = PARCDF(<x>,<gamma>,<a>,<loc>,<scale>) 1588 <SUBSET/EXCEPT/FOR qualification> 1589 where <x> is a variable, a number, or a parameter; 1590 <gamma> is a number or parameter that specifies the 1591 tail length shape parameter; 1592 <a> is a number or parameter that specifies the 1593 optional lower bound shape parameter; 1594 <loc> is a number or parameter that specifies the 1595 optional location parameter; 1596 <scale> is a number or parameter that specifies the 1597 optional scale parameter; 1598 <y> is a variable or a parameter (depending on what <x> is) 1599 where the computed Pareto cdf value is saved; 1600 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 1601 1602 The a, loc, and scale parameters are all optional. 1603 1604Examples: 1605 LET A = PARCDF(3,1.5) 1606 LET A = PARCDF(3,1.5,2) 1607 LET Y = PARCDF(X,GAMMA,A,LOC,SCALE) 1608 1609Note: 1610 The Pareto cumulative distribution can be extended with 1611 location and scale parameters by using the relationship 1612 1613 F(x;gamma,a,loc,scale) = F((x-loc)/scale;gamma,a,0,1) 1614 1615 Since a defines the lower bound, the location parameter is 1616 typically set to zero. 1617 1618Note: 1619 Library functions are distinguished from let subcommands 1620 in the following ways. 1621 1) Functions enclose the input value in parenthesis. Let 1622 subcommands use spaces. 1623 2) Functions can accept (and return) either parameters 1624 (i.e., single values) or variables (i.e., an array of 1625 values) while let subcommands are specific in which they 1626 accept as input and what they return as output. 1627 3) Functions can accept expressions while let subcommands 1628 do not. For example, the following is legal: 1629 LET Y2 = ABS(Y1-INT(Y1)) 1630 For let subcommands, you typically have to do something 1631 like the following: 1632 LET YTEMP = Y**2 + 8 1633 LET A = SUM YTEMP 1634 1635Default: 1636 None 1637 1638Synonyms: 1639 None 1640 1641Related Commands: 1642 PARPDF = Compute the Pareto probability density function. 1643 PARPPF = Compute the Pareto percent point function. 1644 GEPPDF = Compute the generalized Pareto probability density 1645 function. 1646 EV1PDF = Compute the extreme value type I probability density 1647 function. 1648 WEIPDF = Compute the Weibull probability density function. 1649 EXPPDF = Compute the exponential probability density function. 1650 1651Reference: 1652 "Continuous Univariate Distributions: Volume 1", Second Edition, 1653 Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 19. 1654 1655Applications: 1656 Distributional Modeling 1657 1658Implementation Date: 1659 1994/4 1660 1661Program: 1662 MULTIPLOT 2 2 1663 MULTIPLOT CORNER COORDINATES 0 0 100 95 1664 MULTIPLOT SCALE FACTOR 2 1665 . 1666 CASE ASIS 1667 TITLE CASE ASIS 1668 LABEL CASE ASIS 1669 TITLE DISPLACEMENT 2 1670 Y1LABEL DISPLACEMENT 15 1671 X1LABEL DISPLACEMENT 12 1672 Y1LABEL Probability 1673 X1LABEL X 1674 . 1675 TITLE Gamma = 1 1676 PLOT PARCDF(X,1) FOR X = 1 0.1 10 1677 TITLE Gamma = 2 1678 PLOT PARCDF(X,2) FOR X = 1 0.1 10 1679 TITLE Gamma = 5 1680 PLOT PARCDF(X,5) FOR X = 1 0.1 10 1681 TITLE Gamma = 0.5 1682 PLOT PARCDF(X,0.5) FOR X = 1 0.1 10 1683 END OF MULTIPLOT 1684 MOVE 50 97 1685 JUSTIFICATION CENTER 1686 TEXT Pareto CDF Functions 1687 1688-----PARCHAZ (LET)-------------------------------- 1689 1690PARCHAZ 1691 1692Name: 1693 PARCHAZ (LET) 1694 1695Type: 1696 Library Function 1697 1698Purpose: 1699 Compute the Pareto cumulative hazard function with shape 1700 parameters gamma and a. 1701 1702Description: 1703 The standard form of the Pareto cumulative hazard function 1704 is: 1705 1706 H(x;gamma,a) = gamma*LOG(x/a) x >= a; a, gamma > 0 1707 1708 with gamma and a denoting the tail length shape parameter 1709 and the lower bound parameter, respectively. 1710 1711 Note that although the a parameter is typically called a 1712 location parameter (and it is in the sense that it defines 1713 the lower bound), it is not a location parameter in the 1714 technical sense that the following relation does not hold: 1715 1716 H(x;gamma,a) = H((x-a);gamma,0) 1717 1718 with H denoting the cumulative hazard function. 1719 1720 For this reason, Dataplot treats a as a shape parameter. 1721 In Dataplot, the a shape parameter is optional with a 1722 default value of 1. 1723 1724Syntax: 1725 LET <y> = PARCHAZ(<x>,<gamma>,<a>,<loc>,<scale>) 1726 <SUBSET/EXCEPT/FOR qualification> 1727 where <x> is a variable, a number, or a parameter; 1728 <gamma> is a number or parameter that specifies the 1729 tail length shape parameter; 1730 <a> is a number or parameter that specifies the 1731 optional lower bound shape parameter; 1732 <loc> is a number or parameter that specifies the 1733 optional location parameter; 1734 <scale> is a number or parameter that specifies the 1735 optional scale parameter; 1736 <y> is a variable or a parameter (depending on what <x> is) 1737 where the computed Pareto cumulative hazard value 1738 is saved; 1739 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 1740 1741 The a, loc, and scale parameters are all optional. 1742 1743Examples: 1744 LET A = PARCHAZ(3,1.5) 1745 LET A = PARCHAZ(3,1.5,2) 1746 LET Y = PARCHAZ,GAMMA,A,LOC,SCALE) 1747 PLOT PARCHAZ(X,GAMMA,A,LOC,SCALE) FOR X = XSTART 0.01 XSTOP 1748 1749Note: 1750 The Pareto cumulative hazard function can be extended with 1751 location and scale parameters by using the relationship 1752 1753 H(x;gamma,a,loc,scale) = H((x-loc)/scale;gamma,a,0,1) 1754 1755 Since a defines the lower bound, the location parameter is 1756 typically set to zero. 1757 1758Note: 1759 Library functions are distinguished from let subcommands 1760 in the following ways. 1761 1) Functions enclose the input value in parenthesis. Let 1762 subcommands use spaces. 1763 2) Functions can accept (and return) either parameters 1764 (i.e., single values) or variables (i.e., an array of 1765 values) while let subcommands are specific in which they 1766 accept as input and what they return as output. 1767 3) Functions can accept expressions while let subcommands 1768 do not. For example, the following is legal: 1769 LET Y2 = ABS(Y1-INT(Y1)) 1770 For let subcommands, you typically have to do something 1771 like the following: 1772 LET YTEMP = Y**2 + 8 1773 LET A = SUM YTEMP 1774 1775Default: 1776 None 1777 1778Synonyms: 1779 None 1780 1781Related Commands: 1782 PARCDF = Compute the Pareto cumulative distribution function. 1783 PARHAZ = Compute the Pareto hazard function. 1784 PARPDF = Compute the Pareto probability density function. 1785 PARPPF = Compute the Pareto percent point function. 1786 GEPPDF = Compute the generalized Pareto probability density 1787 function. 1788 EV1PDF = Compute the extreme value type I probability density 1789 function. 1790 WEIPDF = Compute the Weibull probability density function. 1791 EXPPDF = Compute the exponential probability density function. 1792 1793Reference: 1794 "Continuous Univariate Distributions: Volume 1", Second Edition, 1795 Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 19. 1796 1797Applications: 1798 Distributional Modeling 1799 1800Implementation Date: 1801 1998/4 1802 1803Program: 1804 MULTIPLOT 2 2 1805 MULTIPLOT CORNER COORDINATES 0 0 100 95 1806 MULTIPLOT SCALE FACTOR 2 1807 . 1808 CASE ASIS 1809 TITLE CASE ASIS 1810 LABEL CASE ASIS 1811 TITLE DISPLACEMENT 2 1812 Y1LABEL DISPLACEMENT 15 1813 X1LABEL DISPLACEMENT 12 1814 Y1LABEL Cumulative Hazard 1815 X1LABEL X 1816 . 1817 TITLE Gamma = 1 1818 PLOT PARCHAZ(X,1) FOR X = 1 0.1 10 1819 TITLE Gamma = 2 1820 PLOT PARCHAZ(X,2) FOR X = 1 0.1 10 1821 TITLE Gamma = 5 1822 PLOT PARCHAZ(X,5) FOR X = 1 0.1 10 1823 TITLE Gamma = 0.5 1824 PLOT PARCHAZ(X,0.5) FOR X = 1 0.1 10 1825 END OF MULTIPLOT 1826 MOVE 50 97 1827 JUSTIFICATION CENTER 1828 TEXT Pareto Cumulative Hazard Functions 1829 1830-----PARETO PLOT--------------------------------------------------- 1831 1832PARETO PLOT 1833 1834Name: 1835 PARETO PLOT 1836 1837Type: 1838 Graphics Command 1839 1840Purpose: 1841 Generates a Pareto plot. 1842 1843Description: 1844 A Pareto plot is an ordered (largest to smallest) histogram with 1845 carry-along tags. The Pareto plot is used to answer the question-- 1846 "Which data values are most important, and which are least 1847 important?". The Pareto plot consists of: 1848 Vertical axis = ordered response value; 1849 Horizontal axis = dummy index (1 to n) where n is the number of 1850 response values. 1851 Like usual, the appearance of the trace is controlled by the first 1852 setting of the LINES, CHARACTERS, SPIKES, BARS, and similar 1853 attributes. 1854 1855Syntax: 1856 PARETO PLOT <y> <SUBSET/EXCEPT/FOR/qualification> 1857 where <y> is the response variable; 1858 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 1859 1860Examples: 1861 PARETO PLOT Y 1862 PARETO PLOT Y1 1863 PARETO PLOT Y SUBSET LAB 2 1864 1865Default: 1866 None 1867 1868Synonyms: 1869 None 1870 1871Related Commands: 1872 CHARACTERS = Sets the type for plot characters. 1873 CHARACTER FILL = Sets the fill switch (on/off) for characters. 1874 CHARACTER OFFSET = Sets the horizontal and vertical offset for 1875 characters. 1876 CHARACTER ANGLE = Sets the angle for characters 1877 LINES = Sets the type for plot lines. 1878 SPIKES = Sets the on/off switches for plot spikes. 1879 BARS = Sets the on/off switches for plot bars. 1880 BAR FILL = Sets the on/off switches for plot bar fills. 1881 BAR DIMENSION = Sets the dimension (2 or 3) for bars. 1882 BAR WIDTH = Sets the widths for plot bars. 1883 FONT = Sets the font. 1884 1885Applications: 1886 Quality Management 1887 1888Implementation Date: 1889 88/9 1890 1891Program: 1892 LET Y = DATA 9 4 13 11 19 8 11 10 1893 CHARACTERS CA FL IL MA NE NY OR TX 1894 CHARACTERS OFFSET 2 2 ALL 1895 CHARACTER ANGLE 45 ALL 1896 SPIKE ON ALL 1897 TITLE 1986 AUTO GAS TAX 1898 PARETO PLOT Y 1899 1900-----PARHAZ (LET)-------------------------------- 1901 1902PARHAZ 1903 1904Name: 1905 PARHAZ (LET) 1906 1907Type: 1908 Library Function 1909 1910Purpose: 1911 Compute the Pareto hazard function with shape parameters 1912 gamma and a. 1913 1914Description: 1915 The standard form of the Pareto hazard function is: 1916 1917 h(x;gamma,a) = gamma/x x >= a; a, gamma > 0 1918 1919 with gamma and a denoting the tail length shape parameter 1920 and the lower bound parameter, respectively. 1921 1922 Note that although the a parameter is typically called a 1923 location parameter (and it is in the sense that it defines 1924 the lower bound), it is not a location parameter in the 1925 technical sense that the following relation does not hold: 1926 1927 h(x;gamma,a) = h((x-a);gamma,0) 1928 1929 with h denoting the hazard function. 1930 1931 For this reason, Dataplot treats a as a shape parameter. 1932 In Dataplot, the a shape parameter is optional with a 1933 default value of 1. 1934 1935Syntax: 1936 LET <y> = PARHAZ(<x>,<gamma>,<a>,<loc>,<scale>) 1937 <SUBSET/EXCEPT/FOR qualification> 1938 where <x> is a variable, a number, or a parameter; 1939 <gamma> is a number or parameter that specifies the 1940 tail length shape parameter; 1941 <a> is a number or parameter that specifies the 1942 optional lower bound shape parameter; 1943 <loc> is a number or parameter that specifies the 1944 optional location parameter; 1945 <scale> is a number or parameter that specifies the 1946 optional scale parameter; 1947 <y> is a variable or a parameter (depending on what <x> is) 1948 where the computed Pareto hazard value is saved; 1949 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 1950 1951 The a, loc, and scale parameters are all optional. 1952 1953Examples: 1954 LET A = PARHAZ(3,1.5) 1955 LET A = PARHAZ(3,1.5,2) 1956 LET Y = PARHAZ,GAMMA,A,LOC,SCALE) 1957 PLOT PARHAZ(X,GAMMA,A,LOC,SCALE) FOR X = XSTART 0.01 XSTOP 1958 1959Note: 1960 The Pareto hazard function can be extended with location and 1961 scale parameters by using the relationship 1962 1963 h(x;gamma,a,loc,scale) = (1/scale)* 1964 h((x-loc)/scale;gamma,a,0,1) 1965 1966 Since a defines the lower bound, the location parameter is 1967 typically set to zero. 1968 1969Note: 1970 Library functions are distinguished from let subcommands 1971 in the following ways. 1972 1) Functions enclose the input value in parenthesis. Let 1973 subcommands use spaces. 1974 2) Functions can accept (and return) either parameters 1975 (i.e., single values) or variables (i.e., an array of 1976 values) while let subcommands are specific in which they 1977 accept as input and what they return as output. 1978 3) Functions can accept expressions while let subcommands 1979 do not. For example, the following is legal: 1980 LET Y2 = ABS(Y1-INT(Y1)) 1981 For let subcommands, you typically have to do something 1982 like the following: 1983 LET YTEMP = Y**2 + 8 1984 LET A = SUM YTEMP 1985 1986Default: 1987 None 1988 1989Synonyms: 1990 None 1991 1992Related Commands: 1993 PARCDF = Compute the Pareto cumulative distribution function. 1994 PARPDF = Compute the Pareto probability density function. 1995 PARPPF = Compute the Pareto percent point function. 1996 GEPPDF = Compute the generalized Pareto probability density 1997 function. 1998 EV1PDF = Compute the extreme value type I probability density 1999 function. 2000 WEIPDF = Compute the Weibull probability density function. 2001 EXPPDF = Compute the exponential probability density function. 2002 2003Reference: 2004 "Continuous Univariate Distributions: Volume 1", Second Edition, 2005 Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 19. 2006 2007Applications: 2008 Distributional Modeling 2009 2010Implementation Date: 2011 1998/4 2012 2013Program: 2014 MULTIPLOT 2 2 2015 MULTIPLOT CORNER COORDINATES 0 0 100 95 2016 MULTIPLOT SCALE FACTOR 2 2017 . 2018 CASE ASIS 2019 TITLE CASE ASIS 2020 LABEL CASE ASIS 2021 TITLE DISPLACEMENT 2 2022 Y1LABEL DISPLACEMENT 15 2023 X1LABEL DISPLACEMENT 12 2024 Y1LABEL Hazard 2025 X1LABEL X 2026 . 2027 TITLE Gamma = 1 2028 PLOT PARHAZ(X,1) FOR X = 1 0.1 10 2029 TITLE Gamma = 2 2030 PLOT PARHAZ(X,2) FOR X = 1 0.1 10 2031 TITLE Gamma = 5 2032 PLOT PARHAZ(X,5) FOR X = 1 0.1 10 2033 TITLE Gamma = 0.5 2034 PLOT PARHAZ(X,0.5) FOR X = 1 0.1 10 2035 END OF MULTIPLOT 2036 MOVE 50 97 2037 JUSTIFICATION CENTER 2038 TEXT Pareto Hazard Functions 2039 2040-----PARPDF (LET)-------------------------------- 2041 2042PARPDF 2043 2044Name: 2045 PARPDF (LET) 2046 2047Type: 2048 Library Function 2049 2050Purpose: 2051 Compute the Pareto probability density function with 2052 shape parameters gamma and a. 2053 2054Description: 2055 The standard form of the Pareto probability density 2056 function is: 2057 2058 f(x;gamma,a) = gammaa*a**gamma/(x**(gamma+1)) 2059 x >= a, a, gamma > 0 2060 2061 with gamma and a denoting the tail length shape parameter 2062 and the lower bound parameter, respectively. The default 2063 value of a is 1. 2064 2065 Note that although the a parameter is typically called a 2066 location parameter (and it is in the sense that it defines 2067 the lower bound), it is not a location parameter in the 2068 technical sense that the following relation does not hold: 2069 2070 f(x;gamma,a) = f((x-a);gamma,0) 2071 2072 For this reason, Dataplot treats a as a shape parameter. 2073 In Dataplot, the a shape parameter is optional with a 2074 default value of 1. 2075 2076Syntax: 2077 LET <y> = PARPDF(<x>,<gamma>,<a>,<loc>,<scale>) 2078 <SUBSET/EXCEPT/FOR qualification> 2079 where <x> is a variable, a number, or a parameter; 2080 <gamma> is a number or parameter that specifies the 2081 tail length shape parameter; 2082 <a> is a number or parameter that specifies the 2083 optional lower bound shape parameter; 2084 <loc> is a number or parameter that specifies the 2085 optional location parameter; 2086 <scale> is a number or parameter that specifies the 2087 optional scale parameter; 2088 <y> is a variable or a parameter (depending on what <x> is) 2089 where the computed Pareto pdf value is saved; 2090 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 2091 2092 The a, loc, and scale parameters are all optional. 2093 2094Examples: 2095 LET A = PARPDF(3,1.5) 2096 LET A = PARPDF(3,1.5,2) 2097 LET Y = PARPDF(X,GAMMA,A,LOC,SCALE) 2098 PLOT PARPDF(X,GAMMA,A,LOC,SCALE) FOR X = XSTART 0.01 XSTOP 2099 2100Note: 2101 The Pareto distribution can be extended with location and 2102 scale parameters by using the relationship 2103 2104 f(x;gamma,a,loc,scale) = (1/scale)*f(x;gamma,a,0,1) 2105 2106 Since a defines the lower bound, the location parameter is 2107 typically set to zero. 2108 2109Note: 2110 Pareto random numbers, probability plots, and goodness 2111 of fit tests can be generated with the commands: 2112 2113 LET GAMMA = <value> 2114 LET A = <value> 2115 LET Y = PARETO RANDOM NUMBERS FOR I = 1 1 N 2116 PARETO PROBABILITY PLOT Y 2117 PARETO PROBABILITY PLOT Y X 2118 PARETO PROBABILITY PLOT Y XLOW XHIGH 2119 PARETO KOLMOGOROV SMIRNOV GOODNESS OF FIT Y 2120 PARETO CHI-SQUARE GOODNESS OF FIT Y X 2121 PARETO CHI-SQUARE GOODNESS OF FIT Y XLOW XHIGH 2122 2123 The following commands can be used to estimate the shape 2124 parameters for the Pareto distribution: 2125 2126 LET GAMMA1 = <value> 2127 LET GAMMA2 = <value> 2128 LET A = <value> 2129 PARETO PPCC PLOT Y 2130 PARETO PPCC PLOT Y X 2131 PARETO PPCC PLOT Y XLOW XHIGH 2132 PARETO KS PLOT Y 2133 PARETO KS PLOT Y X 2134 PARETO KS PLOT Y XLOW XHIGH 2135 2136 The default values for gamma1 and gamma2 are 0.2 and 10, 2137 respectively. Note that only the gamma parameter is 2138 estimated for these plots. The default value of A is 1. 2139 If the value of A is greater than the data minimum, then 2140 it is automatically set to the data minimum. 2141 2142 You can generate maximum likelihood estimates for the Pareto 2143 distribution with the command 2144 2145 PARETO MAXIMUM LIKELIHOOD Y 2146 2147Note: 2148 Library functions are distinguished from let subcommands 2149 in the following ways. 2150 1) Functions enclose the input value in parenthesis. Let 2151 subcommands use spaces. 2152 2) Functions can accept (and return) either parameters 2153 (i.e., single values) or variables (i.e., an array of 2154 values) while let subcommands are specific in which they 2155 accept as input and what they return as output. 2156 3) Functions can accept expressions while let subcommands 2157 do not. For example, the following is legal: 2158 LET Y2 = ABS(Y1-INT(Y1)) 2159 For let subcommands, you typically have to do something 2160 like the following: 2161 LET YTEMP = Y**2 + 8 2162 LET A = SUM YTEMP 2163 2164Default: 2165 None 2166 2167Synonyms: 2168 None 2169 2170Related Commands: 2171 PARCDF = Compute the Pareto cumulative distribution function. 2172 PARPPF = Compute the Pareto percent point function. 2173 GEPPDF = Compute the generalized Pareto probability density 2174 function. 2175 EV1PDF = Compute the extreme value type I probability density 2176 function. 2177 WEIPDF = Compute the Weibull probability density function. 2178 EXPPDF = Compute the exponential probability density function. 2179 2180Reference: 2181 "Continuous Univariate Distributions: Volume 1", Second Edition, 2182 Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 19. 2183 2184Applications: 2185 Distributional Modeling 2186 2187Implementation Date: 2188 1994/4 2189 2190Program: 2191 MULTIPLOT 2 2 2192 MULTIPLOT CORNER COORDINATES 0 0 100 95 2193 MULTIPLOT SCALE FACTOR 2 2194 . 2195 CASE ASIS 2196 TITLE CASE ASIS 2197 LABEL CASE ASIS 2198 TITLE DISPLACEMENT 2 2199 Y1LABEL DISPLACEMENT 15 2200 X1LABEL DISPLACEMENT 12 2201 Y1LABEL Probability Density 2202 X1LABEL X 2203 . 2204 TITLE Gamma = 1 2205 PLOT PARPDF(X,1) FOR X = 1 0.1 10 2206 TITLE Gamma = 2 2207 PLOT PARPDF(X,2) FOR X = 1 0.1 10 2208 TITLE Gamma = 5 2209 PLOT PARPDF(X,5) FOR X = 1 0.1 10 2210 TITLE Gamma = 0.5 2211 PLOT PARPDF(X,0.5) FOR X = 1 0.1 10 2212 END OF MULTIPLOT 2213 . 2214 MOVE 50 97 2215 JUSTIFICATION CENTER 2216 TEXT Pareto PDF Functions 2217 2218-----PARPPF (LET)-------------------------------- 2219 2220PARPPF 2221 2222Name: 2223 PARPPF (LET) 2224 2225Type: 2226 Library Function 2227 2228Purpose: 2229 Compute the Pareto percent point function with shape 2230 parameters gamma and a. 2231 2232Description: 2233 The standard form of the Pareto percent point function is: 2234 2235 G(p;gamma,a) = a*(1-p)**(-1/gamma) 0 <= p < 1; 2236 a, gamma > 0 2237 2238 with gamma and a denoting the tail length shape parameter 2239 and the lower bound parameter, respectively. The default 2240 value of a is 1. 2241 2242 Note that although the a parameter is typically called a 2243 location parameter (and it is in the sense that it defines 2244 the lower bound), it is not a location parameter in the 2245 technical sense that the following relation does not hold: 2246 2247 G(p;gamma,a) = a + G(p;gamma,0) 2248 2249 For this reason, Dataplot treats a as a shape parameter. 2250 In Dataplot, the a shape parameter is optional with a 2251 default value of 1. 2252 2253Syntax: 2254 LET <y> = PARPPF(<p>,<gamma>,<a>,<loc>,<scale>) 2255 <SUBSET/EXCEPT/FOR qualification> 2256 where <p> is a variable, a number, or a parameter in the 2257 interval (0,1); 2258 <gamma> is a number or parameter that specifies the 2259 tail length shape parameter; 2260 <a> is a number or parameter that specifies the 2261 optional lower bound shape parameter; 2262 <loc> is a number or parameter that specifies the 2263 optional location parameter; 2264 <scale> is a number or parameter that specifies the 2265 optional scale parameter; 2266 <y> is a variable or a parameter (depending on what <p> 2267 is) where the computed Pareto ppf value is saved; 2268 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 2269 2270Examples: 2271 LET A = PARPPF(0.95,1.5) 2272 LET A = PARPPF(0.95,1.5,2) 2273 LET Y = PARPPF(P,GAMMA,A,LOC,SCALE) 2274 PLOT PARPPF(P,GAMMA,A,LOC,SCALE) FOR P = 0 0.01 0.99 2275 2276Note: 2277 The Pareto percent point function can be extended with 2278 location and scale parameters by using the relationship 2279 2280 G(p;gamma,a,loc,scale) = loc + scale*G(p;gamma,a,0,1) 2281 2282 Since a defines the lower bound, the location parameter is 2283 typically set to zero. 2284 2285Note: 2286 Library functions are distinguished from let subcommands 2287 in the following ways. 2288 1) Functions enclose the input value in parenthesis. Let 2289 subcommands use spaces. 2290 2) Functions can accept (and return) either parameters 2291 (i.e., single values) or variables (i.e., an array of 2292 values) while let subcommands are specific in which they 2293 accept as input and what they return as output. 2294 3) Functions can accept expressions while let subcommands 2295 do not. For example, the following is legal: 2296 LET Y2 = ABS(Y1-INT(Y1)) 2297 For let subcommands, you typically have to do something 2298 like the following: 2299 LET YTEMP = Y**2 + 8 2300 LET A = SUM YTEMP 2301 2302Default: 2303 None 2304 2305Synonyms: 2306 None 2307 2308Related Commands: 2309 PARCDF = Compute the Pareto cumulative distribution function. 2310 PARPDF = Compute the Pareto probability density function. 2311 GEPPDF = Compute the generalized Pareto probability density 2312 function. 2313 EV1PDF = Compute the extreme value type I probability density 2314 function. 2315 WEIPDF = Compute the Weibull probability density function. 2316 EXPPDF = Compute the exponential probability density function. 2317 2318Reference: 2319 "Continuous Univariate Distributions: Volume 1", Second Edition, 2320 Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 19. 2321 2322Applications: 2323 Distributional Modeling 2324 2325Implementation Date: 2326 1994/4 2327 2328Program: 2329 MULTIPLOT 2 2 2330 MULTIPLOT CORNER COORDINATES 0 0 100 95 2331 MULTIPLOT SCALE FACTOR 2 2332 . 2333 CASE ASIS 2334 TITLE CASE ASIS 2335 LABEL CASE ASIS 2336 TITLE DISPLACEMENT 2 2337 Y1LABEL DISPLACEMENT 15 2338 X1LABEL DISPLACEMENT 12 2339 X1LABEL Probability 2340 Y1LABEL X 2341 . 2342 TITLE Gamma = 1 2343 PLOT PARPPF(P,1) FOR P = 0 0.01 0.99 2344 TITLE Gamma = 2 2345 PLOT PARPPF(P,2) FOR P = 0 0.01 0.99 2346 TITLE Gamma = 5 2347 PLOT PARPPF(P,5) FOR P = 0 0.01 0.99 2348 TITLE Gamma = 0.5 2349 PLOT PARPPF(P,0.5) FOR P = 0 0.01 0.99 2350 END OF MULTIPLOT 2351 MOVE 50 97 2352 JUSTIFICATION CENTER 2353 TEXT Pareto PPF Functions 2354 2355-----PA2CDF (LET)-------------------------------- 2356 2357PA2CDF 2358 2359Name: 2360 PA2CDF (LET) 2361 2362Type: 2363 Library Function 2364 2365Purpose: 2366 Compute the Pareto cumulative distribution of the second 2367 kind with shape parameters gamma and a. 2368 2369Description: 2370 The standard form of the Pareto cumulative distribution 2371 function of the second kind is: 2372 2373 F(x;gamma,a) = 1 - a**gamma/(x+a)**gamma 2374 x, gamma, a > 0 2375 2376 with gamma and a denoting the shape parameters. The a 2377 parameter is optional and has a default value of 1. 2378 2379 The Pareto distribution of the second kind is sometimes 2380 referred to as the Lomax distribution. 2381 2382Syntax: 2383 LET <y> = PA2CDF(<x>,<gamma>,<a>,<loc>,<scale>) 2384 <SUBSET/EXCEPT/FOR qualification> 2385 where <x> is a variable, a number, or a parameter; 2386 <gamma> is a number or parameter that specifies the 2387 tail length shape parameter; 2388 <a> is a number or parameter that specifies the 2389 optional lower bound shape parameter; 2390 <loc> is a number or parameter that specifies the 2391 optional location parameter; 2392 <scale> is a number or parameter that specifies the 2393 optional scale parameter; 2394 <y> is a variable or a parameter (depending on what <x> is) 2395 where the computed Pareto cdf value is saved; 2396 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 2397 2398 The a, loc, and scale parameters are all optional. 2399 2400Examples: 2401 LET A = PA2CDF(3,1.5) 2402 LET X2 = PA2CDF(X1,GAMMA) 2403 2404Note: 2405 The Pareto cumulative distribution of the second kind can 2406 be extended with location and scale parameters by using the 2407 relationship 2408 2409 F(x;gamma,a,loc,scale) = F((x-loc)/scale;gamma,a,0,1) 2410 2411Note: 2412 Johnson, Kotz, and Balakrishnan (see Reference section below) 2413 define Pareto distributions of the first, second, third, and 2414 fourth kinds. Dataplot supports Pareto distributions of the 2415 first and second kinds. 2416 2417Note: 2418 Library functions are distinguished from let subcommands 2419 in the following ways. 2420 1) Functions enclose the input value in parenthesis. Let 2421 subcommands use spaces. 2422 2) Functions can accept (and return) either parameters 2423 (i.e., single values) or variables (i.e., an array of 2424 values) while let subcommands are specific in which they 2425 accept as input and what they return as output. 2426 3) Functions can accept expressions while let subcommands 2427 do not. For example, the following is legal: 2428 LET Y2 = ABS(Y1-INT(Y1)) 2429 For let subcommands, you typically have to do something 2430 like the following: 2431 LET YTEMP = Y**2 + 8 2432 LET A = SUM YTEMP 2433 2434Default: 2435 None 2436 2437Synonyms: 2438 None 2439 2440Related Commands: 2441 PA2PDF = Compute the Pareto second kind probability density 2442 function. 2443 PA2PPF = Compute the Pareto second kind percent point function. 2444 PARPDF = Compute the Pareto probability density function. 2445 GEPPDF = Compute the generalized Pareto probability density 2446 function. 2447 EV1PDF = Compute the extreme value type I probability density 2448 function. 2449 WEIPDF = Compute the Weibull probability density function. 2450 NORPDF = Compute the normal probability density function. 2451 LGNPDF = Compute the lognormal probability density function. 2452 EXPPDF = Compute the exponential probability density function. 2453 2454Reference: 2455 "Continuous Univariate Distributions: Volume 1", 2nd. Ed., 2456 Johnson, Kotz, and Balakrishnan, John Wiley, 1994, (chapter 20). 2457 2458Applications: 2459 Distributional Modeling, Income Distributions 2460 2461Implementation Date: 2462 1995/10 2463 2464Program: 2465 MULTIPLOT 2 2 2466 MULTIPLOT CORNER COORDINATES 0 0 100 95 2467 MULTIPLOT SCALE FACTOR 2 2468 . 2469 CASE ASIS 2470 TITLE CASE ASIS 2471 LABEL CASE ASIS 2472 TITLE DISPLACEMENT 2 2473 Y1LABEL DISPLACEMENT 15 2474 X1LABEL DISPLACEMENT 12 2475 Y1LABEL Probability 2476 X1LABEL X 2477 . 2478 LET A = 1 2479 TITLE Gamma = 0.1 2480 PLOT PA2CDF(X,0.1,A) FOR X = 0.01 0.01 5 2481 TITLE Gamma = 1 2482 PLOT PA2CDF(X,1,A) FOR X = 0.01 0.01 5 2483 TITLE Gamma = 2 2484 PLOT PA2CDF(X,2,A) FOR X = 0.01 0.01 5 2485 TITLE Gamma = 5 2486 PLOT PA2CDF(X,5,A) FOR X = 0.01 0.01 5 2487 END OF MULTIPLOT 2488 . 2489 MOVE 50 97 2490 JUSTIFICATION CENTER 2491 TEXT Pareto Second Kind CDF Functions 2492 2493-----PA2PDF (LET)-------------------------------- 2494 2495PA2PDF 2496 2497Name: 2498 PA2PDF (LET) 2499 2500Type: 2501 Library Function 2502 2503Purpose: 2504 Compute the Pareto probability density function of the second 2505 kind with shape parameters gamma and a. 2506 2507Description: 2508 The standard form of the Pareto probability density function 2509 of the second kind is: 2510 2511 f(x;gamma,a) = gamma*a**gamma/((a+x)**(gamma+1)) 2512 x, gamma > 0 2513 2514 with gamma and a denoting the shape parameters. The a 2515 parameter is optional and has a default value of 1. 2516 2517 The Pareto distribution of the second kind is sometimes 2518 referred to as the Lomax distribution. 2519 2520Syntax: 2521 LET <y> = PA2PDF(<x>,<gamma>,<a>,<loc>,<scale>) 2522 <SUBSET/EXCEPT/FOR qualification> 2523 where <x> is a variable, a number, or a parameter; 2524 <gamma> is a number or parameter that specifies the 2525 tail length shape parameter; 2526 <a> is a number or parameter that specifies the 2527 optional second shape parameter; 2528 <loc> is a number or parameter that specifies the 2529 optional location parameter; 2530 <scale> is a number or parameter that specifies the 2531 optional scale parameter; 2532 <y> is a variable or a parameter (depending on what <x> is) 2533 where the computed Pareto pdf value is saved; 2534 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 2535 2536 The a, loc, and scale parameters are all optional. 2537 2538Examples: 2539 LET A = PA2PDF(3,1.5) 2540 LET A = PA2PDF(3,1.5,0.5) 2541 LET X2 = PA2PDF(X1,GAMMA,A) 2542 PLOT PA2PDF(X,GAMMA,A) FOR X = 0 0.01 10 2543 2544Note: 2545 The Pareto distribution of the second kind can be extended with 2546 location and scale parameters by using the relationship 2547 2548 f(x;gamma,a,loc,scale) = (1/scale)*f(x;gamma,a,0,1) 2549 2550Note: 2551 Pareto second kind random numbers, probability plots, and 2552 goodness of fit tests can be generated with the commands: 2553 2554 LET GAMMA = <value> 2555 LET A = <value> 2556 LET Y = PARETO SECOND KIND RANDOM NUMBERS FOR I = 1 1 N 2557 PARETO SECOND KIND PROBABILITY PLOT Y 2558 PARETO SECOND KIND PROBABILITY PLOT Y X 2559 PARETO SECOND KIND PROBABILITY PLOT Y XLOW XHIGH 2560 PARETO SECOND KIND KOLMOGOROV SMIRNOV GOODNESS OF FIT Y 2561 PARETO SECOND KIND CHI-SQUARE GOODNESS OF FIT Y X 2562 PARETO SECOND KIND CHI-SQUARE GOODNESS OF FIT Y XLOW XHIGH 2563 2564 The following commands can be used to estimate the shape 2565 parameters for the Pareto distribution of the second kind: 2566 2567 LET GAMMA1 = <value> 2568 LET GAMMA2 = <value> 2569 LET A = <value> 2570 PARETO SECOND KIND PPCC PLOT Y 2571 PARETO SECOND KIND PPCC PLOT Y X 2572 PARETO SECOND KIND PPCC PLOT Y XLOW XHIGH 2573 PARETO SECOND KIND KS PLOT Y 2574 PARETO SECOND KIND KS PLOT Y X 2575 PARETO SECOND KIND KS PLOT Y XLOW XHIGH 2576 2577 The default values for gamma1 and gamma2 are 0.2 and 10, 2578 respectively. Note that only the gamma parameter is 2579 estimated for these plots. The default value of A is 1. 2580 2581Note: 2582 Johnson, Kotz, and Balakrishnan (see Reference section below) 2583 define Pareto distributions of the first, second, third, and 2584 fourth kinds. Dataplot supports Pareto distributions of the 2585 first and second kinds. 2586 2587Note: 2588 Library functions are distinguished from let subcommands 2589 in the following ways. 2590 1) Functions enclose the input value in parenthesis. Let 2591 subcommands use spaces. 2592 2) Functions can accept (and return) either parameters 2593 (i.e., single values) or variables (i.e., an array of 2594 values) while let subcommands are specific in which they 2595 accept as input and what they return as output. 2596 3) Functions can accept expressions while let subcommands 2597 do not. For example, the following is legal: 2598 LET Y2 = ABS(Y1-INT(Y1)) 2599 For let subcommands, you typically have to do something 2600 like the following: 2601 LET YTEMP = Y**2 + 8 2602 LET A = SUM YTEMP 2603 2604Default: 2605 None 2606 2607Synonyms: 2608 None 2609 2610Related Commands: 2611 PA2CDF = Compute the Pareto second kind cumulative 2612 distribution function. 2613 PA2PPF = Compute the Pareto second kind percent point function. 2614 PARPDF = Compute the Pareto probability density function. 2615 GEPPDF = Compute the generalized Pareto probability density 2616 function. 2617 EV1PDF = Compute the extreme value type I probability density 2618 function. 2619 WEIPDF = Compute the Weibull probability density function. 2620 NORPDF = Compute the normal probability density function. 2621 LGNPDF = Compute the lognormal probability density function. 2622 EXPPDF = Compute the exponential probability density function. 2623 2624Reference: 2625 "Continuous Univariate Distributions: Volume 1", 2nd. Ed., 2626 Johnson, Kotz, and Balakrishnan, John Wiley, 1994, (chapter 20). 2627 2628Applications: 2629 Distributional Modeling, Income Distributions 2630 2631Implementation Date: 2632 1995/10 2633 2634Program: 2635 MULTIPLOT 2 2 2636 MULTIPLOT CORNER COORDINATES 0 0 100 95 2637 MULTIPLOT SCALE FACTOR 2 2638 . 2639 CASE ASIS 2640 TITLE CASE ASIS 2641 LABEL CASE ASIS 2642 TITLE DISPLACEMENT 2 2643 Y1LABEL DISPLACEMENT 15 2644 X1LABEL DISPLACEMENT 12 2645 Y1LABEL Probability Density 2646 X1LABEL X 2647 . 2648 LET A = 1 2649 TITLE Gamma = 0.1 2650 PLOT PA2PDF(X,0.1,A) FOR X = 0.01 0.01 5 2651 TITLE Gamma = 1 2652 PLOT PA2PDF(X,1,A) FOR X = 0.01 0.01 5 2653 TITLE Gamma = 2 2654 PLOT PA2PDF(X,2,A) FOR X = 0.01 0.01 5 2655 TITLE Gamma = 5 2656 PLOT PA2PDF(X,5,A) FOR X = 0.01 0.01 5 2657 END OF MULTIPLOT 2658 . 2659 MOVE 50 97 2660 JUSTIFICATION CENTER 2661 TEXT Pareto Second Kind PDF Functions 2662 2663-----PA2PPF (LET)-------------------------------- 2664 2665PA2PPF 2666 2667Name: 2668 PA2PPF (LET) 2669 2670Type: 2671 Library Function 2672 2673Purpose: 2674 Compute the Pareto percent point function of the second 2675 kind with shape parameters gamma and a. 2676 2677Description: 2678 The standard form of the Pareto percent point function of 2679 the second kind is: 2680 2681 G(p;gamma,a) = (a**gamma/(1-p))**(1/gamma) - a 2682 0 < p < 1; gamma, a > 0 2683 2684 with gamma and a denoting the shape parameters. The a 2685 parameter is optional and has a default value of 1. 2686 2687 The Pareto distribution of the second kind is sometimes 2688 referred to as the Lomax distribution. 2689 2690Syntax: 2691 LET <y> = PA2PPF(<p>,<gamma>,<a>,<loc>,<scale>) 2692 <SUBSET/EXCEPT/FOR qualification> 2693 where <p> is a variable, a number, or a parameter in the 2694 interval (0,1); 2695 <gamma> is a number or parameter that specifies the 2696 tail length shape parameter; 2697 <a> is a number or parameter that specifies the 2698 optional lower bound shape parameter; 2699 <loc> is a number or parameter that specifies the 2700 optional location parameter; 2701 <scale> is a number or parameter that specifies the 2702 optional scale parameter; 2703 <y> is a variable or a parameter (depending on what <p> is) 2704 where the computed Pareto ppf value is saved; 2705 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 2706 2707 The a, loc, and scale parameters are all optional. 2708 2709Examples: 2710 LET A = PA2PPF(0.95,1.5) 2711 LET X2 = PA2PPF(X1,GAMMA) 2712 LET X2 = PA2PPF(X1,GAMMA,A) 2713 PLOT PA2PPF(X,GAMMA,A) FOR P = 0.01 0.01 0.99 2714 2715Note: 2716 The Pareto percent point of the second kind can be extended 2717 with location and scale parameters by using the relationship 2718 2719 G(p;gamma,a,loc,scale) = loc + scale*G(p;gamma,a,0,1) 2720 2721Note: 2722 Johnson, Kotz, and Balakrishnan (see Reference section below) 2723 define Pareto distributions of the first, second, third, and 2724 fourth kinds. Dataplot supports Pareto distributions of the 2725 first and second kinds. 2726 2727Note: 2728 Library functions are distinguished from let subcommands 2729 in the following ways. 2730 1) Functions enclose the input value in parenthesis. Let 2731 subcommands use spaces. 2732 2) Functions can accept (and return) either parameters 2733 (i.e., single values) or variables (i.e., an array of 2734 values) while let subcommands are specific in which they 2735 accept as input and what they return as output. 2736 3) Functions can accept expressions while let subcommands 2737 do not. For example, the following is legal: 2738 LET Y2 = ABS(Y1-INT(Y1)) 2739 For let subcommands, you typically have to do something 2740 like the following: 2741 LET YTEMP = Y**2 + 8 2742 LET A = SUM YTEMP 2743 2744Default: 2745 None 2746 2747Synonyms: 2748 None 2749 2750Related Commands: 2751 PA2CDF = Compute the Pareto second kind cumulative 2752 distribution function. 2753 PA2PDF = Compute the Pareto second kind probability density 2754 function. 2755 PARPDF = Compute the Pareto probability density function. 2756 GEPPDF = Compute the generalized Pareto probability density 2757 function. 2758 EV1PDF = Compute the extreme value type I probability density 2759 function. 2760 WEIPDF = Compute the Weibull probability density function. 2761 NORPDF = Compute the normal probability density function. 2762 LGNPDF = Compute the lognormal probability density function. 2763 EXPPDF = Compute the exponential probability density function. 2764 2765Reference: 2766 "Continuous Univariate Distributions: Volume 1", 2nd. Ed., 2767 Johnson, Kotz, and Balakrishnan, John Wiley, 1994, (chapter 20). 2768 2769Applications: 2770 Distributional Modeling, Income Distributions 2771 2772Implementation Date: 2773 1995/10 2774 2775Program: 2776 MULTIPLOT 2 2 2777 MULTIPLOT CORNER COORDINATES 0 0 100 95 2778 MULTIPLOT SCALE FACTOR 2 2779 . 2780 CASE ASIS 2781 TITLE CASE ASIS 2782 LABEL CASE ASIS 2783 TITLE DISPLACEMENT 2 2784 Y1LABEL DISPLACEMENT 15 2785 X1LABEL DISPLACEMENT 12 2786 X1LABEL Probability 2787 Y1LABEL X 2788 . 2789 LET A = 1 2790 TITLE Gamma = 0.1 2791 PLOT PA2PPF(P,0.1,A) FOR P = 0.01 0.01 0.99 2792 TITLE Gamma = 1 2793 PLOT PA2PPF(P,1,A) FOR P = 0.01 0.01 0.99 2794 TITLE Gamma = 2 2795 PLOT PA2PPF(P,2,A) FOR P = 0.01 0.01 0.99 2796 TITLE Gamma = 5 2797 PLOT PA2PPF(P,5,A) FOR P = 0.01 0.01 0.99 2798 END OF MULTIPLOT 2799 . 2800 MOVE 50 97 2801 JUSTIFICATION CENTER 2802 TEXT Pareto Second Kind PPF Functions 2803 2804-----PARTIAL CORRELATION (LET)-------------------------------- 2805 2806PARTIAL CORRELATION 2807 2808Name: 2809 PARTIAL CORRELATION (LET) 2810 2811Type: 2812 Let Subcommand 2813 2814Purpose: 2815 Compute the partial correlation coefficient between two variables 2816 given the effect of a third variable. 2817 2818Description: 2819 The standard correlation coefficient is a measure of the linear 2820 relationship between two variables. It is computed as: 2821 2822 r = Sxy/SQRT(Sxx*Syy) 2823 2824 where 2825 2826 Sxx = SUM[i=1 to N][(X(i)-XMEAN)**2] 2827 Syy = SUM[i=1 to N][(Y(i)-YMEAN)**2] 2828 Sxy = SUM[i=1 to N][(X(i)-XMEAN)*(Y(i)-YMEAN)] 2829 2830 A perfect linear relationship yields a correlation coefficient of 2831 +1 (or -1 for a negative relationship) and no linear relationship 2832 yields a correlation coefficient of 0. 2833 2834 Partial correlation is the correlation between two variables 2835 after removing the effect of one or more additional variables. This 2836 command is specifcally for the the case of one additional variable. 2837 In this case, the partial correlation can be computed based on 2838 standard correlations between the three variables as follows: 2839 2840 r12.3 = (r12 - r13*r23)/SQRT((1 - r13**2)*(1 - r23**2)) 2841 2842 with rxy denoting the correlation between x and y. 2843 2844 As with the standard correlation coefficient, a value of +1 indicates 2845 a perfect positive linear relationship, a value of -1 indicates a 2846 perfect negative linear relationship, and a value of 0 indicates no 2847 linear relationship. 2848 2849 It may be of interest to determine if the partial correlation 2850 is significantly different than 0. The CDF value for this 2851 test is 2852 2853 CDF = FCDF(VAL,1,N-3) 2854 2855 where FCDF is the F cumulative distribution function with 2856 1 and N - 3 degrees of freedom (N is the number of observations) 2857 and VAL = ABS((N-3)*R**2/(1 - R**2)) with R denoting the 2858 computed partial correlation. The pvalue is 1 - CDF. 2859 2860Syntax 1: 2861 LET <par> = PARTIAL CORRELATION <y1> <y2> <y3> 2862 <SUBSET/EXCEPT/FOR qualification> 2863 where <y1> is the first response variable; 2864 <y2> is the second response variable; 2865 <y3> is the third response variable; 2866 <par> is a parameter where the computed partial correlation is 2867 saved; 2868 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 2869 2870Syntax 2: 2871 LET <par> = PARTIAL CORRELATION ABSOLUTE VALUE <y1> <y2> <y3> 2872 <SUBSET/EXCEPT/FOR qualification> 2873 where <y1> is the first response variable; 2874 <y2> is the second response variable; 2875 <y3> is the third response variable; 2876 <par> is a parameter where the absolute value of the computed 2877 partial correlation is saved; 2878 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 2879 2880 This syntax computes the absolute value of the partial correlation 2881 coefficient. This is typically used in screening applications where 2882 there is an interest in identifying high magnitude correlations 2883 regardless of the direction of the correlation. 2884 2885Syntax 3: 2886 LET <par> = PARTIAL CORRELATION PVALUE <y1> <y2> <y3> 2887 <SUBSET/EXCEPT/FOR qualification> 2888 where <y1> is the first response variable; 2889 <y2> is the second response variable; 2890 <y3> is the third response variable; 2891 <par> is a parameter where the computed partial correlation 2892 pvalue is saved; 2893 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 2894 2895 This syntax computes the pvalue (described above) of the partial 2896 correlation. 2897 2898Syntax 4: 2899 LET <par> = PARTIAL CORRELATION CDF <y1> <y2> <y3> 2900 <SUBSET/EXCEPT/FOR qualification> 2901 where <y1> is the first response variable; 2902 <y2> is the second response variable; 2903 <y3> is the third response variable; 2904 <par> is a parameter where the computed partial correlation 2905 cdf is saved; 2906 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 2907 2908 This syntax computes the cdf (described above) of the partial 2909 correlation. 2910 2911Examples: 2912 LET A = PARTIAL CORRELATION Y1 Y2 Z 2913 LET A = PARTIAL CORRELATION Y1 Y2 Z SUBSET TAG > 2 2914 LET A = PARTIAL CORRELATION ABSOLUTE VALUE Y1 Y2 Z 2915 LET A = PARTIAL CORRELATION PVALUE Y1 Y2 Z 2916 LET A = PARTIAL CORRELATION CDF Y1 Y2 Z 2917 2918Note: 2919 The three variables must have the same number of elements. 2920 2921Note: 2922 Dataplot statistics can be used in a number of commands. For 2923 details, enter 2924 2925 HELP STATISTICS 2926 2927Default: 2928 None 2929 2930Synonyms: 2931 None 2932 2933Related Commands: 2934 PARTIAL CORRELATION MATRIX = Compute the matrix of partial 2935 correlations. 2936 PARTIAL RANK CORRELATION = Compute the partial rank 2937 correlation. 2938 PARTIAL KENDALL TAU CORRELATION = Compute the partial Kendall tau 2939 correlation. 2940 CORRELATION MATRIX = Compute the matrix of correlations. 2941 CORRELATION = Compute the correlation. 2942 RANK CORRELATION = Compute the rank correlation. 2943 KENDALL TAU CORRELATION = Compute the Kendall tau correlation. 2944 2945Reference: 2946 Conover (1999), "Practical Nonparametric Statistics", Third Edition, 2947 Wiley, p. 327. 2948 2949 Peavy, Bremer, Varner, Hogben (1986), "OMNITAB 80: 2950 An Interpretive System for Statistical and Numerical 2951 Data Analysis," NBS Special Publication 701. 2952 2953Applications: 2954 Linear Regression 2955 2956Implementation Date: 2957 2012/06 2958 2959Program: 2960 . This data is from page 202 of 2961 . 2962 . Peavy, Bremer, Varner, Hogben (1986), "OMNITAB 80: 2963 . An Interpretive System for Statistical and Numerical 2964 . Data Analysis," NBS Special Publication 701. 2965 . 2966 . Original source of the data is from 2967 . Draper and Smith (1981), "Applied Regression Analysis", 2968 . Wiley, p. 373. 2969 . 2970 dimension 40 columns 2971 . 2972 read matrix m 2973 42.2 11.2 31.9 167.1 2974 48.6 10.6 13.2 174.4 2975 42.6 10.6 28.7 160.8 2976 39.0 10.4 26.1 162.0 2977 34.7 9.3 30.1 140.8 2978 44.5 10.8 8.5 174.6 2979 39.1 10.7 24.3 163.7 2980 40.1 10.0 18.6 174.5 2981 45.9 12.0 20.4 185.7 2982 end of data 2983 . 2984 set write decimals 4 2985 let c1 = partial correlation m1 m2 m3 2986 let c2 = partial correlation absolute value m1 m2 m3 2987 let c3 = partial correlation cdf m1 m2 m3 2988 let c4 = partial correlation pvalue m1 m2 m3 2989 print c1 c2 c3 c4 2990 2991-----PARTIAL CORRELATION MATRIX (LET)-------------------------------- 2992 2993PARTIAL CORRELATION MATRIX 2994 2995Name: 2996 PARTIAL CORRELATION MATRIX (LET) 2997 2998Type: 2999 Let Subcommand 3000 3001Purpose: 3002 Compute the partial correlation matrix of a matrix. 3003 3004Description: 3005 The partial correlation matrix computes the partial correlation 3006 coefficients of the columns of a matrix. That is, row i and column j 3007 of the partial correlation matrix is the partial correlation between 3008 column i and column j of the original matrix. This partial 3009 correlation between column i and column j is the correlation 3010 between these two columns after removing the effects of the 3011 remaining columns. Note that the diagonal elements of the 3012 partial correlation matrix will be 1 (since they are the partial 3013 correlation of a column with itself). The partial correlation matrix 3014 is also symmetric (since the partial correlation of column i with 3015 column j is the same as the partial correlation of column j with 3016 column i). 3017 3018 The algorithm for computing the partial correlations is: 3019 3020 1) Compute the standard correlation matrix. 3021 3022 2) Invert this correlation matrix. 3023 3024 3) Compute 3025 3026 r(ij.) = -r(ij)/SQRT(r(ii)*r(jj)) 3027 3028 where r(ij) is the (i,j)-th element of the inverted 3029 correlation matrix. 3030 3031 Alternatively, you can compute the CDF or the p-value for the 3032 partial correlation coefficients (i.e., to see if the partial 3033 correlation coefficient is significantly different than zero). 3034 The CDF value is 3035 3036 CDF = FCDF(VAL,1,N-NC) 3037 3038 where FCDF is the F cumulative distribution function with 3039 1 and N - NC degrees of freedom (N is the number of observations 3040 and NC is the number of columns in the input matrix), and 3041 3042 VAL = ABS((N-NC)*R**2/(1 - R**2)) 3043 3044 with R denoting the computed partial correlation. The pvalue is 3045 1 - CDF. 3046 3047Syntax 1: 3048 LET <mat2> = PARTIAL CORRELATION MATRIX <mat1> 3049 <SUBSET/EXCEPT/FOR qualification> 3050 where <mat1> is a matrix for which the partial correlations are to be 3051 computed; 3052 <mat2> is a matrix where the resulting partial correlations are 3053 saved; 3054 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 3055 rarely used in this context. 3056 3057Syntax 2: 3058 LET <mat2> = PARTIAL CORRELATION CDF MATRIX <mat1> 3059 <SUBSET/EXCEPT/FOR qualification> 3060 where <mat1> is a matrix for which the partial correlation CDF's are 3061 to be computed; 3062 <mat2> is a matrix where the resulting partial correlation CDF's 3063 are saved; 3064 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 3065 rarely used in this context. 3066 3067 This syntax computes the CDF's of the partial correlation 3068 coefficients. 3069 3070Syntax 3: 3071 LET <mat2> = PARTIAL CORRELATION PVALUE MATRIX <mat1> 3072 <SUBSET/EXCEPT/FOR qualification> 3073 where <mat1> is a matrix for which the partial correlation p-value's 3074 are to be computed; 3075 <mat2> is a matrix where the resulting partial correlation 3076 p-values's are saved; 3077 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 3078 rarely used in this context. 3079 3080 This syntax computes the p-values of the partial correlation 3081 coefficients. 3082 3083Examples: 3084 LET C = PARTIAL CORRELATION MATRIX A 3085 3086Note: 3087 By default, the partial correlation matrices are computed on the 3088 columns. That is, element (i,j) of the partial correlation matrix 3089 is the partial correlation between column i and column j of the 3090 input matrix. 3091 3092 To specify a partial correlation matrix based on rows rather than 3093 columns, enter the command 3094 3095 SET MATRIX CORRELATION DIRECTION ROW 3096 3097 To reset column based partial correlations, enter 3098 3099 SET MATRIX CORRELATION DIRECTION COLUMN 3100 3101Note: 3102 By default the Pearson correlation coefficient is computed. 3103 To specify a different type of correlation, enter the command 3104 3105 SET CORRELATION TYPE <DEFAULT/RANK/WINSORIZED/ 3106 BIWEIGHT MIDCORRELATION/PERCENTAGE BEND/KENDALL TAU> 3107 3108 To see the definitions for these, enter 3109 3110 HELP RANK CORRELATION 3111 HELP KENDALLS TAU 3112 HELP BIWEIGHT MIDCORRELATION 3113 HELP PERCENTAGE BEND 3114 3115Note: 3116 Matrices are created with either the READ MATRIX command or the 3117 MATRIX DEFINITION command. Enter HELP MATRIX DEFINITION and HELP 3118 READ MATRIX for details. 3119 3120Note: 3121 The columns of a matrix are accessible as variables by appending an 3122 index to the matrix name. For example, the 4x4 matrix C has 3123 columns C1, C2, C3, and C4. These columns can be operated on like 3124 any other DATAPLOT variable. 3125 3126Note: 3127 The maximum size matrix that DATAPLOT can handle is set when 3128 DATAPLOT is built on a particular site. The default maximums are 3129 100 columns and 100 rows. 3130 3131Default: 3132 None 3133 3134Synonyms: 3135 None 3136 3137Related Commands: 3138 PARTIAL CORRELATION = Compute the partial correlation of three 3139 variables. 3140 CORRELATION MATRIX = Generate the correlation matrix. 3141 CORRELATION = Compute the correlation of two variables. 3142 RANK CORRELATION = Compute the rank correlation of two 3143 variables. 3144 KENDALLS TAU = Compute the Kendall tau correlation of two 3145 variables. 3146 WINSORIZED CORRELATION = Compute the Winsorized correlation of two 3147 variables. 3148 BIWEIGHT MIDCORRELATION = Compute the biweight mid-correlation of 3149 two variables. 3150 PERCENTAGE BEND CORRELATION = Compute the percentage bend correlation of 3151 two variables. 3152 COVARIANCE = Compute the covariance of two variables. 3153 3154Applications: 3155 Linear Fitting 3156 3157Implementation Date: 3158 2012/06 3159 3160Program: 3161 . This data is from page 202 of 3162 . 3163 . Peavy, Bremer, Varner, Hogben (1986), "OMNITAB 80: 3164 . An Interpretive System for Statistical and Numerical 3165 . Data Analysis," NBS Special Publication 701. 3166 . 3167 . Original source of the data is from 3168 . Draper and Smith (1981), "Applied Regression Analysis", 3169 . Wiley, p. 373. 3170 . 3171 dimension 40 columns 3172 . 3173 read matrix m 3174 42.2 11.2 31.9 167.1 3175 48.6 10.6 13.2 174.4 3176 42.6 10.6 28.7 160.8 3177 39.0 10.4 26.1 162.0 3178 34.7 9.3 30.1 140.8 3179 44.5 10.8 8.5 174.6 3180 39.1 10.7 24.3 163.7 3181 40.1 10.0 18.6 174.5 3182 45.9 12.0 20.4 185.7 3183 end of data 3184 . 3185 set write decimals 4 3186 let pcorr = partial correlation matrix m 3187 print pcorr 3188 3189-----PARTIAL KENDALLS TAU CORRELATION (LET)------------------------------ 3190 3191PARTIAL KENDALLS TAU CORRELATION 3192 3193Name: 3194 PARTIAL KENDALLS TAU (LET) 3195 3196Type: 3197 Let Subcommand 3198 3199Purpose: 3200 Compute the partial Kendall's tau correlation coefficient between 3201 two variables given the effect of a third variable. 3202 3203Description: 3204 Kendall's tau coefficient is a measure of concordance 3205 between two paired variables. Given the pairs (X(i),Y(i)) and 3206 (X(j),Y(j)), then 3207 3208 (Y(j) - Y(i))/(X(j) - X(i)) > 0 - pair is concordant 3209 (Y(j) - Y(i))/(X(j) - X(i)) < 0 - pair is discordant 3210 (Y(j) - Y(i))/(X(j) - X(i)) = 0 - pair is considered a tie 3211 X(i) = X(j) - pair is not compared 3212 3213 Kendall's tau is computed as 3214 3215 tau = (Nc - Nd)/(Nc + Nd) 3216 3217 with Nc and Nd denoting the number of concordant pairs and 3218 the number of discordant pairs, respectively, in the sample. 3219 Ties add 0.5 to both the concordant and discordant counts. 3220 There are (n 2) possible pairs in the bivariate sample. 3221 3222 A perfect linear relationship between the ranks yields a 3223 Kendall's tau correlation coefficient of +1 (or -1 for a negative 3224 relationship) and no linear relationship between the ranks 3225 yields a rank correlation coefficient of 0. 3226 3227 Partial Kendall's tau correlation is the Kendall's tau correlation 3228 between two variables after removing the effect of one or more 3229 additional variables. This command is specifcally for the the case 3230 of one additional variable. In this case, the partial Kendall's tau 3231 correlation can be computed based on standard Kendall's tau 3232 correlations between the three variables as follows: 3233 3234 r12.3 = (r12 - r13*r23)/SQRT((1 - r13**2)*(1 - r23**2)) 3235 3236 with rxy denoting the Kendall's tau correlation between x and y. 3237 3238 As with the standard Kendall's tau correlation coefficient, a value 3239 of +1 indicates a perfect positive linear relationship, a value of -1 3240 indicates a perfect negative linear relationship, and a value of 0 3241 indicates no linear relationship. 3242 3243Syntax 1: 3244 LET <par> = PARTIAL KENDALLS TAU CORRELATION <y1> <y2> <y3> 3245 <SUBSET/EXCEPT/FOR qualification> 3246 where <y1> is the first response variable; 3247 <y2> is the second response variable; 3248 <y3> is the third response variable; 3249 <par> is a parameter where the computed partial Kendall's 3250 tau correlation is saved; 3251 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 3252 3253Syntax 2: 3254 LET <par> = PARTIAL KENDALLS TAU CORRELATION ABSOLUTE VALUE 3255 <y1> <y2> <y3> 3256 <SUBSET/EXCEPT/FOR qualification> 3257 where <y1> is the first response variable; 3258 <y2> is the second response variable; 3259 <y3> is the third response variable; 3260 <par> is a parameter where the absolute value of the computed 3261 partial Kendall's tau correlation absolute value is saved; 3262 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 3263 3264 This syntax computes the absolute value of the partial Kendall's 3265 tau correlation coefficient. This is typically used in screening 3266 applications where there is an interest in identifying high magnitude 3267 correlations regardless of the direction of the correlation. 3268 3269Examples: 3270 LET A = PARTIAL KENDALLS TAU CORRELATION Y1 Y2 Z 3271 LET A = PARTIAL KENDALLS TAU CORRELATION Y1 Y2 Z SUBSET TAG > 2 3272 LET A = PARTIAL KENDALLS TAU CORRELATION ABSOLUTE VALUE Y1 Y2 Z 3273 3274Note: 3275 The three variables must have the same number of elements. 3276 3277Note: 3278 The command PARTIAL CORRELATION MATRIX can be used to compute 3279 the matrix of partial correlations. This command has options 3280 to compute several robust forms of the partial correlation 3281 including the Kendall's tau correlation discussed here. 3282 3283Note: 3284 Dataplot statistics can be used in a number of commands. For 3285 details, enter 3286 3287 HELP STATISTICS 3288 3289Default: 3290 None 3291 3292Synonyms: 3293 None 3294 3295Related Commands: 3296 KENDALL TAU CORRELATION = Compute the Kendall tau correlation. 3297 RANK CORRELATION = Compute the rank correlation. 3298 PARTIAL CORRELATION = Compute the partial correlation. 3299 PARTIAL RANK CORRELATION = Compute the partial rank 3300 correlation. 3301 PARTIAL CORRELATION MATRIX = Compute the matrix of partial 3302 correlations. 3303 CORRELATION MATRIX = Compute the matrix of correlations. 3304 CORRELATION = Compute the correlation. 3305 3306Reference: 3307 Conover (1999), "Practical Nonparametric Statistics", Third Edition, 3308 Wiley, p. 327. 3309 3310 Peavy, Bremer, Varner, Hogben (1986), "OMNITAB 80: 3311 An Interpretive System for Statistical and Numerical 3312 Data Analysis," NBS Special Publication 701. 3313 3314Applications: 3315 Linear Regression 3316 3317Implementation Date: 3318 2012/06 3319 3320Program: 3321 . This data is from page 202 of 3322 . 3323 . Peavy, Bremer, Varner, Hogben (1986), "OMNITAB 80: 3324 . An Interpretive System for Statistical and Numerical 3325 . Data Analysis," NBS Special Publication 701. 3326 . 3327 . Original source of the data is from 3328 . Draper and Smith (1981), "Applied Regression Analysis", 3329 . Wiley, p. 373. 3330 . 3331 dimension 40 columns 3332 . 3333 read matrix m 3334 42.2 11.2 31.9 167.1 3335 48.6 10.6 13.2 174.4 3336 42.6 10.6 28.7 160.8 3337 39.0 10.4 26.1 162.0 3338 34.7 9.3 30.1 140.8 3339 44.5 10.8 8.5 174.6 3340 39.1 10.7 24.3 163.7 3341 40.1 10.0 18.6 174.5 3342 45.9 12.0 20.4 185.7 3343 end of data 3344 . 3345 set write decimals 4 3346 let c1 = partial kendall tau correlation m1 m2 m3 3347 let c2 = partial kendall tau correlation absolute value m1 m2 m3 3348 print c1 c2 3349 3350-----PARTIAL RANK CORRELATION (LET)-------------------------------- 3351 3352PARTIAL RANK CORRELATION 3353 3354Name: 3355 PARTIAL RANK CORRELATION (LET) 3356 3357Type: 3358 Let Subcommand 3359 3360Purpose: 3361 Compute the partial rank correlation coefficient between two 3362 variables given the effect of a third variable. 3363 3364Description: 3365 The Spearman rank correlation coefficient is computed as 3366 3367 R = 1 - 6*SUM[i=1 to N][D(i)]/(N*(N**2-1)) 3368 3369 where D(i) is the difference between the ranks assigned to the 3370 corresponding pairs and N is the sample size. Ties are assigned 3371 average ranks. 3372 3373 A perfect linear relationship between the ranks yields a 3374 rank correlation coefficient of +1 (or -1 for a negative 3375 relationship) and no linear relationship between the ranks 3376 yields a rank correlation coefficient of 0. 3377 3378 Partial rank correlation is the correlation between two variables 3379 after removing the effect of one or more additional variables. This 3380 command is specifcally for the the case of one additional variable. 3381 In this case, the partial rank correlation can be computed based on 3382 standard rank correlations between the three variables as follows: 3383 3384 r12.3 = (r12 - r13*r23)/SQRT((1 - r13**2)*(1 - r23**2)) 3385 3386 with rxy denoting the correlation between x and y. 3387 3388 As with the standard rank correlation coefficient, a value of +1 3389 indicates a perfect positive linear relationship, a value of -1 3390 indicates a perfect negative linear relationship, and a value of 0 3391 indicates no linear relationship. 3392 3393Syntax 1: 3394 LET <par> = PARTIAL RANK CORRELATION <y1> <y2> <y3> 3395 <SUBSET/EXCEPT/FOR qualification> 3396 where <y1> is the first response variable; 3397 <y2> is the second response variable; 3398 <y3> is the third response variable; 3399 <par> is a parameter where the computed partial rank 3400 correlation is saved; 3401 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 3402 3403Syntax 2: 3404 LET <par> = PARTIAL RANK CORRELATION ABSOLUTE VALUE <y1> <y2> <y3> 3405 <SUBSET/EXCEPT/FOR qualification> 3406 where <y1> is the first response variable; 3407 <y2> is the second response variable; 3408 <y3> is the third response variable; 3409 <par> is a parameter where the absolute value of the computed 3410 partial rank correlation absolute value is saved; 3411 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 3412 3413 This syntax computes the absolute value of the partial rank 3414 correlation coefficient. This is typically used in screening 3415 applications where there is an interest in identifying high magnitude 3416 correlations regardless of the direction of the correlation. 3417 3418Examples: 3419 LET A = PARTIAL RANK CORRELATION Y1 Y2 Z 3420 LET A = PARTIAL RANK CORRELATION Y1 Y2 Z SUBSET TAG > 2 3421 LET A = PARTIAL RANK CORRELATION ABSOLUTE VALUE Y1 Y2 Z 3422 3423Note: 3424 The three variables must have the same number of elements. 3425 3426Note: 3427 The command PARTIAL CORRELATION MATRIX can be used to compute 3428 the matrix of partial correlations. This command has options 3429 to compute several robust forms of the partial correlation 3430 including the Spearman rank correlation discussed here. 3431 3432Note: 3433 Dataplot statistics can be used in a number of commands. For 3434 details, enter 3435 3436 HELP STATISTICS 3437 3438Default: 3439 None 3440 3441Synonyms: 3442 None 3443 3444Related Commands: 3445 RANK CORRELATION = Compute the rank correlation. 3446 PARTIAL CORRELATION = Compute the partial correlation. 3447 PARTIAL KENDALL TAU CORRELATION = Compute the Kendall tau partial 3448 correlation. 3449 PARTIAL CORRELATION MATRIX = Compute the matrix of partial 3450 correlations. 3451 CORRELATION MATRIX = Compute the matrix of correlations. 3452 CORRELATION = Compute the correlation. 3453 KENDALL TAU CORRELATION = Compute the Kendall tau correlation. 3454 3455Reference: 3456 Conover (1999), "Practical Nonparametric Statistics", Third Edition, 3457 Wiley, p. 327. 3458 3459 Peavy, Bremer, Varner, Hogben (1986), "OMNITAB 80: 3460 An Interpretive System for Statistical and Numerical 3461 Data Analysis," NBS Special Publication 701. 3462 3463Applications: 3464 Linear Regression 3465 3466Implementation Date: 3467 2012/06 3468 3469Program: 3470 . This data is from page 202 of 3471 . 3472 . Peavy, Bremer, Varner, Hogben (1986), "OMNITAB 80: 3473 . An Interpretive System for Statistical and Numerical 3474 . Data Analysis," NBS Special Publication 701. 3475 . 3476 . Original source of the data is from 3477 . Draper and Smith (1981), "Applied Regression Analysis", 3478 . Wiley, p. 373. 3479 . 3480 dimension 40 columns 3481 . 3482 read matrix m 3483 42.2 11.2 31.9 167.1 3484 48.6 10.6 13.2 174.4 3485 42.6 10.6 28.7 160.8 3486 39.0 10.4 26.1 162.0 3487 34.7 9.3 30.1 140.8 3488 44.5 10.8 8.5 174.6 3489 39.1 10.7 24.3 163.7 3490 40.1 10.0 18.6 174.5 3491 45.9 12.0 20.4 185.7 3492 end of data 3493 . 3494 set write decimals 4 3495 let c1 = partial rank correlation m1 m2 m3 3496 let c2 = partial rank correlation absolute value m1 m2 m3 3497 print c1 c2 3498 3499-----PARTIAL LEVERAGE PLOT-------------------------------------- 3500 3501PARTIAL LEVERAGE PLOT 3502 3503Name: 3504 PARTIAL LEVERAGE PLOT 3505 3506Type: 3507 Graphics Command 3508 3509Purpose: 3510 Generate a partial leverage plot. 3511 3512Description: 3513 In multi-linear regression, high leverage points are those 3514 that are outliers with respect to the independent variables. 3515 Influential points are those that cause large changes in the 3516 parameter estimates when they are deleted. Although an 3517 influential point will typically have high leverage, a 3518 high leverage point is not necessarily an influential 3519 point. The leverage is typically defined as the diagonal of the 3520 hat matrix (hat matrix = H = X(X'X)**(-1)X'). Dataplot 3521 currently writes a number of measure of influence and leverage 3522 to the file DPST3F.DAT (e.g., the diagonal of the hat matrix, 3523 Cook's distance, DFFITS). 3524 3525 Partial leverage is used to measure the contribution of the 3526 individual independent variables to the leverage of each 3527 observation. That is, if h(i) is the ith row of the 3528 diagonal of the hat matrix, how does h(i) change as we add 3529 a variable to the regression model. 3530 3531 The partial leverage is computed as: 3532 3533 PL(j)(i) = (X(j.[j])(i))**2/[SUM[k=1 to n][(X(j.[j])k)**2] 3534 3535 where 3536 3537 j = jth independent variable 3538 i = the ith observation 3539 X(j.[j]) = residuals from regressing X(j) against the 3540 remaining indpependent variables. 3541 3542 Note that the partial leverage is the leverage of the ith 3543 point in the partial regression plot for the jth variable 3544 (enter HELP PARTIAL REGRESSION PLOT for details on the 3545 partial regression plot). 3546 3547 The interpretation of the partial leverage plot is that 3548 data points with large partial leverage for an independent 3549 variable can exert undue influence on the selection of that 3550 variable in automatic regression model building procedures 3551 (e.g., the BEST CP command in Dataplot). 3552 3553 Dataplot provides two forms for the partial leverage 3554 plot. You can generate either a single partial leverage 3555 plot or you can generate a matrix of partial leverage plots 3556 (one plot for each independent variable in the model). 3557 3558 For the matrix form of the command, a number of SET FACTOR PLOT 3559 options can be used to control the appearance of the plot 3560 (not all of the SET FACTOR PLOT options apply). These are 3561 discussed in the Notes section below. 3562 3563Syntax 1: 3564 PARTIAL LEVERAGE PLOT <y> <x1> ... <xk> <xi> 3565 <SUBSET/EXCEPT/FOR qualification> 3566 where <y> is the response variable; 3567 <x1> ... <xk> are the independent variables; 3568 <xi> is the independent variable for which the 3569 partial leverage plot is being generated (note that 3570 <xi> must be one of the variables listed in 3571 <x1> ... <xk>; 3572 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 3573 3574 This is the syntax for generating a single partial leverage 3575 plot. 3576 3577Syntax 2: 3578 MATRIX PARTIAL LEVERAGE PLOT <y> <x1> ... <xk> 3579 <SUBSET/EXCEPT/FOR qualification> 3580 where <y> is the response variable; 3581 <x1> ... <xk> are the independent variables; 3582 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 3583 3584 This syntax is used to generate a matrix of partial leverage 3585 plots. 3586 3587Examples: 3588 PARTIAL LEVERAGE PLOT Y X1 X2 X3 X4 X2 3589 3590 MATRIX PARTIAL LEVERAGE PLOT Y X1 X2 X3 X4 3591 3592 PARTIAL LEVERAGE PLOT Y X1 X2 X3 X4 X2 SUBSET TAG > 2 3593 MATRIX PARTIAL LEVERAGE PLOT Y X1 X2 X3 X4 SUBSET TAG > 2 3594 3595Note: 3596 The following option controls which axis tic marks, tic mark 3597 labels, and axis labels are plotted. 3598 3599 SET FACTOR PLOT LABELS <ON/OFF/XON/YON/BOX> 3600 3601 OFF means that all axis labels are suppressed (this can be 3602 useful if a large number of variables are being plotted). ON 3603 means that both X and Y axis labels are printed. XON only 3604 plots the x axis labels and YON only plots the y axis labels. 3605 3606 BOX is a special option that creates an extra column on the 3607 left and an extra row on the bottom. The axis label is 3608 printed in this box. BOX is typically reserved for the plot 3609 types that plot the variable names in the axes labels. 3610 3611 The default is ON (both x and y axis labels are printed). 3612 3613Note: 3614 The following option controls where the x axis tic marks, 3615 tic mark labels, and axis label are printed. 3616 3617 SET FACTOR PLOT X AXIS <BOTTOM/TOP/ALTERNATE> 3618 3619 BOTTOM specifies that the x axis labels are printed on the 3620 bottom axis (on the last row only). TOP specifies that 3621 the x axis labels are printed on the top axis (first row 3622 only). ALTERNATE specifies that the x axis labels alternate 3623 between the top (first row) and bottom axis (last row). 3624 We recommend using the TIC OFFSET command to avoid overlap 3625 of axis labels and tic marks. 3626 3627 The default is ALTERNATE. 3628 3629Note: 3630 The following option controls where the y axis tic marks, 3631 tic mark labels, and axis label are printed. 3632 3633 SET FACTOR PLOT Y AXIS <LEFT/RIGHT/ALTERNATE> 3634 3635 LEFT specifies that the y axis labels are printed on the 3636 left axis (on the first column only). RIGHT specifies that 3637 the y axis labels are printed on the right axis (last column 3638 only). ALTERNATE specifies that the y axis labels alternate 3639 between the left (first column) and right axis (last column). 3640 We recommend using the TIC OFFSET command to avoid overlap 3641 of axis labels and tic marks. 3642 3643 The default is ALTERNATE. 3644 3645Note: 3646 Users have different preferences in terms of whether the 3647 plot frames for neighboring plots are connected or not. 3648 This is controlled with the following option. 3649 3650 SET FACTOR PLOT FRAME <DEFAULT/CONNECTED/USER> 3651 3652 DEFAULT connects neighboring frames (i.e., the FRAME CORNER 3653 COORDINATES are set to 0 0 100 100). USER uses whatever 3654 frame coordinates are currently set (15 20 85 90 by default) 3655 and makes no special provisions for axis labels and tic marks 3656 (i.e., you set them as you normally would, each plot uses 3657 whatever you have set). CONNECTED uses whatever frame 3658 coordinates have been set by the user, but it draws the axis 3659 labels and tic marks as if DEFAULT were being used (that is, as 3660 determined by the SET FACTOR PLOT <LABELS/X AXIS/Y AXIS> 3661 commands described above). Typically, CONNECTED is used to 3662 put a small bit of space between plots. For example, you 3663 might use FRAME CORNER COORDINATES 3 3 97 97 before the 3664 PARTIAL RESIDUAL PLOT command. 3665 3666 Since the plots can often have different limits for the axes, 3667 the default is USER. 3668 3669Note: 3670 When the tic marks and tic mark labels are all plotted on the 3671 same side (i.e., SET FACTOR PLOT Y AXIS is 3672 set to LEFT or RIGHT or SET PARTIAL RESIDUAL PLOT X AXIS is 3673 set to BOTTOM or TOP), then overlap between plots is possible. 3674 The TIC OFFSET command can be used to avoid this. In addition, 3675 you can stagger the tic labels with the following command: 3676 3677 SET FACTOR PLOT LABEL DISPLACEMENT <NORMAL/STAGGERED/VALUE> 3678 3679 NORMAL means that all tic labels are plotted at a distance 3680 determined by the TIC LABEL DISPLACEMENT command. STAGGERED 3681 means that alternating plots will be staggered. That is, one 3682 will use the standard displacement while the next uses a 3683 staggered value. Entering this command with a numeric value 3684 specifies the amount of the displacement for the staggered 3685 tic labels. For example, 3686 3687 TIC MARK LABEL DISPLACEMENT 10 3688 SET FACTOR PLOT LABEL DISPLACEMENT STAGGERED 3689 SET FACTOR PLOT LABEL DISPLACEMENT 25 3690 3691 These commands specify that the default tic label displacement 3692 is 10 and the staggered tic mark label displacement is 25. 3693 3694Note: 3695 It is often helpful on scatter plot matrices to overlay a 3696 fitted line on the plots. The following command is used 3697 to specify the type of fit. 3698 3699 SET FACTOR PLOT FIT <NONE/LOWESS/LINE/QUAD/SMOOTH> 3700 3701 NONE means that no fitted line is plotted. LOWESS means 3702 that a locally weighted least squares line will be overlaid. 3703 LINE means that a linear fit (Y = A0 + A1*X) will be overlaid. 3704 QUAD means that a quadratic fit (Y = A0 + A1*X + A2*X**2) will 3705 be overlaid. SMOOTH means that a least squares smoothing will 3706 be overlaid. 3707 3708 For LOWESS, it is recommended that the lowess fraction be set 3709 fairly high (e.g., LOWESS FRACTION 0.6). 3710 3711 The fitted line is currently only generated if the factor plot 3712 type is PLOT. 3713 3714 The default is for no fitted line to be overlaid on the plot. 3715 If a overlaid fit is desired, the most common choice is to use 3716 LOWESS. 3717 3718Note: 3719 Dataplot allows you to set axis limits with the LIMITS command. 3720 For the factor plot, it is often desirable to set 3721 the axis limits for each plot. This can be done with the 3722 command 3723 3724 SET FACTOR PLOT YLIMITS <LOW1> <UPP1> <LOW2> <UPP2> ... 3725 SET FACTOR PLOT XLIMITS <LOW1> <UPP1> <LOW2> <UPP2> ... 3726 3727 The default is to allow the axis limits to float with the data. 3728 3729Note: 3730 You can use standard plot control commands to control the 3731 appearance of the factor plot. 3732 3733 For example, 3734 3735 MULTIPLOT CORNER COORDINATES 5 5 95 95 3736 MULTIPLOT SCALE FACTOR 3 3737 TIC OFFSET UNITS SCREEN 3738 TIC OFFSET 5 5 3739 3740Default: 3741 None 3742 3743Synonyms: 3744 None 3745 3746Related Commands: 3747 FIT = Perform a multi-linear fit. 3748 CCPR PLOT = Generates a component and component 3749 plus residual plot. 3750 PARTIAL RESIDUAL PLOT = Generates a partial residual plot. 3751 PARTIAL REGRESSION PLOT = Generates a partial regression plot. 3752 VIF = Compute variance inflation factors 3753 for a multi-linear fit. 3754 CONDITION INDICES = Compute condition indices for a design 3755 matrix. 3756 SCATTER PLOT MATIRX = Generate a factor plot. 3757 FACTOR PLOT = Generate a plot for a response 3758 against a number of different 3759 independent variables. 3760 CONDITIONAL PLOT = Generate a conditional (subset) plot. 3761 3762Reference: 3763 "Modern Regression Methods", Tom Ryan, John Wiley, 1997. 3764 3765 "Applied Linear Statistical Models", 3rd ed., Neter, Wasserman, 3766 and Kunter, 1990, Irwin. 3767 3768 "Applied Regression Analysis", 3rd. ed., Draper and Smith, John 3769 Wiley, 1998. 3770 3771 "Residuals and Influence in Regression", Cook and Weisberg, 3772 Chapman and Hall, 1982. 3773 3774 "Regression Diagnostics", Belsley, Kuh, and Welsch, John Wiley, 3775 1980. 3776 3777 "Efficient Computing of Regression Diagnostiocs", 3778 Paul Velleman and Roy Welsch, The American Statistician, 3779 November, 1981, Vol. 35, No. 4, pp. 234-242. 3780 3781Applications: 3782 Multi-linear Regression 3783 3784Implementation Date: 3785 2002/6 3786 3787Program: 3788 SKIP 25 3789 READ HALD647.DAT Y X1 X2 X3 X4 3790 . 3791 MULTIPLOT CORNER COORDINATES 5 5 95 95 3792 MULTIPLOT SCALE FACTOR 2 3793 LINE BLANK 3794 CHARACTER X 3795 . 3796 MATRIX PARTIAL LEVERAGE PLOT Y X1 X2 X3 X4 3797 3798-----PARTIAL REGRESSION PLOT-------------------------------------- 3799 3800PARTIAL REGRESSION PLOT 3801 3802Name: 3803 PARTIAL REGRESSION PLOT 3804 3805Type: 3806 Graphics Command 3807 3808Purpose: 3809 Generate a partial regression plot. Note that partial 3810 regression plots are also referred to as added variable 3811 plots, adjusted variable plots, and individual coefficient 3812 plots. 3813 3814Description: 3815 When performing a linear regression with a single independent 3816 variable, a scatter plot of the response variable against 3817 the independent variable provides a good indication of 3818 the nature of the relationship. If there is more than one 3819 independent variable, things become more complicated. 3820 Although it can still be useful to generate scatter plots 3821 of the response variable against each of the independent 3822 variables, this does not take into account the effect of the 3823 other independent variables in the model. 3824 3825 Partial regression plots attempt to show the effect of 3826 adding an additional variable to the model (given that 3827 one or more indpendent variables are already in the model). 3828 3829 Partial regression plots are formed by: 3830 3831 1) Compute the residuals of regressing the response 3832 variable against the indpendent variables but omitting 3833 X(i). 3834 3835 2) Compute the residuals from regressing X(i) against 3836 the remaining indpendent variables. 3837 3838 3) Plot the residuals from (1) against the residuals 3839 from (2). 3840 3841 Velleman and Welsch (see References below) express this 3842 mathematically as: 3843 3844 Y(.[i]) versus X(i.[i]) 3845 3846 where 3847 3848 Y(.[i]) = residuals from regressing Y (the response 3849 variable) against all the indpendent variables 3850 except X(i). 3851 X(i.[i]) = residuals from regressing X(i) against the 3852 remaining indpependent variables. 3853 3854 Velleman and Welsch list the following useful properties 3855 for this plot: 3856 3857 1) The least squares linear fit to this plot has the 3858 slope Beta(i) and intercept zero. 3859 3860 2) The residuals from the least squares linear fit to 3861 this plot are identical to the residuals from the 3862 least squares fit of the original model (Y against 3863 all the independent variables including X(i)). 3864 3865 3) The influences of individual data values on the 3866 estimation of a coefficient are easy to see in this 3867 plot. 3868 3869 4) It is easy to see many kinds of failures of the 3870 model or violations of the underlying assumptions 3871 (nonlinearity, heteroscedasticity, unusual patterns). 3872 3873 Partial regression plots are widely discussed in the regression 3874 diagnostics literature (e.g., see the References section below). 3875 Since the strengths and weaknesses of partial regression 3876 plots are widely discussed in the literature, we will not 3877 discuss that in any detail here. 3878 3879 Partial regression plots are related to, but distinct from, 3880 partial residual plots. Partial regression plots are most 3881 commonly used to identify leverage points and influential 3882 data points that might not be leverage points. Partial residual 3883 plots are most commonly used to identify the nature of the 3884 relationship between Y and X(i) (given the effect of the 3885 other indpendent variables in the model). Note that since 3886 the simple correlation betweeen the two sets of residuals 3887 plotted is equal to the partial correlation between the 3888 response variable and X(i), partial regression plots will show 3889 the correct strength of the linear relationship between the 3890 response variable and X(i). This is not true for partial 3891 residual plots. On the other hand, for the partial 3892 regression plot, the x axis is not X(i). This limits its 3893 usefulness in determining the need for a transformation 3894 (which is the primary purpose of the partial residual plot). 3895 3896 Dataplot provides two forms for the partial regression 3897 plot. You can generate either a single partial regression 3898 plot or you can generate a matrix of partial regression plots 3899 (one plot for each independent variable in the model). 3900 3901 For the matrix form of the command, a number of SET FACTOR PLOT 3902 options can be used to control the appearance of the plot 3903 (not all of the SET FACTOR PLOT options apply). These are 3904 discussed in the Notes section below. 3905 3906Syntax 1: 3907 PARTIAL REGRESSION PLOT <y> <x1> ... <xk> <xi> 3908 <SUBSET/EXCEPT/FOR qualification> 3909 where <y> is the response variable; 3910 <x1> ... <xk> are the independent variables; 3911 <xi> is the independent variable for which the 3912 partial regression plot is being generated (note that 3913 <xi> must be one of the variables listed in 3914 <x1> ... <xk>; 3915 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 3916 3917 This is the syntax for generating a single partial regression 3918 plot. 3919 3920Syntax 2: 3921 MATRIX PARTIAL REGRESSION PLOT <y> <x1> ... <xk> 3922 <SUBSET/EXCEPT/FOR qualification> 3923 where <y> is the response variable; 3924 <x1> ... <xk> are the independent variables; 3925 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 3926 3927 This syntax is used to generate a matrix of partial regression 3928 plots. 3929 3930Examples: 3931 PARTIAL REGRESSION PLOT Y X1 X2 X3 X4 X2 3932 3933 MATRIX PARTIAL REGRESSION PLOT Y X1 X2 X3 X4 3934 3935 PARTIAL REGRESSION PLOT Y X1 X2 X3 X4 X2 SUBSET TAG > 2 3936 MATRIX PARTIAL REGRESSION PLOT Y X1 X2 X3 X4 SUBSET TAG > 2 3937 3938Note: 3939 The following option controls which axis tic marks, tic mark 3940 labels, and axis labels are plotted. 3941 3942 SET FACTOR PLOT LABELS <ON/OFF/XON/YON/BOX> 3943 3944 OFF means that all axis labels are suppressed (this can be 3945 useful if a large number of variables are being plotted). ON 3946 means that both X and Y axis labels are printed. XON only 3947 plots the x axis labels and YON only plots the y axis labels. 3948 3949 BOX is a special option that creates an extra column on the 3950 left and an extra row on the bottom. The axis label is 3951 printed in this box. BOX is typically reserved for the plot 3952 types that plot the variable names in the axes labels. 3953 3954 The default is ON (both x and y axis labels are printed). 3955 3956Note: 3957 The following option controls where the x axis tic marks, 3958 tic mark labels, and axis label are printed. 3959 3960 SET FACTOR PLOT X AXIS <BOTTOM/TOP/ALTERNATE> 3961 3962 BOTTOM specifies that the x axis labels are printed on the 3963 bottom axis (on the last row only). TOP specifies that 3964 the x axis labels are printed on the top axis (first row 3965 only). ALTERNATE specifies that the x axis labels alternate 3966 between the top (first row) and bottom axis (last row). 3967 We recommend using the TIC OFFSET command to avoid overlap 3968 of axis labels and tic marks. 3969 3970 The default is ALTERNATE. 3971 3972Note: 3973 The following option controls where the y axis tic marks, 3974 tic mark labels, and axis label are printed. 3975 3976 SET FACTOR PLOT Y AXIS <LEFT/RIGHT/ALTERNATE> 3977 3978 LEFT specifies that the y axis labels are printed on the 3979 left axis (on the first column only). RIGHT specifies that 3980 the y axis labels are printed on the right axis (last column 3981 only). ALTERNATE specifies that the y axis labels alternate 3982 between the left (first column) and right axis (last column). 3983 We recommend using the TIC OFFSET command to avoid overlap 3984 of axis labels and tic marks. 3985 3986 The default is ALTERNATE. 3987 3988Note: 3989 Users have different preferences in terms of whether the 3990 plot frames for neighboring plots are connected or not. 3991 This is controlled with the following option. 3992 3993 SET FACTOR PLOT FRAME <DEFAULT/CONNECTED/USER> 3994 3995 DEFAULT connects neighboring frames (i.e., the FRAME CORNER 3996 COORDINATES are set to 0 0 100 100). USER uses whatever 3997 frame coordinates are currently set (15 20 85 90 by default) 3998 and makes no special provisions for axis labels and tic marks 3999 (i.e., you set them as you normally would, each plot uses 4000 whatever you have set). CONNECTED uses whatever frame 4001 coordinates have been set by the user, but it draws the axis 4002 labels and tic marks as if DEFAULT were being used (that is, as 4003 determined by the SET FACTOR PLOT <LABELS/X AXIS/Y AXIS> 4004 commands described above). Typically, CONNECTED is used to 4005 put a small bit of space between plots. For example, you 4006 might use FRAME CORNER COORDINATES 3 3 97 97 before the 4007 PARTIAL RESIDUAL PLOT command. 4008 4009 Since the plots can often have different limits for the axes, 4010 the default is USER. 4011 4012Note: 4013 When the tic marks and tic mark labels are all plotted on the 4014 same side (i.e., SET FACTOR PLOT Y AXIS is 4015 set to LEFT or RIGHT or SET PARTIAL RESIDUAL PLOT X AXIS is 4016 set to BOTTOM or TOP), then overlap between plots is possible. 4017 The TIC OFFSET command can be used to avoid this. In addition, 4018 you can stagger the tic labels with the following command: 4019 4020 SET FACTOR PLOT LABEL DISPLACEMENT <NORMAL/STAGGERED/VALUE> 4021 4022 NORMAL means that all tic labels are plotted at a distance 4023 determined by the TIC LABEL DISPLACEMENT command. STAGGERED 4024 means that alternating plots will be staggered. That is, one 4025 will use the standard displacement while the next uses a 4026 staggered value. Entering this command with a numeric value 4027 specifies the amount of the displacement for the staggered 4028 tic labels. For example, 4029 4030 TIC MARK LABEL DISPLACEMENT 10 4031 SET FACTOR PLOT LABEL DISPLACEMENT STAGGERED 4032 SET FACTOR PLOT LABEL DISPLACEMENT 25 4033 4034 These commands specify that the default tic label displacement 4035 is 10 and the staggered tic mark label displacement is 25. 4036 4037Note: 4038 It is often helpful on scatter plot matrices to overlay a 4039 fitted line on the plots. The following command is used 4040 to specify the type of fit. 4041 4042 SET FACTOR PLOT FIT <NONE/LOWESS/LINE/QUAD/SMOOTH> 4043 4044 NONE means that no fitted line is plotted. LOWESS means 4045 that a locally weighted least squares line will be overlaid. 4046 LINE means that a linear fit (Y = A0 + A1*X) will be overlaid. 4047 QUAD means that a quadratic fit (Y = A0 + A1*X + A2*X**2) will 4048 be overlaid. SMOOTH means that a least squares smoothing will 4049 be overlaid. 4050 4051 For LOWESS, it is recommended that the lowess fraction be set 4052 fairly high (e.g., LOWESS FRACTION 0.6). 4053 4054 The fitted line is currently only generated if the factor plot 4055 type is PLOT. 4056 4057 The default is for no fitted line to be overlaid on the plot. 4058 If a overlaid fit is desired, the most common choice is to use 4059 LOWESS. 4060 4061Note: 4062 Dataplot allows you to set axis limits with the LIMITS command. 4063 For the factor plot, it is often desirable to set 4064 the axis limits for each plot. This can be done with the 4065 command 4066 4067 SET FACTOR PLOT YLIMITS <LOW1> <UPP1> <LOW2> <UPP2> ... 4068 SET FACTOR PLOT XLIMITS <LOW1> <UPP1> <LOW2> <UPP2> ... 4069 4070 The default is to allow the axis limits to float with the data. 4071 4072Note: 4073 You can use standard plot control commands to control the 4074 appearance of the factor plot. 4075 4076 For example, 4077 4078 MULTIPLOT CORNER COORDINATES 5 5 95 95 4079 MULTIPLOT SCALE FACTOR 3 4080 TIC OFFSET UNITS SCREEN 4081 TIC OFFSET 5 5 4082 4083Default: 4084 None 4085 4086Synonyms: 4087 None 4088 4089Related Commands: 4090 FIT = Perform a multi-linear fit. 4091 CCPR PLOT = Generates a component and component 4092 plus residual plot. 4093 PARTIAL RESIDUAL PLOT = Generates a partial residual plot. 4094 PARTIAL LEVERAGE PLOT = Generates a partial leverage plot. 4095 VIF = Compute variance inflation factors 4096 for a multi-linear fit. 4097 CONDITION INDICES = Compute condition indices for a design 4098 matrix. 4099 SCATTER PLOT MATIRX = Generate a factor plot. 4100 FACTOR PLOT = Generate a plot for a response 4101 against a number of different 4102 independent variables. 4103 CONDITIONAL PLOT = Generate a conditional (subset) plot. 4104 4105Reference: 4106 "Modern Regression Methods", Tom Ryan, John Wiley, 1997. 4107 4108 "Applied Linear Statistical Models", 3rd ed., Neter, Wasserman, 4109 and Kunter, 1990, Irwin. 4110 4111 "Applied Regression Analysis", 3rd. ed., Draper and Smith, John 4112 Wiley, 1998. 4113 4114 "Residuals and Influence in Regression", Cook and Weisberg, 4115 Chapman and Hall, 1982. 4116 4117 "Regression Diagnostics", Belsley, Kuh, and Welsch, John Wiley, 4118 1980. 4119 4120 "Efficient Computing of Regression Diagnostiocs", 4121 Paul Velleman and Roy Welsch, The American Statistician, 4122 November, 1981, Vol. 35, No. 4, pp. 234-242. 4123 4124Applications: 4125 Multi-linear Regression 4126 4127Implementation Date: 4128 2002/6 4129 4130Program: 4131 SKIP 25 4132 READ HALD647.DAT Y X1 X2 X3 X4 4133 . 4134 MULTIPLOT CORNER COORDINATES 5 5 95 95 4135 MULTIPLOT SCALE FACTOR 2 4136 LINE BLANK 4137 CHARACTER X 4138 . 4139 MATRIX PARTIAL REGRESSION PLOT Y X1 X2 X3 X4 4140 4141-----PARTIAL RESIDUAL PLOT-------------------------------------- 4142 4143PARTIAL RESIDUAL PLOT 4144 4145Name: 4146 PARTIAL RESIDUAL PLOT 4147 4148Type: 4149 Graphics Command 4150 4151Purpose: 4152 Generate a partial residual plot. 4153 4154Description: 4155 When performing a linear regression with a single independent 4156 variable, a scatter plot of the response variable against 4157 the independent variable provides a good indication of 4158 the nature of the relationship. If there is more than one 4159 independent variable, things become more complicated. 4160 Although it can still be useful to generate scatter plots 4161 of the response variable against each of the independent 4162 variables, this does not take into account the effect of the 4163 other independent variables in the model. 4164 4165 Partial residual plots attempt to show the relationship between 4166 a given independent variable and the response variable given 4167 that other independent variables are also in the model. 4168 4169 Partial residual plots are formed as: 4170 4171 Res + Betahat(i)*X(i) versus X(i) 4172 4173 where 4174 4175 Res = residuals from the full model 4176 Betahat(i) = regression coefficient from the ith 4177 independent variable in the full model 4178 X(i) = the ith independent variable 4179 4180 Partial residual plots are widely discussed in the regression 4181 diagnostics literature (e.g., see the References section below). 4182 Although they can often be useful, be aware that they can 4183 also fail to indicate the proper relationship. In 4184 particular, if X(i) is highly correlated with any of the 4185 other independent variables, the variance indicated by the 4186 partial residual plot can be much less than the actual 4187 variance. These issues are discussed in more detail in the 4188 references given below. 4189 4190 Dataplot provides two forms for the partial residual 4191 plot. You can generate either a single partial residual 4192 plot or you can generate a matrix of partial residual plots 4193 (one plot for each independent variable in the model). 4194 4195 For the matrix form of the command, a number of SET FACTOR PLOT 4196 options can be used to control the appearance of the plot 4197 (not all of the SET FACTOR PLOT options apply). These are 4198 discussed in the Notes section below. 4199 4200 The CCPR plot is a variation of the PARTIAL RESIDUAL PLOT. 4201 Enter HELP CCPR PLOT for details. 4202 4203Syntax 1: 4204 PARTIAL RESIDUAL PLOT <y> <x1> ... <xk> <xi> 4205 <SUBSET/EXCEPT/FOR qualification> 4206 where <y> is the response variable; 4207 <x1> ... <xk> are the independent variables; 4208 <xi> is the independent variable for which the 4209 partial residual plot is being generated (note that 4210 <xi> must be one of the variables listed in 4211 <x1> ... <xk>; 4212 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 4213 4214 This is the syntax for generating a single partial residual 4215 plot. 4216 4217Syntax 2: 4218 MATRIX PARTIAL RESIDUAL PLOT <y> <x1> ... <xk> 4219 <SUBSET/EXCEPT/FOR qualification> 4220 where <y> is the response variable; 4221 <x1> ... <xk> are the independent variables; 4222 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 4223 4224 This syntax is used to generate a matrix of partial residual 4225 plots. 4226 4227Examples: 4228 PARTIAL RESIDUAL PLOT Y X1 X2 X3 X4 X2 4229 4230 MATRIX PARTIAL RESIDUAL PLOT Y X1 X2 X3 X4 4231 4232 PARTIAL RESIDUAL PLOT Y X1 X2 X3 X4 X2 SUBSET TAG > 2 4233 MATRIX PARTIAL RESIDUAL PLOT Y X1 X2 X3 X4 SUBSET TAG > 2 4234 4235Note: 4236 The following option controls which axis tic marks, tic mark 4237 labels, and axis labels are plotted. 4238 4239 SET FACTOR PLOT LABELS <ON/OFF/XON/YON/BOX> 4240 4241 OFF means that all axis labels are suppressed (this can be 4242 useful if a large number of variables are being plotted). ON 4243 means that both X and Y axis labels are printed. XON only 4244 plots the x axis labels and YON only plots the y axis labels. 4245 4246 BOX is a special option that creates an extra column on the 4247 left and an extra row on the bottom. The axis label is 4248 printed in this box. BOX is typically reserved for the plot 4249 types that plot the variable names in the axes labels. 4250 4251 The default is ON (both x and y axis labels are printed). 4252 4253Note: 4254 The following option controls where the x axis tic marks, 4255 tic mark labels, and axis label are printed. 4256 4257 SET FACTOR PLOT X AXIS <BOTTOM/TOP/ALTERNATE> 4258 4259 BOTTOM specifies that the x axis labels are printed on the 4260 bottom axis (on the last row only). TOP specifies that 4261 the x axis labels are printed on the top axis (first row 4262 only). ALTERNATE specifies that the x axis labels alternate 4263 between the top (first row) and bottom axis (last row). 4264 We recommend using the TIC OFFSET command to avoid overlap 4265 of axis labels and tic marks. 4266 4267 The default is ALTERNATE. 4268 4269Note: 4270 The following option controls where the y axis tic marks, 4271 tic mark labels, and axis label are printed. 4272 4273 SET FACTOR PLOT Y AXIS <LEFT/RIGHT/ALTERNATE> 4274 4275 LEFT specifies that the y axis labels are printed on the 4276 left axis (on the first column only). RIGHT specifies that 4277 the y axis labels are printed on the right axis (last column 4278 only). ALTERNATE specifies that the y axis labels alternate 4279 between the left (first column) and right axis (last column). 4280 We recommend using the TIC OFFSET command to avoid overlap 4281 of axis labels and tic marks. 4282 4283 The default is ALTERNATE. 4284 4285Note: 4286 Users have different preferences in terms of whether the 4287 plot frames for neighboring plots are connected or not. 4288 This is controlled with the following option. 4289 4290 SET FACTOR PLOT FRAME <DEFAULT/CONNECTED/USER> 4291 4292 DEFAULT connects neighboring frames (i.e., the FRAME CORNER 4293 COORDINATES are set to 0 0 100 100). USER uses whatever 4294 frame coordinates are currently set (15 20 85 90 by default) 4295 and makes no special provisions for axis labels and tic marks 4296 (i.e., you set them as you normally would, each plot uses 4297 whatever you have set). CONNECTED uses whatever frame 4298 coordinates have been set by the user, but it draws the axis 4299 labels and tic marks as if DEFAULT were being used (that is, as 4300 determined by the SET FACTOR PLOT <LABELS/X AXIS/Y AXIS> 4301 commands described above). Typically, CONNECTED is used to 4302 put a small bit of space between plots. For example, you 4303 might use FRAME CORNER COORDINATES 3 3 97 97 before the 4304 PARTIAL RESIDUAL PLOT command. 4305 4306 Since the plots can often have different limits for the axes, 4307 the default is USER. 4308 4309Note: 4310 When the tic marks and tic mark labels are all plotted on the 4311 same side (i.e., SET FACTOR PLOT Y AXIS is 4312 set to LEFT or RIGHT or SET PARTIAL RESIDUAL PLOT X AXIS is 4313 set to BOTTOM or TOP), then overlap between plots is possible. 4314 The TIC OFFSET command can be used to avoid this. In addition, 4315 you can stagger the tic labels with the following command: 4316 4317 SET FACTOR PLOT LABEL DISPLACEMENT <NORMAL/STAGGERED/VALUE> 4318 4319 NORMAL means that all tic labels are plotted at a distance 4320 determined by the TIC LABEL DISPLACEMENT command. STAGGERED 4321 means that alternating plots will be staggered. That is, one 4322 will use the standard displacement while the next uses a 4323 staggered value. Entering this command with a numeric value 4324 specifies the amount of the displacement for the staggered 4325 tic labels. For example, 4326 4327 TIC MARK LABEL DISPLACEMENT 10 4328 SET FACTOR PLOT LABEL DISPLACEMENT STAGGERED 4329 SET FACTOR PLOT LABEL DISPLACEMENT 25 4330 4331 These commands specify that the default tic label displacement 4332 is 10 and the staggered tic mark label displacement is 25. 4333 4334Note: 4335 It is often helpful on scatter plot matrices to overlay a 4336 fitted line on the plots. The following command is used 4337 to specify the type of fit. 4338 4339 SET FACTOR PLOT FIT <NONE/LOWESS/LINE/QUAD/SMOOTH> 4340 4341 NONE means that no fitted line is plotted. LOWESS means 4342 that a locally weighted least squares line will be overlaid. 4343 LINE means that a linear fit (Y = A0 + A1*X) will be overlaid. 4344 QUAD means that a quadratic fit (Y = A0 + A1*X + A2*X**2) will 4345 be overlaid. SMOOTH means that a least squares smoothing will 4346 be overlaid. 4347 4348 For LOWESS, it is recommended that the lowess fraction be set 4349 fairly high (e.g., LOWESS FRACTION 0.6). 4350 4351 The fitted line is currently only generated if the factor plot 4352 type is PLOT. 4353 4354 The default is for no fitted line to be overlaid on the plot. 4355 If a overlaid fit is desired, the most common choice is to use 4356 LOWESS. 4357 4358Note: 4359 Dataplot allows you to set axis limits with the LIMITS command. 4360 For the factor plot, it is often desirable to set 4361 the axis limits for each plot. This can be done with the 4362 command 4363 4364 SET FACTOR PLOT YLIMITS <LOW1> <UPP1> <LOW2> <UPP2> ... 4365 SET FACTOR PLOT XLIMITS <LOW1> <UPP1> <LOW2> <UPP2> ... 4366 4367 The default is to allow the axis limits to float with the data. 4368 4369Note: 4370 You can use standard plot control commands to control the 4371 appearance of the factor plot. 4372 4373 For example, 4374 4375 MULTIPLOT CORNER COORDINATES 5 5 95 95 4376 MULTIPLOT SCALE FACTOR 3 4377 TIC OFFSET UNITS SCREEN 4378 TIC OFFSET 5 5 4379 4380Default: 4381 None 4382 4383Synonyms: 4384 None 4385 4386Related Commands: 4387 FIT = Perform a multi-linear fit. 4388 CCPR PLOT = Generates a component and component 4389 plus residual plot. 4390 PARTIAL REGRESSION PLOT = Generates a partial regression plot. 4391 PARTIAL LEVERAGE PLOT = Generates a partial leverage plot. 4392 VIF = Compute variance inflation factors 4393 for a multi-linear fit. 4394 CONDITION INDICES = Compute condition indices for a design 4395 matrix. 4396 SCATTER PLOT MATIRX = Generate a factor plot. 4397 FACTOR PLOT = Generate a plot for a response 4398 against a number of different 4399 independent variables. 4400 CONDITIONAL PLOT = Generate a conditional (subset) plot. 4401 4402Reference: 4403 "Modern Regression Methods", Tom Ryan, John Wiley, 1997. 4404 4405 "Applied Linear Statistical Models", 3rd ed., Neter, Wasserman, 4406 and Kunter, 1990, Irwin. 4407 4408 "Applied Regression Analysis", 3rd. ed., Draper and Smith, John 4409 Wiley, 1998. 4410 4411 "Residuals and Influence in Regression", Cook and Weisberg, 4412 Chapman and Hall, 1982. 4413 4414 "Regression Diagnostics", Belsley, Kuh, and Welsch, John Wiley, 4415 1980. 4416 4417 "Efficient Computing of Regression Diagnostiocs", 4418 Paul Velleman and Roy Welsch, The American Statistician, 4419 November, 1981, Vol. 35, No. 4, pp. 234-242. 4420 4421Applications: 4422 Multi-linear Regression 4423 4424Implementation Date: 4425 2002/6 4426 4427Program: 4428 SKIP 25 4429 READ HALD647.DAT Y X1 X2 X3 X4 4430 . 4431 MULTIPLOT CORNER COORDINATES 5 5 95 95 4432 MULTIPLOT SCALE FACTOR 2 4433 LINE BLANK 4434 CHARACTER X 4435 . 4436 MATRIX PARTIAL RESIDUAL PLOT Y X1 X2 X3 X4 4437 4438-----PATH (SET)-------------------------------------------- 4439 4440PATH 4441 4442Name: 4443 PATH (SET) 4444 4445Type: 4446 Set Subcommand 4447 4448Purpose: 4449 Specify the name of the directory where Dataplot's auxiliary files 4450 are stored. 4451 4452Description: 4453 The Dataplot distribution comes with a large number of sample data 4454 files, macro and program files, and experiment design files. 4455 Typically, these files can be accessed in the READ, CALL, and LIST 4456 commands without specifying a path name. However, if the local 4457 implementor has not specified this path correctly in the Dataplot 4458 source code, the SET PATH command can be used to tell Dataplot where 4459 to locate them. Check with your local implementor for the correct 4460 path. 4461 4462 On Microsoft Windows platforms, the Install Shield installation sets 4463 the DATAPLO$ environment variable in the Windows registry that defines 4464 the default location. 4465 4466 For Unix/Linux and Mac OS X installations, you will typically add a 4467 line in your .cshrc file (for c-shell or t-shell users) or your 4468 .bashrc (for Bourne-shell users) that defines the DATAPLOT_FILES 4469 environment variable. 4470 4471 So for those systems where an appropriate environment variable has 4472 been properly defined, there is no need to enter a SET PATH command. 4473 4474 The SET PATH command is most typically used by developers who would 4475 like to set the default Dataplot directory to a test directory 4476 rather than the default installation directory. 4477 4478Syntax: 4479 SET PATH <string> 4480 where <string> specifies the desired path name. 4481 4482 This string is currently limited to a maxium of 80 characters. 4483 4484Examples: 4485 SET PATH D:\DATAPLOT 4486 SET PATH /usr/local/lib/dataplot 4487 PROBE PATH 4488 4489Note: 4490 Starting with the 2019/04 version, Linux and MacOS systems allow 4491 the default path to be set in the Makefile. So it is no longer 4492 neccessary to create a DATAPLOT_FILES environment variable on 4493 these systems. 4494 4495 The order of determining the default path for Linux/MacOS 4496 platforms is: 4497 4498 1. First check for the DATAPLOT_FILES environment variable. 4499 4500 2. If DATAPLOT_FILES has not been defined, use the path 4501 specified in the Makefile (this will be called DPLIBDIR). 4502 4503 3. If DATAPLOT_FILES has not been defined and DPLIBDIR has 4504 not been defined in the Makefile, then default to 4505 /usr/local/lib/dataplot. 4506 4507Note: 4508 When Dataplot attempts to open a file, it will first do so in the 4509 current directory. If Dataplot is unable to locate the file in the 4510 current directory, it will look in the directory containing the 4511 Dataplot auxillary files. 4512 4513 You can use the SET SEARCH DIRECTORY command to define an additional 4514 directory where Dataplot will look for the file. 4515 4516Default: 4517 On Microsoft Windows platforms, the default path is determined by the 4518 Install Shield installation and the DATAPLO$ environment variable is 4519 set to this directory. For English-based platforms, this is either 4520 "C:\Program Files\NIST\DATAPLOT" (for 32-bit systems) or 4521 "C:\Program Files (x86)\NIST\DATAPLOT". Non-English platforms will 4522 typically have a different name for "Program Files". 4523 4524 On Linux/Unix and MacOS systems, the default path is determined by 4525 the DATAPLOT_FILES environment variable. If the this environment 4526 variable is not defined, then check to see if DPLIBDIR was defined 4527 in the Makefile. If neither of these has been set, the default path is 4528 "/usr/local/lib/dataplot". 4529 4530Synonyms: 4531 None 4532 4533Related Commands: 4534 LIST = List the contents of a file. 4535 READ = Read data from a file. 4536 CALL = Execute commands stored in a file. 4537 SEARCH DIRECTORY = Define an additional directory that will be 4538 searched. 4539 4540Applications: 4541 File Usage 4542 4543Implementation Date: 4544 1994/01 4545 2019/08: Use of DPLIBDIR in Makefile for Linux/MacOS systems 4546 4547Program: 4548 SET PATH /home/heckert/lib/dataplot/ 4549 LIST BERGER1.DAT 4550 4551-----PATTERN (LET)--------------------------------------------------- 4552 4553PATTERN 4554 4555Name: 4556 PATTERN (LET) 4557 4558Type: 4559 Let Subcommand 4560 4561Purpose: 4562 Generate numbers with a specific pattern. 4563 4564Description: 4565 The SEQUENCE command is used to generate sequences with a constant 4566 increment. The PATTERN command can be used for those cases where 4567 there is a non-constant increment. 4568 4569Syntax 1: 4570 LET <resp> = PATTERN <list> 4571 where <list> is a list of numbers or parameters; 4572 and <resp> is a variable where the given numbers are saved. 4573 4574 With this syntax, only one iteration of the pattern is saved. 4575 4576Syntax 2: 4577 LET <resp> = PATTERN <list> FOR I = <start> <inc> <stop> 4578 where <list> is a list of numbers or parameters; 4579 <resp> is a variable where the given numbers are saved; 4580 <start> is the first row in <resp> where the pattern is saved 4581 (typically has a value of 1); 4582 <inc> is the row increment for saving values in <resp> 4583 (typically has a value of 1); 4584 and <stop> is the last row in <resp> for saving values. 4585 4586 With this syntax, the pattern is repeated in <resp> until all the 4587 rows specified by the FOR are filled. 4588 4589Examples: 4590 LET X = PATTERN 1 3 4 1 1 1 0 0 2 4591 LET X = PATTERN 1 3 4 1 1 1 0 0 2 FOR I = 1 1 100 4592 4593Default: 4594 None 4595 4596Synonyms: 4597 The DATA command is equivalent to SYNTAX 1. 4598 4599Related Commands: 4600 SEQUENCE = Generate a sequence of numbers. 4601 FIBONNACCI NUMBERS = Generate Fibonnacci numbers. 4602 PRIME NUMBERS = Generate prime numbers. 4603 DATA = Place numbers in a variable. 4604 LOGISTIC NUMBERS = Generate numbers from a logistic sequence. 4605 CANTOR NUMBERS = Generate numbers from a Cantor set. 4606 4607Applications: 4608 Data Input 4609 4610Implementation Date: 4611 Pre-1987 4612 4613Program: 4614 XX 4615 4616-----PAUSE LINES (SET)------------------------------------------- 4617 4618PAUSE LINES (SET) 4619 4620Name: 4621 SET PAUSE LINES 4622 4623Type: 4624 Support Command 4625 4626Purpose: 4627 Specify the number of lines that will be printed to the screen 4628 before pausing and prompting for a carriage return. 4629 4630Description: 4631 For some implementations (e.g., Windows) with a limited number 4632 of scroll lines or for cases where a large amount of output is 4633 printed to the screen, it can be useful to pause after a given 4634 number of lines have been printed in order to view the output. 4635 4636 This command allows you to specify a given number of lines. 4637 When this number of lines has been printed to the terminal 4638 screen, a "?" is printed and execution is halted until a carriage 4639 return is entered. 4640 4641 This is similar to a PAUSE command. However, a PAUSE command 4642 only pauses the output when a PAUSE is explicitly entered. 4643 In contrast, a SET PAUSE LINES needs to be entered only once 4644 and the pause will be activated automatically when the specified 4645 number of lines has been printed. 4646 4647 If the number of pause lines is set to zero or a negative value, 4648 no pause will be generated. 4649 4650 If you have activated the pause and wish to de-activate it later 4651 in the session, you can do this by entering a "0" at the "?" 4652 prompt. You can also enter a SET PAUSE LINES 0 command. 4653 4654Syntax: 4655 SET PAUSE LINES <value> 4656 where <value> specifies the number of lines to output to the 4657 screen before pausing and prompting for a carriage return. 4658 4659Examples: 4660 PAUSE 4661 4662Note: 4663 This command will not be active if you are running the 4664 graphical user interface (GUI). 4665 4666Default: 4667 No pauses are generated 4668 4669Synonyms: 4670 None 4671 4672Related Commands: 4673 PAUSE = Initiate an explicit pause. 4674 4675Applications: 4676 Interactive Usage 4677 4678Implementation Date: 4679 2010/09 4680 4681Program: 4682 XX 4683 4684-----PAUSE------------------------------------------------------- 4685 4686PAUSE 4687 4688Name: 4689 PAUSE 4690 4691Type: 4692 Support Command 4693 4694Purpose: 4695 A "?" is printed to the screen and execution is halted until 4696 a carriage return is entered. 4697 4698Description: 4699 This command is typically used in macros to allow the analyst to 4700 look at the current plot (or terminal output) before the next plot 4701 is generated. 4702 4703Syntax: 4704 PAUSE 4705 4706Examples: 4707 PAUSE 4708 4709Default: 4710 None 4711 4712Synonyms: 4713 None 4714 4715Related Commands: 4716 PLOT = Generate a data or function plot. 4717 4718Applications: 4719 Interactive Usage 4720 4721Implementation Date: 4722 Pre-1987 4723 4724Program: 4725 XX 4726 4727-----PB (LET)-------------------------------- 4728 4729PB 4730 4731Name: 4732 PB (LET) 4733 4734Type: 4735 Library Function 4736 4737Purpose: 4738 Compute the parabolic cylinder functions or the derivatives 4739 of the parabolic cylinder functions. 4740 4741Description: 4742 The parabolic cylinder functions are defined as: 4743 4744 1) D(x,v) = COS(PI*v/2)*w1(x) + SIN(PI*v/2)*w2(x) 4745 4746 where 4747 4748 w1(x) = (1/SQRT(PI))*GAMMA(0.5 + 0.5*v)*y1(x)/(2**(-v/2)) 4749 w2(x) = (1/SQRT(PI))*GAMMA(1 + 0.5*v)*y2(x)/(2**(-v/2 - 0.5)) 4750 4751 where 4752 4753 y1(x) = SUM(a(2*m))*x**(2*m)/(2*m)! 4754 y2(x) = SUM(a(2*m+1))*x**(2*m+1)/(2*m+1)! 4755 4756 where the summation is from m = 0 to infinity and 4757 4758 a(0) = a(1) = 1 4759 a(2) = a(3) = a = -v - 0.5 4760 a(n) = a*a(n-2) + (1/4)*(n-2)(n-3)*a(n-4) (n >= 4) 4761 4762 2) V(x,v) =[1/(GAMMA(1+v)]*[-SIN(PI*v/2)w1(x) + COS(PI*v/2)w2(x)] 4763 4764 where w1 and w2 are defined as for the D(x,v) function 4765 and GAMMA is the gamma function. 4766 4767 3) W(+/-x,a) =[(COSH(PI*a)**(1/4)]*[G1y1(x) -/+ SQRT(2)*G2y2(x)] 4768 4769 where y1 and y2 are defined as for the D(x,v) function, 4770 COSH is the hyperbolic cosine function, and 4771 4772 G1 = ABS(GAMMA(0.25 + 0.5ia)) 4773 G2 = ABS(GAMMA(0.75 + 0.5ia)) 4774 4775 Note that there are alternative formulations for the above 4776 functions. More details are provided in the sources listed 4777 in the References section. 4778 4779 In addition, Dataplot provides functions for computing the 4780 derivatives of each of these functions. 4781 4782 Dataplot computes these function using the PDBV, PBVV, and 4783 PBWA routines from "Computation of Special Functions" (see 4784 the References section below). 4785 4786Syntax 1: 4787 LET <y> = PBDV(<x>,<v>) <SUBSET/EXCEPT/FOR qualification> 4788 where <x> is a variable, number, or parameter containing 4789 positive values; 4790 <v> is a variable, number, or parameter that defines 4791 the order of the parabolic function; 4792 <y> is a variable or a parameter (depending on what 4793 <x> and <v> are) where the computed parabolic 4794 cylinder values are stored; 4795 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 4796 4797 This syntax computes the first form of the parabolic 4798 cylinder functions (D(x,v)). 4799 4800Syntax 2: 4801 LET <y> = PBDV1(<x>,<v>) <SUBSET/EXCEPT/FOR qualification> 4802 where <x> is a variable, number, or parameter containing 4803 positive values; 4804 <v> is a variable, number, or parameter that defines 4805 the order of the parabolic cylinder function; 4806 <y> is a variable or a parameter (depending on what 4807 <x> and <v> are) where the computed parabolic 4808 cylinder values are stored; 4809 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 4810 4811 This syntax computes the derivative of the first form of the 4812 parabolic cylinder functions (D(x,v)). 4813 4814Syntax 3: 4815 LET <y> = PBVV(<x>,<v>) <SUBSET/EXCEPT/FOR qualification> 4816 where <x> is a variable, number, or parameter containing 4817 positive values; 4818 <v> is a variable, number, or parameter that defines 4819 the order of the parabolic function; 4820 <y> is a variable or a parameter (depending on what 4821 <x> and <v> are) where the computed parabolic 4822 cylinder values are stored; 4823 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 4824 4825 This syntax computes the second form of the parabolic 4826 cylinder functions (V(x,v)). 4827 4828Syntax 4: 4829 LET <y> = PBVV1(<x>,<v>) <SUBSET/EXCEPT/FOR qualification> 4830 where <x> is a variable, number, or parameter containing 4831 positive values; 4832 <v> is a variable, number, or parameter that defines 4833 the order of the parabolic function; 4834 <y> is a variable or a parameter (depending on what 4835 <x> and <v> are) where the computed parabolic 4836 cylinder values are stored; 4837 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 4838 4839 This syntax computes the derivative of the second form of 4840 the parabolic cylinder functions (V(x,v)). 4841 4842Syntax 5: 4843 LET <y> = PBWA(<x>,<a>) <SUBSET/EXCEPT/FOR qualification> 4844 where <x> is a variable, number, or parameter containing 4845 positive values; 4846 <a> is a variable, number, or parameter that defines 4847 the order of the parabolic function; 4848 <y> is a variable or a parameter (depending on what 4849 <x> and <v> are) where the computed parabolic 4850 cylinder values are stored; 4851 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 4852 4853 This syntax computes the third form of the parabolic 4854 cylinder functions (W(x,a)). 4855 4856 This function is limited to the case when the absolute 4857 value of <x> is less than 5. 4858 4859Syntax 6: 4860 LET <y> = PBWA1(<x>,<a>) <SUBSET/EXCEPT/FOR qualification> 4861 where <x> is a variable, number, or parameter containing 4862 positive values; 4863 <a> is a variable, number, or parameter that defines 4864 the order of the parabolic function; 4865 <y> is a variable or a parameter (depending on what 4866 <x> and <v> are) where the computed parabolic 4867 cylinder values are stored; 4868 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 4869 4870 This syntax computes the derivative of the third form of 4871 the parabolic cylinder functions (W(x,a)). 4872 4873 This function is limited to the case when the absolute 4874 value of <x> is less than 5. 4875 4876Examples: 4877 LET A = PBDV(1.5,2) 4878 LET A = PBDV1(1.5,2) 4879 4880 LET Y = PBVV(X,2) 4881 LET YPRIME = PBVV1(X,2) 4882 4883 LET Y = PBWA(X,1) FOR X = -3 0.1 3 4884 LET YPRIME = PBWA1(X,1) FOR X = -3 0.1 3 4885 4886Note: 4887 Library functions are distinguished from let subcommands 4888 in the following ways. 4889 1) Functions enclose the input value in parenthesis. Let 4890 subcommands use spaces. 4891 2) Functions can accept (and return) either parameters 4892 (i.e., single values) or variables (i.e., an array of 4893 values) while let subcommands are specific in which they 4894 accept as input and what they return as output. 4895 3) Functions can accept expressions while let subcommands 4896 do not. For example, the following is legal: 4897 LET Y2 = ABS(Y1-INT(Y1)) 4898 For let subcommands, you typically have to do something 4899 like the following: 4900 LET YTEMP = Y**2 + 8 4901 LET A = SUM YTEMP 4902 4903Default: 4904 None 4905 4906Synonyms: 4907 None 4908 4909Related Commands: 4910 CLNGAM = Compute the complex log gamma function. 4911 CBETA = Compute the complex beta function. 4912 CLNBETA = Compute the complex log beta function. 4913 GAMMA = Compute the Gamma function. 4914 GAMMAI = Compute the incomplete Gamma function. 4915 DIGAMMA = Compute the digamma function. 4916 4917Reference: 4918 "Computation of Special Functions", Shanjie Zhang and Jianming 4919 Jin, John Wiley and Sons, 1996, chapter 13. 4920 4921 "Handbook of Mathematical Functions, Applied Mathematics Series, 4922 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 4923 1964, pp. 685-720. 4924 4925Applications: 4926 Special Functions 4927 4928Implementation Date: 4929 1997/12 4930 4931Program 1: 4932 LINE SOLID DASH 4933 MULTIPLOT 2 2 4934 MULTIPLOT CORNER COORDINATES 5 5 95 95 4935 TITLE V = 1 4936 PLOT PBDV(X,1) FOR X = 0.1 0.1 5 AND 4937 PLOT PBDV1(X,1) FOR X = 0.1 0.1 5 4938 TITLE V = 2 4939 PLOT PBDV(X,2) FOR X = 0.1 0.1 5 AND 4940 PLOT PBDV1(X,2) FOR X = 0.1 0.1 5 4941 TITLE V = 3 4942 PLOT PBDV(X,3) FOR X = 0.1 0.1 5 AND 4943 PLOT PBDV1(X,3) FOR X = 0.1 0.1 5 4944 TITLE V = 4 4945 PLOT PBDV(X,4) FOR X = 0.1 0.1 5 AND 4946 PLOT PBDV1(X,4) FOR X = 0.1 0.1 5 4947 END OF MULTIPLOT 4948 MOVE 50 95 4949 JUSTIFICATION CENTER 4950 TEXT PBDV (AND DERIVATIVE) FUNCTIONS 4951 4952Program 2: 4953 LINE SOLID DASH 4954 MULTIPLOT 2 2 4955 MULTIPLOT CORNER COORDINATES 5 5 95 95 4956 TITLE V = 1 4957 PLOT PBVV(X,1) FOR X = 0.1 0.1 5 AND 4958 PLOT PBVV1(X,1) FOR X = 0.1 0.1 5 4959 TITLE V = 2 4960 PLOT PBVV(X,2) FOR X = 0.1 0.1 5 AND 4961 PLOT PBVV1(X,2) FOR X = 0.1 0.1 5 4962 TITLE V = 3 4963 PLOT PBVV(X,3) FOR X = 0.1 0.1 5 AND 4964 PLOT PBVV1(X,3) FOR X = 0.1 0.1 5 4965 TITLE V = 4 4966 PLOT PBVV(X,4) FOR X = 0.1 0.1 5 AND 4967 PLOT PBVV1(X,4) FOR X = 0.1 0.1 5 4968 END OF MULTIPLOT 4969 MOVE 50 95 4970 JUSTIFICATION CENTER 4971 TEXT PBVV (AND DERIVATIVE) FUNCTIONS 4972 4973Program 3: 4974 LINE SOLID DASH 4975 MULTIPLOT 2 2 4976 MULTIPLOT CORNER COORDINATES 5 5 95 95 4977 TITLE V = 1 4978 PLOT PBWA(X,1) FOR X = 0.1 0.1 5 AND 4979 PLOT PBWA1(X,1) FOR X = 0.1 0.1 5 4980 TITLE V = 2 4981 PLOT PBWA(X,2) FOR X = 0.1 0.1 5 AND 4982 PLOT PBWA1(X,2) FOR X = 0.1 0.1 5 4983 TITLE V = 3 4984 PLOT PBWA(X,3) FOR X = 0.1 0.1 5 AND 4985 PLOT PBWA1(X,3) FOR X = 0.1 0.1 5 4986 TITLE V = 4 4987 PLOT PBWA(X,4) FOR X = 0.1 0.1 5 AND 4988 PLOT PBWA1(X,4) FOR X = 0.1 0.1 5 4989 END OF MULTIPLOT 4990 MOVE 50 95 4991 JUSTIFICATION CENTER 4992 TEXT PBWA (AND DERIVATIVE) FUNCTIONS 4993 4994-----PEAKS OF FREQUENCY TABLE (LET)---------------------------------- 4995 4996PEAKS OF FREQUENCY TABLE 4997 4998Name: 4999 PEAKS OF FREQUENCY TABLE (LET) 5000 5001Type: 5002 Let Subcommand 5003 5004Purpose: 5005 Bin (i.e., create a frequency table) a response variable and 5006 then thin the frequency table by extracting the peaks. 5007 5008Description: 5009 Binning a data variable means to divide it into classes 5010 and compute the frequency for each class. This is the 5011 numerical equivalent of a histogram. 5012 5013 Peaks are determined as follows: 5014 5015 1) Compute the difference of the frequency counts. 5016 5017 2) Where the differences change sign indicates a peak. 5018 5019 Also, you can specify that relative frequencies rather than 5020 counts be computed. The command 5021 5022 SET RELATIVE HISTOGRAM <AREA/PERCENT> 5023 5024 can be used to specify whether relative frequencies are 5025 computed so that the area sums to 1 or so that frequencies 5026 sum to 1. The first option, which is the default, is useful 5027 for when using the relative binning as an estimate of a 5028 probability distribution. The second option is useful when 5029 you want to see what percentage of the data falls in a given 5030 class. 5031 5032Syntax 1: 5033 LET <y2> <x2> = PEAKS OF FREQUENCY TABLE <y> 5034 <SUBSET/EXCEPT/FOR qualification> 5035 where <y> is the response variable; 5036 <y2> is a variable where the computed counts (or 5037 frequencies) are stored; 5038 <x2> is a variable where the computed bin mid-points 5039 are stored; 5040 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 5041 5042 This syntax is used for the case where the frequencies are 5043 expressed as raw counts. 5044 5045Syntax 2: 5046 LET <y2> <x2> = RELATIVE PEAKS OF FREQUENCY TABLE <y> 5047 <SUBSET/EXCEPT/FOR qualification> 5048 where <y> is the response variable; 5049 <y2> is a variable where the computed counts (or 5050 frequencies) are stored; 5051 <x2> is a variable where the computed bin mid-points 5052 are stored; 5053 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 5054 5055 This syntax is used for the case where the frequencies are 5056 expressed as relative frequencies. 5057 5058Examples: 5059 LET Y2 X2 = PEAKS OF FREQUENCY TABLE Y 5060 LET Y2 X2 = PEAKS OF FREQUENCY TABLE Y SUBSET TAG > 2 5061 LET Y2 X2 = RELATIVE PEAKS OF FREQUENCY TABLE Y 5062 5063Note: 5064 As with the histogram, you can use the CLASS WIDTH, CLASS 5065 LOWER, and CLASS UPPER commands to override these defaults. 5066 5067 By default, DATAPLOT uses a class width of 0.3 times the standard 5068 deviation of the variable. A number of alternative choices for 5069 class width can be set with the command 5070 5071 SET HISTOGRAM CLASS WIDTH 5072 5073 Enter HELP HISTOGRAM CLASS WIDTH for details. 5074 5075Default: 5076 None 5077 5078Synonyms: 5079 None 5080 5081Related Commands: 5082 BINNED = Compute a frequency table. 5083 COMBINE FREQUENCY TABLE = Combine low frequency classes in a 5084 frequency table. 5085 HISTOGRAM = Generate a histogram. 5086 CLASS WIDTH = Set class widths for histograms and 5087 other related commands. 5088 HISTOGRAM CLASS WIDTH = Specify the algorithm used to 5089 determine the class width. 5090 5091Applications: 5092 Data Analysis 5093 5094Implementation Date: 5095 2008/4 5096 5097Program: 5098 let u1 = 0 5099 let sd1 = 1 5100 let u2 = 5 5101 let sd2 = 3 5102 let p = 0.6 5103 let y = normal mixture rand numb for i = 1 1 500 5104 . 5105 set write decimals 4 5106 let y2 x2 = binned y 5107 print x2 y2 5108 . 5109 let y3 x3 = peaks of frequency table y 5110 print x3 y3 5111 . 5112 xlimits -5 15 5113 histogram y 5114 . 5115 line color blue 5116 line dash 5117 line thickness 0.2 5118 let ycoor1 = 0 5119 let npeak = size x3 5120 . 5121 loop for k = 1 1 npeak 5122 let xtemp = x3(k) 5123 let ytemp = y3(k) 5124 drawdata xtemp ycoor1 xtemp ytemp 5125 end of loop 5126 5127-----PEAKS OVER THRESHOLD PLOT-------------------------------------- 5128 5129PEAKS OVER THRESHOLD PLOT 5130 5131Name: 5132 PEAKS OVER THRESHOLD PLOT 5133 5134Type: 5135 Graphics Command 5136 5137Purpose: 5138 Generates a peaks over threshold plot. 5139 5140Description: 5141 In univariate extreme value analysis, there are two basic 5142 approaches for extracting the extreme data. 5143 5144 1) We find the maximum (or minimum) value in equal 5145 length intervals. For example, we could extract the 5146 maximum wind speed for each year and then develop a 5147 distributional model for these yearly maximums. 5148 5149 This is commonly referred to as the "epochal" method. 5150 5151 2) An alternative is to define an overall threshold. 5152 We then extract all points above that threshold and 5153 develop a distributional model for these points. Note 5154 that in this case, the number of points extracted in 5155 each interval is not necessarily equal. 5156 5157 The generalized Pareto distribution provides a useful 5158 distributional model for univariate extreme value data since 5159 it indicates what type of extreme value model is appropriate: 5160 5161 1) gamma = 0 - this is equivalent to an extreme value 5162 type I (Gumbel) distribution. 5163 2) gamma > 0 - this is equivalent to an extreme value 5164 type II (Frechet) distribution. 5165 3) gamma < 0 - this is equivalent to a reverse Weibull 5166 distribution (in Dataplot, this is a 5167 Weibull with SET MINMAX MAXIMUM). The 5168 shape parameter for the reverse Weibull 5169 is -1/gamma. 5170 5171 The purpose of the PEAKS OVER THRESHOLD PLOT is to see 5172 how the estimated value of gamma changes as the threshold 5173 is changed. Specifically, the plot is generated as follows: 5174 5175 1) Define an initial threshold. In Dataplot, you can 5176 specify either the starting number of points above the 5177 threshold or a particular value for the threshold. 5178 5179 To specify the intial number of points above the 5180 threshold, enter the command 5181 5182 SET PEAKS OVER THRESHOLD INITIAL POINTS <value> 5183 5184 To specify a starting value for the threshold, enter 5185 the command 5186 5187 SET PEAKS OVER THRESHOLD INITIAL THRESHOLD <value> 5188 5189 If neither command is given, Dataplot will start 5190 with a threshold that gives 2.5% of the data set. 5191 If both are specified, the INITIAL THRESHOLD takes 5192 precedence over the INITIAL POINTS. 5193 5194 2) For the points above the threshold, estimate the 5195 parameters for the generalized Pareto distribution 5196 (see the Note section below for details on how this 5197 is done). 5198 5199 In addition, calculate a confidence interval for 5200 the shape parameter. For the de Haan and CME methods 5201 (see the Note section below), we compute the standard 5202 deviation of the estimate of gamma. We then use 5203 gamma +/- 2*sd(gamma) as an estimate of the confidence 5204 interval. For the PPCC plot method, the confidence 5205 interval is computed using bootstrapping. 5206 5207 3) Decrement the threshold. To specify how much to 5208 decrement the threshold at each interval, enter the 5209 command 5210 5211 SET PEAKS OVER THRESHOLD INCREMENT <value> 5212 5213 The default increment is -1. 5214 5215 4) This is repeated for a pre-specified number of 5216 iterations. The default number of iterations is 30. 5217 To change the number of iterations, enter the command 5218 5219 SET PEAKS OVER THRESHOLDS ITERATIONS <value> 5220 5221 The plot then consists of three curves: 5222 5223 1) The point estimates of gamma. 5224 2) The lower confidence limit for gamma. 5225 3) The upper confidence limit for gamma. 5226 5227 Each of these is plotted against the number of points above 5228 the threshold. To have the actual threshold plotted on the 5229 horizontal axis, enter the command 5230 5231 SET PEAKS OVER THRESHOLD X AXIS THRESHOLD 5232 5233 To restore the default of the number of points above the 5234 threshold, enter the command 5235 5236 SET PEAKS OVER THRESHOLD X AXIS POINTS 5237 5238 The basic interpretation of this plot is: 5239 5240 When the threshold is high, few points are included so 5241 the variance of gamma is also high (and so the resulting 5242 confidence intervals are wide). As the threshold 5243 decreases (and more points are included), the variance 5244 of gamma decreases with resulting narrower confidence 5245 intervals. However, as the number of points increases, 5246 the bias of the estimate of gamma increases. This will 5247 often be indicated by a downward slope of the graph. 5248 Over intervals where the bias error is small, the 5249 graph will be nearly horizontal. When choosing a 5250 reasonable value of gamma from the graph, it should 5251 be noted that larger estimates of gamma imply a 5252 longer tail and are therefore conservative from a 5253 structural engineering point of view. 5254 5255 In addition to the plot, this command will also generate 5256 the following tables at each iteration. 5257 5258 1) The first table contains the threshold, the number 5259 of points above the threshold, and the parameter 5260 estimates. 5261 5262 2) In engineering applications, the mean recurrence 5263 interval (this is also referred to as the return 5264 interval or recurrence interval) is of interest. 5265 5266 The return interval of a given wind speed, in years, is 5267 defined as the inverse of the probability that the wind 5268 speed will be exceeded in any one year. It is defined as 5269 5270 1/(1 - F(x)) 5271 5272 with F(x) denoting the cumulative distribution function. 5273 Mean recurrence intervals are discussed in more detail 5274 in Simiu and Scanlon (see References section below). 5275 5276 More often, we would like to compute the wind speed 5277 that corresponds to a given return interval. The 5278 solution to this is given by solving the above 5279 equation for x. 5280 5281 X(R) = G(1 - (1/R)) 5282 5283 with G and R denoting the percent point function and 5284 the desired mean recurrence interval, respectively. 5285 5286 The above formula is for the case of a single yearly 5287 maximum. If lambda is the mean number of threshold 5288 crossings per year, the formula is 5289 5290 X(R) = G(1 - (1/(lambda*R))) 5291 5292 In the Dataplot PEAKS OVER THRESHOLD PLOT command, you 5293 can optionally give a second variable that specifies the 5294 desired mean recurrence intervals. If you specify mean 5295 return intervals, Dataplot will print a table showing 5296 the mean return interval along with the corresponding 5297 wind speed (called XR). 5298 5299 3) In wind engineering applications, the load factor is 5300 also of interest. This is commonly computed as 5301 5302 (XMAX/XR(50))**2 5303 5304 with XMAX denoting the maximum value of the fitted 5305 generalized Pareto distribution (the generalized 5306 Pareto is bounded above if the shape parameter is 5307 negative) and XR(50) denoting the wind speed 5308 corresponding to a mean recurrence interval of 50 5309 years. 5310 5311 To print the value of the maximum wind speed and the 5312 load factor, enter the command 5313 5314 SET PEAKS OVER THRESHOLD LOAD FACTOR OFF 5315 5316 Since this is specific to extreme wind applications, 5317 it is OFF by default. 5318 5319Syntax 1: 5320 PEAKS OVER THRESHOLD PLOT <y> <SUBSET/EXCEPT/FOR qualification> 5321 where <y> is a response variable; 5322 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 5323 5324Syntax 2: 5325 PEAKS OVER THRESHOLD PLOT <y> <r> 5326 <SUBSET/EXCEPT/FOR qualification> 5327 where <y> is a response variable; 5328 <r> is a variable containing mean recurrence intervals; 5329 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 5330 5331Examples: 5332 PEAKS OVER THRESHOLD PLOT Y 5333 PEAKS OVER THRESHOLD PLOT Y R 5334 PEAKS OVER THRESHOLD PLOT Y SUBSET TAG > 1 5335 5336Note: 5337 There are a number of methods for estimating the parameters 5338 for the generalized Pareto distribution. To specify the 5339 method, enter the command 5340 5341 SET PEAKS OVER THRESHOLD METHOD <value> 5342 5343 where <value> is one of the following: 5344 5345 DEHAAN - use the de Haan method (enter HELP DEHAAN 5346 for the details of this method) 5347 CME - use the conditional mean exceedance method 5348 (enter HELP CME for the details of this method) 5349 PPCC - use the PPCC (probability plot correlation 5350 coefficient plot) to estimate gamma and a 5351 probability plot to estimate the location and 5352 scale parameters. A 95% confidence interval 5353 for the gamma parameter is obtained via the 5354 bootstrap. For details of these methods, enter 5355 HELP PPCC PLOT, HELP PROBABILITY PLOT, and 5356 HELP DISTRIBUTIONAL BOOTSTRAP). 5357 5358 You can obtain more accurate estimates for 5359 gamma by restricting the range for the PPCC 5360 plot. Enter the commands 5361 5362 LET GAMMA1 = <lower limit> 5363 LET GAMMA2 = <upper limit> 5364 5365 One recommendation is to run the plot with the 5366 default limits and then rerun it with tighter 5367 limits based on the first plot (be sure to keep 5368 them wide enough to accomodate the bootstrap 5369 estimates). 5370 5371 Additional methods will be added in future releases of 5372 Dataplot. The default is DEHAAN. 5373 5374Note: 5375 Since this command generates a large number of tables, it 5376 is typically desired to save them to file. To do this, 5377 enter the commands 5378 5379 CAPTURE POT.OUT 5380 PEAKS OVER THRESHOLD PLOT Y R 5381 END OF CAPTURE 5382 5383 You can alternatively choose to save the output in HTML, 5384 Latek, or RTF (Rich Text Format) formats. For example, 5385 5386 CAPTURE HTML POT.HTM 5387 PEAKS OVER THRESHOLD PLOT Y R 5388 END OF CAPTURE 5389 5390 CAPTURE LATEX POT.TEK 5391 PEAKS OVER THRESHOLD PLOT Y R 5392 END OF CAPTURE 5393 5394 CAPTURE RTF POT.RTF 5395 PEAKS OVER THRESHOLD PLOT Y R 5396 END OF CAPTURE 5397 5398 The HTML and Latex formats can incorporate the plot as 5399 well. For details, enter 5400 5401 HELP CAPTURE HTML 5402 HELP CAPTURE LATEX 5403 5404Note: 5405 Dataplot automatically writes the following values to the 5406 file dpst1f.dat (there is one row for each distinct value 5407 of the threshold, the following correspond to the columns 5408 in dpst1f.dat): 5409 5410 1. Number of points above the threshold 5411 2. The threshold 5412 3. The estimate of the shape parameter, gamma 5413 4. The estimate of the location parameter 5414 5. The estimate of the scale parameter 5415 5416 If mean recurrence intervals have been specified (see 5417 Syntax 2), Dataplot additionally writes the following values 5418 to the 5419 file dpst2f.dat: 5420 5421 1. Iteration 5422 2. Number of points above the threshold 5423 3. The threshold 5424 4. The requested mean recurrence interval 5425 5. The XR corresponding to the requested mean 5426 recurrence interval 5427 6. The load factor corresponding to the mean recurrence 5428 interval 5429 5430 Note that the last column, the load factor, is only printed 5431 if the SET LOAD FACTOR ON command is entered. This load 5432 factor is 5433 5434 (XR/XR50)**2 5435 5436 A -99.0 is printed for mean recurrence intervals less than 5437 or equal to 50. 5438 5439 The purpose of writing these values to files is to allow 5440 you to perform additional analyses. For example, you may 5441 want to plot the XR corresponding to the various return 5442 intervals. This is demonstrated in the program example 5443 below. 5444 5445Note: 5446 Some sources reverse the sign in the definition of the 5447 generalized Pareto distribution. For details, enter 5448 the command 5449 5450 HELP GEPPDF 5451 5452 If you use the reversed sign definition, then adjust the 5453 role of positive and negative values of gamma in the 5454 discussion above. 5455 5456Default: 5457 None 5458 5459Synonyms: 5460 POT is a synonym for PEAKS OVER THRESHOLD 5461 5462Related Commands: 5463 DEHAAN = Compute the estimates for the parameters 5464 of the generalized Pareto distribution 5465 using the de Haan method. 5466 CME = Compute the estimates for the parameters 5467 of the generalized Pareto distribution 5468 using the CME method. 5469 GEPPPF = Computes the percent point function of 5470 the generalized Pareto distribution. 5471 PPCC PLOT = Generates a ppcc plot. 5472 PROBABILITY PLOT = Generates a probability plot. 5473 DISTRIBUTIONAL = Perform a bootstrap analysis for a 5474 BOOTSTRAP univariate distribution. 5475 CME PLOT = Generates a conditional mean exceedance plot. 5476 5477Reference: 5478 E. Simiu, N. A. Heckert, and T. Whalen (April, 1996). "Estimates 5479 of Hurricane Wind Speeds by the 'Peaks Over Threshold' Method", 5480 NIST Technical Note 1416. 5481 5482 E. Simiu and N. A. Heckert (March 1995). "Extreme Wind 5483 Distribution Tails: A 'Peak Over Threshold' Approach", 5484 NIST Building Science Series 174. 5485 5486 Alan Heckert, Emil Simiu, and Tim Whalen (April,1998). 5487 "Estimates of Hurricane Wind Speeds by the 'Peaks Over 5488 Threshold' Approach", Journal of Structural Engineering, 5489 pp. 445-449. 5490 5491 J. A. Lechner, E. Simiu, N. A. Heckert (1993). "Assessment of 5492 'peak over threshold' Methods for Estimating Extreme Value 5493 Distribution Tails", Structural Safety, 12, pp. 305-314. 5494 5495 E. Simiu and N. A. Heckert (1996). "Extreme Wind Distribution 5496 Tails: A 'Peaks Over Threshold' Approach", Journal of Structural 5497 Engineering, Vol. 122, No. 5, 1996. 5498 5499Applications: 5500 Extreme Value Analysis 5501 5502Implementation Date: 5503 2005/5 5504 5505Program: 5506 DIMENSION 40 COLUMNS 5507 SKIP 2 5508 READ PARAMETER MPOST550.DAT URATE 5509 SKIP 3 5510 READ MPOST550.DAT Y1 TO Y17 5511 . 5512 TITLE Peaks Over Threshold Plot (Milepost 550)CR()de Haan Method 5513 TITLE DISPLACEMENT 5 5514 Y1LABEL Gamma 5515 X1LABEL Number of Points Above Threshold 5516 TITLE CASE ASIS 5517 LABEL CASE ASIS 5518 LINE SOLID DOT DOT 5519 LINE THICKNESS 0.2 0.1 0.1 5520 . 5521 SET PEAKS OVER THRESHOLD ITERATIONS 50 5522 SET PEAKS OVER THRESHOLD PERIOD URATE 5523 SET PEAKS OVER THRESHOLD METHOD DEHAAN 5524 . 5525 LET R = DATA 25 50 100 200 500 1000 5526 . 5527 CAPTURE POT.OUT 5528 PEAKS OVER THRESHOLD PLOT Y17 R 5529 END OF CAPTURE 5530 . 5531 SKIP 0 5532 READ DPST2F.DAT ITER NPOINTS THRESH R2 XR 5533 . 5534 TITLE Mean Recurrence Intervals (Milepost 550) 5535 TITLE DISPLACEMENT 2 5536 Y1LABEL XR 5537 LINE SOLID ALL 5538 LINE THICKNESS 0.1 ALL 5539 . 5540 PLOT XR NPOINTS R2 5541 . 5542 CRLF ON 5543 MARGIN 87 5544 MOVE 87 88 5545 TEXT 1,000 - yr 5546 TEXT 500 5547 TEXT 200 5548 TEXT 100 5549 TEXT 50 5550 TEXT 25 5551 5552-----PEARSON CONTINGENCY COEFICIENT (LET)-------------------------------- 5553 5554PEARSON CONTINGENCY COEFICIENT 5555 5556Name: 5557 PEARSON CONTINGENCY COEFICIENT (LET) 5558 5559Type: 5560 Let Subcommand 5561 5562Purpose: 5563 Compute Pearson's contingency coefficient for an RxC contingency 5564 table. 5565 5566Description: 5567 If we have N observations with two variables where each 5568 observation can be classified into one of R mutually exclusive 5569 categories for variable one and one of C mutually exclusive 5570 categories for variable two, then a cross-tabulation of the 5571 data results in a two-way contingency table (also referred to 5572 as an RxC contingency table). The resulting contingency table 5573 has R rows and C columns. 5574 5575 A common question with regards to a two-way contingency 5576 table is whether we have independence. By independence, we 5577 mean that the row and column variables are unassociated 5578 (i.e., knowing the value of the row variable will not 5579 help us predict the value of column variable and likewise 5580 knowing the value of the column variable will not help us 5581 predict the value of the row variable). 5582 5583 A more technical definition for independence is that 5584 5585 P(row i, column j) = P(row i)*P(column j) for all i,j 5586 5587 The standard test statistic for determing independence is 5588 the chi-square test statistic: 5589 5590 T = SUM[i=1 to r][j=1 to c][(O(ij) - E(ij)**2/E(ij)] 5591 5592 where 5593 5594 r = the number of rows in the contingency table 5595 c = the number of columns in the contingency table 5596 O(ij) = the observed frequency of the ith row and 5597 jth column 5598 E(ij) = the expected frequency of the ith row and 5599 jth column 5600 = R(i)*C(j)/N 5601 R(i) = the sum of the observed frequencies for row i 5602 C(j) = the sum of the observed frequencies for column j 5603 N = the total sample size 5604 5605 One criticism of this statistic is that it does not give a 5606 meaningful description of the degree of dependence (or strength of 5607 association). That is, it is useful for determining whether there 5608 is dependence. However, since the strength of that association also 5609 depends on the degrees of freedom as well as the value of the test 5610 statistic, it is not easy to interpert the strength of association. 5611 5612 The Pearson's contingency coefficient is one method to provide an 5613 easier to interpret measure of strength of association. Specifically, 5614 it is: 5615 5616 Pearson's Coefficient = SQRT(T/(N+T)) 5617 5618 where 5619 5620 T = the chi-square test statistic given above 5621 N = the total sample size 5622 5623 So this statistic basically scales the chi-square statistic to 5624 a value between 0 (no association) and 1 (maximum association). 5625 It has the desirable property of scale invariance. That is, 5626 if the sample size increases, the value of Pearson's contingency 5627 coefficient does not change as long as values in the table change 5628 the same relative to each other. 5629 5630 The data for the contingency table can be specified in either of 5631 the following two ways: 5632 5633 1) raw data 5634 5635 In this case, you will have two variables. The first 5636 will contain r distinct values and the second will contain 5637 c distinct values. Dataplot will automatically perform the 5638 cross-tabulation to obtain the counts for each cell. Although 5639 the distinct values will typically be integers, this is not 5640 strictly required. 5641 5642 2) table data 5643 5644 If you only have the resulting contingency table (i.e., the 5645 counts for each cell), then you can use the READ MATRIX (or 5646 CREATE MATRIX) command to create a matrix with the data. This 5647 is demonstrated in the example program below. 5648 5649 In this case, your data should contain non-negative integers 5650 since they represent the counts for each cell. 5651 5652Syntax 1: 5653 LET <par> = PEARSON CONTINGENCY COEFICIENT <y1> <y2> 5654 <SUBSET/EXCEPT/FOR qualification> 5655 where <y1> is the first response variable; 5656 <y2> is the second response variable; 5657 <par> is a parameter where the computed Pearson contingency 5658 coefficient is stored; 5659 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 5660 5661 Use this syntax for raw data. 5662 5663Syntax 2: 5664 LET <par> = MATRIX GRAND PEARSON CONTINGENCY COEFICIENT <y1> <y2> 5665 <SUBSET/EXCEPT/FOR qualification> 5666 where <m> is a matrix containing the contingency table; 5667 <par> is a parameter where the computed Pearson contingency 5668 coefficient is stored; 5669 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 5670 5671 Use this syntax if your data is a contingency table. 5672 5673Examples: 5674 LET A = PEARSON CONTINGENCY COEFICIENT Y1 Y2 5675 LET A = MATRIX GRAND PEARSON CONTINGENCY COEFICIENT M 5676 5677Note: 5678 The Cramer contingency coefficient is more commonly used 5679 than the Pearson contingency coefficient. 5680 5681Note: 5682 For the raw data case, the two variables should have the same 5683 number of elements. 5684 5685Note: 5686 The following additional commands are supported 5687 5688 TABULATE PEARSON CONTINGENCY COEFICIENT Y1 Y2 X 5689 CROSS TABULATE PEARSON CONTINGENCY COEFICIENT Y1 Y2 X1 X2 5690 5691 PEARSON CONTINGENCY COEFICIENT PLOT Y1 Y2 X 5692 CROSS TABULATE PEARSON CONTINGENCY COEFICIENT PLOT Y1 Y2 X1 X2 5693 5694 BOOTSTRAP PEARSON CONTINGENCY COEFICIENT PLOT Y1 Y2 5695 JACKNIFE PEARSON CONTINGENCY COEFICIENT PLOT Y1 Y2 5696 5697 Note that the above commands expect the variables to have 5698 the same number of observations. 5699 5700 Note that the above commands are only available if you have 5701 raw data. 5702 5703Default: 5704 None 5705 5706Synonyms: 5707 None 5708 5709Related Commands: 5710 CHI-SQUARE INDEPENDENCE TEST = Perform a chi-square test for 5711 independence. 5712 CRAMER CONTINGENCY COEFFICIENT = Compute Cramer's contingency 5713 coefficient. 5714 ASSOCIATION PLOT = Generate an association plot. 5715 SIEVE PLOT = Generate a sieve plot. 5716 ODDS RATIO INDEPENDENCE TEST = Perform a log(odds ratio) test for 5717 independence. 5718 FISHER EXACT TEST = Perform Fisher's exact test. 5719 ROSE PLOT = Generate a Rose plot. 5720 BINARY TABULATION PLOT = Generate a binary tabulation plot. 5721 ROC CURVE = Generate a ROC curve. 5722 ODDS RATIO = Compute the bias corrected odds 5723 ratio. 5724 LOG ODDS RATIO = Compute the bias corrected 5725 log(odds ratio). 5726 5727Reference: 5728 Conover (1999), "Practical Nonparametric Statistics", 5729 Third Edition, Wiley, pp. 229-230. 5730 5731 Friendly (2000), "Visualizing Categorical Data", SAS Institute 5732 Inc., p. 61. 5733 5734Applications: 5735 Categorical Data Analysis 5736 5737Implementation Date: 5738 2007/5 5739 5740Program: 5741 . Sample data from page 61 of Friendly 5742 read matrix m 5743 5 29 14 16 5744 15 54 14 10 5745 20 84 17 94 5746 68 119 26 7 5747 end of data 5748 . 5749 let a = matrix pearson contingency coefficient m 5750 5751-----PEARSON DISSIMILARITY (LET)-------------------------------- 5752 5753PEARSON DISSIMILARITY 5754 5755Name: 5756 PEARSON DISSIMILARITY (LET) 5757 PEARSON SIMILARITY (LET) 5758 5759Type: 5760 Let Subcommand 5761 5762Purpose: 5763 Compute the Pearson correlation coefficient transformed to a 5764 dissimilarity measure between two variables. 5765 5766Description: 5767 The correlation coefficient is a measure of the linear relationship 5768 between two variables. It is computed as: 5769 5770 Sxx = SUM[i=1 to N][(X(i)-XMEAN)**2] 5771 Syy = SUM[i=1 to N]([Y(i)-YMEAN)**2] 5772 Sxy = SUM[i=1 to N][(X(i)-XMEAN)*(Y(i)-YMEAN)] 5773 r = Sxy/SQRT(Sxx*Syy) 5774 5775 A perfect linear relationship yields a correlation coefficient of 5776 +1 (or -1 for a negative relationship) and no linear relationship 5777 yields a correlation coefficient of 0. 5778 5779 In some applications, such as clustering, it can be useful to 5780 transform the correlation coefficient to a dissimilarity measure. 5781 The transformation used here is 5782 5783 d = (1 - r)/2 5784 5785 This converts the correlation coefficient with values between -1 and 5786 1 to a score between 0 and 1. High positive correlation (i.e., very 5787 similar) results in a dissimilarity near 0 and high negative 5788 correlation (i.e., very dissimilar) results in a dissimilarity near 1. 5789 5790 If a similarity score is preferred, you can use 5791 5792 s = 1 - d 5793 5794 where d is defined as above. 5795 5796Syntax 1: 5797 LET <par> = PEARSON DISSIMILARITY <y1> <y2> 5798 <SUBSET/EXCEPT/FOR qualification> 5799 where <y1> is the first response variable; 5800 <y2> is the second response variable; 5801 <par> is a parameter where the computed Pearson dissimilarity 5802 is stored; 5803 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 5804 5805Syntax 2: 5806 LET <par> = PEARSON SIMILARITY <y1> <y2> 5807 <SUBSET/EXCEPT/FOR qualification> 5808 where <y1> is the first response variable; 5809 <y2> is the second response variable; 5810 <par> is a parameter where the computed Pearson similarity 5811 is stored; 5812 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 5813 5814Examples: 5815 LET A = PEARSON DISSIMILARITY Y1 Y2 5816 LET A = PEARSON DISSIMILARITY Y1 Y2 SUBSET TAG > 2 5817 LET A = PEARSON SIMILARITY Y1 Y2 5818 5819Note: 5820 The two variables must have the same number of elements. 5821 5822Default: 5823 None 5824 5825Synonyms: 5826 PEARSON DISTANCE is a synonym for PEARSON DISSIMILARITY 5827 5828Related Commands: 5829 CORRELATION = Compute the Pearson correlation of two 5830 variables. 5831 SPEARMAN DISSIMILARITY = Compute the dissimilarity of two variables 5832 based on Spearman's rank correlation. 5833 KENDALL TAU DISSIMILARITY = Compute the dissimilarity of two variables 5834 based on Kendall's tau correlation. 5835 COSINE DISTANCE = Compute the cosine distance. 5836 MANHATTAN DISTANCE = Compute the Euclidean distance. 5837 EUCLIDEAN DISTANCE = Compute the Euclidean distance. 5838 MATRIX DISTANCE = Compute various distance metrics for a 5839 matrix. 5840 GENERATE MATRIX <stat> = Compute a matrix of pairwise statistic 5841 values. 5842 CLUSTER = Perform a cluster analysis. 5843 5844Reference: 5845 Kaufman and Rousseeuw (1990), "Finding Groups in Data: An 5846 Introduction To Cluster Analysis", Wiley. 5847 5848Applications: 5849 Clustering 5850 5851Implementation Date: 5852 2017/08: 5853 2018/10: Added PEARSON SIMILARITY 5854 5855Program 1: 5856 SKIP 25 5857 READ BERGER1.DAT Y X 5858 LET CORR = CORRELATION Y X 5859 LET D = PEARSON DISSIMILARITY Y X 5860 SET WRITE DECIMALS 3 5861 PRINT CORR D 5862 5863Program 2: 5864 SKIP 25 5865 READ IRIS.DAT Y1 Y2 Y3 Y4 5866 SET WRITE DECIMALS 3 5867 . 5868 LET M = GENERATE MATRIX PEARSON DISSIMILARITY Y1 Y2 Y3 Y4 5869 PRINT M 5870 5871Program 3: 5872 SKIP 25 5873 READ IRIS.DAT Y1 Y2 Y3 Y4 TAG 5874 . 5875 CASE ASIS 5876 TITLE CASE ASIS 5877 TITLE OFFSET 2 5878 LABEL CASE ASIS 5879 TIC MARK OFFSET UNITS DATA 5880 YLIMITS 0 1 5881 MAJOR YTIC MARK NUMBER 6 5882 MINOR YTIC MARK NUMBER 1 5883 Y1TIC MARK LABEL DECIMAL 1 5884 Y1LABEL DISPLACEMENT 20 5885 X1LABEL Species 5886 XLIMITS 1 3 5887 MAJOR XTIC MARK NUMBER 3 5888 MINOR XTIC MARK NUMBER 0 5889 XTIC MARK OFFSET 0.3 0.3 5890 X1LABEL DISPLACEMENT 14 5891 CHARACTER X BLANK 5892 LINES BLANK SOLID 5893 . 5894 MULTIPLOT CORNER COORDINATES 5 5 95 95 5895 MULTIPLOT SCALE FACTOR 2 5896 MULTIPLOT 2 3 5897 . 5898 TITLE Sepal Length vs Sepal Width 5899 CORRELATION PLOT Y1 Y2 TAG 5900 . 5901 TITLE Sepal Length vs Petal Length 5902 CORRELATION PLOT Y1 Y3 TAG 5903 . 5904 TITLE Sepal Length vs Petal Width 5905 CORRELATION PLOT Y1 Y4 TAG 5906 . 5907 TITLE Sepal Width vs Petal Length 5908 CORRELATION PLOT Y2 Y3 TAG 5909 . 5910 TITLE Sepal Width vs Petal Width 5911 CORRELATION PLOT Y2 Y4 TAG 5912 . 5913 TITLE Petal Length vs Petal Width 5914 CORRELATION PLOT Y3 Y4 TAG 5915 . 5916 END OF MULTIPLOT 5917 . 5918 JUSTIFICATION CENTER 5919 MOVE 50 97 5920 TEXT Pearson Dissimilarity Coefficient 5921 5922-----PEDESTAL------------------------------------------------------- 5923 5924PEDESTAL 5925 5926Note: 5927 THIS COMMAND IS NOT CURRENTLY OPERATIONAL!!!! 5928 5929Name: 5930 PEDESTAL 5931 5932Type: 5933 Plot Control Command 5934 5935Purpose: 5936 Specifies whether or not a pedestal will appear on subsequent 5937 3-d plots (as generated via the 3D-PLOT command). 5938 5939Description: 5940 A pedestal is a base upon which 3-dimensional surfaces may rest. 5941 It is the preferred representation of 3-d surfaces by some 5942 analysts. 5943 5944Syntax: 5945 PEDESTAL <ON or OFF> 5946 where ON specifies that the pedestal will be generated while OFF 5947 specifies that it will not. 5948 5949Examples: 5950 PEDESTAL ON 5951 PEDESTAL OFF 5952 PEDESTAL 5953 5954Default: 5955 Off 5956 5957Synonyms: 5958 None 5959 5960Related Commands: 5961 3D-PLOT = Generates a 3-d data or function plot. 5962 EYE COORDINATES = Sets the location of the eye for 3-d plots. 5963 PEDESTAL COLOR = Sets the pedestal color for 3-d plots. 5964 PEDESTAL SIZE = Sets the pedestal height for 3-d plots. 5965 VISIBLE = Allows/suppress hidden lines in 3-d plots. 5966 5967Applications: 5968 3D plots 5969 5970Implementation Date: 5971 XX 5972 5973Program: 5974 XX 5975 5976-----PEDESTAL COLOR---------------------------------------------------- 5977 5978PEDESTAL COLOR 5979 5980Note: 5981 The PEDESTAL command is not currently operational, so this command 5982 has no effect. 5983 5984Name: 5985 PEDESTAL COLOR 5986 5987Type: 5988 Plot Control Command 5989 5990Purpose: 5991 Specifies the color of the lines which constitute the pedestal in 5992 subsequent 3-d plots. 5993 5994Syntax: 5995 PEDESTAL COLOR <color> 5996 where <color> specifies the desired color. 5997 5998Examples: 5999 PEDESTAL COLOR GREEN 6000 PEDESTAL COLOR YELLOW 6001 PEDESTAL COLOR 6002 6003Note: 6004 The PEDESTAL COLOR command with no arguments reverts the pedestal 6005 color to default. 6006 6007Default: 6008 The default is black (but the default is for the pedestal lines 6009 themselves to be off.) 6010 6011Synonyms: 6012 None 6013 6014Related Commands: 6015 PEDESTAL = Allows/suppresses the pedestal for 3-d plots. 6016 PEDESTAL SIZE = Sets the pedestal height for 3-d plots. 6017 3D-PLOT = Generates a 3-d data or function plot. 6018 EYE COORDINATES = Sets the location of eye for 3-d plots. 6019 6020Applications: 6021 XX 6022 6023Implementation Date: 6024 XX 6025 6026Program: 6027 XX 6028 6029-----PEDESTAL SIZE---------------------------------------------------- 6030 6031PEDESTAL SIZE 6032 6033Note: 6034 The PEDESTAL command is not currently operational, so this command 6035 has no effect. 6036 6037Name: 6038 PEDESTAL SIZE 6039 6040Type: 6041 Plot Control Command 6042 6043Purpose: 6044 Specifies the vertical height of the pedestal in subsequent 3-d 6045 plots. 6046 6047Description: 6048 The size is in units of the vertical axis variable on the 3-d plot. 6049 6050Syntax: 6051 PEDESTAL SIZE <size> 6052 where <size> is a number or parameter in units of the 3-d vertical 6053 axis variable that specifies the size. 6054 6055Examples: 6056 PEDESTAL SIZE 2000 6057 PEDESTAL SIZE 4500 6058 PEDESTAL SIZE 0.0025 6059 6060Default: 6061 The default size is (zmax - zmin) where 6062 zmax = the data maximum for the vertical axis variable; 6063 zmin = the data minimum for the vertical axis variable. 6064 6065Synonyms: 6066 None 6067 6068Related Commands: 6069 PEDESTAL = Allows/suppresses the pedestal for 3-d plots. 6070 PEDESTAL COLOR = Sets the pedestal color for 3-d plots. 6071 3D-PLOT = Generates a 3-d data or function plot. 6072 EYE COORDINATES = Sets the location of the eye for 3-d plots. 6073 6074Applications: 6075 XX 6076 6077Implementation Date: 6078 XX 6079 6080Program: 6081 XX 6082 6083-----PEN MAP------------------------------------------------------- 6084 6085PEN MAP 6086 6087Name: 6088 PEN MAP 6089 6090Type: 6091 Output Devices Command 6092 6093Purpose: 6094 Allows the mapping of colors to pen slots to be defined by 6095 the user for selected pen plotters. 6096 6097Description: 6098 Pen plotters allow different color pens to be loaded into each pen 6099 slot. Previously, the color to pen slot mapping was hard coded in 6100 DATAPLOT. The PEN MAP allows the user to re-define the default 6101 mapping for the HP-GL, ZETA, and CALCOMP devices. 6102 6103 For each of the supported devices, up to 16 pens can be defined. 6104 Also, specifying "LIST/SHOW/PRINT" for the color will print the 6105 current mapping and "DEFAULT" will reset the default mapping. 6106 6107 DATAPLOT also supports the Tektronix 4662 and HP 7221 plotters. 6108 However, these are now essentially obsolete, so they are not 6109 supported with this command. 6110 6111Syntax 1: 6112 <device> PEN MAP <color> <index> 6113 where <device> is one of the following: 6114 HPGL - for HPGL plotters 6115 CALCOMP - for CALCOMP plotters 6116 ZETA - for Zeta plotters; 6117 <color> is a character string that specifies one of the 6118 colors available on the plotter; 6119 and <index> is an integer number or parameter between 1 and 16. 6120 6121Syntax 2: 6122 <device> PEN MAP <keyword> 6123 where <device> is one of the following: 6124 HPGL - for HPGL plotters 6125 CALCOMP - for CALCOMP plotters 6126 ZETA - for Zeta plotters; 6127 and <keyword> is one of the following: 6128 LIST - print the current mapping 6129 SHOW - print the current mapping 6130 PRINT - print the current mapping 6131 DEFAULT - reset the default mapping. 6132 6133Examples: 6134 HPGL PEN MAP DEFAULT 6135 HPGL PEN MAP SHOW 6136 HPGL PEN MAP RED 4 6137 CALCOMP PEN MAP BLUE 2 6138 ZETA PEN MAP GREEN 4 6139 6140Note: 6141 If a color is defined more than once, it is mapped to lowest pen 6142 slot. 6143 6144Note: 6145 In earlier versions of DATAPLOT, specifying a color by index 6146 would cause penplotters to use the slot corresponding to the index 6147 number (i.e., color 1 would go to slot 1). However, to make the 6148 use of color names and color indices consistent across devices, 6149 an index now maps to a specific color (e.g., color 1 maps to 6150 black). This color is then mapped to a particular slot number 6151 (which is not necessarily the same as the index number). To see 6152 the default color to slot mapping, enter one of the following 6153 DATAPLOT commands: 6154 SHOW COLORS CALCOMP 6155 SHOW COLORS ZETA 6156 SHOW COLORS HPGL 6157 The PEN MAP command can be used to override the default color to 6158 slot mapping. 6159 6160Note: 6161 If your plotter always has the same color pens in the same slots 6162 with an order different than the default DATAPLOT order, then a 6163 series of PEN MAP commands can be placed in the start-up file 6164 DPLOGF.DAT. 6165 6166Default: 6167 The following is the default color to slot mapping for an eight 6168 slot penplotter: 6169 BLACK 1 6170 RED 2 6171 BLUE 3 6172 GREEN 4 6173 MAGENTA 5 6174 ORANGE 6 6175 CYAN 7 6176 YELLOW 8 6177 6178Synonyms: 6179 None 6180 6181Related Commands: 6182 SHOW COLORS = Print the available colors. 6183 6184Applications: 6185 XX 6186 6187Implementation Date: 6188 90/6 6189 6190Program: 6191 HPGL PEN MAP BLACK 1 6192 HPGL PEN MAP BLUE 2 6193 HPGL PEN MAP GREEN 3 6194 HPGL PEN MAP RED 4 6195 6196-----PEQ (LET)---------------------------------------------- 6197 6198PEQ 6199 6200Name: 6201 PEQ (LET) 6202 6203Type: 6204 Library Function 6205 6206Purpose: 6207 Compute the real component of the Weierstrass P elliptic function 6208 of a complex number (equianharmonic case with unit period 6209 parallelogram). 6210 6211Description: 6212 The Weierstrass elliptic function is described in detail in the 6213 Handbook of Mathematical Functions (see REFERENCE section below). 6214 6215Syntax: 6216 LET <a> = PEQ(<xr>,<xc>) <SUBSET/EXCEPT/FOR qualification> 6217 where <xr> is a number, parameter, or variable that specifies the 6218 the real component of the input; 6219 <xc> is a number, parameter, or variable that specifies the 6220 the complex component of the input; 6221 <a> is a variable or a parameter (depending on what <xr> and 6222 <xc> are) where the computed values are stored; 6223 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 6224 6225Examples: 6226 LET A = PEQ(2,1) 6227 LET A = PEQ(X,4) 6228 LET X2 = PEQ(1,Y) 6229 6230Note: 6231 The Weierstrass elliptic functions are computed using algorithm 6232 549 from the ACM Transactions on Mathematical Software (see the 6233 REFERENCE section below). 6234 6235Note: 6236 If the input value corresponds to a lattice point, an error 6237 message is printed and the output value is set to the largest 6238 real number on the machine. 6239 6240Note: 6241 Library functions are distinguished from let subcommands 6242 in the following ways. 6243 1) Functions enclose the input value in parenthesis. Let 6244 subcommands use spaces. 6245 2) Functions can accept (and return) either parameters 6246 (i.e., single values) or variables (i.e., an array of 6247 values) while let subcommands are specific in which they 6248 accept as input and what they return as output. 6249 3) Functions can accept expressions while let subcommands 6250 do not. For example, the following is legal: 6251 LET Y2 = ABS(Y1-INT(Y1)) 6252 For let subcommands, you typically have to do something 6253 like the following: 6254 LET YTEMP = Y**2 + 8 6255 LET A = SUM YTEMP 6256 6257Default: 6258 None 6259 6260Synonyms: 6261 None 6262 6263Related Commands: 6264 PEQI = Compute the complex component of the Weierstrass elliptic 6265 function (equianharmonic case). 6266 PEQ1 = Compute the real component of the first derivative of 6267 the Weierstrass elliptic function (equianharmonic case). 6268 PEQ1I = Compute the complex component of the first derivative of 6269 the Weierstrass elliptic function (equianharmonic case). 6270 PLEM = Compute the real component of the Weierstrass elliptic 6271 function (lemniscatic case). 6272 PLEMI = Compute the complex component of the Weierstrass elliptic 6273 function (lemniscatic case). 6274 PLEM1 = Compute the real component of the first derivative of 6275 the Weierstrass elliptic function (lemniscatic case). 6276 PLEM1I = Compute the complex component of the first derivative of 6277 the Weierstrass elliptic function (lemniscatic case). 6278 SN = Compute the Jacobi elliptic function sn. 6279 CN = Compute the Jacobi elliptic function cn. 6280 DN = Compute the Jacobi elliptic function dn. 6281 RF = Compute the Carlson elliptic integral of the first kind. 6282 RD = Compute the Carlson elliptic integral of the second kind. 6283 RJ = Compute the Carlson elliptic integral of the third kind. 6284 ELLIPC1 = Compute the Legendre complete elliptic integral of the 6285 first kind. 6286 ELLIPC2 = Compute the Legendre complete elliptic integral of the 6287 second kind. 6288 ELLIP1 = Compute the Legendre elliptic integral of the first 6289 kind. 6290 ELLIP2 = Compute the Legendre elliptic integral of the second 6291 kind. 6292 ELLIP3 = Compute the Legendre's elliptic integral of the third 6293 kind. 6294 6295Reference: 6296 "Algorithm 549: Weierstrass' Elliptic Functions", Eckhardt, ACM 6297 Transactions on Mathematical Software, vol. 6 (pp. 112-120). 6298 6299 "Handbook of Mathematical Functions, Applied Mathematics Series, 6300 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 6301 1964 (chapter 18). 6302 6303Applications: 6304 Special Functions 6305 6306Implementation Date: 6307 94/11 6308 6309Program: 6310 TITLE WEIERSTRASS ELLIPTIC FUNCTIONS 6311 LINE SOLID DASH 6312 PLOT PEQ(X,0.5) FOR X = 0 0.01 5 AND 6313 PLOT PEQI(X,0.5) FOR X = 0 0.01 5 6314 6315-----PEQI (LET)---------------------------------------------- 6316 6317PEQI 6318 6319Name: 6320 PEQI (LET) 6321 6322Type: 6323 Library Function 6324 6325Purpose: 6326 Compute the complex component of the Weierstrass P elliptic 6327 function of a complex number (equianharmonic case with unit period 6328 parallelogram). 6329 6330Description: 6331 The Weierstrass elliptic function is described in detail in the 6332 Handbook of Mathematical Functions (see REFERENCE section below). 6333 6334Syntax: 6335 LET <a> = PEQI(<xr>,<xc>) <SUBSET/EXCEPT/FOR qualification> 6336 where <xr> is a number, parameter, or variable that specifies the 6337 the real component of the input; 6338 <xc> is a number, parameter, or variable that specifies the 6339 the complex component of the input; 6340 <a> is a variable or a parameter (depending on what <xr> and 6341 <xc> are) where the computed values are stored; 6342 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 6343 6344Examples: 6345 LET A = PEQI(2,1) 6346 LET A = PEQI(X,4) 6347 LET X2 = PEQI(1,Y) 6348 6349Note: 6350 The Weierstrass elliptic functions are computed using algorithm 6351 549 from the ACM Transactions on Mathematical Software (see the 6352 REFERENCE section below). 6353 6354Note: 6355 If the input value corresponds to a lattice point, an error 6356 message is printed and the output value is set to the largest 6357 real number on the machine. 6358 6359Note: 6360 Library functions are distinguished from let subcommands 6361 in the following ways. 6362 1) Functions enclose the input value in parenthesis. Let 6363 subcommands use spaces. 6364 2) Functions can accept (and return) either parameters 6365 (i.e., single values) or variables (i.e., an array of 6366 values) while let subcommands are specific in which they 6367 accept as input and what they return as output. 6368 3) Functions can accept expressions while let subcommands 6369 do not. For example, the following is legal: 6370 LET Y2 = ABS(Y1-INT(Y1)) 6371 For let subcommands, you typically have to do something 6372 like the following: 6373 LET YTEMP = Y**2 + 8 6374 LET A = SUM YTEMP 6375 6376Default: 6377 None 6378 6379Synonyms: 6380 None 6381 6382Related Commands: 6383 PEQ = Compute the real component of the Weierstrass elliptic 6384 function (equianharmonic case). 6385 PEQ1 = Compute the real component of the first derivative of 6386 the Weierstrass elliptic function (equianharmonic case). 6387 PEQ1I = Compute the complex component of the first derivative of 6388 the Weierstrass elliptic function (equianharmonic case). 6389 PLEM = Compute the real component of the Weierstrass elliptic 6390 function (lemniscatic case). 6391 PLEMI = Compute the complex component of the Weierstrass elliptic 6392 function (lemniscatic case). 6393 PLEM1 = Compute the real component of the first derivative of 6394 the Weierstrass elliptic function (lemniscatic case). 6395 PLEM1I = Compute the complex component of the first derivative of 6396 the Weierstrass elliptic function (lemniscatic case). 6397 SN = Compute the Jacobi elliptic function sn. 6398 CN = Compute the Jacobi elliptic function cn. 6399 DN = Compute the Jacobi elliptic function dn. 6400 RF = Compute the Carlson elliptic integral of the first kind. 6401 RD = Compute the Carlson elliptic integral of the second kind. 6402 RJ = Compute the Carlson elliptic integral of the third kind. 6403 ELLIPC1 = Compute the Legendre complete elliptic integral of the 6404 first kind. 6405 ELLIPC2 = Compute the Legendre complete elliptic integral of the 6406 second kind. 6407 ELLIP1 = Compute the Legendre elliptic integral of the first 6408 kind. 6409 ELLIP2 = Compute the Legendre elliptic integral of the second 6410 kind. 6411 ELLIP3 = Compute the Legendre's elliptic integral of the third 6412 kind. 6413 6414Reference: 6415 "Algorithm 549: Weierstrass' Elliptic Functions", Eckhardt, ACM 6416 Transactions on Mathematical Software, vol. 6 (pp. 112-120). 6417 6418 "Handbook of Mathematical Functions, Applied Mathematics Series, 6419 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 6420 1964 (chapter 18). 6421 6422Applications: 6423 Special Functions 6424 6425Implementation Date: 6426 94/11 6427 6428Program: 6429 TITLE WEIERSTRASS ELLIPTIC FUNCTIONS 6430 LINE SOLID DASH 6431 PLOT PEQI(X,0.5) FOR X = 0 0.01 5 AND 6432 PLOT PEQ(X,0.5) FOR X = 0 0.01 5 6433 6434-----PEQ1 (LET)---------------------------------------------- 6435 6436PEQ1 6437 6438Name: 6439 PEQ1 (LET) 6440 6441Type: 6442 Library Function 6443 6444Purpose: 6445 Compute the real component of the first derivative of the 6446 Weierstrass P elliptic function of a complex number (equianharmonic 6447 case with unit period parallelogram). 6448 6449Description: 6450 The Weierstrass elliptic function is described in detail in the 6451 Handbook of Mathematical Functions (see REFERENCE section below). 6452 6453Syntax: 6454 LET <a> = PEQ1(<xr>,<xc>) <SUBSET/EXCEPT/FOR qualification> 6455 where <xr> is a number, parameter, or variable that specifies the 6456 the real component of the input; 6457 <xc> is a number, parameter, or variable that specifies the 6458 the complex component of the input; 6459 <a> is a variable or a parameter (depending on what <xr> and 6460 <xc> are) where the computed values are stored; 6461 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 6462 6463Examples: 6464 LET A = PEQ1(2,1) 6465 LET A = PEQ1(X,4) 6466 LET X2 = PEQ1(1,Y) 6467 6468Note: 6469 The Weierstrass elliptic functions are computed using algorithm 6470 549 from the ACM Transactions on Mathematical Software (see the 6471 REFERENCE section below). 6472 6473Note: 6474 If the input value corresponds to a lattice point, an error 6475 message is printed and the output value is set to the largest 6476 real number on the machine. 6477 6478Note: 6479 Library functions are distinguished from let subcommands 6480 in the following ways. 6481 1) Functions enclose the input value in parenthesis. Let 6482 subcommands use spaces. 6483 2) Functions can accept (and return) either parameters 6484 (i.e., single values) or variables (i.e., an array of 6485 values) while let subcommands are specific in which they 6486 accept as input and what they return as output. 6487 3) Functions can accept expressions while let subcommands 6488 do not. For example, the following is legal: 6489 LET Y2 = ABS(Y1-INT(Y1)) 6490 For let subcommands, you typically have to do something 6491 like the following: 6492 LET YTEMP = Y**2 + 8 6493 LET A = SUM YTEMP 6494 6495Default: 6496 None 6497 6498Synonyms: 6499 None 6500 6501Related Commands: 6502 PEQ = Compute the real component of the Weierstrass elliptic 6503 function (equianharmonic case). 6504 PEQI = Compute the complex component of the Weierstrass elliptic 6505 function (equianharmonic case). 6506 PEQ1I = Compute the complex component of the first derivative of 6507 the Weierstrass elliptic function (equianharmonic case). 6508 PLEM = Compute the real component of the Weierstrass elliptic 6509 function (lemniscatic case). 6510 PLEMI = Compute the complex component of the Weierstrass elliptic 6511 function (lemniscatic case). 6512 PLEM1 = Compute the real component of the first derivative of 6513 the Weierstrass elliptic function (lemniscatic case). 6514 PLEM1I = Compute the complex component of the first derivative of 6515 the Weierstrass elliptic function (lemniscatic case). 6516 SN = Compute the Jacobi elliptic function sn. 6517 CN = Compute the Jacobi elliptic function cn. 6518 DN = Compute the Jacobi elliptic function dn. 6519 RF = Compute the Carlson elliptic integral of the first kind. 6520 RD = Compute the Carlson elliptic integral of the second kind. 6521 RJ = Compute the Carlson elliptic integral of the third kind. 6522 ELLIPC1 = Compute the Legendre complete elliptic integral of the 6523 first kind. 6524 ELLIPC2 = Compute the Legendre complete elliptic integral of the 6525 second kind. 6526 ELLIP1 = Compute the Legendre elliptic integral of the first 6527 kind. 6528 ELLIP2 = Compute the Legendre elliptic integral of the second 6529 kind. 6530 ELLIP3 = Compute the Legendre's elliptic integral of the third 6531 kind. 6532 6533Reference: 6534 "Algorithm 549: Weierstrass' Elliptic Functions", Eckhardt, ACM 6535 Transactions on Mathematical Software, vol. 6 (pp. 112-120). 6536 6537 "Handbook of Mathematical Functions, Applied Mathematics Series, 6538 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 6539 1964 (chapter 18). 6540 6541Applications: 6542 Special Functions 6543 6544Implementation Date: 6545 94/11 6546 6547Program: 6548 TITLE WEIERSTRASS ELLIPTIC FUNCTIONS 6549 LINE SOLID DASH 6550 PLOT PEQ1(X,0.5) FOR X = 0 0.01 5 AND 6551 PLOT PEQ1I(X,0.5) FOR X = 0 0.01 5 6552 6553-----PEQ1I (LET)---------------------------------------------- 6554 6555PEQ1I 6556 6557Name: 6558 PEQ1I (LET) 6559 6560Type: 6561 Library Function 6562 6563Purpose: 6564 Compute the complex component of the first derivative of the 6565 Weierstrass P elliptic function of a complex number (equianharmonic 6566 case with unit period parallelogram). 6567 6568Description: 6569 The Weierstrass elliptic function is described in detail in the 6570 Handbook of Mathematical Functions (see REFERENCE section below). 6571 6572Syntax: 6573 LET <a> = PEQ1I(<xr>,<xc>) <SUBSET/EXCEPT/FOR qualification> 6574 where <xr> is a number, parameter, or variable that specifies the 6575 the real component of the input; 6576 <xc> is a number, parameter, or variable that specifies the 6577 the complex component of the input; 6578 <a> is a variable or a parameter (depending on what <xr> and 6579 <xc> are) where the computed values are stored; 6580 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 6581 6582Examples: 6583 LET A = PEQ1I(2,1) 6584 LET A = PEQ1I(X,4) 6585 LET X2 = PEQ1I(1,Y) 6586 6587Note: 6588 The Weierstrass elliptic functions are computed using algorithm 6589 549 from the ACM Transactions on Mathematical Software (see the 6590 REFERENCE section below). 6591 6592Note: 6593 If the input value corresponds to a lattice point, an error 6594 message is printed and the output value is set to the largest 6595 real number on the machine. 6596 6597Note: 6598 Library functions are distinguished from let subcommands 6599 in the following ways. 6600 1) Functions enclose the input value in parenthesis. Let 6601 subcommands use spaces. 6602 2) Functions can accept (and return) either parameters 6603 (i.e., single values) or variables (i.e., an array of 6604 values) while let subcommands are specific in which they 6605 accept as input and what they return as output. 6606 3) Functions can accept expressions while let subcommands 6607 do not. For example, the following is legal: 6608 LET Y2 = ABS(Y1-INT(Y1)) 6609 For let subcommands, you typically have to do something 6610 like the following: 6611 LET YTEMP = Y**2 + 8 6612 LET A = SUM YTEMP 6613 6614Default: 6615 None 6616 6617Synonyms: 6618 None 6619 6620Related Commands: 6621 PEQ = Compute the real component of the Weierstrass elliptic 6622 function (equianharmonic case). 6623 PEQI = Compute the complex component of the Weierstrass elliptic 6624 function (equianharmonic case). 6625 PEQ1 = Compute the real component of the first derivative of 6626 the Weierstrass elliptic function (equianharmonic case). 6627 PLEM = Compute the real component of the Weierstrass elliptic 6628 function (lemniscatic case). 6629 PLEMI = Compute the complex component of the Weierstrass elliptic 6630 function (lemniscatic case). 6631 PLEM1 = Compute the real component of the first derivative of 6632 the Weierstrass elliptic function (lemniscatic case). 6633 PLEM1I = Compute the complex component of the first derivative of 6634 the Weierstrass elliptic function (lemniscatic case). 6635 SN = Compute the Jacobi elliptic function sn. 6636 CN = Compute the Jacobi elliptic function cn. 6637 DN = Compute the Jacobi elliptic function dn. 6638 RF = Compute the Carlson elliptic integral of the first kind. 6639 RD = Compute the Carlson elliptic integral of the second kind. 6640 RJ = Compute the Carlson elliptic integral of the third kind. 6641 ELLIPC1 = Compute the Legendre complete elliptic integral of the 6642 first kind. 6643 ELLIPC2 = Compute the Legendre complete elliptic integral of the 6644 second kind. 6645 ELLIP1 = Compute the Legendre elliptic integral of the first 6646 kind. 6647 ELLIP2 = Compute the Legendre elliptic integral of the second 6648 kind. 6649 ELLIP3 = Compute the Legendre's elliptic integral of the third 6650 kind. 6651 6652Reference: 6653 "Algorithm 549: Weierstrass' Elliptic Functions", Eckhardt, ACM 6654 Transactions on Mathematical Software, vol. 6 (pp. 112-120). 6655 6656 "Handbook of Mathematical Functions, Applied Mathematics Series, 6657 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 6658 1964 (chapter 18). 6659 6660Applications: 6661 Special Functions 6662 6663Implementation Date: 6664 94/11 6665 6666Program: 6667 TITLE WEIERSTRASS ELLIPTIC FUNCTIONS 6668 LINE SOLID DASH 6669 PLOT PEQ1(X,0.5) FOR X = 0 0.01 5 AND 6670 PLOT PEQ1I(X,0.5) FOR X = 0 0.01 5 6671 6672-----PERCDIF (LET)-------------------------------- 6673 6674PERCDIF 6675 6676Name: 6677 PERCDIF (LET) 6678 6679Type: 6680 Library Function 6681 6682Purpose: 6683 Return the percent difference of two numbers. 6684 6685Description: 6686 The definition of the percent difference between X1 and X2 used 6687 by Dataplot is: 6688 6689 Percent Difference = 100*ABS(X1 - X2)/MAX(ABS(X1),ABS(X2)) 6690 6691 Dataplot also supports the alternative formula 6692 6693 Percent Difference = 100*ABS((X1 - X2)/((X1 + X2)/2)) 6694 6695Syntax 1: 6696 LET <y> = PERCDIF(<y1>,<y2>) <SUBSET/EXCEPT/FOR qualification> 6697 where <y1> is a variable or a parameter; 6698 <y2> is a variable or a parameter; 6699 <y> is a variable or a parameter (depending on what <y1> and 6700 <y2> are) where the computed percent difference values 6701 are stored; 6702 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 6703 6704 This syntax implements the first formula given above (the 6705 denominator is the maximum of the two values). 6706 6707Syntax 2: 6708 LET <y> = PERCDIF2(<y1>,<y2>) <SUBSET/EXCEPT/FOR qualification> 6709 where <y1> is a variable or a parameter; 6710 <y2> is a variable or a parameter; 6711 <y> is a variable or a parameter (depending on what <y1> and 6712 <y2> are) where the computed percent difference values 6713 are stored; 6714 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 6715 6716 This syntax implements the second formula given above (the 6717 denominator is the average of the two values). 6718 6719Examples: 6720 LET A = PERCDIF(14,10) 6721 LET A = PERCDIF(A1,A2) 6722 LET X2 = PERCDIF(X1,X4) 6723 LET X2 = PERCDIF(X1-4,X2+6) 6724 6725Note: 6726 Library functions are distinguished from let subcommands 6727 in the following ways. 6728 1) Functions enclose the input value in parenthesis. Let 6729 subcommands use spaces. 6730 2) Functions can accept (and return) either parameters 6731 (i.e., single values) or variables (i.e., an array of 6732 values) while let subcommands are specific in which they 6733 accept as input and what they return as output. 6734 3) Functions can accept expressions while let subcommands 6735 do not. For example, the following is legal: 6736 LET Y2 = ABS(Y1-INT(Y1)) 6737 For let subcommands, you typically have to do something 6738 like the following: 6739 LET YTEMP = Y**2 + 8 6740 LET A = SUM YTEMP 6741 6742Default: 6743 None 6744 6745Synonyms: 6746 None 6747 6748Related Commands: 6749 PERCERR = Compute the percent error of two numbers. 6750 RELDIF = Compute the relative difference of two numbers. 6751 RELERR = Compute the relative error of two numbers. 6752 MIN = Compute the minimum of two numbers. 6753 MAX = Compute the maximum of two numbers. 6754 ABS = Compute the absolute value of a number. 6755 6756Applications: 6757 Data Management 6758 6759Implementation Date: 6760 2010/12 6761 6762Program: 6763 LET X = SEQUENCE 0.1 0.1 3 6764 LET Y1 = X**2 6765 LET Y2 = X**(1/2) 6766 LET Y3 = PERCDIF(Y1,Y2) 6767 SET WRITE DECIMALS 5 6768 PRINT Y1 Y2 Y3 6769 6770-----PERCENT AGREE (LET)------------------------------------------------ 6771 6772PERCENT AGREE 6773 6774Name: 6775 PERCENT AGREE (LET) 6776 6777Type: 6778 Let Subcommand 6779 6780Purpose: 6781 Compute the percentage of values that agree in two response 6782 variables. This is pairwise agreement (i.e., how often does 6783 Y1(I) = Y2(I) for I = 1, ..., N). 6784 6785Description: 6786 Given two methods (or two labortories), it may sometimes be useful 6787 to know how often they reach the same conclusion. 6788 6789 For example, if we have two sensors that either detect or do not 6790 detect the presence of some quantity of interest, how often do 6791 the two detectors agree? 6792 6793 This command is typically used when there a discrete number of 6794 values for the variable. Often this will be two (e.g., Yes/No 6795 type data), but it is not restricted to two. 6796 6797 If you want to compare values for two response variables when 6798 the data is continuous, the YOUDEN PLOT is recommended. 6799 6800Syntax: 6801 LET <par> = PERCENT AGREE <y1> <y2> <SUBSET/EXCEPT/FOR qualification> 6802 where <y1> is the first response variable; 6803 <y2> is the second response variable; 6804 <par> is a parameter where the percent agree is saved; 6805 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 6806 6807Examples: 6808 LET A = PERCENT AGREE Y1 Y2 6809 LET A = PERCENT AGREE Y1 Y2 SUBSET TAG > 1 6810 6811Note: 6812 Dataplot statistics can be used in a number of commands. For 6813 details, enter 6814 6815 HELP STATISTICS 6816 6817Default: 6818 None 6819 6820Synonyms: 6821 None 6822 6823Related Commands: 6824 PERCENT DISAGREE = Compute the percentage of values that disagree 6825 in two response variables. 6826 FALSE NEGATIVES = Compute the proportion of false negatives. 6827 FALSE POSITIVES = Compute the proportion of false positives. 6828 TRUE NEGATIVES = Compute the proportion of true negatives. 6829 TRUE POSITIVES = Compute the proportion of true positives. 6830 TEST SENSITIVITY = Compute the test sensitivity. 6831 TEST SPECIFICITY = Compute the test specificity. 6832 ODDS RATIO = Compute the bias corrected log(odds ratio). 6833 YOUDEN PLOT = Generate a Youden plot. 6834 6835Applications: 6836 Categorical Data Analysis 6837 6838Implementation Date: 6839 2011/7 6840 6841Program: 6842 . Step 1: Read the Data 6843 . 6844 . Column 1: Method 1 (low => live cell, high => dead cell) 6845 . Column 2: Method 2 (high => live cell, low => dead cell) 6846 . 6847 dimension 40 columns 6848 read percmat intensity 6849 7.1 39.8 6850 8.5 29.6 6851 72.7 4.2 6852 32.3 12.3 6853 5.4 21.5 6854 71.1 4.4 6855 100.0 13.5 6856 55.0 22.4 6857 15.0 25.9 6858 8.7 38.5 6859 0.9 16.6 6860 19.0 48.5 6861 100.0 4.3 6862 100.0 7.9 6863 5.2 42.6 6864 21.8 47.2 6865 90.0 1.0 6866 2.0 23.5 6867 98.0 2.2 6868 100.0 6.2 6869 100.0 2.0 6870 100.0 5.6 6871 100.0 3.0 6872 30.0 14.3 6873 100.0 1.0 6874 end of data 6875 . 6876 . Step 3: Generate fluctuation plot based on different levels of 6877 . the 2 methods 6878 . 6879 . Use intensity levels of 5%, 10%, 15%, 20%, 25% 6880 . Use percent matching levels of 80%, 90%, 95%, 99.5% 6881 . 6882 let n = size intensity 6883 let intcut = data 5 10 15 20 25 6884 let nint = size intcut 6885 let matcut = data 80 90 95 99.5 6886 let nmat = size matcut 6887 . 6888 let int2 = intensity 6889 let mat2 = percmat 6890 let xgroup = 1 for i = 1 1 n 6891 let ygroup = 1 for i = 1 1 n 6892 let icnt = 0 6893 . 6894 loop for k = 1 1 nint 6895 let acut = intcut(k) 6896 loop for l = 1 1 nmat 6897 let bcut = matcut(l) 6898 let icnt = icnt + 1 6899 if icnt = 1 6900 let xgroupal = xgroup 6901 let ygroupal = ygroup 6902 let intcor = 0 for i = 1 1 n 6903 let intcor = 1 subset int2 > acut 6904 let intall = intcor 6905 let matcor = 0 for i = 1 1 n 6906 let matcor = 1 subset mat2 < bcut 6907 let matall = matcor 6908 else 6909 let xgroup2 = k for i = 1 1 n 6910 extend xgroupal xgroup2 6911 let ygroup2 = l for i = 1 1 n 6912 extend ygroupal ygroup2 6913 let intcor = 0 for i = 1 1 n 6914 let intcor = 1 subset int2 > acut 6915 extend intall intcor 6916 let matcor = 0 for i = 1 1 n 6917 let matcor = 1 subset mat2 < bcut 6918 extend matall matcor 6919 end of if 6920 end of loop 6921 end of loop 6922 . 6923 label case asis 6924 tic mark label case asis 6925 title case asis 6926 title offset 2 6927 . 6928 title Percent Agreement Between Method 1 and Method 2 6929 y1label Method 1 6930 x1label Method 2 6931 tic offset units data 6932 xlimits 1 nmat 6933 major xtic mark number nmat 6934 minor xtic mark number 0 6935 xtic mark offset 0.7 0.7 6936 x1tic mark label format alpha 6937 x1tic mark label content 80% 90% 95% 99.5% 6938 ylimits 1 nint 6939 major ytic mark number nint 6940 minor ytic mark number 0 6941 ytic mark offset 0.7 0.7 6942 y1tic mark label format alpha 6943 y1tic mark label content 5% 10% 15% 20% 25% 6944 . 6945 let ylevel = data 60 70 80 85 90 101 6946 . 6947 let string color = g90 g20 green cyan blue orange red 6948 line color ^color 6949 region fill color ^color 6950 region border color ^color 6951 . 6952 set fluctuation plot floor 0 6953 set fluctuation plot ceiling 100 6954 fluctuation percent agreement contour plot ... 6955 intall matall xgroupal ygroupal ylevel 6956 . 6957 box fill pattern solid 6958 box shadow hw 0 0 6959 . 6960 box fill color g20 6961 box 86 90 90 86 6962 move 91 87; text <= 60 6963 . 6964 box fill color green 6965 box 86 86 90 82 6966 move 91 83; text 60 - 70 6967 . 6968 box fill color cyan 6969 box 86 82 90 78 6970 move 91 79; text 70 - 80 6971 . 6972 box fill color blue 6973 box 86 78 90 74 6974 move 91 75; text 80 - 85 6975 . 6976 box fill color orange 6977 box 86 74 90 70 6978 move 91 71; text 85 - 90 6979 . 6980 box fill color red 6981 box 86 70 90 66 6982 move 91 67; text > 90 6983 6984-----PERCENTAGE BEND CORRELATION (LET)------------------------------- 6985 6986PERCENTAGE BEND CORRELATION 6987 6988Name: 6989 PERCENTAGE BEND CORRELATION (LET) 6990 6991Type: 6992 Let Subcommand 6993 6994Purpose: 6995 Compute the percentage bend correlation for a variable. 6996 6997Description: 6998 Mosteller and Tukey (see Reference section below) define 6999 two types of robustness: 7000 7001 1) resistance means that changing a small part, even by a 7002 large amount, of the data does not cause a large change 7003 in the estimate 7004 7005 2) robustness of efficiency means that the statistic has 7006 high efficiency in a variety of situations rather than 7007 in any one situation. Efficiency means that the estimate 7008 is close to optimal estimate given that we know what 7009 distribution that the data comes from. A useful measure 7010 of efficiency is: 7011 7012 Efficiency = (lowest variance feasible)/ 7013 (actual variance) 7014 7015 Many statistics have one of these properties. However, 7016 it can be difficult to find statistics that are both 7017 resistant and have robustness of efficiency. 7018 7019 The Pearson correlation coefficient is an optimal estimator for 7020 Gaussian data. However, it is not resistant and it does not 7021 have robustness of efficiency. 7022 7023 The percentage bend correlation estimator, discussed in 7024 Shoemaker and Hettmansperger and also by Wilcox, is both 7025 resistant and robust of efficiency. The rationale and 7026 derivation for this estimate is given in these references. 7027 7028 The percentage bend correlation between two variables X and 7029 Y is computed as follows: 7030 7031 1. Set m = [(1-beta)*n + 0.5]. This is the value of 7032 (1-beta)*m + 0.5 rounded down to the nearest integer. 7033 7034 2. Let W(i) = |X(i) - M(x)| for i = 1, ..., n where M(x) 7035 is the median of X. 7036 7037 3. Sort the W(i) in ascending order. 7038 7039 4. what(x) = W(m) (i. e., the mth order statistic). 7040 W(m) is the estimate of the (1-beta) quantile of W. 7041 7042 5. Sort the X values. Compute the number of values 7043 of (X(i) - M(x))/whatx(beta) that are less than -1 7044 and the number that are greater than +1 and store in 7045 i1 and i2 respectively. Then compute 7046 7047 S(x) = SUM[i=i1+1 to n-i2][X(i)] 7048 phihat(x) = (what(x)*(i2-i1) + S(x))/(n - i1 - i2) 7049 U(i) = (X(i) - phihat(x)/what(x) 7050 7051 6. Repeat the above calculations on the Y variable. 7052 Store corresponding quantities in what(y), phihat(y), 7053 and V(i). 7054 7055 7. Define the function 7056 7057 PSI(x) = MAX[-1, MIN(1,x)] 7058 7059 8. Compute 7060 7061 A(i) = PSI(U(i)) 7062 B(i) = PSI(V(i)) 7063 7064 8. rho(pb) = SUM[i=1 to n][A(i)*B(i)]/ 7065 SQRT(SUM[i=1 to n][A(i)**2]*SUM[i=1 o n][B(i)**2]) 7066 7067 The value of beta is selected between 0 and 0.5. Higher 7068 values of beta result in a higher breakdown point at the 7069 expense of lower efficiency. 7070 7071Syntax: 7072 LET <par> = PERCENTAGE BEND CORRELATION <y1> <y2> 7073 <SUBSET/EXCEPT/FOR qualification> 7074 where <y1> is the first response variable; 7075 <y2> is the second response variable; 7076 <par> is a parameter where the computed percentage bend 7077 correlation is stored; 7078 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 7079 7080Examples: 7081 LET A = PERCENTAGE BEND CORRELATION Y1 Y2 7082 LET A = PERCENTAGE BEND CORRELATION Y1 Y2 SUBSET TAG > 2 7083 7084Note: 7085 To set the value of beta, enter the command 7086 7087 LET BETA = <value> 7088 7089 where <value> is greater than 0 and less than or equal to 7090 0.5. The default value for beta is 0.1. 7091 7092Note: 7093 Dataplot statistics can be used in a number of commands. For 7094 details, enter 7095 7096 HELP STATISTICS 7097 7098Default: 7099 None 7100 7101Synonyms: 7102 None 7103 7104Related Commands: 7105 PERCENTAGE BEND MIDVARI = Compute the percentage bend 7106 midvariance of a variable. 7107 BIWEIGHT CORRELATION = Compute a biweight correlation 7108 estimate of a variable. 7109 WINSORIZED CORRELATION = Compute a Winsorized correlation 7110 estimate of a variable. 7111 CORRELATION = Compute the correlation between 7112 two variables. 7113 RANK CORRELATION = Compute the rank correlation between 7114 two variables. 7115 VARIANCE = Compute the variance of a variable. 7116 STATISTIC PLOT = Generate a statistic versus group 7117 plot for a given statistic. 7118 CROSS TABULATE PLOT = Generate a statistic versus group 7119 plot for a given statistic and two 7120 group variables. 7121 BOOTSTRAP PLOT = Generate a bootstrap plot for a 7122 given statistic. 7123 DEX PLOT = Generate various types of design 7124 of experiment plots. 7125 INFLUENCE CURVE = Generate an influence curve for a 7126 given statistic. 7127 INTERACTION STATISTIC PLOT = Generate an interaction plot for a 7128 given statistic. 7129 7130Reference: 7131 "Robust Estimates of and Tests for the One- and Two-Sample 7132 Scale Models", Shoemaker and Hettmansperger, Biometrika 69, 7133 1982, pp. 47-54. 7134 7135 "Introduction to Robust Estimation and Hypothesis Testing", 7136 Rand Wilcox, Academic Press, 1997. 7137 7138 "Data Analysis and Regression: A Second Course in Statistics", 7139 Mosteller and Tukey, Addison-Wesley, 1977, pp. 203-209. 7140 7141Applications: 7142 Robust Data Analysis 7143 7144Implementation Date: 7145 2002/7 7146 7147Program 1: 7148 SKIP 25 7149 READ MATRIX IRIS.DAT Y1 Y2 Y3 Y4 X 7150 LET M = CREATE MATRIX Y1 Y2 Y3 Y4 7151 SET CORRELATION TYPE PERCENTAGE BEND 7152 LET B = CORRELATION MATRIX Y1 Y2 Y3 Y4 7153 7154Program 2: 7155 SKIP 25 7156 READ IRIS.DAT Y1 Y2 Y3 Y4 X 7157 . 7158 MULTIPLOT CORNER COORDINATES 0 0 100 95 7159 MULTIPLOT 2 1 7160 BOOTSTRAP SAMPLES 500 7161 BOOTSTRAP PERCENTAGE BEND CORRELATION PLOT Y1 Y2 7162 X1LABEL B025 = ^B025, B975=^B975 7163 HISTOGRAM YPLOT 7164 END OF MULTIPLOT 7165 MOVE 50 96 7166 JUSTIFICATION CENTER 7167 TEXT PERCENTAGE BEND CORRELATION BOOTSTRAP: IRIS DATA 7168 7169-----PERCENTAGE BEND MIDVARIANCE (LET)------------------------------- 7170 7171PERCENTAGE BEND MIDVARIANCE 7172 7173Name: 7174 PERCENTAGE BEND MIDVARIANCE (LET) 7175 7176Type: 7177 Let Subcommand 7178 7179Purpose: 7180 Compute the percentage bend midvariance for a variable. 7181 7182Description: 7183 Mosteller and Tukey (see Reference section below) define 7184 two types of robustness: 7185 7186 1) resistance means that changing a small part, even by a 7187 large amount, of the data does not cause a large change 7188 in the estimate 7189 7190 2) robustness of efficiency means that the statistic has 7191 high efficiency in a variety of situations rather than 7192 in any one situation. Efficiency means that the estimate 7193 is close to optimal estimate given that we know what 7194 distribution that the data comes from. A useful measure 7195 of efficiency is: 7196 7197 Efficiency = (lowest variance feasible)/ 7198 (actual variance) 7199 7200 Many statistics have one of these properties. However, 7201 it can be difficult to find statistics that are both 7202 resistant and have robustness of efficiency. 7203 7204 For scale estimators, the variance is an optimal estimator for 7205 Gaussian data. However, it is not resistant and it does not 7206 have robustness of efficiency. 7207 7208 The percentage bend midvariance estimator, discussed in 7209 Shoemaker and Hettmansperger and also by Wilcox, is both 7210 resistant and robust of efficiency. The rationale and 7211 derivation for this estimate is given in these references. 7212 7213 The percentage bend midvariance of a a variable X is computed 7214 as follows: 7215 7216 1. Set m = [(1-beta)*n + 0.5]. This is the value of 7217 (1-beta)*m + 0.5 rounded down to the nearest integer. 7218 7219 2. Let W(i) = |X(i) - M| for i = 1, ..., n where M is 7220 the median of X. 7221 7222 3. Sort the W(i) in ascending order. 7223 7224 4. what(beta) = W(m) (i. e., the mth order statistic). 7225 W(m) is the estimate of the (1-beta) quantile of W. 7226 7227 7228 5. Y(i) = (X(i) - M)/what(beta) 7229 7230 6. a(i) = 1 if |Y(i)| < 1 7231 = 0 if |Y(i)| >= 1 7232 7233 7. phi(x) = max[-1, min(1,x)] 7234 7235 8. PBV = n*what(beta)**2*SUM[{phi(Y(i))}**2]/ 7236 (SUM[a(i)])**2 7237 7238 The value of beta is selected between 0 and 0.5. Higher 7239 values of beta result in a higher breakdown point at the 7240 expense of lower efficiency. 7241 7242Syntax: 7243 LET <par> = PERCENTAGE BEND MIDVARIANCE <y> 7244 <SUBSET/EXCEPT/FOR qualification> 7245 where <y> is the response variable; 7246 <par> is a parameter where the computed percentage bend 7247 midvariance is stored; 7248 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 7249 7250Examples: 7251 LET A = PERCENTAGE BEND MIDVARIANCE Y1 7252 LET A = PERCENTAGE BEND MIDVARIANCE Y1 SUBSET TAG > 2 7253 7254Note: 7255 To set the value of beta, enter the command 7256 7257 LET BETA = <value> 7258 7259 where <value> is greater than 0 and less than or equal to 7260 0.5. The default value for beta is 0.1. 7261 7262Note: 7263 Dataplot statistics can be used in a number of commands. For 7264 details, enter 7265 7266 HELP STATISTICS 7267 7268Default: 7269 None 7270 7271Synonyms: 7272 None 7273 7274Related Commands: 7275 BIWEIGHT MIDVARIANCE = Compute a biweight midvariance 7276 estimate of a variable. 7277 BIWEIGHT SCALE = Compute a biweight scale estimate 7278 of a variable. 7279 BIWEIGHT LOCATION = Compute a biweight location estimate 7280 of a variable. 7281 BIWEIGHT CONFIDENCE LIMITS = Compute a biweight based confidence 7282 interval. 7283 WINSORIZED VARIANCE = Compute the Winsorized variance of a 7284 variable. 7285 MEDIAN ABSOLUTE DEVIATION = Compute the median absolute 7286 deviation of a variable. 7287 VARIANCE = Compute the variance of a variable. 7288 STATISTIC PLOT = Generate a statistic versus group 7289 plot for a given statistic. 7290 CROSS TABULATE PLOT = Generate a statistic versus group 7291 plot for a given statistic and two 7292 group variables. 7293 BOOTSTRAP PLOT = Generate a bootstrap plot for a 7294 given statistic. 7295 DEX PLOT = Generate various types of design 7296 of experiment plots. 7297 INFLUENCE CURVE = Generate an influence curve for a 7298 given statistic. 7299 INTERACTION STATISTIC PLOT = Generate an interaction plot for a 7300 given statistic. 7301 7302Reference: 7303 "Robust Estimates of and Tests for the One- and Two-Sample 7304 Scale Models", Shoemaker and Hettmansperger, Biometrika 69, 7305 1982, pp. 47-54. 7306 7307 "Introduction to Robust Estimation and Hypothesis Testing", 7308 Rand Wilcox, Academic Press, 1997. 7309 7310 "Data Analysis and Regression: A Second Course in Statistics", 7311 Mosteller and Tukey, Addison-Wesley, 1977, pp. 203-209. 7312 7313Applications: 7314 Robust Data Analysis 7315 7316Implementation Date: 7317 2002/7 7318 7319Program 1: 7320 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 7321 LET Y2 = LOGISTIC RANDOM NUMBERS FOR I = 1 1 100 7322 LET Y3 = CAUCHY RANDOM NUMBERS FOR I = 1 1 100 7323 LET Y4 = DOUBLE EXPONENTIAL RANDOM NUMBERS FOR I = 1 1 100 7324 LET A1 = PERCENTAGE BEND MIDVARIANCE Y1 7325 LET A2 = PERCENTAGE BEND MIDVARIANCE Y2 7326 LET A3 = PERCENTAGE BEND MIDVARIANCE Y3 7327 LET A4 = PERCENTAGE BEND MIDVARIANCE Y4 7328 7329Program 2: 7330 MULTIPLOT 2 2 7331 MULTIPLOT CORNER COORDINATES 0 0 100 100 7332 MULTIPLOT SCALE FACTOR 2 7333 X1LABEL DISPLACEMENT 12 7334 . 7335 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 200 7336 LET Y2 = CAUCHY RANDOM NUMBERS FOR I = 1 1 200 7337 . 7338 BOOTSTRAP SAMPLES 500 7339 BOOTSTRAP PERCENTAGE BEND MIDVARIANCE PLOT Y1 7340 X1LABEL B025 = ^B025, B975=^B975 7341 HISTOGRAM YPLOT 7342 X1LABEL 7343 . 7344 BOOTSTRAP PERCENTAGE BEND MIDVARIANCE PLOT Y1 7345 X1LABEL B025 = ^B025, B975=^B975 7346 HISTOGRAM YPLOT 7347 . 7348 END OF MULTIPLOT 7349 JUSTIFICATION CENTER 7350 MOVE 50 96 7351 TEXT PERCENTAGE BEND MIDVARIANCE BOOTSTRAP: NORMAL 7352 MOVE 50 46 7353 TEXT PERCENTAGE BEND MIDVARIANCE BOOTSTRAP: CAUCHY 7354 7355-----PERCENT DEFECTIVE (LET)------------------------------------------ 7356 7357PERCENT DEFECTIVE 7358 7359Name: 7360 PERCENT DEFECTIVE (LET) 7361 7362Type: 7363 Let Subcommand 7364 7365Purpose: 7366 Compute the percentage of defectives for a variable. 7367 7368Description: 7369 The percent defective is the number of values of a variable 7370 (expressed as a percentage) that fall outside some user specified 7371 tolerance limits. 7372 7373Syntax: 7374 LET <par> = PERCENT DEFECTIVE <x> <SUBSET/EXCEPT/FOR qualification> 7375 where <x> is the variable for which the percent defectives is 7376 computed; 7377 <par> is a parameter where the computed percentage of 7378 defectives is saved; 7379 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 7380 7381Examples: 7382 LET A = PERCENT DEFECTIVE Y1 7383 LET A = PERCENT DEFECTIVE Y1 SUBSET TAG > 2 7384 7385Note: 7386 The upper and lower specification limits must be specified by the 7387 user as follows: 7388 LET LSL = <value> 7389 LET USL = <value> 7390 7391Default: 7392 None 7393 7394Synonyms: 7395 None 7396 7397Related Commands: 7398 CONTROL CHART = Generate a control chart. 7399 CP (LET) = Compute the CP index. 7400 CPK (LET) = Compute the CPK index. 7401 EXPECTED LOSS (LET) = Compute the expected loss of a sample. 7402 7403Applications: 7404 Quality Control 7405 7406Implementation Date: 7407 XX 7408 7409Program: 7410 LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 100 7411 LET LSL = -2 7412 LET USL = 2 7413 LET A = PERCENT DEFECTIVE Y 7414 7415-----PERCENT DEFECTIVE PLOT----------------------------------------- 7416 7417PERCENT DEFECTIVE PLOT 7418 7419Name: 7420 PERCENT DEFECTIVE PLOT 7421 7422Type: 7423 Graphics Command 7424 7425Purpose: 7426 Generates a percent defective plot. 7427 7428Description: 7429 A percent defective plot consists of subsample percent defective 7430 versus subsample index. The subsample percent defective index is 7431 the percent defective of the data in the subsample. The percent 7432 defective plot is used to answer the question--"Does the subsample 7433 percent defective index change over different subsamples?" The 7434 plot consists of: 7435 Vertical axis = subsample percent defective index; 7436 Horizontal axis = subsample index. 7437 The percent defective plot yields 2 traces: 7438 1. a subsample percent defective trace; and 7439 2. a full-sample percent defective reference line. 7440 Like usual, the appearance of these 2 traces is controlled by 7441 the first 2 settings of the LINES, CHARACTERS, SPIKES, BARS, 7442 and similar attributes. 7443 7444Syntax: 7445 PERCENT DEFECTIVE PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 7446 where <y> is the response (= dependent) variable; 7447 <x> is the subsample identifier variable (this variable 7448 appears on the horizontal axis); 7449 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 7450 7451Examples: 7452 PERCENT DEFECTIVE PLOT Y X 7453 PERCENT DEFECTIVE PLOT Y X SUBSET X > 6 7454 7455Note: 7456 The percent defective computes the number of defectives for a 7457 variable (i.e., the number of values that fall outside of some user 7458 specified tolerance limits) and expresses it as a percentage. 7459 specified cost. 7460 7461Note: 7462 The upper and lower specification limits must be specified by the 7463 user as follows: 7464 LET USL = <value> 7465 LET LSL = <value> 7466 7467Default: 7468 None 7469 7470Synonyms: 7471 None 7472 7473Related Commands: 7474 CHARACTERS = Sets the type for plot characters. 7475 LINES = Sets the type for plot lines. 7476 CP PLOT = Generates a Cp plot. 7477 CPK PLOT = Generates a Cpk plot. 7478 EXPECTED LOSS PLOT = Generates an expected loss plot. 7479 BOX PLOT = Generates a box plot. 7480 XBAR CHART = Generates an xbar control chart. 7481 PLOT = Generates a data or function plot. 7482 7483Applications: 7484 Quality Control 7485 7486Implementation Date: 7487 93/10 7488 7489Program: 7490 SKIP 25 7491 READ GEAR.DAT DIAMETER BATCH 7492 . 7493 TITLE CASE ASIS; LABEL CASE ASIS 7494 TITLE Gear Diameter Analysis 7495 Y1LABEL PERCENT DEFECTIVE 7496 X1LABEL Batch 7497 LEGEND 1 Process Capability 7498 LEGEND 2 PERCENT DEFECTIVE Plot 7499 XTIC OFFSET 0.5 0.5 7500 YTIC OFFSET 2.0 2.0 7501 CHARACTER CIRCLE BLANK 7502 CHARACTER FILL ON 7503 CHARACTER SIZE 1.2 7504 SPIKE ON 7505 SPIKE DOTTED 7506 LINE BLANK SOLID 7507 . 7508 LET LSL = 0.99 7509 LET USL = 1.01 7510 . 7511 PERCENT DEFECTIVE PLOT DIAMETER BATCH 7512 7513-----PERCENT DISAGREE (LET)-------------------------------------------- 7514 7515PERCENT DISAGREE 7516 7517Name: 7518 PERCENT DISAGREE (LET) 7519 7520Type: 7521 Let Subcommand 7522 7523Purpose: 7524 Compute the percentage of values that disagree in two response 7525 variables. This is pairwise disagreement (i.e., how often does 7526 Y1(I) not equal Y2(I) for I = 1, ..., N). 7527 7528Description: 7529 Given two methods (or two labortories), it may sometimes be useful 7530 to know how often they reach a different conclusion. 7531 7532 For example, if we have two sensors that either detect or do not 7533 detect the presence of some quantity of interest, how often do 7534 the two detectors disagree? 7535 7536 This command is typically used when there a discrete number of 7537 values for the variable. Often this will be two (e.g., Yes/No 7538 type data), but it is not restricted to two. 7539 7540 If you want to compare values for two response variables when 7541 the data is continuous, the YOUDEN PLOT is recommended. 7542 7543Syntax: 7544 LET <par> = PERCENT DISAGREE <y1> <y2> 7545 <SUBSET/EXCEPT/FOR qualification> 7546 where <y1> is the first response variable; 7547 <y2> is the second response variable; 7548 <par> is a parameter where the percent agree is saved; 7549 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 7550 7551Examples: 7552 LET A = PERCENT DISAGREE Y1 Y2 7553 LET A = PERCENT DISAGREE Y1 Y2 SUBSET TAG > 1 7554 7555Note: 7556 Dataplot statistics can be used in a number of commands. For 7557 details, enter 7558 7559 HELP STATISTICS 7560 7561Default: 7562 None 7563 7564Synonyms: 7565 None 7566 7567Related Commands: 7568 PERCENT AGREE = Compute the percentage of values that agree 7569 in two response variables. 7570 FALSE NEGATIVES = Compute the proportion of false negatives. 7571 FALSE POSITIVES = Compute the proportion of false positives. 7572 TRUE NEGATIVES = Compute the proportion of true negatives. 7573 TRUE POSITIVES = Compute the proportion of true positives. 7574 TEST SENSITIVITY = Compute the test sensitivity. 7575 TEST SPECIFICITY = Compute the test specificity. 7576 ODDS RATIO = Compute the bias corrected log(odds ratio). 7577 YOUDEN PLOT = Generate a Youden plot. 7578 7579Applications: 7580 Categorical Data Analysis 7581 7582Implementation Date: 7583 2011/7 7584 7585Program: 7586 . Step 1: Read the Data 7587 . 7588 . Column 1: Method 1 (low => live cell, high => dead cell) 7589 . Column 2: Method 2 (high => live cell, low => dead cell) 7590 dimension 40 columns 7591 read percmat intensity 7592 7.1 39.8 7593 8.5 29.6 7594 72.7 4.2 7595 32.3 12.3 7596 5.4 21.5 7597 71.1 4.4 7598 100.0 13.5 7599 55.0 22.4 7600 15.0 25.9 7601 8.7 38.5 7602 0.9 16.6 7603 19.0 48.5 7604 100.0 4.3 7605 100.0 7.9 7606 5.2 42.6 7607 21.8 47.2 7608 90.0 1.0 7609 2.0 23.5 7610 98.0 2.2 7611 100.0 6.2 7612 100.0 2.0 7613 100.0 5.6 7614 100.0 3.0 7615 30.0 14.3 7616 100.0 1.0 7617 end of data 7618 . 7619 . Step 3: Generate fluctuation plot based on different levels of 7620 . the 2 methods 7621 . 7622 . Use intensity levels of 5%, 10%, 15%, 20%, 25% 7623 . Use percent matching levels of 80%, 90%, 95%, 99.5% 7624 . 7625 let n = size intensity 7626 let intcut = data 5 10 15 20 25 7627 let nint = size intcut 7628 let matcut = data 80 90 95 99.5 7629 let nmat = size matcut 7630 . 7631 let int2 = intensity 7632 let mat2 = percmat 7633 let xgroup = 1 for i = 1 1 n 7634 let ygroup = 1 for i = 1 1 n 7635 let icnt = 0 7636 . 7637 loop for k = 1 1 nint 7638 let acut = intcut(k) 7639 loop for l = 1 1 nmat 7640 let bcut = matcut(l) 7641 let icnt = icnt + 1 7642 if icnt = 1 7643 let xgroupal = xgroup 7644 let ygroupal = ygroup 7645 let intcor = 0 for i = 1 1 n 7646 let intcor = 1 subset int2 > acut 7647 let intall = intcor 7648 let matcor = 0 for i = 1 1 n 7649 let matcor = 1 subset mat2 < bcut 7650 let matall = matcor 7651 else 7652 let xgroup2 = k for i = 1 1 n 7653 extend xgroupal xgroup2 7654 let ygroup2 = l for i = 1 1 n 7655 extend ygroupal ygroup2 7656 let intcor = 0 for i = 1 1 n 7657 let intcor = 1 subset int2 > acut 7658 extend intall intcor 7659 let matcor = 0 for i = 1 1 n 7660 let matcor = 1 subset mat2 < bcut 7661 extend matall matcor 7662 end of if 7663 end of loop 7664 end of loop 7665 . 7666 label case asis 7667 tic mark label case asis 7668 title case asis 7669 title offset 2 7670 . 7671 title Percent Disagreement Between Method 1 and Method 2 7672 y1label Method 1 7673 x1label Method 2 7674 tic offset units data 7675 xlimits 1 nmat 7676 major xtic mark number nmat 7677 minor xtic mark number 0 7678 xtic mark offset 0.7 0.7 7679 x1tic mark label format alpha 7680 x1tic mark label content 80% 90% 95% 99.5% 7681 ylimits 1 nint 7682 major ytic mark number nint 7683 minor ytic mark number 0 7684 ytic mark offset 0.7 0.7 7685 y1tic mark label format alpha 7686 y1tic mark label content 5% 10% 15% 20% 25% 7687 . 7688 let ylevel = data 60 70 80 85 90 101 7689 let ylevel = data 10 15 20 30 41 7690 . 7691 let string color = g90 green cyan blue orange red 7692 line color ^color 7693 region fill color ^color 7694 region border color ^color 7695 . 7696 set fluctuation plot floor 0 7697 set fluctuation plot ceiling 40 7698 fluctuation percent disagreement contour plot ... 7699 intall matall xgroupal ygroupal ylevel 7700 . 7701 box fill pattern solid 7702 box shadow hw 0 0 7703 . 7704 box fill color green 7705 box 86 90 90 86 7706 move 91 87; text <= 10 7707 . 7708 box fill color cyan 7709 box 86 86 90 82 7710 move 91 83; text 10 - 15 7711 . 7712 box fill color blue 7713 box 86 82 90 78 7714 move 91 79; text 15 - 20 7715 . 7716 box fill color orange 7717 box 86 78 90 74 7718 move 91 75; text 20 - 30 7719 . 7720 box fill color red 7721 box 86 74 90 70 7722 move 91 71; text > 30 7723 7724-----PERCENTAGE RANK (LET)--------------------------------------------------- 7725 7726PERCENTAGE RANK 7727 7728Name: 7729 PERCENTAGE RANK (LET) 7730 7731Type: 7732 Let Subcommand 7733 7734Purpose: 7735 Compute the percentage ranks of a variable. 7736 7737Description: 7738 The percentage rank is computed as 7739 7740 PR(i) = 100*(RANK(i) - 0.5)/N 7741 7742 with RANK(i) and N denoting the rank of the i-th element and the 7743 number of observations, respectively. 7744 7745 Ranks are frequently used in nonparametric statistical analysis. Some 7746 analysts like to the think of the ranks in terms of percentages. 7747 7748Syntax: 7749 LET <y2> = PERCENTAGE RANK <y1> <SUBSET/EXCEPT/FOR qualification> 7750 where <y1> is a response variable; 7751 <y2> is a variable where the percentage ranks are saved; 7752 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 7753 7754Examples: 7755 LET PERCRANK = PERCENTAGE RANK Y1 7756 7757Note: 7758 Ties are assigned an average rank. For example, if the 2nd and 3rd 7759 highest values are equal, each is assigned a rank of 2.5. 7760 7761Default: 7762 None 7763 7764Synonyms: 7765 None 7766 7767Related Commands: 7768 RANK = Rank the elements in a variable. 7769 RANK2 = Rank the elements in a variable when there are one, 7770 two, or three group-id variables. 7771 RANK INDEX = Rank the elements in a variable where each rank will 7772 be assigned a unique integer value. 7773 SORT = Sort the elements in a variable. 7774 SORTC = Sort the elements in a variable and carry one or 7775 more variables along. 7776 7777Reference: 7778 ISO 13528, First Edition, Statistical Methods for Use 7779 in Proficiency Testing by Interlaboratory Comparisons, 7780 2005, p. 24. 7781 7782Applications: 7783 Nonparametric statistics 7784 7785Implementation Date: 7786 2012/1 7787 7788Program: 7789 let y1 = norm rand numb for i = 1 1 20 7790 let y2 = rank y1 7791 let y3 = percentage rank y1 7792 . 7793 set write decimals 3 7794 print y1 y2 y3 7795 7796-----PERCENTILE (LET)----------------------------------------- 7797 7798PERCENTILE 7799 7800Name: 7801 PERCENTILE (LET) 7802 7803Type: 7804 Let Subcommand 7805 7806Purpose: 7807 Compute a user specified percentile for a variable. 7808 7809Description: 7810 The p-th percentile of a data set is defined as that value 7811 where p percent of the data is below that value and (1-p) 7812 percent of the data is above that value. For example, the 7813 50th percentile is the median. 7814 7815 The default method for computing percentiles in Dataplot is 7816 based on the order statistic. The formula is: 7817 7818 X(p) = (1 - r)*X(NI1) + r*X(NI2) 7819 7820 where 7821 7822 X are the observations sorted in ascending order 7823 NI1 = INT(p*(N+1)) 7824 NI2 = NI1 + 1 7825 r = p*(N+1) - INT(p*(N+1)) 7826 7827 If p is < 1/(N+1), then X(1) is returned. If p > N/(N+1), then X(N) 7828 is returned. 7829 7830Syntax 1: 7831 LET <par> = <value> PERCENTILE <y> 7832 <SUBSET/EXCEPT/FOR qualification> 7833 where <y> is the response variable; 7834 <par> is a parameter where the computed percentile 7835 is stored; 7836 <value> is a parameter in the range 0 to 100 that specifies 7837 which percentile to compute; 7838 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 7839 7840Syntax 2: 7841 LET <par> = PERCENTILE <y> 7842 <SUBSET/EXCEPT/FOR qualification> 7843 where <y> is the response variable; 7844 <par> is a parameter where the computed percentile is stored; 7845 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 7846 7847 With this syntax, the desired percentile is specified by entering the 7848 command 7849 7850 LET P100 = <value> 7851 7852 before entering the PERCENTILE command. 7853 7854Examples: 7855 LET A = 20 PERCENTILE Y 7856 LET A = 50 PERCENTILE Y SUBSET TAG > 2 7857 7858 LET P100 = 90 7859 LET A = PERCENTILE Y 7860 7861Note: 7862 The QUANTILE command is equivalent to the PERCENTILE command. The 7863 only difference is that the requested percentile is given as a 7864 percentage between 0 and 100% while the requested quantile is 7865 specified as a fraction between 0 and 1. 7866 7867Note: 7868 Note that there are a number of other ways of calculating percentiles 7869 in common use. Hyndman and Fan (1996) in an American Statistician 7870 article evaluated nine different methods (we will refer to these as R1 7871 through R9) for computing percentiles relative to six desirable 7872 properties. Their goal was to advocate a "standard" definition for 7873 percentiles that would be implemented in statistical software. Although 7874 this has not in fact happened, the article does provide a useful 7875 summary and evaluation of various methods for computing percentiles. 7876 Most statistical and spreadsheet software use one of the methods 7877 described in Hyndman and Fan. 7878 7879 The default method used by Dataplot described above corresponds to 7880 method R6 of Hyndman and Fan. The description of the methods 7881 here will be in terms of the quantile q = p/100 (where p is 7882 the desired percentile). 7883 7884 The method advocated by Hyndman and Fan is R8. For the R8 method, 7885 7886 X(q) = X(NI1) + r*(X(NI2) - X(NI1)) 7887 7888 where 7889 7890 X are the observations sorted in ascending order 7891 NI1 = INT(q*(N+(1/3)) + (1/3)) 7892 NI2 = NI1 + 1 7893 r = q*(N+1) - INT(q*(N+1)) 7894 7895 If q <= (2/3)/(N+(1/3)) the minimum value will be returned and 7896 if q >= (N-(1/3))/(N+(1/3)) the maximum value will be returned. 7897 7898 Method R7 (this is the default method in R and Excel) is calculated by 7899 7900 X(q) = X(NI1) + r*(X(NI2) - X(NI1)) 7901 7902 where 7903 7904 X are the observations sorted in ascending order 7905 NI1 = INT(q*(N-1) + 1) 7906 NI2 = NI1 + 1 7907 r = q*(N+1) - INT(q*(N+1)) 7908 7909 If q = 1, then X(N) is returned. 7910 7911 The R6, R7, and R8 methods give fairly similar, but not exactly the 7912 same (particularly for small samples), results. For most purposes, 7913 any of these three methods should be acceptable. 7914 7915Note: 7916 The following command is used to determine which method 7917 is used to compute the percentile: 7918 7919 SET QUANTILE METHOD <ORDER/R6/R7/R8> 7920 7921 R6 is equivalent to ORDER. 7922 7923Note: 7924 Dataplot statistics can be used in 20+ commands. For details, enter 7925 7926 HELP STATISTICS 7927 7928 When using these commands, the specific quantile to compute is 7929 specified by entering the following command (before the statistic 7930 command): 7931 7932 LET P100 = <value> 7933 7934 where <value> is a number in the interval (0,100) that specifies 7935 the desired quantile. 7936 7937 7938Default: 7939 The ORDER STATISTIC (R6) method is the default method for calculating 7940 percentiles. 7941 7942Synonyms: 7943 None 7944 7945Related Commands: 7946 QUANTILE = Compute a specified quantile. 7947 MEDIAN = Compute the median. 7948 LOWER QUARTILE = Compute the lower quartile. 7949 UPPER QUARTILE = Compute the upper quartile. 7950 FIRST DECILE = Compute the first decile (the 10th percentile). 7951 ... STATISTIC PLOT = Generate a statistic versus subset plot for 7952 numerous statistics. 7953 7954Reference: 7955 Hyndman and Fan (November 1996), "Sample Quantiles in Statistical 7956 Packages", The American Statistician, Vol. 50, No. 4, pp. 361-365. 7957 7958Applications: 7959 Data Analysis 7960 7961Implementation Date: 7962 1998/12 7963 2015/2: Support for R7 and R8 methods 7964 7965Program 1: 7966 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 7967 LET A1 = 30 PERCENTILE Y1 7968 7969Program 2: 7970 . Step 1: Read the data 7971 . 7972 read y 7973 95.1772 7974 95.1567 7975 95.1937 7976 95.1959 7977 95.1442 7978 95.0610 7979 95.1591 7980 95.1195 7981 95.1065 7982 95.0925 7983 95.1990 7984 95.1682 7985 end of data 7986 . 7987 . Step 2: Compute the percentiles using various methods 7988 . 7989 let p100 = xq 7990 . 7991 let xpr6 = percentile y 7992 let xpr6 = round(xpr6,4) 7993 . 7994 set quantile method r7 7995 let xpr7 = percentile y 7996 let xpr7 = round(xpr7,4) 7997 . 7998 set quantile method r8 7999 let xpr8 = percentile y 8000 let xpr8 = round(xpr8,4) 8001 . 8002 . Step 3: Print the results 8003 . 8004 print "Percentile with R6 method: ^xpr6" 8005 print "Percentile with R7 method: ^xpr7" 8006 print "Percentile with R8 method: ^xpr8" 8007 8008-----PERCENT POINT PLOT------------------------------------------------ 8009 8010PERCENT POINT PLOT 8011 8012Name: 8013 PERCENT POINT PLOT 8014 8015Type: 8016 Graphics Command 8017 8018Purpose: 8019 Generates a percent point plot. 8020 8021Description: 8022 A percent point plot is a graphical data analysis technique for 8023 summarizing the distributional information of a variable. It 8024 consists of: 8025 8026 Vertical axis = percent point; 8027 Horizontal axis = percent (0 to 100). 8028 8029 Thus, for example, if the value of 50 is chosen on the horizontal 8030 axis, then the corresponding value on the vertical axis is the 8031 estimated 50% point (that is, the median) from the data. 8032 8033 The percent point plot can be generated for either raw data or for 8034 binned data. 8035 8036 For raw data, the percentile plot is constructed by plotting the 8037 sorted data on the vertical axis. The corresponding horizontal axis 8038 value for the i-th point is 100*Y(i)/N with Y(i) and N denoting the 8039 i-th observation of the sorted data and the sample size, respectively. 8040 The multiplication by 100 is to covert the horizontal axis to a 8041 percentage value. 8042 8043 For binned data, the vertical axis value is the mid-point of the 8044 bin. The corresponding horizontal axis values are the cumulative 8045 sums of the frequencies of the bins divided by the sum of the 8046 frequencies for all bins. This value is multiplied by 100 to convert 8047 the horizontal axis to a percentage value. 8048 8049 By default, raw data is first binned into frequency data. To 8050 suppress this binning (i.e., generate the raw data version of 8051 the plot), enter the command 8052 8053 SET PERCENT POINT PLOT UNBINNED 8054 8055 To restore the default of binning raw data, enter 8056 8057 SET PERCENT POINT PLOT BINNED 8058 8059 Typically no binning is preferred for small to moderate size data 8060 sets. Binning can be helpful for large data sets in that it 8061 reduces the number of points that are plotted. 8062 8063Syntax 1: 8064 PERCENT POINT PLOT <x> <SUBSET/EXCEPT/FOR qualification> 8065 where <x> is the variable of raw data; 8066 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 8067 8068 This syntax is used for the case where you have raw data. 8069 8070Syntax 2: 8071 PERCENT POINT PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 8072 where <y> is the variable of pre-computed frequencies; 8073 <x> is the variable of distinct values; 8074 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 8075 8076 This syntax is used for the case where you have pre-computed 8077 frequencies at each data level. This syntax is used when you 8078 have equal width bins. 8079 8080Syntax 3: 8081 PERCENT POINT PLOT <y> <xlow> <xhigh> 8082 <SUBSET/EXCEPT/FOR qualification> 8083 where <y> is the variable of pre-computed frequencies; 8084 <xlow> is the variable containing the lower limits of the bins; 8085 <xhigh> is the variable containing the upper limits of the bins; 8086 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 8087 8088 This syntax is used for the case where you have pre-computed 8089 frequencies at each data level. This syntax is used when you have 8090 unequal width bins. 8091 8092Syntax 4: 8093 MULTIPLE PERCENT POINT PLOT <y1> ... <yk> 8094 <SUBSET/EXCEPT/FOR qualification> 8095 where <y1> ... <yk> is a list of 1 to 30 response variables; 8096 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 8097 8098 This syntax will generate percent point plots of each of the 8099 listed response variables on the same plot. You can specify 8100 different plot attributes for each response variable. 8101 8102 This syntax is only supported for raw data (i.e., no binned data). 8103 8104Syntax 5: 8105 REPLICATED PERCENT POINT PLOT <y> <x1> ... <xk> 8106 <SUBSET/EXCEPT/FOR qualification> 8107 where <y> is the response variable; 8108 <x1> ... <xk> is a list of 1 to 6 group-id variables; 8109 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 8110 8111 From one to six group-id variables can be specified (most 8112 commonly there is a single group-id variable). 8113 8114 Note that with this syntax, the plot points corresponding to each 8115 group are drawn with different attributes (i.e., the first group 8116 uses the first setting for the CHARACTER and LINE and related 8117 attribute setting commands, the second group uses the second 8118 setting, and so on). For example, this syntax can be used to label 8119 the plot points with the group-id. 8120 8121 If there is more than one group-id variable, the attribute settings 8122 work from right to left. That is, if X1 has 2 levels and X2 has 8123 2 levels, then 8124 8125 trace 1 = Level 1 of X1 and Level 1 of X2 8126 trace 2 = Level 1 of X1 and Level 2 of X2 8127 trace 3 = Level 2 of X1 and Level 1 of X2 8128 trace 4 = Level 2 of X1 and Level 1 of X2 8129 8130Syntax 6: 8131 HIGHLIGHTED PERCENT POINT PLOT <y> <x> 8132 <SUBSET/EXCEPT/FOR qualification> 8133 where <y> is the response variable; 8134 <x> is a group-id variable; 8135 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 8136 8137 Although this syntax is similar to the REPLICATION case, it 8138 is generally used in a different way. The REPLICATION case is 8139 used when we have distinct groups of data and we want to generate 8140 separate percent point plots for each group. Highlighting is 8141 used when we have a single group of data, but we want to draw 8142 some of the points with different attributes. For example, we 8143 may want to emphasize the extreme points in the plot. 8144 8145Example: 8146 PERCENT POINT PLOT Y 8147 PERCENT POINT Y X 8148 PERCENT POINT Y XLOW XHIGH 8149 HIGHTLIGHTED PERCENT POINT Y TAG 8150 MULTIPLE PERCENT POINT Y1 Y2 Y3 8151 PERCENT POINT Y X SUBSET X > 2 8152 8153Note: 8154 When raw data is binned, Dataplot divides the raw data into classes 8155 in the same manner as it does for a histogram or frequency polygon. 8156 The percent points are calculated at the mid-points of these histogram 8157 classes. The defaults are the same as for histograms (the class 8158 width is 0.3*standard deviation, 6 classes above and 6 classes 8159 below the mean). You can specify your own binning with the 8160 CLASS LOWER, CLASS UPPER, and CLASS WIDTH commands. This is 8161 demonstrated in the sample program below. 8162 8163 The SET HISTOGRAM CLASS WIDTH can be used to define several other 8164 algorithms for binning the data (HELP HISTOGRAM CLASS WIDTH for 8165 details). The SET HISTOGRAM OUTLIERS command also applies to 8166 the PERCENT POINT PLOT if raw data is being binned. 8167 8168Note: 8169 Percent point plots are also referred to as quantile plots in 8170 the statistical literature. 8171 8172Note: 8173 The attributes of the plot can be set by the first setting of the 8174 LINE, CHARACTER, SPIKE, and BAR commands (and there corresponding 8175 attribute setting commands). This is demonstrated in the sample 8176 program below. 8177 8178Default: 8179 None 8180 8181Synonyms: 8182 None 8183 8184Related Commands: 8185 QUAN-QUAN PLOT = Generates a quantile-quantile plot. 8186 HISTOGRAM = Generates a histogram. 8187 FREQUENCY PLOT = Generates a frequency plot. 8188 PIE CHART = Generates a pie chart. 8189 PROBABILITY PLOT = Generates a probability plot. 8190 PPCC PLOT = Generates probability plot correlation 8191 coefficient plot. 8192 PLOT = Generates a plot (including bar plots). 8193 CLASS LOWER = Sets the lower class minimum for histograms, 8194 frequency plots, and pie charts. 8195 CLASS UPPER = Sets the upper class maximum for histograms, 8196 frequency plots, and pie charts. 8197 CLASS WIDTH = Sets the class width for histograms, frequency 8198 plots, and pie charts. 8199 8200Applications: 8201 Distributional Analysis 8202 8203Reference: 8204 Chambers, Cleveland, Kleiner, and Tukey (1983), "Graphical Methods 8205 for Data Analysis", Wadsworth. 8206 8207Implementation Date: 8208 Pre-1987 8209 1998/09: Support for SET PERCENT POINT PLOT command. 8210 2011/02: Support for REPLICATION and MULTIPLE options. 8211 2011/02: Support for HIGHLIGHT option. 8212 8213Program 1: 8214 SKIP 25 8215 READ SUNSPOT2.DAT Y 8216 . 8217 LET ALOW = MINIMUM Y 8218 LET AHIGH = MAXIMUM Y 8219 CLASS LOWER ALOW 8220 CLASS UPPER AHIGH 8221 CLASS WIDTH 1.0 8222 CHARACTER CIRCLE 8223 CHARACTER FILL ON 8224 CHARACTER SIZE 1.2 8225 X1LABEL PERCENT POINT 8226 Y1LABEL DATA VALUE 8227 TITLE AUTOMATIC 8228 . 8229 PERCENT POINT PLOT Y 8230 8231Program 2: 8232 let y1 = norm rand numb for i = 1 1 100 8233 . 8234 title case asis 8235 title offset 2 8236 title automatic 8237 label case asis 8238 tic mark offset units screen 8239 tic mark offset 3 3 8240 . 8241 char circle 8242 char fill on 8243 char hw 0.5 0.375 8244 line blank 8245 . 8246 multiplot corner coordinates 5 5 95 95 8247 multiplot scale factor 2 8248 multiplot 2 2 8249 . 8250 set percent point plot unbinned 8251 set histogram outliers on 8252 set histogram empty bins off 8253 title Unbinned Data 8254 percent point plot y1 8255 . 8256 set percent point plot binned 8257 title Data Binned by Command 8258 percent point plot y1 8259 . 8260 title User Created Bins: Equi-Spaced Bins 8261 let z2 x2 = binned y1 8262 percent point plot z2 x2 8263 . 8264 let minsize = 5 8265 let z3 xlow xhigh = combine frequency table z2 x2 8266 title User Created Bins: Unequal-Spaced Bins 8267 percent point plot z3 xlow xhigh 8268 . 8269 end of multiplot 8270 justification center 8271 move 50 97 8272 text Percent Point Plots for 100 Normal Random Numbers 8273 move 50 5 8274 text Percentile 8275 direction vertical 8276 move 3 50 8277 text Response Value 8278 8279Program 3: 8280 dimension 500 rows 8281 skip 25 8282 read iris.dat y1 y2 y3 y4 8283 let m = create matrix y1 y2 y3 y4 8284 . 8285 title case asis 8286 title offset 2 8287 label case asis 8288 . 8289 char circle all 8290 char color black 8291 char fill on all 8292 char hw 0.5 0.375 all 8293 line blank all 8294 . 8295 y1label Response Value 8296 x1label Percentile 8297 title IRIS Data (all species combined) 8298 . 8299 set percent point plot unbinned 8300 set histogram outliers on 8301 set histogram empty bins off 8302 percent point plot m 8303 . 8304 char color red blue cyan green 8305 title IRIS Data (species plotted separately) 8306 multiple percent point plot y1 to y4 8307 8308Program 4: 8309 skip 25 8310 read gear.dat y x 8311 . 8312 title case asis 8313 title offset 2 8314 label case asis 8315 tic mark offset units screen 8316 tic mark offset 5 5 8317 . 8318 char circle all 8319 char color black red blue green cyan grey brown magenta dgreen orange 8320 char fill on all 8321 char hw 0.5 0.375 all 8322 line blank all 8323 . 8324 title Percent Point Plots for GEAR.DAT 8325 y1label Response Value 8326 x1label Percentile 8327 . 8328 set percent point plot unbinned 8329 set histogram outliers on 8330 set histogram empty bins off 8331 replicated percent point plot y x 8332 8333-----PERCERR (LET)-------------------------------- 8334 8335PERCERR 8336 8337Name: 8338 PERCERR (LET) 8339 8340Type: 8341 Library Function 8342 8343Purpose: 8344 Return the percent error of two numbers. 8345 8346Description: 8347 The definition of the percent error between a "true" value 8348 X(t) and an observed value X(o) used by Dataplot is: 8349 8350 Percent Error = 100*(X(t) - X(o))/X(t) 8351 8352 There may be some slight differences for this formula in other 8353 sources. Specifically, 8354 8355 1) Some sources take the absolute value of the above 8356 quantity. In Dataplot, you can use the ABS function 8357 to obtain this form. 8358 8359 2) Some sources may reverse the order of the X(t) and X(o) values. 8360 This changes the sign of the result, but not the magnitude. 8361 8362Syntax: 8363 LET <y> = PERCERR(<y1>,<y2>) <SUBSET/EXCEPT/FOR qualification> 8364 where <y1> is a variable or a parameter; 8365 <y2> is a variable or a parameter; 8366 <y> is a variable or a parameter (depending on what <y1> and 8367 <y2> are) where the computed percent error values 8368 are stored; 8369 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 8370 8371Examples: 8372 LET A = PERCERR(14,10) 8373 LET A = PERCERR(A1,A2) 8374 LET X2 = PERCERR(X1,X4) 8375 LET X2 = PERCERR(X1-4,X2+6) 8376 8377Note: 8378 Library functions are distinguished from let subcommands 8379 in the following ways. 8380 1) Functions enclose the input value in parenthesis. Let 8381 subcommands use spaces. 8382 2) Functions can accept (and return) either parameters 8383 (i.e., single values) or variables (i.e., an array of 8384 values) while let subcommands are specific in which they 8385 accept as input and what they return as output. 8386 3) Functions can accept expressions while let subcommands 8387 do not. For example, the following is legal: 8388 LET Y2 = ABS(Y1-INT(Y1)) 8389 For let subcommands, you typically have to do something 8390 like the following: 8391 LET YTEMP = Y**2 + 8 8392 LET A = SUM YTEMP 8393 8394Default: 8395 None 8396 8397Synonyms: 8398 None 8399 8400Related Commands: 8401 PERCDIF = Compute the percent difference of two numbers. 8402 RELDIF = Compute the relative difference of two numbers. 8403 MIN = Compute the minimum of two numbers. 8404 MAX = Compute the maximum of two numbers. 8405 ABS = Compute the absolute value of a number. 8406 8407Applications: 8408 Data Management 8409 8410Implementation Date: 8411 2010/12 8412 8413Program: 8414 LET X = SEQUENCE 0.1 0.1 3 8415 LET Y1 = X**2 8416 LET Y2 = X**(1/2) 8417 LET Y3 = PERCERR(Y1,Y2) 8418 SET WRITE DECIMALS 5 8419 PRINT Y1 Y2 Y3 8420 8421-----PERIODOGRAM------------------------------------------------------- 8422 8423PERIODOGRAM 8424 8425Name: 8426 PERIODOGRAM 8427 8428Type: 8429 Graphics Command 8430 8431Purpose: 8432 Generates an auto-periodogram. 8433 8434Description: 8435 A periodogram is a time series technique which carries out a 8436 Fourier decomposition of the time series. It consists of: 8437 Vertical axis = sum of squared Fourier coefficients 8438 (a(i)**2 + b(i)**2); 8439 Horizontal axis = Fourier frequencies (1/n, 2/n, 3/n, ..., 1/2) 8440 where n is the number of observations in the 8441 time series. 8442 8443Syntax 1: (one time series, produces an auto-periodogram) 8444 PERIODOGRAM <y> <SUBSET/EXCEPT/FOR qualification> 8445 where <y> is a response variable; 8446 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 8447 8448Examples: 8449 PERIODOGRAM Y 8450 PERIODOGRAM Y2 SUBSET Y2 > 2 8451 8452Note: 8453 The periodogram assumes equi-spaced data. Equi-spaced time series 8454 are inherently limited to detecting frequencies between 0 and 0.5. 8455 8456Note: 8457 The spectral plot is an improved form of the periodogram and is 8458 generally recommended in its place. See the SPECTRUM command for 8459 details. 8460 8461Note: 8462 The CROSS-PERIODOGRAM, CO-PERIODOGRAM, and QUADRATURE PERIODOGRAM 8463 commands are recognized. However, these variations are not 8464 implemented at this time. These commands will generate a page 8465 erase, but no plot is generated. These options are recognized for 8466 the SPECTRUM command. 8467 8468Default: 8469 None 8470 8471Synonyms: 8472 None 8473 8474Related Commands: 8475 SPECTRUM = Generates a spectral plot. 8476 CORRELATION PLOT = Generates a correlation plot. 8477 COMPLEX DEMOD PLOT = Generates a complex demodulation plot. 8478 LAG PLOT = Generates a lag plot. 8479 PLOT = Generates a data or function plot. 8480 4-PLOT = Generates 4-plot univariate analysis. 8481 CHARACTERS = Sets the types for plot characters. 8482 LINES = Sets the types for plot lines. 8483 SPIKES = Sets the on/off switches for plot spikes. 8484 SUMMARY = Generates a table of summary statistics. 8485 LET = Generates sin/cos transformations (plus 8486 much more). 8487 FIT = Carries out a least squares fit. 8488 8489Reference: 8490 "Spectral Analysis of Time Series", Jenkins and Watts, ... 8491 8492Applications: 8493 Frequency Time Series Analysis 8494 8495Implementation Date: 8496 Pre-1987 8497 8498Program: 8499 . THIS SAMPLE PROGRAM READS THE FILE LEW.DAT IN THE 8500 . DATAPLOT REFERENCE DIRECTORY. SINCE IT CONTAINS 200 8501 . DATA POINTS, IT IS NOT REPRODUCED HERE. THESE DATA ARE 8502 . BEAM DEFLECTION DATA. 8503 . 8504 SKIP 25 8505 READ LEW.DAT DEFLECT 8506 . 8507 SPIKE ON 8508 LINE BLANK 8509 YLIMITS 0 40000 8510 YTIC OFFSET 0 2000 8511 . 8512 PERIODOGRAM DEFLECT 8513 8514-----PERPINDICULAR LINES-------------------------------------------------- 8515 8516PERPINDICULAR LINES 8517 8518Name: 8519 PERPINDICULAR LINES 8520 8521Type: 8522 LET Subcommand 8523 8524Purpose: 8525 Given a line defined by two points and a third point, find the line 8526 perpindicular to the first line and containing the third point. 8527 8528Syntax: 8529 LET <yout> <xout>= PERPINDICULAR LINES <x1> <y1> <x2> <y2> <x3> <y3> 8530 <SUBSET/EXPCEPT/FOR qualification> 8531 where <x1> is a variable or parameter containing the x-coordinates for the 8532 first point of line one; 8533 <y1> is a variable or parameter containing the y-coordinates for the 8534 first point of line one; 8535 <x2> is a variable or parameter containing the x-coordinates for the 8536 second point of line one; 8537 <y2> is a variable or parameter containing the y-coordinates for the 8538 second point of line one; 8539 <x3> is a variable or parameter containing the x-coordinates for the 8540 third point; 8541 <y3> is a variable or parameter containing the y-coordinates for the 8542 third point; 8543 <yout> is a variable containing the y-coordinates of the 8544 second point of the perpindicular line; 8545 <xout> is a variable containing the x-coordinates of the 8546 second point of the perpindicular line; 8547 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 8548 8549Examples: 8550 LET YOUT XOUT = PERPINDICULAR LINES X1 Y1 X2 Y2 X3 Y3 X4 Y4 8551 8552Default: 8553 None 8554 8555Synonyms: 8556 None 8557 8558Related Commands: 8559 PARALLEL LINE = Determine the coordinates for a point that defines 8560 a parallel line determined by a point and a line 8561 defined by two points. 8562 POINTS IN POLYGON = Determine whether points are in the interior 8563 of a convex polygon. 8564 CONVEX HULL = Determine the convex hull of a set of points. 8565 TRANSFORM POINTS = Perform location, scale, and rotation 8566 transformation for a set of points. 8567 EXTREME POINTS = Determine the extreme points of a set of points. 8568 LINE INTERSECTIONS = Determine the intersection points for a set of 8569 lines. 8570 8571Applications: 8572 Computational Geometry 8573 8574Implementation Date: 8575 2012/10 8576 8577Program: 8578 dimension 40 columns 8579 skip 25 8580 read convhull.dat x y 8581 . 8582 let y2 x2 = 2d convex hull y x 8583 let xtemp = x2(1) 8584 let ytemp = y2(1) 8585 let y2 = combine y2 ytemp 8586 let x2 = combine x2 xtemp 8587 let x3 = x2 8588 let y3 = y2 8589 let n = size y2 8590 let nm1 = n - 1 8591 retain x2 y2 for i = 1 1 nm1 8592 retain x3 y3 for i = 2 1 n 8593 let slope = slope(x2,y2,x3,y3) 8594 let pdist = dpntline(xtemp,ytemp,x3,y3,slope) 8595 let xtempv = xtemp for i = 1 1 nm1 8596 let ytempv = ytemp for i = 1 1 nm1 8597 let y5 x5 = perpindicular line x2 y2 x3 y3 xtempv ytempv 8598 . 8599 set write decimals 4 8600 print "Anchor Point: (^xtemp,^ytemp)" 8601 print " " 8602 print " " 8603 print x2 y2 x3 y3 x5 y5 8604 8605-----PEXCDF (LET)-------------------------------- 8606 8607PEXCDF 8608 8609Name: 8610 PEXCDF (LET) 8611 8612Type: 8613 Library Function 8614 8615Purpose: 8616 Compute the exponential power cumulative distribution function 8617 with shape parameter beta. 8618 8619Description: 8620 The exponential power distribution has the following cumulative 8621 distribution function: 8622 8623 F(x;beta) = 1 - EXP(1 - EXP(X**BETA)) 8624 x > 0; beta > 0 8625 8626 with beta denoting the shape parameter. 8627 8628 This distribution can be generalized with location and 8629 scale parameters using the relation 8630 8631 F(x;beta,loc,scale) = F((x-loc)/scale;beta,0,1) 8632 8633 This distribution was proposed by Dhillon as useful 8634 distribution for reliability applications since it can 8635 have increasing, decreasing, or bathtub shaped hazard 8636 functions. 8637 8638Syntax: 8639 LET <y> = PEXCDF(<x>,<beta>,<loc>,<scale>) 8640 <SUBSET/EXCEPT/FOR qualification> 8641 where <x> is a number, parameter, or variable containing positive 8642 values; 8643 <y> is a variable or a parameter (depending on what <x> is) 8644 where the computed exponential power cdf value is 8645 stored; 8646 <beta> is a positive number, parameter, or variable that 8647 specifies the shape parameter; 8648 <loc> is a number, parameter, or variable that specifies 8649 the location parameter; 8650 <scale> is a positive number, parameter, or variable that 8651 specifies the scale parameter; 8652 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 8653 8654 If <loc> and <scale> are omitted, they default to 0 and 1, 8655 respectively. 8656 8657Examples: 8658 LET A = PEXCDF(0.3,2.5) 8659 LET A = PEXCDF(X1,2.5,0,10) 8660 PLOT PEXCDF(X,2.5,0,3) FOR X = 0.1 0.1 10 8661 8662Note: 8663 The 11/2007 version changed the syntax for this function 8664 from 8665 8666 LET A = PEXCDF(X,ALPHA,BETA,LOC,SCALE) 8667 8668 to 8669 8670 LET A = PEXCDF(X,BETA,LOC,SCALE) 8671 8672 This was done since ALPHA is in fact a scale parameter 8673 (in the articles listed in the References section, ALPHA 8674 is actually the reciprocal of the scale parameter). 8675 8676Note: 8677 Library functions are distinguished from let subcommands 8678 in the following ways. 8679 1) Functions enclose the input value in parenthesis. Let 8680 subcommands use spaces. 8681 2) Functions can accept (and return) either parameters 8682 (i.e., single values) or variables (i.e., an array of 8683 values) while let subcommands are specific in which they 8684 accept as input and what they return as output. 8685 3) Functions can accept expressions while let subcommands 8686 do not. For example, the following is legal: 8687 LET Y2 = ABS(Y1-INT(Y1)) 8688 For let subcommands, you typically have to do something 8689 like the following: 8690 LET YTEMP = Y**2 + 8 8691 LET A = SUM YTEMP 8692 8693Default: 8694 None 8695 8696Synonyms: 8697 None 8698 8699Related Commands: 8700 PEXPDF = Compute the exponential power probability density 8701 function. 8702 PEXPPF = Compute the exponential power percent point function. 8703 PEXHAZ = Compute the exponential power hazard function. 8704 PEXCHAZ = Compute the exponential power cumulative hazard 8705 function. 8706 ALPPDF = Compute the alpha probability density function. 8707 WEIPDF = Compute the Weibull probability density function. 8708 LGNPDF = Compute the log-normal probability density function. 8709 NORCDF = Compute the normal cumulative distribution function. 8710 NORPDF = Compute the normal probability density function. 8711 8712References: 8713 Johnson, Kotz, and Balakrishnan (1994), "Continuous Univariate 8714 Distributions--Volume 2", Second Edition, John Wiley and Sons, 8715 pp. 643-644. 8716 8717 Dhillon (1981), "Life Distributions", IEEE Transactions on 8718 Reliability, Vol. R-30, No. 5, pp. 457-459. 8719 8720Applications: 8721 Reliability, accelerated life testing 8722 8723Implementation Date: 8724 1998/4 8725 2007/11: Corrected the second shape parameter to be the 8726 scale parameter 8727 8728Program: 8729 LABEL CASE ASIS 8730 TITLE CASE ASIS 8731 TITLE OFFSET 2 8732 . 8733 MULTIPLOT 2 2 8734 MULTIPLOT CORNER COORDINATES 0 0 100 95 8735 MULTIPLOT SCALE FACTOR 2 8736 . 8737 LET BETA = 0.5 8738 TITLE BETA = ^beta 8739 PLOT PEXCDF(X,BETA) FOR X = 0.01 0.01 2 8740 . 8741 LET BETA = 1 8742 TITLE BETA = ^beta 8743 PLOT PEXCDF(X,BETA) FOR X = 0.01 0.01 2 8744 . 8745 LET BETA = 2 8746 TITLE BETA = ^beta 8747 PLOT PEXCDF(X,BETA) FOR X = 0.01 0.01 2 8748 . 8749 LET BETA = 5 8750 TITLE BETA = ^beta 8751 PLOT PEXCDF(X,BETA) FOR X = 0.01 0.01 2 8752 . 8753 END OF MULTIPLOT 8754 . 8755 JUSTIFICATION CENTER 8756 MOVE 50 97 8757 TEXT Exponential Power Cumulative Distribution Functions 8758 8759-----PEXCHAZ (LET)-------------------------------- 8760 8761PEXCHAZ 8762 8763Name: 8764 PEXCHAZ (LET) 8765 8766Type: 8767 Library Function 8768 8769Purpose: 8770 Compute the exponential power cumulative hazard function 8771 with shape parameter beta. 8772 8773Description: 8774 The exponential power distribution has the following cumulative 8775 hazard function: 8776 8777 H(x;beta) = EXP(x**beta) - 1 8778 x > 0; beta > 0 8779 8780 with beta denoting the shape parameter. 8781 8782 This distribution can be generalized with location and 8783 scale parameters using the relation 8784 8785 H(x;beta,loc,scale) = H((x-loc)/scale;beta,0,1) 8786 8787 This distribution was proposed by Dhillon as useful 8788 distribution for reliability applications since it can 8789 have increasing, decreasing, or bathtub shaped hazard 8790 functions. 8791 8792Syntax: 8793 LET <y> = PEXCHAZ(<x>,<beta>,<loc>,<scale>) 8794 <SUBSET/EXCEPT/FOR qualification> 8795 where <x> is a number, parameter, or variable containing positive 8796 values; 8797 <y> is a variable or a parameter (depending on what <x> is) 8798 where the computed exponential power cumulative 8799 hazard value is stored; 8800 <beta> is a positive number, parameter, or variable that 8801 specifies the shape parameter; 8802 <loc> is a number, parameter, or variable that specifies 8803 the location parameter; 8804 <scale> is a positive number, parameter, or variable that 8805 specifies the scale parameter; 8806 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 8807 8808 If <loc> and <scale> are omitted, they default to 0 and 1, 8809 respectively. 8810 8811Examples: 8812 LET A = PEXCHAZ(0.3,2.5) 8813 LET A = PEXCHAZ(X1,2.5,0,10) 8814 PLOT PEXCHAZ(X,2.5,0,3) FOR X = 0.1 0.1 10 8815 8816Note: 8817 The 11/2007 version changed the syntax for this function 8818 from 8819 8820 LET A = PEXCHAZ(X,ALPHA,BETA,LOC,SCALE) 8821 8822 to 8823 8824 LET A = PEXCHAZ(X,BETA,LOC,SCALE) 8825 8826 This was done since ALPHA is in fact a scale parameter 8827 (in the articles listed in the References section, ALPHA 8828 is actually the reciprocal of the scale parameter). 8829 8830Note: 8831 Library functions are distinguished from let subcommands 8832 in the following ways. 8833 1) Functions enclose the input value in parenthesis. Let 8834 subcommands use spaces. 8835 2) Functions can accept (and return) either parameters 8836 (i.e., single values) or variables (i.e., an array of 8837 values) while let subcommands are specific in which they 8838 accept as input and what they return as output. 8839 3) Functions can accept expressions while let subcommands 8840 do not. For example, the following is legal: 8841 LET Y2 = ABS(Y1-INT(Y1)) 8842 For let subcommands, you typically have to do something 8843 like the following: 8844 LET YTEMP = Y**2 + 8 8845 LET A = SUM YTEMP 8846 8847Default: 8848 None 8849 8850Synonyms: 8851 None 8852 8853Related Commands: 8854 PEXCDF = Compute the exponential power cumulative distribution 8855 function. 8856 PEXPDF = Compute the exponential power probability density 8857 function. 8858 PEXPPF = Compute the exponential power percent point function. 8859 PEXHAZ = Compute the exponential power hazard function. 8860 ALPPDF = Compute the alpha probability density function. 8861 WEIPDF = Compute the Weibull probability density function. 8862 LGNPDF = Compute the log-normal probability density function. 8863 NORCDF = Compute the normal cumulative distribution function. 8864 NORPDF = Compute the normal probability density function. 8865 8866References: 8867 Johnson, Kotz, and Balakrishnan (1994), "Continuous Univariate 8868 Distributions--Volume 2", Second Edition, John Wiley and Sons, 8869 pp. 643-644. 8870 8871 Dhillon (1981), "Life Distributions", IEEE Transactions on 8872 Reliability, Vol. R-30, No. 5, pp. 457-459. 8873 8874Applications: 8875 Reliability, accelerated life testing 8876 8877Implementation Date: 8878 1998/4 8879 2007/11: Corrected the second shape parameter to be the 8880 scale parameter 8881 8882Program: 8883 LABEL CASE ASIS 8884 TITLE CASE ASIS 8885 TITLE OFFSET 2 8886 . 8887 MULTIPLOT 2 2 8888 MULTIPLOT CORNER COORDINATES 0 0 100 95 8889 MULTIPLOT SCALE FACTOR 2 8890 . 8891 LET BETA = 0.5 8892 TITLE BETA = ^beta 8893 PLOT PEXCHAZ(X,BETA) FOR X = 0.01 0.01 2 8894 . 8895 LET BETA = 1 8896 TITLE BETA = ^beta 8897 PLOT PEXCHAZ(X,BETA) FOR X = 0.01 0.01 2 8898 . 8899 LET BETA = 2 8900 TITLE BETA = ^beta 8901 PLOT PEXCHAZ(X,BETA) FOR X = 0.01 0.01 2 8902 . 8903 LET BETA = 5 8904 TITLE BETA = ^beta 8905 PLOT PEXCHAZ(X,BETA) FOR X = 0.01 0.01 2 8906 . 8907 END OF MULTIPLOT 8908 . 8909 JUSTIFICATION CENTER 8910 MOVE 50 97 8911 TEXT Exponential Power Cumulative Hazard Functions 8912 8913-----PEXHAZ (LET)-------------------------------- 8914 8915PEXHAZ 8916 8917Name: 8918 PEXHAZ (LET) 8919 8920Type: 8921 Library Function 8922 8923Purpose: 8924 Compute the exponential power hazard function with shape 8925 parameter beta. 8926 8927Description: 8928 The exponential power distribution has the following hazard 8929 function: 8930 8931 h(x;beta) = beta*x**(beta-1)*EXP(x**beta) 8932 x > 0; beta > 0 8933 8934 with beta denoting the shape parameter. 8935 8936 This distribution can be generalized with location and 8937 scale parameters using the relation 8938 8939 h(x;beta,loc,scale) = (1/scale)*h((x-loc)/scale;beta,0,1) 8940 8941 This distribution was proposed by Dhillon as useful 8942 distribution for reliability applications since it can 8943 have increasing, decreasing, or bathtub shaped hazard 8944 functions. 8945 8946Syntax: 8947 LET <y> = PEXHAZ(<x>,<beta>,<loc>,<scale>) 8948 <SUBSET/EXCEPT/FOR qualification> 8949 where <x> is a number, parameter, or variable containing positive 8950 values; 8951 <y> is a variable or a parameter (depending on what <x> is) 8952 where the computed exponential power hazard value is 8953 stored; 8954 <beta> is a positive number, parameter, or variable that 8955 specifies the shape parameter; 8956 <loc> is a number, parameter, or variable that specifies 8957 the location parameter; 8958 <scale> is a positive number, parameter, or variable that 8959 specifies the scale parameter; 8960 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 8961 8962 If <loc> and <scale> are omitted, they default to 0 and 1, 8963 respectively. 8964 8965Examples: 8966 LET A = PEXHAZ(0.3,2.5) 8967 LET A = PEXHAZ(X1,2.5,0,10) 8968 PLOT PEXHAZ(X,2.5,0,3) FOR X = 0.1 0.1 10 8969 8970Note: 8971 The 11/2007 version changed the syntax for this function 8972 from 8973 8974 LET A = PEXHAZ(X,ALPHA,BETA,LOC,SCALE) 8975 8976 to 8977 8978 LET A = PEXHAZ(X,BETA,LOC,SCALE) 8979 8980 This was done since ALPHA is in fact a scale parameter 8981 (in the articles listed in the References section, ALPHA 8982 is actually the reciprocal of the scale parameter). 8983 8984Note: 8985 Library functions are distinguished from let subcommands 8986 in the following ways. 8987 1) Functions enclose the input value in parenthesis. Let 8988 subcommands use spaces. 8989 2) Functions can accept (and return) either parameters 8990 (i.e., single values) or variables (i.e., an array of 8991 values) while let subcommands are specific in which they 8992 accept as input and what they return as output. 8993 3) Functions can accept expressions while let subcommands 8994 do not. For example, the following is legal: 8995 LET Y2 = ABS(Y1-INT(Y1)) 8996 For let subcommands, you typically have to do something 8997 like the following: 8998 LET YTEMP = Y**2 + 8 8999 LET A = SUM YTEMP 9000 9001Default: 9002 None 9003 9004Synonyms: 9005 None 9006 9007Related Commands: 9008 PEXCDF = Compute the exponential power cumulative distribution 9009 function. 9010 PEXCHAZ = Compute the exponential power cumulative hazard 9011 function. 9012 PEXPDF = Compute the exponential power probability density 9013 function. 9014 PEXPPF = Compute the exponential power percent point function. 9015 ALPPDF = Compute the alpha probability density function. 9016 WEIPDF = Compute the Weibull probability density function. 9017 LGNPDF = Compute the log-normal probability density function. 9018 NORCDF = Compute the normal cumulative distribution function. 9019 NORPDF = Compute the normal probability density function. 9020 9021References: 9022 Johnson, Kotz, and Balakrishnan (1994), "Continuous Univariate 9023 Distributions--Volume 2", Second Edition, John Wiley and Sons, 9024 pp. 643-644. 9025 9026 Dhillon (1981), "Life Distributions", IEEE Transactions on 9027 Reliability, Vol. R-30, No. 5, pp. 457-459. 9028 9029Applications: 9030 Reliability, accelerated life testing 9031 9032Implementation Date: 9033 1998/4 9034 2007/11: Corrected the second shape parameter to be the 9035 scale parameter 9036 9037Program: 9038 LABEL CASE ASIS 9039 TITLE CASE ASIS 9040 TITLE OFFSET 2 9041 . 9042 MULTIPLOT 2 2 9043 MULTIPLOT CORNER COORDINATES 0 0 100 95 9044 MULTIPLOT SCALE FACTOR 2 9045 . 9046 LET BETA = 0.5 9047 TITLE BETA = ^beta 9048 PLOT PEXHAZ(X,BETA) FOR X = 0.01 0.01 2 9049 . 9050 LET BETA = 1 9051 TITLE BETA = ^beta 9052 PLOT PEXHAZ(X,BETA) FOR X = 0.01 0.01 2 9053 . 9054 LET BETA = 2 9055 TITLE BETA = ^beta 9056 PLOT PEXHAZ(X,BETA) FOR X = 0.01 0.01 2 9057 . 9058 LET BETA = 5 9059 TITLE BETA = ^beta 9060 PLOT PEXHAZ(X,BETA) FOR X = 0.01 0.01 2 9061 . 9062 END OF MULTIPLOT 9063 . 9064 JUSTIFICATION CENTER 9065 MOVE 50 97 9066 TEXT Exponential Power Hazard Functions 9067 9068-----PEXPDF (LET)-------------------------------- 9069 9070PEXPDF 9071 9072Name: 9073 PEXPDF (LET) 9074 9075Type: 9076 Library Function 9077 9078Purpose: 9079 Compute the exponential power probability density function with 9080 shape parameter beta. 9081 9082Description: 9083 The exponential power distribution has the following probability 9084 density function: 9085 9086 f(x;beta) = beta*x**(beta-1)*EXP(x**beta)* 9087 EXP(1 - EXP(x**beta)) 9088 x > 0; beta > 0 9089 9090 with beta denoting the shape parameter. 9091 9092 This distribution can be generalized with location and 9093 scale parameters using the relation 9094 9095 f(x;beta,loc,scale) = (1/scale)*f((x-loc)/scale;beta,0,1) 9096 9097 This distribution was proposed by Dhillon as useful 9098 distribution for reliability applications since it can 9099 have increasing, decreasing, or bathtub shaped hazard 9100 functions. 9101 9102Syntax: 9103 LET <y> = PEXPDF(<x>,<beta>,<loc>,<scale>) 9104 <SUBSET/EXCEPT/FOR qualification> 9105 where <x> is a number, parameter, or variable containing positive 9106 values; 9107 <y> is a variable or a parameter (depending on what <x> is) 9108 where the computed exponential power pdf value is 9109 stored; 9110 <beta> is a positive number, parameter, or variable that 9111 specifies the shape parameter; 9112 <loc> is a number, parameter, or variable that specifies 9113 the location parameter; 9114 <scale> is a positive number, parameter, or variable that 9115 specifies the scale parameter; 9116 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 9117 9118 If <loc> and <scale> are omitted, they default to 0 and 1, 9119 respectively. 9120 9121Examples: 9122 LET A = PEXPDF(0.3,2.5) 9123 LET A = PEXPDF(X1,2.5,0,10) 9124 PLOT PEXPDF(X,2.5,0,3) FOR X = 0.1 0.1 10 9125 9126Note: 9127 The 11/2007 version changed the syntax for this function 9128 from 9129 9130 LET A = PEXPDF(X,ALPHA,BETA,LOC,SCALE) 9131 9132 to 9133 9134 LET A = PEXPDF(X,BETA,LOC,SCALE) 9135 9136 This was done since ALPHA is in fact a scale parameter 9137 (in the articles listed in the References section, ALPHA 9138 is actually the reciprocal of the scale parameter). 9139 9140Note: 9141 Exponential power random numbers, probability plots, and 9142 goodness of fit tests can be generated with the commands: 9143 9144 LET BETA = <value> 9145 LET Y = EXPONENTIAL POWER RANDOM NUMBERS FOR I = 1 1 N 9146 EXPONENTIAL POWER PROBABILITY PLOT Y 9147 EXPONENTIAL POWER PROBABILITY PLOT Y2 X2 9148 EXPONENTIAL POWER PROBABILITY PLOT Y3 XLOW XHIGH 9149 EXPONENTIAL POWER KOLMOGOROV SMIRNOV GOODNESS OF FIT Y 9150 EXPONENTIAL POWER CHI-SQUARE GOODNESS OF FIT Y2 X2 9151 EXPONENTIAL POWER CHI-SQUARE GOODNESS OF FIT Y3 XLOW XHIGH 9152 9153 The following commands can be used to estimate the beta 9154 shape parameter for the exponential power distribution: 9155 9156 LET BETA1 = <value> 9157 LET BETA2 = <value> 9158 EXPONENTIAL POWER PPCC PLOT Y 9159 EXPONENTIAL POWER PPCC PLOT Y2 X2 9160 EXPONENTIAL POWER PPCC PLOT Y3 XLOW XHIGH 9161 EXPONENTIAL POWER KS PLOT Y 9162 EXPONENTIAL POWER KS PLOT Y2 X2 9163 EXPONENTIAL POWER KS PLOT Y3 XLOW XHIGH 9164 9165 The default values for BETA1 and BETA2 are 0.5 and 10. 9166 9167 The probability plot can then be used to estimate the 9168 location and scale (location = PPA0, scale = PPA1). 9169 9170 The 2-parameter exponential power maximum likelihood 9171 estimates can be obtained using the command 9172 9173 EXPONENTIAL POWER MAXIMUM LIKELIHOOD Y 9174 9175 9176 solution of the following simultaneous equations: 9177 9178 (n/beta) + n*LOG(alpha) + SUM[i=1 to n][A(i)] - 9179 SUM[i=1 to n][B(i)*C(i)*EXP(B(i))] + 9180 SUM[i=1 to n][B(i)*C(i)] = 0 9181 9182 (beta*n/alpha) - 9183 (beta/alpha)*SUM[i=1 to n][B(i)*EXP(B(i))] + 9184 SUM[i=1 to n][B(i)] = 0 9185 9186 where 9187 9188 alpha = 1/scale 9189 A(i) = LOG(X(i)) 9190 B(i) = (alpha*X(i))**beta 9191 C(i) = LOG(alpha*X(i)) 9192 9193 Our experience indicates that the maximum likelihood 9194 can fail, particularly when the scale parameter is > 1. 9195 Specifying improved starting values can sometimes help 9196 (for example, use the estimates obtained from the ppcc/ 9197 probability plot method as starting values). These can 9198 be specified with the commands 9199 9200 LET ALPHASV = <value> 9201 LET BETASV = <value> 9202 9203 In this context, ALPHASV is the starting value for the 9204 scale parameter, not the reciprocal of the scale parameter. 9205 9206 The BOOTSTRAP DISTRIBUTION command can be used to find 9207 uncertainty intervals for the ppcc plot and the ks plot 9208 methods. 9209 9210Note: 9211 Library functions are distinguished from let subcommands 9212 in the following ways. 9213 1) Functions enclose the input value in parenthesis. Let 9214 subcommands use spaces. 9215 2) Functions can accept (and return) either parameters 9216 (i.e., single values) or variables (i.e., an array of 9217 values) while let subcommands are specific in which they 9218 accept as input and what they return as output. 9219 3) Functions can accept expressions while let subcommands 9220 do not. For example, the following is legal: 9221 LET Y2 = ABS(Y1-INT(Y1)) 9222 For let subcommands, you typically have to do something 9223 like the following: 9224 LET YTEMP = Y**2 + 8 9225 LET A = SUM YTEMP 9226 9227Default: 9228 None 9229 9230Synonyms: 9231 None 9232 9233Related Commands: 9234 PEXCDF = Compute the exponential power cumulative distribution 9235 function. 9236 PEXPPF = Compute the exponential power percent point function. 9237 PEXHAZ = Compute the exponential power hazard function. 9238 PEXCHAZ = Compute the exponential power cumulative hazard 9239 function. 9240 ALPPDF = Compute the alpha probability density function. 9241 WEIPDF = Compute the Weibull probability density function. 9242 LGNPDF = Compute the log-normal probability density function. 9243 NORCDF = Compute the normal cumulative distribution function. 9244 NORPDF = Compute the normal probability density function. 9245 9246References: 9247 Johnson, Kotz, and Balakrishnan (1994), "Continuous Univariate 9248 Distributions--Volume 2", Second Edition, John Wiley and Sons, 9249 pp. 643-644. 9250 9251 Dhillon (1981), "Life Distributions", IEEE Transactions on 9252 Reliability, Vol. R-30, No. 5, pp. 457-459. 9253 9254Applications: 9255 Reliability, accelerated life testing 9256 9257Implementation Date: 9258 1998/4 9259 2007/11: Corrected the second shape parameter to be the 9260 scale parameter 9261 9262Program 1: 9263 LABEL CASE ASIS 9264 TITLE CASE ASIS 9265 TITLE OFFSET 2 9266 . 9267 MULTIPLOT 2 2 9268 MULTIPLOT CORNER COORDINATES 0 0 100 95 9269 MULTIPLOT SCALE FACTOR 2 9270 . 9271 LET BETA = 0.5 9272 TITLE BETA = ^beta 9273 PLOT PEXPDF(X,BETA) FOR X = 0.01 0.01 2 9274 . 9275 LET BETA = 1 9276 TITLE BETA = ^beta 9277 PLOT PEXPDF(X,BETA) FOR X = 0.01 0.01 2 9278 . 9279 LET BETA = 2 9280 TITLE BETA = ^beta 9281 PLOT PEXPDF(X,BETA) FOR X = 0.01 0.01 2 9282 . 9283 LET BETA = 5 9284 TITLE BETA = ^beta 9285 PLOT PEXPDF(X,BETA) FOR X = 0.01 0.01 2 9286 . 9287 END OF MULTIPLOT 9288 . 9289 JUSTIFICATION CENTER 9290 MOVE 50 97 9291 TEXT Exponential Power Probability Density Functions 9292 9293Program 2: 9294 let beta = 2.4 9295 let y = exponential power random numbers for i = 1 1 200 9296 let y = 0.6*y 9297 let betasav = beta 9298 let amax = maximum y 9299 . 9300 exponential power ppcc plot y 9301 let beta1 = beta - 1 9302 let beta1 = max(beta1,0.1) 9303 let beta2 = beta + 1 9304 y1label Correlation Coefficient 9305 x1label Beta 9306 exponential power ppcc plot y 9307 justification center 9308 move 50 6 9309 let beta = shape 9310 text Betahat = ^beta (True Value: ^betasav) 9311 . 9312 char x 9313 line bl 9314 y1label Data 9315 x1label Theoretical 9316 exponential power prob plot y 9317 move 50 6 9318 text Location = ^ppa0, Scale = ^ppa1 9319 move 50 2 9320 text PPCC = ^ppcc 9321 char bl 9322 line so 9323 label 9324 . 9325 relative histogram y 9326 limits freeze 9327 pre-erase off 9328 plot pexpdf(x,beta,ppa0,ppa1) for x = 0.01 .01 amax 9329 limits 9330 pre-erase on 9331 . 9332 let ksloc = ppa0 9333 let ksscale = ppa1 9334 exponential power kolm smir goodness of fit y 9335 . 9336 exponential power mle y 9337 . 9338 let beta = betaml 9339 let ksloc = ppa0 9340 let ksscale = alphaml 9341 exponential power kolm smir goodness of fit y 9342 9343-----PEXPPF (LET)-------------------------------- 9344 9345PEXPPF 9346 9347Name: 9348 PEXPPF (LET) 9349 9350Type: 9351 Library Function 9352 9353Purpose: 9354 Compute the exponential power percent point function 9355 with shape parameter beta. 9356 9357Description: 9358 The exponential power distribution has the following percent 9359 point function: 9360 9361 G(p;beta) = -{LOG[1 - LOG(1-p)]}**(1/beta) 9362 0 < p < 1; beta > 0 9363 9364 with beta denoting the shape parameter. 9365 9366 This distribution can be generalized with location and 9367 scale parameters using the relation 9368 9369 G(p;beta,loc,scale) = loc + scale*G(p;beta,0,1) 9370 9371 This distribution was proposed by Dhillon as useful 9372 distribution for reliability applications since it can 9373 have increasing, decreasing, or bathtub shaped hazard 9374 functions. 9375 9376Syntax: 9377 LET <y> = PEXPPF(<x>,<beta>,<loc>,<scale>) 9378 <SUBSET/EXCEPT/FOR qualification> 9379 where <x> is a number, parameter, or variable containing positive 9380 values; 9381 <y> is a variable or a parameter (depending on what <x> is) 9382 where the computed exponential power ppf value is 9383 stored; 9384 <beta> is a positive number, parameter, or variable that 9385 specifies the shape parameter; 9386 <loc> is a number, parameter, or variable that specifies 9387 the location parameter; 9388 <scale> is a positive number, parameter, or variable that 9389 specifies the scale parameter; 9390 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 9391 9392 If <loc> and <scale> are omitted, they default to 0 and 1, 9393 respectively. 9394 9395Examples: 9396 LET A = PEXPPF(0.95,2.5) 9397 LET A = PEXPPF(P1,2.5,0,10) 9398 PLOT PEXPPF(P,2.5,0,3) FOR P = 0.01 0.01 0.99 9399 9400Note: 9401 The 11/2007 version changed the syntax for this function 9402 from 9403 9404 LET A = PEXPPF(P,ALPHA,BETA,LOC,SCALE) 9405 9406 to 9407 9408 LET A = PEXPPF(P,BETA,LOC,SCALE) 9409 9410 This was done since ALPHA is in fact a scale parameter 9411 (in the articles listed in the References section, ALPHA 9412 is actually the reciprocal of the scale parameter). 9413 9414Note: 9415 Library functions are distinguished from let subcommands 9416 in the following ways. 9417 1) Functions enclose the input value in parenthesis. Let 9418 subcommands use spaces. 9419 2) Functions can accept (and return) either parameters 9420 (i.e., single values) or variables (i.e., an array of 9421 values) while let subcommands are specific in which they 9422 accept as input and what they return as output. 9423 3) Functions can accept expressions while let subcommands 9424 do not. For example, the following is legal: 9425 LET Y2 = ABS(Y1-INT(Y1)) 9426 For let subcommands, you typically have to do something 9427 like the following: 9428 LET YTEMP = Y**2 + 8 9429 LET A = SUM YTEMP 9430 9431Default: 9432 None 9433 9434Synonyms: 9435 None 9436 9437Related Commands: 9438 PEXCDF = Compute the exponential power cumulative distribution 9439 function. 9440 PEXPDF = Compute the exponential power probability density 9441 function. 9442 PEXHAZ = Compute the exponential power hazard function. 9443 PEXCHAZ = Compute the exponential power cumulative hazard 9444 function. 9445 ALPPDF = Compute the alpha probability density function. 9446 WEIPDF = Compute the Weibull probability density function. 9447 LGNPDF = Compute the log-normal probability density function. 9448 NORCDF = Compute the normal cumulative distribution function. 9449 NORPDF = Compute the normal probability density function. 9450 9451References: 9452 Johnson, Kotz, and Balakrishnan (1994), "Continuous Univariate 9453 Distributions--Volume 2", Second Edition, John Wiley and Sons, 9454 pp. 643-644. 9455 9456 Dhillon (1981), "Life Distributions", IEEE Transactions on 9457 Reliability, Vol. R-30, No. 5, pp. 457-459. 9458 9459Applications: 9460 Reliability, accelerated life testing 9461 9462Implementation Date: 9463 1998/4 9464 2007/11: Corrected the second shape parameter to be the 9465 scale parameter 9466 9467Program: 9468 LABEL CASE ASIS 9469 TITLE CASE ASIS 9470 TITLE OFFSET 2 9471 . 9472 MULTIPLOT 2 2 9473 MULTIPLOT CORNER COORDINATES 0 0 100 95 9474 MULTIPLOT SCALE FACTOR 2 9475 . 9476 LET BETA = 0.5 9477 TITLE BETA = ^beta 9478 PLOT PEXPPF(P,BETA) FOR P = 0.01 0.01 0.99 9479 . 9480 LET BETA = 1 9481 TITLE BETA = ^beta 9482 PLOT PEXPPF(P,BETA) FOR P = 0.01 0.01 0.99 9483 . 9484 LET BETA = 2 9485 TITLE BETA = ^beta 9486 PLOT PEXPPF(P,BETA) FOR P = 0.01 0.01 0.99 9487 . 9488 LET BETA = 5 9489 TITLE BETA = ^beta 9490 PLOT PEXPPF(P,BETA) FOR P = 0.01 0.01 0.99 9491 . 9492 END OF MULTIPLOT 9493 . 9494 JUSTIFICATION CENTER 9495 MOVE 50 97 9496 TEXT Exponential Power Percent Point Functions 9497 9498-----PHASE PLANE DIAGRAM-------------------------------------- 9499 9500PHASE PLANE DIAGRAM 9501 9502Name: 9503 PHASE PLANE DIAGRAM 9504 9505Type: 9506 Graphics Command 9507 9508Purpose: 9509 Generates a phase plane diagram. 9510 9511Description: 9512 A first order differential equation is one of the form: 9513 y'=F(t,y) 9514 where t is an independent variable (often it is time) and y is a 9515 dependent variable. A second order differential equation is one 9516 of the form: 9517 y''=F(t,y,y') 9518 Second (and higher order) differential equations are commonly 9519 reordered as a system of first order differential equations. For 9520 the second order equation, this is done as: 9521 y1=y 9522 y2=y1' = y' 9523 y3=y2' = y'' 9524 and the system of equations is: 9525 y1'=y2 9526 y2'=y3 9527 For example, the differential equation 9528 y''+y'=x**2 + y**2 9529 can be transformed into the two equations 9530 y1'=y2 9531 y2'=x**2+y**2-y2 9532 9533 The phase space is the coordinate system determined by the 9534 dependent variables (y for first order equation, y1 and y2 for the 9535 second order case). For the second order differential equation, 9536 the phase diagram (or phase portrait) plots the points: 9537 (y1(ti),y2(ti)) 9538 where ti is the time at i = 0, 1, 2, ..., n. In the original 9539 equations these points are: 9540 (y(ti),y'(ti)) 9541 This idea extends to higher dimensions as well. 9542 9543 If the functional forms are known, then the RUNGE KUTTA command 9544 can be used to find y and y', and the phase diagram can be plotted 9545 from those variables. 9546 9547 The PHASE PLANE DIAGRAM is used for the case where the functional 9548 form of the differential equation is unknown. It works on a set of 9549 data points (i.e., values for y and optionally for time) to give 9550 a graphical estimate of the phase diagram. It uses the fact that 9551 y'=dy/dx (i.e., the change in y divided by the change in x). The 9552 one variable case (i.e., y only) plots the following: 9553 Vertical axis = Y(i+1) - Y(i); 9554 Horizontal axis = Y(i). 9555 The two variable case plots the following: 9556 Vertical axis = (Y(i+1) - Y(i))/(X(i+1)-X(i)); 9557 Horizontal axis = Y(i). 9558 For the one variable case, the X values are assumed to be equally 9559 spaced and equal to 1 (that is, dx=1) and Y(i+1) - Y(i) is an 9560 estimate of dy. For the two variable case, X(i+1) - X(i) is an 9561 estimate of dx and Y(i+1) - Y(i) is an estimate of dy. In either 9562 case, the vertical axis is an estimate of the derivative of Y. 9563 9564Syntax 1: 9565 PHASE PLANE DIAGRAM <y> <SUBSET/EXCEPT/FOR qualification> 9566 where <y> is a response variable; 9567 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 9568 9569Syntax 2: 9570 PHASE PLANE DIAGRAM <y> <x> <SUBSET/EXCEPT/FOR qualification> 9571 where <y> is a response variable; 9572 <x> is the independent variable (usually time); 9573 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 9574 9575Examples: 9576 PHASE PLANE DIAGRAM Y1 X 9577 PHASE PLANE DIAGRAM Y1 9578 PHASE PLANE DIAGRAM Y1 Y2 SUBSET TAG > 3 9579 9580Note: 9581 A related technique is to plot y(t+1) vs. y(t). This can be done 9582 in DATAPLOT with the LAG PLOT command. 9583 9584Default: 9585 None 9586 9587Synonyms: 9588 None 9589 9590Related Commands: 9591 LINES = Sets type for plot lines. 9592 CHARACTER = Sets type for plot characters. 9593 LAG PLOT = Generates a lag plot. 9594 PLOT = Generates a data/function plot. 9595 MULTIPLOT = Allows multiple plots per page 9596 RUNGE KUTTA = Numerically solve a first or second order 9597 differential equation. 9598 9599Reference: 9600 "Differential Equations, Dynamical Systems, and Linear Algebra", 9601 Hirsch and Smale, Academic Press, 1974 (pp. 2-4). 9602 9603 "Chaos", James Gleick, Penguin Press, 1987 (pp. 264-266). 9604 9605Applications: 9606 Differential Equations 9607 9608Implementation Date: 9609 88/9 9610 9611Program: 9612 . SOURCE--DORN, WILLIAM S. AND MCCRACKEN, DANIEL D., NUMERICAL METHODS 9613 . WITH FORTRAN IV CASE STUDIES, JOHN WILEY AND SONS, INC., 9614 . NEW YORK, 1972, PAGES 391-401. 9615 . TO FIND--DEFLECTION VALUE FOR VARIOUS DISTANCES OUT ONTO THE BEAM 9616 . NOTE--THE ELASTIC DEFLECTION SATISFIES THE DIFFERENTIAL EQUATION-- 9617 . Y'' / (1 + (Y')**2 )**(3/2) = P*(L-X) / (E*I) 9618 . Y'' = P*(L-X) / (E*I) * (1 + (Y')**2 )**(3/2) 9619 . WITH Y(0) = 0 AND Y'(0) = 0 9620 . WHERE 9621 . Y = DEFLECTION FROM HORIZONTAL (IN INCHES) 9622 . X = DISTANCE OUT ONTO BEAM (X = 0, 2, 4, 6, ..., 100 INCHES) 9623 . P = LOAD (IN POUNDS) AT FREE END (HERE = 64) 9624 . L = LENGTH (IN INCHES) OF BEAM (HERE = 100) 9625 . E = YOUNG'S MODULUS (= 6 * 10**6) 9626 . I = MOMENT OF INERTIA OF CROSS SECTION (HERE = 0.128 INCHES**4) 9627 . -----START POINT----------------------------------- 9628 . 9629 . STEP 1--DEFINE THE PHYSICAL PARAMETERS OF THE BEAM 9630 LET P = 64 9631 LET L = 100 9632 LET E = 6*10**6 9633 LET I = 0.128 9634 . STEP 2--DEFINE THE RIGHT-SIDE FUNCTION OF Y''(X) = F 9635 LET FUNCTION F1 = P*(L-X)/(E*I) 9636 LET FUNCTION F2 = (1+YP**2)**(3/2) 9637 LET FUNCTION F = F1*F2 9638 . STEP 3--DEFINE INITIAL CONDITIONS AND DEFINE THE DESIRED SEQUENCE 9639 . OF POINTS AT WHICH TO COMPUTE THE SOLUTION CURVE. 9640 LET Y(1) = 0 9641 LET YP(1) = 0 9642 LET X = SEQUENCE 0 2 100 9643 . STEP 4--SOLVE THE DIFFERENTIAL EQUATION 9644 LET Y YP = RUNGA-KUTTA F X 9645 . 9646 X1LABEL Y 9647 Y1LABEL Y' DERIVED FROM DATA 9648 PHASE PLANE DIAGRAM Y X 9649 9650-----PI------------------------------------------------------- 9651 9652PI 9653 9654Name: 9655 PI 9656 9657Type: 9658 Keyword 9659 9660Purpose: 9661 An internal DATAPLOT parameter which has the value 3.1415926. 9662 9663Description: 9664 This parameter is automatically-provided and can be used like 9665 any other parameter. 9666 9667Syntax: 9668 None 9669 9670Examples: 9671 PLOT SIN(PI*X) FOR X = 0 .1 2 9672 LET Y2 = (1/SQRT(2*PI))*EXP(0.5*X**2) 9673 FIT Y = A+B*SIN(OMEGA*PI*T) 9674 9675Note: 9676 When PI is used in a FIT, as in 9677 FIT Y = A+B*SIN(OMEGA*PI*T) 9678 then DATAPLOT recognizes this parameter as a built-in constant (as 9679 one would hope) and so the FIT code will not attempt to produce 9680 least squares estimates of this parameter as it will for all the 9681 other parameters in the model being fitted. 9682 9683Default: 9684 None 9685 9686Synonyms: 9687 None 9688 9689Related Commands: 9690 INFINITY = Built-in parameter with the value machine infinity. 9691 9692Applications: 9693 XX 9694 9695Implementation Date: 9696 XX 9697 9698Program: 9699 XX 9700 9701-----PICTURE POINTS------------------------------------------------- 9702 9703PICTURE POINTS 9704 9705Name: 9706 PICTURE POINTS 9707 9708Type: 9709 Output Device Command 9710 9711Purpose: 9712 This command specifies the number of pixels (horizontal and 9713 vertical) on a device. 9714 9715Description: 9716 Normally, specifying the device sets this value correctly. 9717 However, this command can sometimes be useful when using a 9718 different model number of a supported device. 9719 9720Syntax 1: 9721 PICTURE POINTS <hor> <vert> 9722 where <hor> is a number or parameter that specifies the number of 9723 horizontal pixels; 9724 and <vert> is a number or parameter that specifies the number of 9725 vertical pixels. 9726 9727 This syntax sets the picture points on device 1 (i.e., the 9728 terminal). 9729 9730Syntax 2: 9731 DEVICE <1/2/3> PICTURE POINTS <hor> <vert> 9732 where 1 specifies device 1, 2 specifies device 2, and 3 specifies 9733 device 3; 9734 <hor> is a number or parameter that specifies the number of 9735 horizontal pixels; 9736 and <vert> is a number or parameter that specifies the number of 9737 vertical pixels. 9738 9739 This syntax sets the picture points on the specified device (1, 2, 9740 or 3). 9741 9742Examples: 9743 PICTURE POINTS 1000 500 9744 DEVICE 2 PICTURE POINTS 1000 500 9745 9746Default: 9747 None 9748 9749Synonyms: 9750 DEVICE PICTURE POINTS 9751 9752Related Commands: 9753 DEVICE = Specify the graphics device. 9754 DEVICE COLOR = Specify if the graphics device is color. 9755 DEVICE POWER = Specify if the device is on or not. 9756 9757Applications: 9758 Graphics Output 9759 9760Implementation Date: 9761 Pre-1987 9762 9763Program: 9764 DEVICE 2 GD JPEG 9765 DEVICE 2 PICTURE POINTS 700 450 9766 SKIP 25 9767 READ ZARR15.DAT Y 9768 4-PLOT Y 9769 9770-----PIE CHART------------------------------------------------------- 9771 9772PIE CHART 9773 9774Name: 9775 PIE CHART 9776 9777Type: 9778 Graphics Command 9779 9780Purpose: 9781 Generates a pie chart. 9782 9783Description: 9784 A pie chart is a graphical data analysis technique for summarizing 9785 the distributional information of a variable. It is a circular 9786 plot consisting of wedges where the size of each wedge is 9787 proportional to the frequency (= number of observations) in that 9788 wedge. The plot is to be read clockwise (where the first wedge is 9789 at "9 o'clock). 9790 9791 If a single variable is specified, Dataplot divides the values 9792 into frequency classes in the same manner as for a histogram. The 9793 histogram and the pie chart have the same information except the 9794 histogram has bars at the data values (where the height of the bar 9795 is proportional to the number of observations in the class), 9796 whereas the pie chart has wedges (where the area of the wedge is 9797 proportional to the number of observations in the class). 9798 9799 If two variables are specified, the first variable contains 9800 pre-computed frequencies and the second variable is a group 9801 identifier. This second form is more commonly used. 9802 9803 As mentioned above, by default raw data is first binned into 9804 frequency data. However, in many if not most cases, the response 9805 variable is intended to be interpreted as a frequency (i.e., the 9806 proportion for Y(i) is Y(i)/SUM[Y(i)]). That is, we have an implicit 9807 group-id variable that is simply 1, 2, ..., N where N is the number 9808 of points in the response variable. 9809 9810 To suppress this binning for the single variable case, enter 9811 9812 SET PIE CHART UNBINNED 9813 9814 To restore the default of binning raw data, enter 9815 9816 SET PIE CHART BINNED 9817 9818 Typically no binning is preferred for small size data sets. Binning 9819 can be helpful for larger data sets in that it reduces the number of 9820 pie wedges that are plotted (in this case, we are really treating a 9821 pie chart as an alternative way to graph a histogram). 9822 9823Syntax 1: 9824 PIE CHART <x> <SUBSET/EXCEPT/FOR qualification> 9825 where <x> is the variable of raw data values; 9826 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 9827 9828 This syntax is used for the case where you have raw data. 9829 9830Syntax 2: 9831 PIE CHART <y> <x> <SUBSET/EXCEPT/FOR qualification> 9832 where <y> is the variable of pre-computed frequencies; 9833 <x> is the variable of group identifiers; 9834 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 9835 9836 This syntax is used for the case where you have pre-computed 9837 frequencies at each data level. This assumes that you have 9838 equal width bins. 9839 9840Syntax 3: 9841 PIE CHART <y> <xlow> <xhigh> <SUBSET/EXCEPT/FOR qualification> 9842 where <y> is the variable of pre-computed frequencies; 9843 <xlow> is the variable containing the lower limits of the bins; 9844 <xhigh> is the variable containing the upper limits of the bins; 9845 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 9846 9847 This syntax is used for the case where you have pre-computed 9848 frequencies at each data level. This syntax is used when you have 9849 unequal width bins. 9850 9851Examples: 9852 PIE CHART X 9853 PIE CHART TEMP SUBSET TEMP > 0 9854 PIE CHART F X SUBSET X > 2 9855 PIE CHART COUNTS STATE 9856 9857Note: 9858 Each wedge is drawn with a common set of attributes. The 9859 attributes of the wedge borders are set with the LINE, LINE COLOR, 9860 and LINE THICKNESS commands (typically they are all set the same). 9861 The attributes of the interior are set with the various REGION 9862 commands. Any labels for the wedges must be set with the LEGEND or 9863 TEXT commands. The CROSS HAIR command can help in positioning 9864 labels. The program example below shows how to set the attributes. 9865 Dataplot does not support features such as 3d pie charts or 9866 exploding slices that are common in many business graphics 9867 programs. 9868 9869Note: 9870 Although pie charts are popular in business graphics, they are 9871 generally a poor graphics technique. See the book listed in the 9872 Reference section below for more information. 9873 9874Note: 9875 For the one variable form of the command, Dataplot uses a class 9876 width of 0.3 X the standard deviation of the variable. Use the 9877 CLASS WIDTH to override this default. Dataplot also tends to 9878 generate a large number of zero frequency classes at the lower and 9879 upper tails. The CLASS LOWER and CLASS UPPER commands can be used 9880 to set lower and upper limits for the classes. 9881 9882Default: 9883 None 9884 9885Synonyms: 9886 None 9887 9888Related Commands: 9889 HISTOGRAM = Generates a histogram. 9890 FREQUENCY PLOT = Generates a frequency plot. 9891 PERCENT POINT PLOT = Generates a percent point plot. 9892 PLOT = Generates a plot (including bar plots). 9893 CLASS LOWER = Sets the lower class minimum for histograms, 9894 frequency plots, and pie charts. 9895 CLASS UPPER = Sets the upper class maximum for histograms, 9896 frequency plots, and pie charts. 9897 CLASS WIDTH = Sets the class width for histogram, frequency 9898 plots, and pie charts. 9899 LINE = Sets the types for plot lines. 9900 LINE COLOR = Sets the colors for plot lines. 9901 LINE THICKNESS = Sets the thicknesses for plot lines. 9902 REGION FILL = Sets on/off switches for region fills. 9903 9904Reference: 9905 William Cleveland (1985), "The Elements of Graphing Data", Wadsworth, 9906 p. 264. 9907 9908Applications: 9909 Business Graphics 9910 9911Implementation Date: 9912 Pre-1987 9913 1993/11: Added the ability to set the attributes of the pie wedges. 9914 9915Program: 9916 LET X = DATA 81 82 83 84 85 9917 LET Y = DATA 2 5 9 15 28 9918 . 9919 TITLE SALES IN MILLIONS OF DOLLARS 9920 LINE THICKNESS .3 ALL 9921 REGION FILL ON ALL 9922 REGION PATTERN COLOR G10 G30 G50 G70 G90 9923 REGION FILL COLOR G10 G30 G50 G70 G90 9924 LET N = SIZE X 9925 LOOP FOR K = 1 1 N 9926 LET A = X(K) 9927 LEGEND ^K 19^A 9928 END OF LOOP 9929 LEGEND 1 COORDINATES 8 58 9930 LEGEND 2 COORDINATES 10 71 9931 LEGEND 3 COORDINATES 28 92 9932 LEGEND 4 COORDINATES 68 77 9933 LEGEND 5 COORDINATES 67 30 9934 PIE CHART Y X 9935 9936-----PIXMAP TITLE-------------------------------------------------- 9937 9938PIXMAP TITLE 9939 9940Name: 9941 PIXMAP TITLE 9942 9943Type: 9944 Support Command 9945 9946Purpose: 9947 Specify a title for a plot saved with the SAVE PLOT command. 9948 This is a temporary title used for identification purposes 9949 only and is not saved with the plot. 9950 9951Description: 9952 The SAVE PLOT and REPEAT PLOT commands allow you to save and 9953 recall graphs. The primary use of this is to compare the current 9954 graph to previously created graphs. 9955 9956 The PIXMAP TITLE command applies to the current plot when 9957 the SAVE PLOT command is entered. The order of the plot 9958 command and PIXMAP TITLE command does not matter. 9959 9960 Dataplot maintains a list of saved graphs for the current 9961 session. The "current list" consists of all plots saved in 9962 the current session and any plots from previous Dataplot 9963 sessions explicitly recalled with the REPEAT PLOT command. 9964 9965 These commands are host dependent. They are currently 9966 supported for the following platforms: 9967 9968 1) Unix platforms via the X11 device driver; 9969 2) Windows 95/98/NT command line version built with the 9970 Microsoft Fortran compiler; 9971 3) Dataplot GUI (both Unix and Windows 95/98/NT). 9972 9973Syntax: 9974 PIXMAP TITLE <string> 9975 where <string> specifies the title for the saved plot. 9976 9977Examples: 9978 HISTOGRAM Y1 9979 PIXMAP TITLE HISTOGRAM: Y1 9980 SAVE PLOT HIST.1 9981 9982Default: 9983 None 9984 9985Synonyms: 9986 None 9987 9988Note: 9989 Be aware that for SAVE PLOT AUTOMATIC, the saving for a given 9990 plot is not executed until the next screen erase (typically the 9991 next plot) is encountered to allow for multi-plotting and the 9992 addition of diagrammatic graphics to a plot. The order of 9993 the commands would typically be something like: 9994 9995 SAVE GRAPH AUTOMATIC 9996 4-PLOT Y 9997 PIXMAP TITLE 4-PLOT 9998 PLOT Y 9999 PIXMAP TITLE PLOT Y 10000 HISTOGRAM Y 10001 PIXMAP TITLE HISTOGRAM 10002 10003 The main point here is that the PIXMAP TITLE comes AFTER the 10004 plot command. 10005 10006Note: 10007 Unlike the regular TITLE command, the PIXMAP TITLE command does 10008 not persist. That is, it applies only to the next saved plot and 10009 then reverts to the default of using the file name. 10010 10011Note: 10012 The REPEAT PLOT command is used to display a plot saved 10013 with SAVE PLOT. The LIST PLOT command lists the currently 10014 saved plots (by sequence number, file name, and title). 10015 The CYCLE PLOT command allows you to cycle through the 10016 pixmaps in the current list by clicking mouse buttons. 10017 The PIXMAP TITLE command allows you to specify the title 10018 for a saved plot. This title is simply for ease of 10019 identification in listing the saved plots and is not 10020 saved as part of the plot. 10021 10022Related Commands: 10023 LIST PLOT = List saved plots. 10024 REPEAT PLOT = Redraw a previously saved plot. 10025 SAVE PLOT = Save a plot. 10026 CYCLE PLOT = Cycle through previously saved graphs using 10027 mouse buttons. 10028 10029Applications: 10030 Interactive Usage 10031 10032Implementation Date: 10033 7/1997 10034 10035Program: 10036 READ BERGER1.DAT Y X 10037 FIT Y X 10038 4-PLOT RES 10039 PIXMAP TITLE RESIDUALS FROM LINEAR FIT 10040 SAVE PLOT RES.1 10041 QUADRATIC FIT Y X 10042 4-PLOT RES 10043 PIXMAP TITLE RESIDUALS FROM QUADRATIC FIT 10044 SAVE PLOT RES.2 10045 LIST PLOT 10046 10047-----PLEM (LET)---------------------------------------------- 10048 10049PLEM 10050 10051Name: 10052 PLEM (LET) 10053 10054Type: 10055 Library Function 10056 10057Purpose: 10058 Compute the real component of the Weierstrass P elliptic function 10059 of a complex number (lemniscatic case with unit period 10060 parallelogram). 10061 10062Description: 10063 The Weierstrass elliptic function is described in detail in the 10064 Handbook of Mathematical Functions (see REFERENCE section below). 10065 10066Syntax: 10067 LET <a> = PLEM(<xr>,<xc>) <SUBSET/EXCEPT/FOR qualification> 10068 where <xr> is a number, parameter, or variable that specifies the 10069 the real component of the input; 10070 <xc> is a number, parameter, or variable that specifies the 10071 the complex component of the input; 10072 <a> is a variable or a parameter (depending on what <xr> and 10073 <xc> are) where the computed values are stored; 10074 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 10075 10076Examples: 10077 LET A = PLEM(2,1) 10078 LET A = PLEM(X,4) 10079 LET X2 = PLEM(1,Y) 10080 10081Note: 10082 The Weierstrass elliptic functions are computed using algorithm 10083 549 from the ACM Transactions on Mathematical Software (see the 10084 REFERENCE section below). 10085 10086Note: 10087 If the input value corresponds to a lattice point, an error 10088 message is printed and the output value is set to the largest 10089 real number on the machine. 10090 10091Note: 10092 Library functions are distinguished from let subcommands 10093 in the following ways. 10094 1) Functions enclose the input value in parenthesis. Let 10095 subcommands use spaces. 10096 2) Functions can accept (and return) either parameters 10097 (i.e., single values) or variables (i.e., an array of 10098 values) while let subcommands are specific in which they 10099 accept as input and what they return as output. 10100 3) Functions can accept expressions while let subcommands 10101 do not. For example, the following is legal: 10102 LET Y2 = ABS(Y1-INT(Y1)) 10103 For let subcommands, you typically have to do something 10104 like the following: 10105 LET YTEMP = Y**2 + 8 10106 LET A = SUM YTEMP 10107 10108Default: 10109 None 10110 10111Synonyms: 10112 None 10113 10114Related Commands: 10115 PEQ = Compute the real component of the Weierstrass elliptic 10116 function (equianharmonic case). 10117 PEQI = Compute the complex component of the Weierstrass elliptic 10118 function (equianharmonic case). 10119 PEQ1 = Compute the real component of the first derivative of 10120 the Weierstrass elliptic function (equianharmonic case). 10121 PEQ1I = Compute the complex component of the first derivative of 10122 the Weierstrass elliptic function (equianharmonic case). 10123 PLEMI = Compute the complex component of the Weierstrass elliptic 10124 function (lemniscatic case). 10125 PLEM1 = Compute the real component of the first derivative of 10126 the Weierstrass elliptic function (lemniscatic case). 10127 PLEM1I = Compute the complex component of the first derivative of 10128 the Weierstrass elliptic function (lemniscatic case). 10129 SN = Compute the Jacobi elliptic function sn. 10130 CN = Compute the Jacobi elliptic function cn. 10131 DN = Compute the Jacobi elliptic function dn. 10132 RF = Compute the Carlson elliptic integral of the first kind. 10133 RD = Compute the Carlson elliptic integral of the second kind. 10134 RJ = Compute the Carlson elliptic integral of the third kind. 10135 ELLIPC1 = Compute the Legendre complete elliptic integral of the 10136 first kind. 10137 ELLIPC2 = Compute the Legendre complete elliptic integral of the 10138 second kind. 10139 ELLIP1 = Compute the Legendre elliptic integral of the first 10140 kind. 10141 ELLIP2 = Compute the Legendre elliptic integral of the second 10142 kind. 10143 ELLIP3 = Compute the Legendre's elliptic integral of the third 10144 kind. 10145 10146Reference: 10147 "Algorithm 549: Weierstrass' Elliptic Functions", Eckhardt, ACM 10148 Transactions on Mathematical Software, vol. 6 (pp. 112-120). 10149 10150 "Handbook of Mathematical Functions, Applied Mathematics Series, 10151 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 10152 1964 (chapter 18). 10153 10154Applications: 10155 Special Functions 10156 10157Implementation Date: 10158 94/11 10159 10160Program: 10161 TITLE WEIERSTRASS ELLIPTIC FUNCTIONS 10162 LINE SOLID DASH 10163 PLOT PLEM(X,0.5) FOR X = 0 0.01 5 AND 10164 PLOT PLEMI(X,0.5) FOR X = 0 0.01 5 10165 10166-----PLEMI (LET)---------------------------------------------- 10167 10168PLEMI 10169 10170Name: 10171 PLEMI (LET) 10172 10173Type: 10174 Library Function 10175 10176Purpose: 10177 Compute the complex component of the Weierstrass P elliptic 10178 function of a complex number (lemniscatic case with unit period 10179 parallelogram). 10180 10181Description: 10182 The Weierstrass elliptic function is described in detail in the 10183 Handbook of Mathematical Functions (see REFERENCE section below). 10184 10185Syntax: 10186 LET <a> = PLEMI(<xr>,<xc>) <SUBSET/EXCEPT/FOR qualification> 10187 where <xr> is a number, parameter, or variable that specifies the 10188 the real component of the input; 10189 <xc> is a number, parameter, or variable that specifies the 10190 the complex component of the input; 10191 <a> is a variable or a parameter (depending on what <xr> and 10192 <xc> are) where the computed values are stored; 10193 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 10194 10195Examples: 10196 LET A = PLEMI(2,1) 10197 LET A = PLEMI(X,4) 10198 LET X2 = PLEMI(1,Y) 10199 10200Note: 10201 The Weierstrass elliptic functions are computed using algorithm 10202 549 from the ACM Transactions on Mathematical Software (see the 10203 REFERENCE section below). 10204 10205Note: 10206 If the input value corresponds to a lattice point, an error 10207 message is printed and the output value is set to the largest 10208 real number on the machine. 10209 10210Note: 10211 Library functions are distinguished from let subcommands 10212 in the following ways. 10213 1) Functions enclose the input value in parenthesis. Let 10214 subcommands use spaces. 10215 2) Functions can accept (and return) either parameters 10216 (i.e., single values) or variables (i.e., an array of 10217 values) while let subcommands are specific in which they 10218 accept as input and what they return as output. 10219 3) Functions can accept expressions while let subcommands 10220 do not. For example, the following is legal: 10221 LET Y2 = ABS(Y1-INT(Y1)) 10222 For let subcommands, you typically have to do something 10223 like the following: 10224 LET YTEMP = Y**2 + 8 10225 LET A = SUM YTEMP 10226 10227Default: 10228 None 10229 10230Synonyms: 10231 None 10232 10233Related Commands: 10234 PEQ = Compute the real component of the Weierstrass elliptic 10235 function (equianharmonic case). 10236 PEQI = Compute the complex component of the Weierstrass elliptic 10237 function (equianharmonic case). 10238 PEQ1 = Compute the real component of the first derivative of 10239 the Weierstrass elliptic function (equianharmonic case). 10240 PEQ1I = Compute the complex component of the first derivative of 10241 the Weierstrass elliptic function (equianharmonic case). 10242 PLEM = Compute the real component of the Weierstrass elliptic 10243 function (lemniscatic case). 10244 PLEM1 = Compute the real component of the first derivative of 10245 the Weierstrass elliptic function (lemniscatic case). 10246 PLEM1I = Compute the complex component of the first derivative of 10247 the Weierstrass elliptic function (lemniscatic case). 10248 SN = Compute the Jacobi elliptic function sn. 10249 CN = Compute the Jacobi elliptic function cn. 10250 DN = Compute the Jacobi elliptic function dn. 10251 RF = Compute the Carlson elliptic integral of the first kind. 10252 RD = Compute the Carlson elliptic integral of the second kind. 10253 RJ = Compute the Carlson elliptic integral of the third kind. 10254 ELLIPC1 = Compute the Legendre complete elliptic integral of the 10255 first kind. 10256 ELLIPC2 = Compute the Legendre complete elliptic integral of the 10257 second kind. 10258 ELLIP1 = Compute the Legendre elliptic integral of the first 10259 kind. 10260 ELLIP2 = Compute the Legendre elliptic integral of the second 10261 kind. 10262 ELLIP3 = Compute the Legendre's elliptic integral of the third 10263 kind. 10264 10265Reference: 10266 "Algorithm 549: Weierstrass' Elliptic Functions", Eckhardt, ACM 10267 Transactions on Mathematical Software, vol. 6 (pp. 112-120). 10268 10269 "Handbook of Mathematical Functions, Applied Mathematics Series, 10270 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 10271 1964 (chapter 18). 10272 10273Applications: 10274 Special Functions 10275 10276Implementation Date: 10277 94/11 10278 10279Program: 10280 TITLE WEIERSTRASS ELLIPTIC FUNCTIONS 10281 LINE SOLID DASH 10282 PLOT PLEMI(X,0.5) FOR X = 0 0.01 5 AND 10283 PLOT PLEM(X,0.5) FOR X = 0 0.01 5 10284 10285-----PLEM1 (LET)---------------------------------------------- 10286 10287PLEM1 10288 10289Name: 10290 PLEM1 (LET) 10291 10292Type: 10293 Library Function 10294 10295Purpose: 10296 Compute the real component of the first derivative of the 10297 Weierstrass P elliptic function of a complex number (lemniscatic 10298 case with unit period parallelogram). 10299 10300Description: 10301 The Weierstrass elliptic function is described in detail in the 10302 Handbook of Mathematical Functions (see REFERENCE section below). 10303 10304Syntax: 10305 LET <a> = PLEM1(<xr>,<xc>) <SUBSET/EXCEPT/FOR qualification> 10306 where <xr> is a number, parameter, or variable that specifies the 10307 the real component of the input; 10308 <xc> is a number, parameter, or variable that specifies the 10309 the complex component of the input; 10310 <a> is a variable or a parameter (depending on what <xr> and 10311 <xc> are) where the computed values are stored; 10312 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 10313 10314Examples: 10315 LET A = PLEM1(2,1) 10316 LET A = PLEM1(X,4) 10317 LET X2 = PLEM1(1,Y) 10318 10319Note: 10320 The Weierstrass elliptic functions are computed using algorithm 10321 549 from the ACM Transactions on Mathematical Software (see the 10322 REFERENCE section below). 10323 10324Note: 10325 If the input value corresponds to a lattice point, an error 10326 message is printed and the output value is set to the largest 10327 real number on the machine. 10328 10329Note: 10330 Library functions are distinguished from let subcommands 10331 in the following ways. 10332 1) Functions enclose the input value in parenthesis. Let 10333 subcommands use spaces. 10334 2) Functions can accept (and return) either parameters 10335 (i.e., single values) or variables (i.e., an array of 10336 values) while let subcommands are specific in which they 10337 accept as input and what they return as output. 10338 3) Functions can accept expressions while let subcommands 10339 do not. For example, the following is legal: 10340 LET Y2 = ABS(Y1-INT(Y1)) 10341 For let subcommands, you typically have to do something 10342 like the following: 10343 LET YTEMP = Y**2 + 8 10344 LET A = SUM YTEMP 10345 10346Default: 10347 None 10348 10349Synonyms: 10350 None 10351 10352Related Commands: 10353 PEQ = Compute the real component of the Weierstrass elliptic 10354 function (equianharmonic case). 10355 PEQI = Compute the complex component of the Weierstrass elliptic 10356 function (equianharmonic case). 10357 PEQ1 = Compute the real component of the first derivative of 10358 the Weierstrass elliptic function (equianharmonic case). 10359 PEQ1I = Compute the complex component of the first derivative of 10360 the Weierstrass elliptic function (equianharmonic case). 10361 PLEM = Compute the real component of the Weierstrass elliptic 10362 function (lemniscatic case). 10363 PLEMI = Compute the complex component of the Weierstrass elliptic 10364 function (lemniscatic case). 10365 PLEM1I = Compute the complex component of the first derivative of 10366 the Weierstrass elliptic function (lemniscatic case). 10367 SN = Compute the Jacobi elliptic function sn. 10368 CN = Compute the Jacobi elliptic function cn. 10369 DN = Compute the Jacobi elliptic function dn. 10370 RF = Compute the Carlson elliptic integral of the first kind. 10371 RD = Compute the Carlson elliptic integral of the second kind. 10372 RJ = Compute the Carlson elliptic integral of the third kind. 10373 ELLIPC1 = Compute the Legendre complete elliptic integral of the 10374 first kind. 10375 ELLIPC2 = Compute the Legendre complete elliptic integral of the 10376 second kind. 10377 ELLIP1 = Compute the Legendre elliptic integral of the first 10378 kind. 10379 ELLIP2 = Compute the Legendre elliptic integral of the second 10380 kind. 10381 ELLIP3 = Compute the Legendre's elliptic integral of the third 10382 kind. 10383 10384Reference: 10385 "Algorithm 549: Weierstrass' Elliptic Functions", Eckhardt, ACM 10386 Transactions on Mathematical Software, vol. 6 (pp. 112-120). 10387 10388 "Handbook of Mathematical Functions, Applied Mathematics Series, 10389 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 10390 1964 (chapter 18). 10391 10392Applications: 10393 Special Functions 10394 10395Implementation Date: 10396 94/11 10397 10398Program: 10399 TITLE WEIERSTRASS ELLIPTIC FUNCTIONS 10400 LINE SOLID DASH 10401 PLOT PLEM1(X,0.5) FOR X = 0 0.01 5 AND 10402 PLOT PLEM1I(X,0.5) FOR X = 0 0.01 5 10403 10404-----PLEM1I (LET)---------------------------------------------- 10405 10406PLEM1I 10407 10408Name: 10409 PLEM1I (LET) 10410 10411Type: 10412 Library Function 10413 10414Purpose: 10415 Compute the complex component of the first derivative of the 10416 Weierstrass P elliptic function of a complex number (lemniscatic 10417 case with unit period parallelogram). 10418 10419Description: 10420 The Weierstrass elliptic function is described in detail in the 10421 Handbook of Mathematical Functions (see REFERENCE section below). 10422 10423Syntax: 10424 LET <a> = PLEM1I(<xr>,<xc>) <SUBSET/EXCEPT/FOR qualification> 10425 where <xr> is a number, parameter, or variable that specifies the 10426 the real component of the input; 10427 <xc> is a number, parameter, or variable that specifies the 10428 the complex component of the input; 10429 <a> is a variable or a parameter (depending on what <xr> and 10430 <xc> are) where the computed values are stored; 10431 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 10432 10433Examples: 10434 LET A = PLEM1I(2,1) 10435 LET A = PLEM1I(X,4) 10436 LET X2 = PLEM1I(1,Y) 10437 10438Note: 10439 The Weierstrass elliptic functions are computed using algorithm 10440 549 from the ACM Transactions on Mathematical Software (see the 10441 REFERENCE section below). 10442 10443Note: 10444 If the input value corresponds to a lattice point, an error 10445 message is printed and the output value is set to the largest 10446 real number on the machine. 10447 10448Note: 10449 Library functions are distinguished from let subcommands 10450 in the following ways. 10451 1) Functions enclose the input value in parenthesis. Let 10452 subcommands use spaces. 10453 2) Functions can accept (and return) either parameters 10454 (i.e., single values) or variables (i.e., an array of 10455 values) while let subcommands are specific in which they 10456 accept as input and what they return as output. 10457 3) Functions can accept expressions while let subcommands 10458 do not. For example, the following is legal: 10459 LET Y2 = ABS(Y1-INT(Y1)) 10460 For let subcommands, you typically have to do something 10461 like the following: 10462 LET YTEMP = Y**2 + 8 10463 LET A = SUM YTEMP 10464 10465Default: 10466 None 10467 10468Synonyms: 10469 None 10470 10471Related Commands: 10472 PEQ = Compute the real component of the Weierstrass elliptic 10473 function (equianharmonic case). 10474 PEQI = Compute the complex component of the Weierstrass elliptic 10475 function (equianharmonic case). 10476 PEQ1 = Compute the real component of the first derivative of 10477 the Weierstrass elliptic function (equianharmonic case). 10478 PEQ1I = Compute the complex component of the first derivative of 10479 the Weierstrass elliptic function (equianharmonic case). 10480 PLEM = Compute the real component of the Weierstrass elliptic 10481 function (lemniscatic case). 10482 PLEMI = Compute the complex component of the Weierstrass elliptic 10483 function (lemniscatic case). 10484 PLEM1 = Compute the real component of the first derivative of 10485 the Weierstrass elliptic function (lemniscatic case). 10486 SN = Compute the Jacobi elliptic function sn. 10487 CN = Compute the Jacobi elliptic function cn. 10488 DN = Compute the Jacobi elliptic function dn. 10489 RF = Compute the Carlson elliptic integral of the first kind. 10490 RD = Compute the Carlson elliptic integral of the second kind. 10491 RJ = Compute the Carlson elliptic integral of the third kind. 10492 ELLIPC1 = Compute the Legendre complete elliptic integral of the 10493 first kind. 10494 ELLIPC2 = Compute the Legendre complete elliptic integral of the 10495 second kind. 10496 ELLIP1 = Compute the Legendre elliptic integral of the first 10497 kind. 10498 ELLIP2 = Compute the Legendre elliptic integral of the second 10499 kind. 10500 ELLIP3 = Compute the Legendre's elliptic integral of the third 10501 kind. 10502 10503Reference: 10504 "Algorithm 549: Weierstrass' Elliptic Functions", Eckhardt, ACM 10505 Transactions on Mathematical Software, vol. 6 (pp. 112-120). 10506 10507 "Handbook of Mathematical Functions, Applied Mathematics Series, 10508 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 10509 1964 (chapter 18). 10510 10511Applications: 10512 Special Functions 10513 10514Implementation Date: 10515 94/11 10516 10517Program: 10518 TITLE WEIERSTRASS ELLIPTIC FUNCTIONS 10519 LINE SOLID DASH 10520 PLOT PLEM1I(X,0.5) FOR X = 0 0.01 5 AND 10521 PLOT PLEM1(X,0.5) FOR X = 0 0.01 5 10522 10523-----PLNCDF (LET)-------------------------------- 10524 10525PLNCDF 10526 10527Name: 10528 PLNCDF (LET) 10529 10530Type: 10531 Library Function 10532 10533Purpose: 10534 Compute the standard power-lognormal cumulative distribution 10535 function. 10536 10537Description: 10538 The standard power-lognormal distribution has the following 10539 cumulative distribution function: 10540 F(x,sigma,p) = 1 - {NORCDF(-ln(x)/sigma)}**p 10541 for x, sigma, p > 0 10542 where sigma is a shape parameter, p is a shape (power) parameter, 10543 and NORCDF and NORPDF are the cumulative distribution function 10544 and the probability density function for the standard normal 10545 distribution, respectively. 10546 10547 If p is 1, this distribution reduces to the lognormal 10548 distribution. 10549 10550Syntax: 10551 LET <y> = PLNCDF(<x>,<p>,<s>) <SUBSET/EXCEPT/FOR qualification> 10552 where <x> is a non-negative number, parameter, or variable; 10553 <p> is a positive number, parameter, or variable 10554 that specifies the power parameter; 10555 <s> is an optional positive number, parameter, or variable 10556 that specifies the shape parameter; 10557 <y> is a variable or a parameter (depending on what <x> is) 10558 where the computed power-lognormal cdf value is stored; 10559 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 10560 10561 If the <s> parameter is omitted, it defaults to 1. 10562 10563Examples: 10564 LET A = PLNCDF(3,2,1) 10565 LET X2 = PLNCDF(X1,POW,SD) 10566 LET X2 = PLNCDF(X1,1,0.5) 10567 10568Note: 10569 The general power-lognormal cumulative distribution function 10570 can be expressed in terms of the standard power-lognormal 10571 cumulative distribution function as follows: 10572 F(x,sigma,p,loc,scale)=F((x-loc)/scale,sigma,p) 10573 for x > loc, sigma, p, scale > 0 10574 where loc and scale are the location and scales parameters, 10575 respectively. 10576 10577Note: 10578 Library functions are distinguished from let subcommands 10579 in the following ways. 10580 1) Functions enclose the input value in parenthesis. Let 10581 subcommands use spaces. 10582 2) Functions can accept (and return) either parameters 10583 (i.e., single values) or variables (i.e., an array of 10584 values) while let subcommands are specific in which they 10585 accept as input and what they return as output. 10586 3) Functions can accept expressions while let subcommands 10587 do not. For example, the following is legal: 10588 LET Y2 = ABS(Y1-INT(Y1)) 10589 For let subcommands, you typically have to do something 10590 like the following: 10591 LET YTEMP = Y**2 + 8 10592 LET A = SUM YTEMP 10593 10594Default: 10595 None 10596 10597Synonyms: 10598 None 10599 10600Related Commands: 10601 PLNPDF = Compute the power-lognormal probability density 10602 function. 10603 PLNPPF = Compute the power-lognormal percent point function. 10604 PLNHAZ = Compute the power-lognormal hazard function. 10605 PLNCHAZ = Compute the power-lognormal cumulative hazard function. 10606 PNRPDF = Compute the power-normal probability density function. 10607 LGNPDF = Compute the lognormal probability density function. 10608 HFNPDF = Compute the half-normal probability density function. 10609 NORPDF = Compute the normal probability density function. 10610 10611Reference: 10612 "A Computer Program POWNOR for Fitting the Power-Normal and 10613 -Lognormal Models to Life or Strength Data from Specimens of 10614 Various Sizes", Nelson and Doganaksoy, NIST-IR 4760, March 1992. 10615 10616Applications: 10617 Reliability 10618 10619Implementation Date: 10620 1995/5 10621 10622Program: 10623 LABEL CASE ASIS 10624 X1LABEL X 10625 Y1LABEL Probability 10626 Y1LABEL DISPLACEMENT 12 10627 TITLE CASE ASIS 10628 . 10629 MULTIPLOT 2 2 10630 MULTIPLOT CORNER COORDINATES 0 0 100 95 10631 . 10632 TITLE P = 0.5, SIGMA = 0.2, 0.4, 0.7, 1.0 10633 PLOT PLNCDF(X,0.5,0.2) FOR X = 0.01 .01 3 AND 10634 PLOT PLNCDF(X,0.5,0.4) FOR X = 0.01 .01 3 AND 10635 PLOT PLNCDF(X,0.5,0.7) FOR X = 0.01 .01 3 AND 10636 PLOT PLNCDF(X,0.5,1.0) FOR X = 0.01 .01 3 10637 TITLE P = 1.0, SIGMA = 0.2, 0.4, 0.7, 1.0 10638 PLOT PLNCDF(X,1.0,0.2) FOR X = 0.01 .01 3 AND 10639 PLOT PLNCDF(X,1.0,0.4) FOR X = 0.01 .01 3 AND 10640 PLOT PLNCDF(X,1.0,0.7) FOR X = 0.01 .01 3 AND 10641 PLOT PLNCDF(X,1.0,1.0) FOR X = 0.01 .01 3 10642 TITLE P = 5.0, SIGMA = 0.2, 0.4, 0.7, 1.0 10643 PLOT PLNCDF(X,5.0,0.2) FOR X = 0.01 .01 2 AND 10644 PLOT PLNCDF(X,5.0,0.4) FOR X = 0.01 .01 2 AND 10645 PLOT PLNCDF(X,5.0,0.7) FOR X = 0.01 .01 2 AND 10646 PLOT PLNCDF(X,5.0,1.0) FOR X = 0.01 .01 2 10647 TITLE P = 20, SIGMA = 0.2, 0.4, 0.7, 1.0 10648 PLOT PLNCDF(X,20,0.2) FOR X = 0.01 .01 1 AND 10649 PLOT PLNCDF(X,20,0.4) FOR X = 0.01 .01 1 AND 10650 PLOT PLNCDF(X,20,0.7) FOR X = 0.01 .01 1 AND 10651 PLOT PLNCDF(X,20,1.0) FOR X = 0.01 .01 1 10652 . 10653 END OF MULTIPLOT 10654 MOVE 50 97 10655 JUSTIFICATION CENTER 10656 TEXT Power Lognormal CDF's 10657 10658-----PLNCHAZ (LET)-------------------------------- 10659 10660PLNCHAZ 10661 10662Name: 10663 PLNCHAZ (LET) 10664 10665Type: 10666 Library Function 10667 10668Purpose: 10669 Compute the standard power-lognormal hazard function. 10670 10671Description: 10672 The standard power-lognormal distribution has the following 10673 cumulative hazard function: 10674 H(x,sigma,p)=-LOG[(NORCDF(-LOG(x)/sigma))**p) 10675 for x, p, sigma > 0 10676 where sigma is a shape parameter, p is a shape (power) parameter, 10677 and NORCDF is the cumulative distribution function for the 10678 standard normal distribution. 10679 10680 If p is 1, this distribution reduces to the lognormal 10681 distribution. 10682 10683Syntax: 10684 LET <y> = PLNCHAZ(<x>,<p>,<s>) <SUBSET/EXCEPT/FOR qualification> 10685 where <x> is a non-negative number, parameter, or variable; 10686 <p> is a positive number, parameter, or variable 10687 that specifies the power parameter; 10688 <s> is an optional positive number, parameter, or variable 10689 that specifies the shape parameter; 10690 <y> is a variable or a parameter (depending on what <y1> 10691 is) where the computed power-lognormal cumulative 10692 hazard value is stored; 10693 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 10694 10695 If the <s> parameter is omitted, it defaults to 1. 10696 10697Examples: 10698 LET A = PLNCHAZ(3,2,1) 10699 LET X2 = PLNCHAZ(X1,POW,SD) 10700 LET X2 = PLNCHAZ(X1,0.5,0.5) 10701 10702Note: 10703 The general power-lognormal cumulative hazard function can be 10704 expressed in terms of the standard power-lognormal cumulative 10705 hazard function as follows: 10706 H(x,sigma,p,loc,scale)=H((x-loc)/scale,sigma,p) 10707 for x > loc, sigma, p,scale > 0 10708 where loc and scale are the location and scales parameters, 10709 respectively. 10710 10711Note: 10712 Library functions are distinguished from let subcommands 10713 in the following ways. 10714 1) Functions enclose the input value in parenthesis. Let 10715 subcommands use spaces. 10716 2) Functions can accept (and return) either parameters 10717 (i.e., single values) or variables (i.e., an array of 10718 values) while let subcommands are specific in which they 10719 accept as input and what they return as output. 10720 3) Functions can accept expressions while let subcommands 10721 do not. For example, the following is legal: 10722 LET Y2 = ABS(Y1-INT(Y1)) 10723 For let subcommands, you typically have to do something 10724 like the following: 10725 LET YTEMP = Y**2 + 8 10726 LET A = SUM YTEMP 10727 10728Default: 10729 None 10730 10731Synonyms: 10732 None 10733 10734Related Commands: 10735 PLNCDF = Compute the power-lognormal cumulative distribution 10736 function. 10737 PLNPDF = Compute the power-lognormal probability density 10738 function. 10739 PLNPPF = Compute the power-lognormal percent point function. 10740 PLNHAZ = Compute the power-lognormal hazard function. 10741 PNRPDF = Compute the power-normal probability density function. 10742 LGNPDF = Compute the lognormal probability density function. 10743 HFNPDF = Compute the half-normal probability density function. 10744 NORPDF = Compute the normal probability density function. 10745 10746Reference: 10747 "A Computer Program POWNOR for Fitting the Power-Normal and 10748 -Lognormal Models to Life or Strength Data from Specimens of 10749 Various Sizes", Nelson and Doganaksoy, NIST-IR 4760, March 1992. 10750 10751Applications: 10752 Reliability 10753 10754Implementation Date: 10755 1998/4 10756 10757Program: 10758 LABEL CASE ASIS 10759 X1LABEL X 10760 Y1LABEL Cumulative Hazard 10761 TITLE CASE ASIS 10762 . 10763 MULTIPLOT 2 2 10764 MULTIPLOT CORNER COORDINATES 0 0 100 95 10765 . 10766 TITLE P = 0.5, SIGMA = 0.2, 0.4, 0.7, 1.0 10767 PLOT PLNCHAZ(X,0.5,0.2) FOR X = 0.01 .01 3 AND 10768 PLOT PLNCHAZ(X,0.5,0.4) FOR X = 0.01 .01 3 AND 10769 PLOT PLNCHAZ(X,0.5,0.7) FOR X = 0.01 .01 3 AND 10770 PLOT PLNCHAZ(X,0.5,1.0) FOR X = 0.01 .01 3 10771 TITLE P = 1.0, SIGMA = 0.2, 0.4, 0.7, 1.0 10772 PLOT PLNCHAZ(X,1.0,0.2) FOR X = 0.01 .01 3 AND 10773 PLOT PLNCHAZ(X,1.0,0.4) FOR X = 0.01 .01 3 AND 10774 PLOT PLNCHAZ(X,1.0,0.7) FOR X = 0.01 .01 3 AND 10775 PLOT PLNCHAZ(X,1.0,1.0) FOR X = 0.01 .01 3 10776 TITLE P = 5.0, SIGMA = 0.2, 0.4, 0.7, 1.0 10777 PLOT PLNCHAZ(X,5.0,0.2) FOR X = 0.01 .01 2 AND 10778 PLOT PLNCHAZ(X,5.0,0.4) FOR X = 0.01 .01 2 AND 10779 PLOT PLNCHAZ(X,5.0,0.7) FOR X = 0.01 .01 2 AND 10780 PLOT PLNCHAZ(X,5.0,1.0) FOR X = 0.01 .01 2 10781 TITLE P = 20, SIGMA = 0.2, 0.4, 0.7, 1.0 10782 PLOT PLNCHAZ(X,20,0.2) FOR X = 0.01 .01 1 AND 10783 PLOT PLNCHAZ(X,20,0.4) FOR X = 0.01 .01 1 AND 10784 PLOT PLNCHAZ(X,20,0.7) FOR X = 0.01 .01 1 AND 10785 PLOT PLNCHAZ(X,20,1.0) FOR X = 0.01 .01 1 10786 . 10787 END OF MULTIPLOT 10788 MOVE 50 97 10789 JUSTIFICATION CENTER 10790 TEXT Power Lognormal Cumulative Hazard Functions 10791 10792-----PLNHAZ (LET)-------------------------------- 10793 10794PLNHAZ 10795 10796Name: 10797 PLNHAZ (LET) 10798 10799Type: 10800 Library Function 10801 10802Purpose: 10803 Compute the standard power-lognormal hazard function. 10804 10805Description: 10806 The standard power-lognormal distribution has the following 10807 hazard function: 10808 h(x,sigma,p)=p*(1/(x*sigma))*NORPDF(ln(x)/sigma)/ 10809 NORCDF(-ln(x)/sigma) for x, p, sigma > 0 10810 where sigma is a shape parameter, p is a shape (power) parameter, 10811 and NORCDF and NORPDF are the cumulative distribution function 10812 and the probability density function for the standard normal 10813 distribution respectively. 10814 10815 The hazard function for the power-lognormal distribution is 10816 a multiple (p) of the hazard function of the lognormal 10817 distribution. 10818 10819 If p is 1, this distribution reduces to the lognormal 10820 distribution. 10821 10822Syntax: 10823 LET <y> = PLNHAZ(<x>,<p>,<s>) <SUBSET/EXCEPT/FOR qualification> 10824 where <x> is a non-negative number, parameter, or variable; 10825 <p> is a positive number, parameter, or variable 10826 that specifies the power parameter; 10827 <s> is an optional positive number, parameter, or variable 10828 that specifies the shape parameter; 10829 <y> is a variable or a parameter (depending on what <y1> 10830 is) where the computed power-lognormal hazard value is 10831 stored; 10832 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 10833 10834 If the <s> parameter is omitted, it defaults to 1. 10835 10836Examples: 10837 LET A = PLNHAZ(3,2,1) 10838 LET X2 = PLNHAZ(X1,POW,SD) 10839 LET X2 = PLNHAZ(X1,0.5,0.5) 10840 10841Note: 10842 The general power-lognormal hazard function can be expressed 10843 in terms of the standard power-lognormal hazard function as 10844 follows: 10845 h(x,sigma,p,loc,scale)=h((x-loc)/scale,sigma,p)/scale 10846 for x > loc, sigma, p, scale > 0 10847 where loc and scale are the location and scales parameters, 10848 respectively. 10849 10850Note: 10851 Library functions are distinguished from let subcommands 10852 in the following ways. 10853 1) Functions enclose the input value in parenthesis. Let 10854 subcommands use spaces. 10855 2) Functions can accept (and return) either parameters 10856 (i.e., single values) or variables (i.e., an array of 10857 values) while let subcommands are specific in which they 10858 accept as input and what they return as output. 10859 3) Functions can accept expressions while let subcommands 10860 do not. For example, the following is legal: 10861 LET Y2 = ABS(Y1-INT(Y1)) 10862 For let subcommands, you typically have to do something 10863 like the following: 10864 LET YTEMP = Y**2 + 8 10865 LET A = SUM YTEMP 10866 10867Default: 10868 None 10869 10870Synonyms: 10871 None 10872 10873Related Commands: 10874 PLNCDF = Compute the power-lognormal cumulative distribution 10875 function. 10876 PLNPDF = Compute the power-lognormal probability density 10877 function. 10878 PLNPPF = Compute the power-lognormal percent point function. 10879 PLNCHAZ = Compute the power-lognormal cumulative hazard function. 10880 PNRPDF = Compute the power-normal probability density function. 10881 LGNPDF = Compute the lognormal probability density function. 10882 HFNPDF = Compute the half-normal probability density function. 10883 NORPDF = Compute the normal probability density function. 10884 10885Reference: 10886 "A Computer Program POWNOR for Fitting the Power-Normal and 10887 -Lognormal Models to Life or Strength Data from Specimens of 10888 Various Sizes", Nelson and Doganaksoy, NIST-IR 4760, March 1992. 10889 10890Applications: 10891 Reliability 10892 10893Implementation Date: 10894 1998/4 10895 10896Program: 10897 LABEL CASE ASIS 10898 X1LABEL X 10899 Y1LABEL Hazard 10900 TITLE CASE ASIS 10901 . 10902 MULTIPLOT 2 2 10903 MULTIPLOT CORNER COORDINATES 0 0 100 95 10904 . 10905 TITLE P = 0.5, SIGMA = 0.2, 0.4, 0.7, 1.0 10906 PLOT PLNHAZ(X,0.5,0.2) FOR X = 0.01 .01 3 AND 10907 PLOT PLNHAZ(X,0.5,0.4) FOR X = 0.01 .01 3 AND 10908 PLOT PLNHAZ(X,0.5,0.7) FOR X = 0.01 .01 3 AND 10909 PLOT PLNHAZ(X,0.5,1.0) FOR X = 0.01 .01 3 10910 TITLE P = 1.0, SIGMA = 0.2, 0.4, 0.7, 1.0 10911 PLOT PLNHAZ(X,1.0,0.2) FOR X = 0.01 .01 3 AND 10912 PLOT PLNHAZ(X,1.0,0.4) FOR X = 0.01 .01 3 AND 10913 PLOT PLNHAZ(X,1.0,0.7) FOR X = 0.01 .01 3 AND 10914 PLOT PLNHAZ(X,1.0,1.0) FOR X = 0.01 .01 3 10915 TITLE P = 5.0, SIGMA = 0.2, 0.4, 0.7, 1.0 10916 PLOT PLNHAZ(X,5.0,0.2) FOR X = 0.01 .01 2 AND 10917 PLOT PLNHAZ(X,5.0,0.4) FOR X = 0.01 .01 2 AND 10918 PLOT PLNHAZ(X,5.0,0.7) FOR X = 0.01 .01 2 AND 10919 PLOT PLNHAZ(X,5.0,1.0) FOR X = 0.01 .01 2 10920 TITLE P = 20, SIGMA = 0.2, 0.4, 0.7, 1.0 10921 PLOT PLNHAZ(X,20,0.2) FOR X = 0.01 .01 1 AND 10922 PLOT PLNHAZ(X,20,0.4) FOR X = 0.01 .01 1 AND 10923 PLOT PLNHAZ(X,20,0.7) FOR X = 0.01 .01 1 AND 10924 PLOT PLNHAZ(X,20,1.0) FOR X = 0.01 .01 1 10925 . 10926 END OF MULTIPLOT 10927 MOVE 50 97 10928 JUSTIFICATION CENTER 10929 TEXT Power Lognormal Hazard Functions 10930 10931-----PLNPDF (LET)-------------------------------- 10932 10933PLNPDF 10934 10935Name: 10936 PLNPDF (LET) 10937 10938Type: 10939 Library Function 10940 10941Purpose: 10942 Compute the standard power-lognormal probability density 10943 function. 10944 10945Description: 10946 The standard power-lognormal distribution has the following 10947 probability density function: 10948 f(x,sigma,p)=(p/(x*sigma))*NORPDF(ln(x)/sigma)* 10949 NORCDF(-ln(x)/sigma)**(p-1) 10950 for x, p, sigma > 0 10951 where sigma is a shape parameter, p is a shape (power) parameter, 10952 and NORCDF and NORPDF are the cumulative distribution function 10953 and the probability density function for the standard normal 10954 distribution respectively. 10955 10956 If p is 1, this distribution reduces to the lognormal 10957 distribution. 10958 10959Syntax: 10960 LET <y> = PLNPDF(<x>,<p>,<s>) <SUBSET/EXCEPT/FOR qualification> 10961 where <x> is a non-negative number, parameter, or variable; 10962 <p> is a positive number, parameter, or variable 10963 that specifies the power parameter; 10964 <s> is an optional positive number, parameter, or variable 10965 that specifies the shape parameter; 10966 <y> is a variable or a parameter (depending on what <y1> 10967 is) where the computed power-lognormal pdf value is 10968 stored; 10969 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 10970 10971 If the <s> parameter is omitted, it defaults to 1. 10972 10973Examples: 10974 LET A = PLNPDF(3,2,1) 10975 LET X2 = PLNPDF(X1,POW,SD) 10976 LET X2 = PLNPDF(X1,0.5,0.5) 10977 10978Note: 10979 The general power-lognormal probability density function can 10980 be expressed in terms of the standard power-lognormal 10981 probability density function as follows: 10982 f(x,sigma,p,loc,scale)=f((x-loc)/scale,sigma,p)/scale 10983 for x > loc, sigma, p, scale > 0 10984 where loc and scale are the location and scales parameters, 10985 respectively. 10986 10987Note: 10988 Library functions are distinguished from let subcommands 10989 in the following ways. 10990 1) Functions enclose the input value in parenthesis. Let 10991 subcommands use spaces. 10992 2) Functions can accept (and return) either parameters 10993 (i.e., single values) or variables (i.e., an array of 10994 values) while let subcommands are specific in which they 10995 accept as input and what they return as output. 10996 3) Functions can accept expressions while let subcommands 10997 do not. For example, the following is legal: 10998 LET Y2 = ABS(Y1-INT(Y1)) 10999 For let subcommands, you typically have to do something 11000 like the following: 11001 LET YTEMP = Y**2 + 8 11002 LET A = SUM YTEMP 11003 11004Default: 11005 None 11006 11007Synonyms: 11008 None 11009 11010Related Commands: 11011 PLNCDF = Compute the power-lognormal cumulative distribution 11012 function. 11013 PLNPPF = Compute the power-lognormal percent point function. 11014 PLNHAZ = Compute the power-lognormal hazard function. 11015 PLNCHAZ = Compute the power-lognormal cumulative hazard function. 11016 PNRPDF = Compute the power-normal probability density function. 11017 LGNPDF = Compute the lognormal probability density function. 11018 HFNPDF = Compute the half-normal probability density function. 11019 NORPDF = Compute the normal probability density function. 11020 11021Reference: 11022 "A Computer Program POWNOR for Fitting the Power-Normal and 11023 -Lognormal Models to Life or Strength Data from Specimens of 11024 Various Sizes", Nelson and Doganaksoy, NIST-IR 4760, March 1992. 11025 11026Applications: 11027 Reliability 11028 11029Implementation Date: 11030 1995/5 11031 11032Program: 11033 LABEL CASE ASIS 11034 X1LABEL X 11035 Y1LABEL Probability 11036 TITLE CASE ASIS 11037 . 11038 MULTIPLOT 2 2 11039 MULTIPLOT CORNER COORDINATES 0 0 100 95 11040 . 11041 TITLE P = 0.5, SIGMA = 0.2, 0.4, 0.7, 1.0 11042 PLOT PLNPDF(X,0.5,0.2) FOR X = 0.01 .01 3 AND 11043 PLOT PLNPDF(X,0.5,0.4) FOR X = 0.01 .01 3 AND 11044 PLOT PLNPDF(X,0.5,0.7) FOR X = 0.01 .01 3 AND 11045 PLOT PLNPDF(X,0.5,1.0) FOR X = 0.01 .01 3 11046 TITLE P = 1.0, SIGMA = 0.2, 0.4, 0.7, 1.0 11047 PLOT PLNPDF(X,1.0,0.2) FOR X = 0.01 .01 3 AND 11048 PLOT PLNPDF(X,1.0,0.4) FOR X = 0.01 .01 3 AND 11049 PLOT PLNPDF(X,1.0,0.7) FOR X = 0.01 .01 3 AND 11050 PLOT PLNPDF(X,1.0,1.0) FOR X = 0.01 .01 3 11051 TITLE P = 5.0, SIGMA = 0.2, 0.4, 0.7, 1.0 11052 PLOT PLNPDF(X,5.0,0.2) FOR X = 0.01 .01 2 AND 11053 PLOT PLNPDF(X,5.0,0.4) FOR X = 0.01 .01 2 AND 11054 PLOT PLNPDF(X,5.0,0.7) FOR X = 0.01 .01 2 AND 11055 PLOT PLNPDF(X,5.0,1.0) FOR X = 0.01 .01 2 11056 TITLE P = 20, SIGMA = 0.2, 0.4, 0.7, 1.0 11057 PLOT PLNPDF(X,20,0.2) FOR X = 0.01 .01 1 AND 11058 PLOT PLNPDF(X,20,0.4) FOR X = 0.01 .01 1 AND 11059 PLOT PLNPDF(X,20,0.7) FOR X = 0.01 .01 1 AND 11060 PLOT PLNPDF(X,20,1.0) FOR X = 0.01 .01 1 11061 . 11062 END OF MULTIPLOT 11063 MOVE 50 97 11064 JUSTIFICATION CENTER 11065 TEXT Power Lognormal PDF's 11066 11067-----PLNPPF (LET)-------------------------------- 11068 11069PLNPPF 11070 11071Name: 11072 PLNPPF (LET) 11073 11074Type: 11075 Library Function 11076 11077Purpose: 11078 Compute the power-lognormal percent point function. 11079 11080Description: 11081 The standard lognormal distribution has the following percent 11082 point function: 11083 G(f,sigma,p) = EXP(NORPPF(1-(1-f)**(1/p))/sigma) 11084 for 0 < f < 1, sigma, p > 0 11085 where sigma is a shape parameter, p is a shape (power) parameter, 11086 and NORPPF is the percent point function of the standard normal 11087 distribution. The input value is a real number between 0 and 1 11088 (since it corresponds to a probability). 11089 11090 If p is 1, this distribution reduces to the lognormal 11091 distribution. 11092 11093Syntax: 11094 LET <y> = PLNPPF(<x>,<p>,<s>) <SUBSET/EXCEPT/FOR qualification> 11095 where <x> is a number, parameter, or variable in the range 0 to 1; 11096 <p> is a positive number, parameter, or variable 11097 that specifies the power parameter; 11098 <s> is an optional positive number, parameter, or variable 11099 that specifies the shape parameter; 11100 <y> is a variable or a parameter (depending on what <x> is) 11101 where the computed power-lognormal ppf value is stored; 11102 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 11103 11104 If the <s> parameter is omitted, it defaults to 1. 11105 11106Examples: 11107 LET A = PLNPPF(0.9,2,1) 11108 LET X2 = PLNPPF(X1,P,SD) 11109 LET X2 = PLNPPF(X1,0.5,3) 11110 11111Note: 11112 The general power-lognormal percent point function can be 11113 expressed in terms of the standard power-lognormal percent point 11114 function as follows: 11115 G(f,sigma,p,loc,scale) = loc + scale*G(f,sigma,p) 11116 for 0 < f < 1, sigma, p, scale > 0 11117 where loc and scale are the location and scales parameters, 11118 respectively. 11119 11120Note: 11121 Library functions are distinguished from let subcommands 11122 in the following ways. 11123 1) Functions enclose the input value in parenthesis. Let 11124 subcommands use spaces. 11125 2) Functions can accept (and return) either parameters 11126 (i.e., single values) or variables (i.e., an array of 11127 values) while let subcommands are specific in which they 11128 accept as input and what they return as output. 11129 3) Functions can accept expressions while let subcommands 11130 do not. For example, the following is legal: 11131 LET Y2 = ABS(Y1-INT(Y1)) 11132 For let subcommands, you typically have to do something 11133 like the following: 11134 LET YTEMP = Y**2 + 8 11135 LET A = SUM YTEMP 11136 11137Default: 11138 None 11139 11140Synonyms: 11141 None 11142 11143Related Commands: 11144 PLNCDF = Compute the power-lognormal cumulative distribution 11145 function. 11146 PLNPDF = Compute the power-lognormal probability density 11147 function. 11148 PLNHAZ = Compute the power-lognormal hazard function. 11149 PLNCHAZ = Compute the power-lognormal cumulative hazard function. 11150 PNRPDF = Compute the power-normal probability density function. 11151 LGNPDF = Compute the lognormal probability density function. 11152 HFNPDF = Compute the half-normal probability density function. 11153 NORPDF = Compute the normal probability density function. 11154 11155Reference: 11156 "A Computer Program POWNOR for Fitting the Power-Normal and 11157 -Lognormal Models to Life or Strength Data from Specimens of 11158 Various Sizes", Nelson and Doganaksoy, NIST-IR 4760, March 1992. 11159 11160Applications: 11161 Reliability 11162 11163Implementation Date: 11164 1995/5 11165 11166Program: 11167 LABEL CASE ASIS 11168 Y1LABEL X 11169 X1LABEL Probability 11170 TITLE CASE ASIS 11171 . 11172 MULTIPLOT 2 2 11173 MULTIPLOT CORNER COORDINATES 0 0 100 95 11174 . 11175 TITLE P = 0.5, SIGMA = 0.2, 0.4, 0.7, 1.0 11176 PLOT PLNPPF(F,0.5,0.2) FOR F = 0.01 .01 0.99 AND 11177 PLOT PLNPPF(F,0.5,0.4) FOR F = 0.01 .01 0.99 AND 11178 PLOT PLNPPF(F,0.5,0.7) FOR F = 0.01 .01 0.99 AND 11179 PLOT PLNPPF(F,0.5,1.0) FOR F = 0.01 .01 0.99 11180 TITLE P = 1.0, SIGMA = 0.2, 0.4, 0.7, 1.0 11181 PLOT PLNPPF(F,1.0,0.2) FOR F = 0.01 .01 0.99 AND 11182 PLOT PLNPPF(F,1.0,0.4) FOR F = 0.01 .01 0.99 AND 11183 PLOT PLNPPF(F,1.0,0.7) FOR F = 0.01 .01 0.99 AND 11184 PLOT PLNPPF(F,1.0,1.0) FOR F = 0.01 .01 0.99 11185 TITLE P = 5.0, SIGMA = 0.2, 0.4, 0.7, 1.0 11186 PLOT PLNPPF(F,5.0,0.2) FOR F = 0.01 .01 0.99 AND 11187 PLOT PLNPPF(F,5.0,0.4) FOR F = 0.01 .01 0.99 AND 11188 PLOT PLNPPF(F,5.0,0.7) FOR F = 0.01 .01 0.99 AND 11189 PLOT PLNPPF(F,5.0,1.0) FOR F = 0.01 .01 0.99 11190 TITLE P = 20, SIGMA = 0.2, 0.4, 0.7, 1.0 11191 PLOT PLNPPF(F,20,0.2) FOR F = 0.01 .01 0.99 AND 11192 PLOT PLNPPF(F,20,0.4) FOR F = 0.01 .01 0.99 AND 11193 PLOT PLNPPF(F,20,0.7) FOR F = 0.01 .01 0.99 AND 11194 PLOT PLNPPF(F,20,1.0) FOR F = 0.01 .01 0.99 11195 . 11196 END OF MULTIPLOT 11197 MOVE 50 97 11198 JUSTIFICATION CENTER 11199 TEXT Power Lognormal PPF's 11200 11201-----PLOT------------------------------------------------------- 11202 11203PLOT 11204 11205Name: 11206 PLOT 11207 11208Type: 11209 Graphics Command 11210 11211Purpose: 11212 Generates a plot. 11213 11214Description: 11215 The PLOT command allows the analyst to generate single or 11216 multi-trace plots of data, functions, or both. It is DATAPLOT's 11217 most powerful, most important, and most heavily used graphics 11218 command. There are 7 general plot syntaxes: 11219 1) 1-variable form 11220 2) 2-variable form 11221 3) 3-variable multi-trace form 11222 4) VERSUS form 11223 5) multi-VERSUS form 11224 6) function form 11225 7) AND form 11226 11227 DATAPLOT uses the concept of traces. A trace is a connected set of 11228 points. Points in the same trace are plotted with the same 11229 attributes. In most cases, a single variable is one trace. 11230 However, a single variable can be split into multiple traces if 11231 desired (see SYNTAX 3). 11232 11233Syntax 1: (1-variable form) 11234 PLOT <y> <SUBSET/EXCEPT/FOR qualification> 11235 where <y> is a variable; 11236 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 11237 11238 This form for the PLOT command is used for plotting <y> versus its 11239 dummy index. The resulting plot will have <y> on the vertical 11240 axis and the dummy index 1, 2, 3, ..., n (where n = the number of 11241 elements in <y>) on the horizontal axis. 11242 11243Syntax 2: (2-variable form) 11244 PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 11245 where <y> is an independent (i.e., the vertical axis) variable; 11246 <x> is an independent (i.e., the horizontal axis) variable; 11247 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 11248 11249 This is the 2-argument form for the PLOT command. It is used for 11250 plotting <y> versus <x>. The resulting plot will have <y> on the 11251 vertical axis and <x> on the horizontal axis. 11252 11253Syntax 3: (the 3-variable multi-trace form) 11254 PLOT <y> <x> <tag> <SUBSET/EXPECT/FOR qualification> 11255 where <y> is an independent (i.e., the vertical axis) variable; 11256 <x> is an independent (i.e., the horizontal axis) variable; 11257 <tag> is a variable that identifies groups in <y> and <x> 11258 that are plotted with common attributes; 11259 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 11260 11261 This is the 3-argument form for the PLOT command. It is used for 11262 multi-trace plotting of <y> versus <x>. The resulting plot will 11263 have <y> on the vertical axis, <x> on the horizontal axis, and will 11264 have one trace for each distinct value in the <tag> variable. 11265 11266 If the <x> variable and the <tag> variable are identical, all 11267 points with a common <x> value are treated as a common trace (i.e., 11268 they are plotted with common attributes). 11269 11270 Although DATAPLOT supports a large number of built-in plot formats, 11271 there will be cases where you may want a specialized chart format 11272 that is not available. This syntax for the PLOT command can often 11273 be used for this purpose by defining the <tag> variable in the 11274 right way. Points with a common <tag> value are treated as a 11275 trace, and attributes can be set for each individual trace. 11276 11277Syntax 4: (VERSUS form) 11278 PLOT <y1> <y2> <y3> ... <yk> VERSUS <x> 11279 <SUBSET/EXCEPT/FOR qualification> 11280 where <y1>, <y2>, <y3>, ..., <yk> are dependent (i.e., vertical 11281 axis) variables; 11282 <x> is an independent (i.e., the horizontal axis) variable; 11283 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 11284 11285 This is the single-VERSUS argument form for the PLOT command. It 11286 is used for multi-trace plotting where the dependent variables are 11287 plotted against a common <x> variable. The resulting plot will 11288 have one trace for each <yi> variable: 11289 <y1> (vertically) versus <x> (horizontally) 11290 <y2> (vertically) versus <x> (horizontally) 11291 <y3> (vertically) versus <x> (horizontally) 11292 ... 11293 <yk> (vertically) versus <x> (horizontally) 11294 11295 VS and VS. can also be used for VERSUS. 11296 11297Syntax: 5 (multi-VERSUS form) 11298 PLOT <syntax 4> <syntax 4> ... <syntax 4> 11299 11300 This is the multi-VERSUS argument form for the PLOT command. It 11301 is used for multi-trace plotting where the dependent variables are 11302 plotted against different <x> variables. 11303 11304Syntax: 6 (function form) 11305 PLOT <f> FOR <x> = <start> <increment> <stop> 11306 where <f> is a function (either pre-defined via the LET 11307 FUNCTION command, or explicitly defined herein); 11308 <x> is the dummy variable in the function; 11309 <start> is the desired minimum value for <x> at which the 11310 function is to be evaluated; 11311 <increment> is the desired increment value for <x> at which 11312 the function is to be evaluated; 11313 and <stop> is the desired maximum value for <x> at which the 11314 function is to be evaluated. 11315 11316 This is the function form for the PLOT command. It is used for 11317 plotting a function of one variable. 11318 11319Syntax: 7 (AND form) 11320 <any valid syntax 1 to 6> AND 11321 <any valid syntax 1 to 6> AND 11322 <any valid syntax 1 to 6> AND 11323 ... 11324 <any valid syntax 1 to 6> AND 11325 <any valid syntax 1 to 6> 11326 11327 This is the most general syntax for PLOT. It is used for 11328 generating multi-trace plots of variables, of functions, or of 11329 mixtures of both. 11330 11331Examples: 11332 PLOT Y 11333 PLOT TEMP SUBSET TAG > 4 11334 11335 PLOT Y X 11336 PLOT RES X SUBSET X > -9999 11337 11338 PLOT Y X LAB 11339 PLOT PRES TEMP DAY 11340 PLOT PRES TEMP DAY DAY <> 4 11341 11342 PLOT Y1 Y2 Y3 VERSUS X 11343 PLOT Y PRED VERSUS X 11344 PLOT Y PRED VERSUS X SUBSET X = 10.6 TO 19.7 11345 11346 PLOT Y1 Y2 Y3 VERSUS X1 Y4 Y5 VERSUS X2 11347 PLOT P1 VERSUS T1 P2 VERSUS T2 P3 VERUS T3 11348 11349 PLOT SIN(X)*EXP(-X) FOR X = 0 .1 5 11350 11351 LET FUNCTION F = EXP(-X*SIN(X**2)) 11352 PLOT F FOR X = 0 .1 3 11353 11354 PLOT Y X AND 11355 PLOT A+B*X FOR X = 1 1 10 11356 11357 PLOT Y1 Y2 VS X AND 11358 PLOT Y X AND 11359 PLOT A*SIN(B*X) FOR X = 1 .1 3 AND 11360 PLOT Y3 X3 LAB 11361 11362Note: 11363 Plot points can be plotted as characters, connected lines, spikes, 11364 or bars. These are set independently of each other. The default 11365 is to plot each trace as a connected line with no symbol, no bar, 11366 and no spike. The LINE, CHARACTER, SPIKE, and BAR commands are 11367 used to set the switches for plotting a given trace as a connected 11368 line, a character, a spike, or a bar respectively. 11369 11370 There are attribute setting commands for lines, characters, spikes, 11371 and bars. See the documentation for LINE, CHARACTER, SPIKE, and 11372 BAR for a complete list of these commands. Attributes are set 11373 giving a list of values. The first trace uses the first setting, 11374 the second trace uses the second setting, and so on. For example, 11375 CHARACTER SIZE 2.0 3.0 1.5 sets the character size for trace 1 to 11376 2.0, the character size for trace 2 to 3.0, and the character size 11377 for trace 3 to 1.5. Attributes can be set for up to 100 traces. 11378 11379 As a more complex example, suppose you want to plot a variable Y 11380 as a connected line and every fifth point as a filled circle. You 11381 can do something like the following: 11382 LET N = SIZE Y 11383 LET X = SEQUENCE 1 1 N 11384 LET TAG = PATTERN 1 2 2 2 2 FOR I = 1 1 N 11385 CHARACTER CIRCLE BLANK 11386 CHARACTER FILL ON OFF 11387 CHARACTER SIZE 1.5 11388 PLOT Y X TAG 11389 11390Note: 11391 DATAPLOT provides a large range of plot control features for the 11392 plot. This includes titles, axis labels, legends, and so on. 11393 DATAPLOT sets these with separate commands (as opposed to 11394 arguments on the PLOT command itself). Each of these features 11395 typically has its own attribute setting commands as well. DATAPLOT 11396 simply uses whatever the current setting is for each of these 11397 attributes when it generates a plot. For example, a TITLE command 11398 is entered to define the plot title (nothing is actually generated 11399 until the next PLOT is performed). This title remains in effect 11400 for all subsequent plots until it is changed (another TITLE 11401 command) or deleted (TITLE with no arguments). 11402 11403 Most of the commonly used plot features are listed below. The 11404 attribute setting commands are not listed (e.g., TITLE is listed, 11405 but TITLE COLOR and TITLE SIZE are not). See the documentation 11406 for the plot feature for its attribute setting commands. 11407 11408Note: 11409 Dataplot allows subregions to be added to plots. Enter 11410 HELP SUBREGION for details. 11411 11412 This capability was implemented 2000/1. 11413 11414Note: 11415 DATAPLOT saves the following internal parameters after a plot: 11416 11417 PLOTCORR - correlation of the X and Y coordinates on the plot 11418 PLOTCOR1 - correlation of the X and Y coordinates on the plot 11419 with a tag value of 1. This can be useful for 11420 plots that generate reference lines (which you 11421 do not want included in the correlation computation 11422 PLOTYMAX - maximum Y coordinate 11423 YMAXINDE - index of the maximum Y coordinate 11424 PLOTYMIN - minimum Y coordinate 11425 YMININDE - index of the minimum Y coordinate 11426 PLOTXMAX - maximum X coordinate 11427 XMAXINDE - index of the maximum X coordinate 11428 PLOTXMIN - minimum X coordinate 11429 XMININDE - index of the minimum X coordinate 11430 NACCEPT - number of plot points inside the first subregion 11431 (0 if no subregions defined) 11432 NREJECT - number of plot points outside the first subregion 11433 (0 if no subregions defined) 11434 NTOTAL - number of plot points (NACCEPT + NREJECT) 11435 (0 if no subregions defined) 11436 11437 These internal parameters are actually computed for all plot 11438 types, not just the PLOT command. 11439 11440 This capability was implemented 2000/1. 11441 11442Default: 11443 None 11444 11445Synonyms: 11446 VS and VS. are synonyms for VERSUS. 11447 11448Related Commands: 11449 CHARACTERS = Sets the types for plot characters. 11450 LINES = Sets the types for plot lines. 11451 SPIKES = Sets the on/off switches for plot spikes. 11452 BARS = Sets the on/off switches for plot bars. 11453 TITLE = Sets the plot title. 11454 LABEL = Sets the plot axis labels. 11455 LEGEND = Sets the plot legends. 11456 BOX COORDINATES = Sets the locations for plot boxes. 11457 ARROW COORDINATES = Sets the locations for plot arrows. 11458 SEGMENT COORDINATES = Sets the locations for plot segments. 11459 FRAME = Sets the on/off switch for the plot frame. 11460 FRAME COORDINATES = Sets the location for the plot frame. 11461 GRID = Sets the on/off switch for the plot grid. 11462 LOG = Sets the on/off switch for log scale. 11463 TIC = Sets the on/off switch for the plot tics. 11464 TIC LABEL = Sets the on/off switch for the plot tic 11465 labels. 11466 MARGIN COLOR = Sets the color for the plot margin. 11467 BACKGROUND COLOR = Sets the color for the plot background. 11468 PRE-ERASE = Sets the automatic pre-erase switch for 11469 plots. 11470 SEQUENCE = Sets the automatic sequence switch for plots. 11471 MULTIPLOT = Generate multiple plots per page. 11472 11473Applications: 11474 Graphics 11475 11476Implementation Date: 11477 Pre-1987 11478 11479Program: 11480 . POLLUTION SOURCE ANALYSIS, LLOYD CURRIE, DATE--1990 11481 . SUBSET OF CURRIE.DAT REFERENCE FILE 11482 . 11483 LET ID2 = DATA 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 11484 LET LEAD = DATA 164 426 59 98 312 263 607 497 213 54 160 262 547 325 419 94 70 11485 LET POT = DATA 106 175 61 79 94 121 424 328 107 218 140 179 246 231 245 339 99 11486 . 11487 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 11488 TITLE SCATTER PLOT; X1LABEL LEAD; Y1LABEL POTASSIUM 11489 LINE BLANK ALL; CHARACTER CIRCLE; CHARACTER FILL ON 11490 PLOT POT LEAD 11491 . 11492 CHARACTER CIRCLE SQUARE; CHARACTER FILL OFF ALL 11493 TITLE SCATTER PLOT WITH GROUPS 11494 LEGEND 1 CIRC() - GROUP 1; LEGEND 2 SQUA() - GROUP 2 11495 LEGEND FILL ON; LEGEND FONT DUPLEX 11496 PLOT POT LEAD ID2 11497 . 11498 CHARACTER CIRCLE CIRCLE SQUARE SQUARE; CHARACTER FILL OFF ON OFF ON 11499 LET X = SEQUENCE 1 1 17 11500 LEGEND 1 CIRC() - POTASSIUM; LEGEND 2 SQUA() - LEAD 11501 X1LABEL SEQUENCE; Y1LABEL; TITLE CHARACTER FILL REPRESENTS GROUP ID 11502 PLOT POT X ID2 AND 11503 PLOT LEAD X ID2 11504 . 11505 CHARACTER BLANK ALL; LINE SOLID DASH 11506 SEGMENT 1 COORDINATES 16 85 19 85 11507 SEGMENT 2 COORDINATES 16 81 19 81 11508 SEGMENT 2 PATTERN DASH 11509 TITLE MULTIPLE TRACES AS LINES 11510 PLOT POT LEAD VS X 11511 END OF MULTIPLOT 11512 11513-----PNRCDF (LET)-------------------------------- 11514 11515PNRCDF 11516 11517Name: 11518 PNRCDF (LET) 11519 11520Type: 11521 Library Function 11522 11523Purpose: 11524 Compute the standard power-normal cumulative distribution 11525 function. 11526 11527Description: 11528 The standard power-normal distribution has the following 11529 probability density function: 11530 f(x,p)=p*NORPDF(x)*NORCDF(-x)**(p-1) for x > 0, p > 0 11531 where p is the shape (power) parameter, and NORCDF and NORPDF are 11532 the cumulative distribution function and the probability density 11533 function for the standard normal distribution respectively. 11534 11535 The cumulative distribution is the area under the curve from 11536 negative infinity to x (i.e., the integral of the above function). 11537 It has the formula: 11538 F(x,p) = 1 - (NORCDF(-x))**p for x > 0, p > 0 11539 11540 If p is 1, this distribution reduces to the normal distribution. 11541 11542Syntax: 11543 LET <y2> = PNRCDF(<y1>,<p>) <SUBSET/EXCEPT/FOR qualification> 11544 where <y1> is a non-negative number, parameter, or variable; 11545 <p> is a positive number, parameter, or variable 11546 that specifies the power parameter; 11547 <y2> is a variable or a parameter (depending on what <y1> is) 11548 where the computed power-normal cdf value is stored; 11549 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 11550 11551Examples: 11552 LET A = PNRCDF(3,2) 11553 LET X2 = PNRCDF(X1,POW) 11554 LET X2 = PNRCDF(X1,0.5) 11555 11556Note: 11557 The general power-normal distribution has the following 11558 probability density function: 11559 f(x,u,s,p)=(p/s)*NORPDF((x-u)/s)*NORCDF(-(x-u)/s)**(p-1) 11560 for x > 0, s > 0, p > 0 11561 where u is the location parameter, s is the scale parameter, and p 11562 is the power parameter. The cumulative distribution function has 11563 the formula: 11564 F(x,u,s,p) = 1 - (NORCDF(-(x-u)/s))**p for x > 0, s > 0, p > 0 11565 11566Note: 11567 Library functions are distinguished from let subcommands 11568 in the following ways. 11569 1) Functions enclose the input value in parenthesis. Let 11570 subcommands use spaces. 11571 2) Functions can accept (and return) either parameters 11572 (i.e., single values) or variables (i.e., an array of 11573 values) while let subcommands are specific in which they 11574 accept as input and what they return as output. 11575 3) Functions can accept expressions while let subcommands 11576 do not. For example, the following is legal: 11577 LET Y2 = ABS(Y1-INT(Y1)) 11578 For let subcommands, you typically have to do something 11579 like the following: 11580 LET YTEMP = Y**2 + 8 11581 LET A = SUM YTEMP 11582 11583Default: 11584 None 11585 11586Synonyms: 11587 None 11588 11589Related Commands: 11590 PNRPDF = Compute the power-normal probability density function. 11591 PNRPPF = Compute the power-normal percent point function. 11592 PLNCDF = Compute the power-lognormal cumulative distribution 11593 function. 11594 PLNPDF = Compute the power-lognormal probability density function. 11595 PLNPPF = Compute the power-lognormal percent point function. 11596 LGNCDF = Compute the lognormal cumulative distribution function. 11597 LGNPDF = Compute the lognormal probability density function. 11598 LGNPPF = Compute the lognormal percent point function. 11599 NORCDF = Compute the normal cumulative distribution function. 11600 NORPDF = Compute the normal probability density function. 11601 NORPPF = Compute the normal percent point function. 11602 11603Reference: 11604 "A Computer Program POWNOR for Fitting the Power-Normal and 11605 -Lognormal Models to Life or Strength Data from Specimens of 11606 Various Sizes", Nelson and Doganaksoy, NIST-IR 4760, March 1992. 11607 11608Applications: 11609 Reliability 11610 11611Implementation Date: 11612 1995/5 11613 11614Program: 11615 LABEL CASE ASIS 11616 X1LABEL X 11617 YLIMITS 0 1 11618 Y1LABEL Probability 11619 MAJOR YTIC MARK NUMBER 6 11620 TITLE CASE ASIS 11621 TITLE Power Normal PDF Plot CR() ... 11622 SD=1, P=10000, 3000, 1000, 300, 100, 50, 20, 5, 1, 0.5, 0.2 0.1 11623 . 11624 PLOT PNRCDF(X,10000) FOR X = -5 .05 5 AND 11625 PLOT PNRCDF(X,3000) FOR X = -5 .05 5 AND 11626 PLOT PNRCDF(X,1000) FOR X = -5 .05 5 AND 11627 PLOT PNRCDF(X,300) FOR X = -5 .05 5 AND 11628 PLOT PNRCDF(X,100) FOR X = -5 .05 5 AND 11629 PLOT PNRCDF(X,50) FOR X = -5 .05 5 AND 11630 PLOT PNRCDF(X,20) FOR X = -5 .05 5 AND 11631 PLOT PNRCDF(X,5) FOR X = -5 .05 5 AND 11632 PLOT PNRCDF(X,1) FOR X = -5 .05 5 AND 11633 PLOT PNRCDF(X,0.5) FOR X = -5 .05 5 AND 11634 PLOT PNRCDF(X,0.2) FOR X = -5 .05 5 AND 11635 PLOT PNRCDF(X,0.1) FOR X = -5 .05 5 11636 11637-----PNRCHAZ (LET)-------------------------------- 11638 11639PNRCHAZ 11640 11641Name: 11642 PNRCHAZ (LET) 11643 11644Type: 11645 Library Function 11646 11647Purpose: 11648 Compute the standard power-normal cumulative hazard function. 11649 11650Description: 11651 The standard power-normal distribution has the following 11652 cumulative hazard function: 11653 H(x,p)=-LOG[(NORCDF(-x))**p] for x, p > 0 11654 where p is the shape (power) parameter and NORCDF is the 11655 cumulative distribution function for the standard normal 11656 distribution. 11657 11658 If p is 1, this distribution reduces to the normal distribution. 11659 11660Syntax: 11661 LET <y> = PNRCHAZ(<x>,<p>) <SUBSET/EXCEPT/FOR qualification> 11662 where <x> is a non-negative number, parameter, or variable; 11663 <p> is a positive number, parameter, or variable 11664 that specifies the power parameter; 11665 <y> is a variable or a parameter (depending on what <x> is) 11666 where the computed power-normal cumulative hazard 11667 value is stored; 11668 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 11669 11670Examples: 11671 LET A = PNRCHAZ(3,2) 11672 LET X2 = PNRCHAZ(X1,POW) 11673 LET X2 = PNRCHAZ(X1,0.5) 11674 11675Note: 11676 The general form of the power-normal cumulative hazard function is: 11677 H(x,p,mu,sigma)=-LOG[(NORCDF(-(x-mu)/sigma))**p] 11678 for x, p, sigma > 0 11679 where mu and sigma are the location and scale parameters, 11680 respectively. 11681 11682Default: 11683 None 11684 11685Synonyms: 11686 None 11687 11688Related Commands: 11689 PNRCDF = Compute the power-normal cumulative distribution 11690 function. 11691 PNRPDF = Compute the power-normal probability density function. 11692 PNRPPF = Compute the power-normal percent point function. 11693 PNRHAZ = Compute the power-normal hazard function. 11694 PLNPDF = Compute the power-lognormal probability density function. 11695 LGNPDF = Compute the lognormal probability density function. 11696 NORPDF = Compute the normal probability density function. 11697 11698Reference: 11699 "A Computer Program POWNOR for Fitting the Power-Normal and 11700 -Lognormal Models to Life or Strength Data from Specimens of 11701 Various Sizes", Nelson and Doganaksoy, NIST-IR 4760, March 1992. 11702 11703Applications: 11704 Reliability 11705 11706Implementation Date: 11707 1998/4 11708 11709Program: 11710 LABEL CASE ASIS 11711 X1LABEL X 11712 Y1LABEL Cumulative Hazard 11713 YLIMITS 0 1 11714 MAJOR YTIC MARK NUMBER 6 11715 TITLE CASE ASIS 11716 TITLE Power Normal Cumulative Hazard Plot CR() ... 11717 SD=1, P=10000, 3000, 1000, 300, 100, 50, 20, 5, 1, 0.5, 0.2 0.1 11718 . 11719 PLOT PNRCHAZ(X,10000) FOR X = -5 .05 5 AND 11720 PLOT PNRCHAZ(X,3000) FOR X = -5 .05 5 AND 11721 PLOT PNRCHAZ(X,1000) FOR X = -5 .05 5 AND 11722 PLOT PNRCHAZ(X,300) FOR X = -5 .05 5 AND 11723 PLOT PNRCHAZ(X,100) FOR X = -5 .05 5 AND 11724 PLOT PNRCHAZ(X,50) FOR X = -5 .05 5 AND 11725 PLOT PNRCHAZ(X,20) FOR X = -5 .05 5 AND 11726 PLOT PNRCHAZ(X,5) FOR X = -5 .05 5 AND 11727 PLOT PNRCHAZ(X,1) FOR X = -5 .05 5 AND 11728 PLOT PNRCHAZ(X,0.5) FOR X = -5 .05 5 AND 11729 PLOT PNRCHAZ(X,0.2) FOR X = -5 .05 5 AND 11730 PLOT PNRCHAZ(X,0.1) FOR X = -5 .05 5 11731 11732-----PNRHAZ (LET)-------------------------------- 11733 11734PNRHAZ 11735 11736Name: 11737 PNRHAZ (LET) 11738 11739Type: 11740 Library Function 11741 11742Purpose: 11743 Compute the standard power-normal hazard function. 11744 11745Description: 11746 The standard power-normal distribution has the following 11747 hazard function: 11748 h(x,p)=p*NORPDF(x)/NORCDF(-x) for x > 0, p > 0 11749 where p is the power parameter, and NORCDF and NORPDF are the 11750 cumulative distribution function and the probability density 11751 function for the standard normal distribution respectively. 11752 11753 If p is 1, this distribution reduces to the normal distribution. 11754 11755Syntax: 11756 LET <y> = PNRHAZ(<x>,<p>) <SUBSET/EXCEPT/FOR qualification> 11757 where <x> is a non-negative number, parameter, or variable; 11758 <p> is a positive number, parameter, or variable 11759 that specifies the power parameter; 11760 <y> is a variable or a parameter (depending on what <x> is) 11761 where the computed power-normal hazard value is stored; 11762 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 11763 11764Examples: 11765 LET A = PNRHAZ(3,2) 11766 LET X2 = PNRHAZ(X1,POW) 11767 LET X2 = PNRHAZ(X1,0.5) 11768 11769Note: 11770 The general form of the power-normal hazard function is: 11771 h(x,p,mu,sigma)=p*NORPDF((x-mu)/sigma)/ 11772 [sigma*NORCDF(-(x-mu)/sigma) for x, p, sigma > 0 11773 where mu and sigma are the location and scale parameters, 11774 respectively. 11775 11776Default: 11777 None 11778 11779Synonyms: 11780 None 11781 11782Related Commands: 11783 PNRCDF = Compute the power-normal cumulative distribution 11784 function. 11785 PNRPDF = Compute the power-normal probability density function. 11786 PNRPPF = Compute the power-normal percent point function. 11787 PNRCHAZ = Compute the power-normal cumulative hazard function. 11788 PLNPDF = Compute the power-lognormal probability density function. 11789 LGNPDF = Compute the lognormal probability density function. 11790 NORPDF = Compute the normal probability density function. 11791 11792Reference: 11793 "A Computer Program POWNOR for Fitting the Power-Normal and 11794 -Lognormal Models to Life or Strength Data from Specimens of 11795 Various Sizes", Nelson and Doganaksoy, NIST-IR 4760, March 1992. 11796 11797Applications: 11798 Reliability 11799 11800Implementation Date: 11801 1998/4 11802 11803Program: 11804 LABEL CASE ASIS 11805 X1LABEL X 11806 Y1LABEL Hazard 11807 YLIMITS 0 1 11808 MAJOR YTIC MARK NUMBER 6 11809 TITLE CASE ASIS 11810 TITLE Power Normal Hazard Plot CR() ... 11811 SD=1, P=10000, 3000, 1000, 300, 100, 50, 20, 5, 1, 0.5, 0.2 0.1 11812 . 11813 PLOT PNRHAZ(X,10000) FOR X = -5 .05 5 AND 11814 PLOT PNRHAZ(X,3000) FOR X = -5 .05 5 AND 11815 PLOT PNRHAZ(X,1000) FOR X = -5 .05 5 AND 11816 PLOT PNRHAZ(X,300) FOR X = -5 .05 5 AND 11817 PLOT PNRHAZ(X,100) FOR X = -5 .05 5 AND 11818 PLOT PNRHAZ(X,50) FOR X = -5 .05 5 AND 11819 PLOT PNRHAZ(X,20) FOR X = -5 .05 5 AND 11820 PLOT PNRHAZ(X,5) FOR X = -5 .05 5 AND 11821 PLOT PNRHAZ(X,1) FOR X = -5 .05 5 AND 11822 PLOT PNRHAZ(X,0.5) FOR X = -5 .05 5 AND 11823 PLOT PNRHAZ(X,0.2) FOR X = -5 .05 5 AND 11824 PLOT PNRHAZ(X,0.1) FOR X = -5 .05 5 11825 11826-----PNRPDF (LET)-------------------------------- 11827 11828PNRPDF 11829 11830Name: 11831 PNRPDF (LET) 11832 11833Type: 11834 Library Function 11835 11836Purpose: 11837 Compute the standard power-normal probability density function. 11838 11839Description: 11840 The standard power-normal distribution has the following 11841 probability density function: 11842 f(x,p)=p*NORPDF(x)*NORCDF(-x)**(p-1) for x > 0, p > 0 11843 where p is the power parameter, and NORCDF and NORPDF are the 11844 cumulative distribution function and the probability density 11845 function for the standard normal distribution respectively. 11846 11847 If p is 1, this distribution reduces to the normal distribution. 11848 11849Syntax: 11850 LET <y2> = PNRPDF(<y1>,<p>) <SUBSET/EXCEPT/FOR qualification> 11851 where <y1> is a non-negative number, parameter, or variable; 11852 <p> is a positive number, parameter, or variable 11853 that specifies the power parameter; 11854 <y2> is a variable or a parameter (depending on what <y1> is) 11855 where the computed power-normal pdf value is stored; 11856 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 11857 11858Examples: 11859 LET A = PNRPDF(3,2) 11860 LET X2 = PNRPDF(X1,POW) 11861 LET X2 = PNRPDF(X1,0.5) 11862 11863Note: 11864 The general power-normal distribution has the following 11865 probability density function: 11866 f(x,u,s,p)=(p/s)*NORPDF((x-u)/s)*NORCDF(-(x-u)/s)**(p-1) 11867 for x > 0, s > 0, p > 0 11868 where u is the location parameter, s is the shape parameter, and p 11869 is the power parameter. 11870 11871Default: 11872 None 11873 11874Synonyms: 11875 None 11876 11877Related Commands: 11878 PNRCDF = Compute the power-normal cumulative distribution 11879 function. 11880 PNRPPF = Compute the power-normal percent point function. 11881 PLNCDF = Compute the power-lognormal cumulative distribution 11882 function. 11883 PLNPDF = Compute the power-lognormal probability density function. 11884 PLNPPF = Compute the power-lognormal percent point function. 11885 LGNCDF = Compute the lognormal cumulative distribution function. 11886 LGNPDF = Compute the lognormal probability density function. 11887 LGNPPF = Compute the lognormal percent point function. 11888 NORCDF = Compute the normal cumulative distribution function. 11889 NORPDF = Compute the normal probability density function. 11890 NORPPF = Compute the normal percent point function. 11891 11892Reference: 11893 "A Computer Program POWNOR for Fitting the Power-Normal and 11894 -Lognormal Models to Life or Strength Data from Specimens of 11895 Various Sizes", Nelson and Doganaksoy, NIST-IR 4760, March 1992. 11896 11897Applications: 11898 Reliability 11899 11900Implementation Date: 11901 1995/5 11902 11903Program: 11904 LABEL CASE ASIS 11905 X1LABEL X 11906 YLIMITS 0 1.5 11907 Y1LABEL Probability 11908 MAJOR YTIC MARK NUMBER 6 11909 TITLE CASE ASIS 11910 TITLE Power Normal PDF Plot CR() ... 11911 SD=1, P=10000, 3000, 1000, 300, 100, 50, 20, 5, 1, 0.5, 0.2 0.1 11912 . 11913 PLOT PNRPDF(X,10000) FOR X = -5 .05 5 AND 11914 PLOT PNRPDF(X,3000) FOR X = -5 .05 5 AND 11915 PLOT PNRPDF(X,1000) FOR X = -5 .05 5 AND 11916 PLOT PNRPDF(X,300) FOR X = -5 .05 5 AND 11917 PLOT PNRPDF(X,100) FOR X = -5 .05 5 AND 11918 PLOT PNRPDF(X,50) FOR X = -5 .05 5 AND 11919 PLOT PNRPDF(X,20) FOR X = -5 .05 5 AND 11920 PLOT PNRPDF(X,5) FOR X = -5 .05 5 AND 11921 PLOT PNRPDF(X,1) FOR X = -5 .05 5 AND 11922 PLOT PNRPDF(X,0.5) FOR X = -5 .05 5 AND 11923 PLOT PNRPDF(X,0.2) FOR X = -5 .05 5 AND 11924 PLOT PNRPDF(X,0.1) FOR X = -5 .05 5 11925 11926-----PNRPPF (LET)-------------------------------- 11927 11928PNRPPF 11929 11930Name: 11931 PNRPPF (LET) 11932 11933Type: 11934 Library Function 11935 11936Purpose: 11937 Compute the power-normal percent point function. 11938 11939Description: 11940 The standard power-normal distribution has the following 11941 percent point function: 11942 G(f,p) = NORPPF(1-(1-f)**(1/p)) 0 < f < 1; p > 0 11943 where p is the shape (power) parameter and NORPPF is the percent 11944 point function of the standard normal distribution. The input 11945 value is a real number between 0 and 1 (since it corresponds to a 11946 probability). 11947 11948 If p is 1, this distribution reduces to the normal distribution. 11949 11950Syntax: 11951 LET <y2> = PNRPPF(<y1>,<p>) <SUBSET/EXCEPT/FOR qualification> 11952 where <y1> is a number, parameter, or variable in the range 0 to 1; 11953 <p> is a positive number, parameter, or variable 11954 that specifies the power parameter; 11955 <y2> is a variable or a parameter (depending on what <y1> is) 11956 where the computed power-normal ppf value is stored; 11957 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 11958 11959Examples: 11960 LET A = PNRPPF(0.9,2) 11961 LET X2 = PNRPPF(X1,P) 11962 LET X2 = PNRPPF(X1,0.5) 11963 11964Note: 11965 The general power-normal distribution has the following 11966 percent point function: 11967 G(f,p,mu,sigma) = mu + sigma*NORPPF(1-(1-f)**(1/p)) 11968 for 0 < f < 1; p, sigma > 0 11969 where mu and sigma are the location and scale parameters, 11970 respectively. 11971 11972Note: 11973 Library functions are distinguished from let subcommands 11974 in the following ways. 11975 1) Functions enclose the input value in parenthesis. Let 11976 subcommands use spaces. 11977 2) Functions can accept (and return) either parameters 11978 (i.e., single values) or variables (i.e., an array of 11979 values) while let subcommands are specific in which they 11980 accept as input and what they return as output. 11981 3) Functions can accept expressions while let subcommands 11982 do not. For example, the following is legal: 11983 LET Y2 = ABS(Y1-INT(Y1)) 11984 For let subcommands, you typically have to do something 11985 like the following: 11986 LET YTEMP = Y**2 + 8 11987 LET A = SUM YTEMP 11988 11989Default: 11990 None 11991 11992Synonyms: 11993 None 11994 11995Related Commands: 11996 PNRCDF = Compute the power-normal cumulative density function. 11997 PNRPDF = Compute the power-normal probability density function. 11998 PNRHAZ = Compute the power-normal hazard function. 11999 PNRCHAZ = Compute the power-normal cumulative hazard function. 12000 PLNPDF = Compute the power-lognormal probability density 12001 function. 12002 LGNPDF = Compute the lognormal probability density function. 12003 HFNPDF = Compute the half-normal probability density function. 12004 NORPDF = Compute the normal probability density function. 12005 12006Reference: 12007 "A Computer Program POWNOR for Fitting the Power-Normal and 12008 -Lognormal Models to Life or Strength Data from Specimens of 12009 Various Sizes", Nelson and Doganaksoy, NIST-IR 4760, March 1992. 12010 12011Applications: 12012 Reliability 12013 12014Implementation Date: 12015 1995/5 12016 12017Program: 12018 LABEL CASE ASIS 12019 X1LABEL Probabiulity 12020 Y1LABEL X 12021 YLIMITS -5 10 12022 TITLE CASE ASIS 12023 TITLE Power Normal PPF Plot CR() ... 12024 SD=1, P=10000, 3000, 1000, 300, 100, 50, 20, 5, 1, 0.5, 0.2 0.1 12025 . 12026 PLOT PNRPPF(F,10000) FOR F = 0.01 0.01 0.99 AND 12027 PLOT PNRPPF(F,3000) FOR F = 0.01 0.01 0.99 AND 12028 PLOT PNRPPF(F,1000) FOR F = 0.01 0.01 0.99 AND 12029 PLOT PNRPPF(F,300) FOR F = 0.01 0.01 0.99 AND 12030 PLOT PNRPPF(F,100) FOR F = 0.01 0.01 0.99 AND 12031 PLOT PNRPPF(F,50) FOR F = 0.01 0.01 0.99 AND 12032 PLOT PNRPPF(F,20) FOR F = 0.01 0.01 0.99 AND 12033 PLOT PNRPPF(F,5) FOR F = 0.01 0.01 0.99 AND 12034 PLOT PNRPPF(F,1) FOR F = 0.01 0.01 0.99 AND 12035 PLOT PNRPPF(F,0.5) FOR F = 0.01 0.01 0.99 AND 12036 PLOT PNRPPF(F,0.2) FOR F = 0.01 0.01 0.99 AND 12037 PLOT PNRPPF(F,0.1) FOR F = 0.01 0.01 0.99 12038 12039-----POCH (LET)-------------------------------- 12040 12041POCH 12042 12043Name: 12044 POCH (LET) 12045 12046Type: 12047 Library Function 12048 12049Purpose: 12050 Compute a generalization of Pochhammer's symbol. 12051 12052Description: 12053 Pochhammer's generalized symbol is defined to be: 12054 POCH(X,A) = GAMMA(A+X)/GAMMA(A) 12055 where GAMMA is the gamma function. See the documentation for the 12056 GAMMA command for a description of the gamma function. 12057 12058Syntax: 12059 LET <y> = POCH(<x>,<a>) <SUBSET/EXCEPT/FOR qualification> 12060 where <x> is a number, parameter or variable; 12061 <a> is a number, parameter, or variable; 12062 <y> is a variable or a parameter (depending on what <x> 12063 and <a> are) where the computed values are stored; 12064 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 12065 12066Examples: 12067 LET P = POCH(2.3,1) 12068 LET A = POCH(X,A1) 12069 LET X2 = POCH(X1,4.2) 12070 12071Note: 12072 DATAPLOT uses the routine DPOCH from the SLATEC Common Mathematical 12073 Library to compute this function. SLATEC is a large set of high 12074 quality, portable, public domain Fortran routines for various 12075 mathematical capabilities maintained by seven federal laboratories. 12076 12077Note: 12078 Library functions are distinguished from let subcommands 12079 in the following ways. 12080 1) Functions enclose the input value in parenthesis. Let 12081 subcommands use spaces. 12082 2) Functions can accept (and return) either parameters 12083 (i.e., single values) or variables (i.e., an array of 12084 values) while let subcommands are specific in which they 12085 accept as input and what they return as output. 12086 3) Functions can accept expressions while let subcommands 12087 do not. For example, the following is legal: 12088 LET Y2 = ABS(Y1-INT(Y1)) 12089 For let subcommands, you typically have to do something 12090 like the following: 12091 LET YTEMP = Y**2 + 8 12092 LET A = SUM YTEMP 12093 12094Default: 12095 None 12096 12097Synonyms: 12098 None 12099 12100Related Commands: 12101 POCH1 = Compute a generalization of Pochhammer's symbol 12102 starting from the first order. 12103 GAMMA = Compute the gamma function. 12104 LOGGAMMA = Compute the log (to base e) gamma function. 12105 GAMMAIP = Compute an alternate form of the incomplete gamma 12106 function. 12107 GAMMAIC = Compute the complementary incomplete Gamma function. 12108 GAMMAR = Compute the reciprocal gamma function. 12109 TRICOMI = Compute Tricomi's incomplete gamma function. 12110 DIGAMMA = Compute the digamma function. 12111 12112Reference: 12113 "Handbook of Mathematical Functions, Applied Mathematics Series, 12114 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 12115 1964 (chapter 6). 12116 12117Applications: 12118 Special Functions 12119 12120Implementation Date: 12121 94/9 12122 12123Program: 12124 TITLE AUTOMATIC 12125 PLOT POCH(X,2.5) FOR X = 1 0.1 10 12126 12127-----POCH1 (LET)-------------------------------- 12128 12129POCH1 12130 12131Name: 12132 POCH1 (LET) 12133 12134Type: 12135 Library Function 12136 12137Purpose: 12138 Compute a generalization of Pochhammer's symbol starting from the 12139 first order. 12140 12141Description: 12142 Pochhammer's generalized symbol starting from the first order is 12143 defined to be: 12144 POCH1(X,A) = [GAMMA(A+X)/(GAMMA(A)-1)]/X 12145 where GAMMA is the gamma function. See the documentation for the 12146 GAMMA command for a description of the gamma function. 12147 12148Syntax: 12149 LET <y> = POCH1(<x>,<a>) <SUBSET/EXCEPT/FOR qualification> 12150 where <x> is a number, parameter or variable; 12151 <a> is a number, parameter, or variable; 12152 <y> is a variable or a parameter (depending on what <x> 12153 and <a> are) where the computed values are stored; 12154 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 12155 12156Examples: 12157 LET P = POCH1(2.3,1) 12158 LET A = POCH1(X,A1) 12159 LET X2 = POCH1(X1,4.2) 12160 12161Note: 12162 DATAPLOT uses the routine DPOCH1 from the SLATEC Common 12163 Mathematical Library to compute this function. SLATEC is a large 12164 set of high quality, portable, public domain Fortran routines for 12165 various mathematical capabilities maintained by seven federal 12166 laboratories. 12167 12168Note: 12169 Library functions are distinguished from let subcommands 12170 in the following ways. 12171 1) Functions enclose the input value in parenthesis. Let 12172 subcommands use spaces. 12173 2) Functions can accept (and return) either parameters 12174 (i.e., single values) or variables (i.e., an array of 12175 values) while let subcommands are specific in which they 12176 accept as input and what they return as output. 12177 3) Functions can accept expressions while let subcommands 12178 do not. For example, the following is legal: 12179 LET Y2 = ABS(Y1-INT(Y1)) 12180 For let subcommands, you typically have to do something 12181 like the following: 12182 LET YTEMP = Y**2 + 8 12183 LET A = SUM YTEMP 12184 12185Default: 12186 None 12187 12188Synonyms: 12189 None 12190 12191Related Commands: 12192 POCH = Compute a generalization of Pochhammer's symbol. 12193 GAMMA = Compute the gamma function. 12194 LOGGAMMA = Compute the log (to base e) gamma function. 12195 GAMMAIP = Compute an alternate form of the incomplete gamma 12196 function. 12197 GAMMAIC = Compute the complementary incomplete Gamma function. 12198 GAMMAR = Compute the reciprocal gamma function. 12199 TRICOMI = Compute Tricomi's incomplete gamma function. 12200 DIGAMMA = Compute the digamma function. 12201 12202Reference: 12203 "Handbook of Mathematical Functions, Applied Mathematics Series, 12204 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 12205 1964 (chapter 6). 12206 12207 "The Special Functions and their Approximations, Volume 1", Luke, 12208 Academic Press, 34, (1969). 12209 12210Applications: 12211 Special Functions 12212 12213Implementation Date: 12214 94/9 12215 12216Program: 12217 TITLE AUTOMATIC 12218 PLOT POCH1(X,2.5) FOR X = 1 0.1 10 12219 12220-----POICDF (LET)-------------------------------- 12221 12222POICDF 12223 12224Name: 12225 POICDF (LET) 12226 12227Type: 12228 Library Function 12229 12230Purpose: 12231 Compute the Poisson cumulative distribution function. 12232 12233Description: 12234 The Poisson distribution is the distribution of the number of 12235 events in the interval (0,lambda) when the waiting time between 12236 events is exponentially distributed with mean 1 and standard 12237 deviation 1 (there are alternate interpretations as well). The 12238 Poisson distribution has the following probability density 12239 function: 12240 p(x,lambda) = exp(-lambda)*lambda**x/lambda! 12241 where x is a non-negative integer. The cumulative distribution is 12242 the probability of obtaining x or fewer events. It is the sum of 12243 the Poisson probabilities of 0 to x. The cumulative distribution 12244 is computed via a chi-square approximation. 12245 12246Syntax: 12247 LET <y2> = POICDF(<y1>,<lambda>) <SUBSET/EXCEPT/FOR qualification> 12248 where <y1> is a non-negative integer variable, number, or 12249 parameter (a warning message is printed if it is not); 12250 <y2> is a variable or a parameter (depending on what <y1> is) 12251 where the computed Poisson cdf value is stored; 12252 <lambda> is a number or parameter that specifies the shape 12253 parameter of the Poisson distribution; 12254 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 12255 12256Examples: 12257 LET A = POICDF(3,0.5) 12258 LET X2 = POICDF(X1,0.3) 12259 12260Note: 12261 Library functions are distinguished from let subcommands 12262 in the following ways. 12263 1) Functions enclose the input value in parenthesis. Let 12264 subcommands use spaces. 12265 2) Functions can accept (and return) either parameters 12266 (i.e., single values) or variables (i.e., an array of 12267 values) while let subcommands are specific in which they 12268 accept as input and what they return as output. 12269 3) Functions can accept expressions while let subcommands 12270 do not. For example, the following is legal: 12271 LET Y2 = ABS(Y1-INT(Y1)) 12272 For let subcommands, you typically have to do something 12273 like the following: 12274 LET YTEMP = Y**2 + 8 12275 LET A = SUM YTEMP 12276 12277Default: 12278 None 12279 12280Synonyms: 12281 None 12282 12283Related Commands: 12284 POIPDF = Compute the Poisson probability density function. 12285 POIPPF = Compute the Poisson percent point function. 12286 BINCDF = Compute the binomial cumulative distribution function. 12287 BINPDF = Compute the binomial probability density function. 12288 BINPPF = Compute the binomial percent point function. 12289 NBCDF = Compute the negative binomial cumulative distribution 12290 function. 12291 NBPDF = Compute the negative binomial probability density 12292 function. 12293 NBPPF = Compute the negative binomial percent point function. 12294 GEOCDF = Compute the geometric cumulative distribution function. 12295 GEOPDF = Compute the geometric probability density function. 12296 GEOPPF = Compute the geometric percent point function. 12297 12298Reference: 12299 "Discrete Univariate Distributions", Johnson and Kotz, Houghton 12300 Mifflin, 1970 (chapter 4). 12301 12302Applications: 12303 XX 12304 12305Implementation Date: 12306 94/4 12307 12308Program: 12309 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 12310 YLIMITS 0 1 12311 MAJOR YTIC NUMBER 6 12312 MINOR YTIC NUMBER 1 12313 YTIC DECIMAL 1 12314 XLIMITS 0 50 12315 XTIC OFFSET 0.5 0.5 12316 LINE BLANK 12317 SPIKE ON 12318 SPIKE LINE DASH 12319 CHARACTER CIRCLE 12320 CHARACTER FILL ON 12321 CHARACTER SIZE 1.2 12322 TITLE AUTOMATIC 12323 X1LABEL NUMBER OF SUCCESSES 12324 Y1LABEL PROBABILITY 12325 TITLE AUTOMATIC; TITLE SIZE 3 12326 PLOT POICDF(X,5) FOR X = 0 1 50 12327 PLOT POICDF(X,15) FOR X = 0 1 50 12328 PLOT POICDF(X,25) FOR X = 0 1 50 12329 PLOT POICDF(X,35) FOR X = 0 1 50 12330 END OF MULTIPLOT 12331 12332-----POINTS IN POLYGON-------------------------------------------------- 12333 12334POINTS IN POLYGON 12335 12336Name: 12337 POINTS IN POLYGON 12338 12339Type: 12340 LET Subcommand 12341 12342Purpose: 12343 Given a polygon and a set of points, determine if each of these 12344 points are interior points, exterior points, edge points, or 12345 equal to a vertex. 12346 12347Description: 12348 A basic problem in computational geometry is to determine if a 12349 point is inside or outside of a polygon. In a Dataplot context, 12350 the most common application for this basic problem is to determine 12351 whether a point should be plotted or not plotted. 12352 12353 Given a set of one or more points, this command returns a tag 12354 value (where each row of the tag variable corresponds to the 12355 row of the variables containing the x and y coordinates of the 12356 points being tested). Each value of the tag variable will contain 12357 either a 1, 2, 3, or 4 where 12358 12359 1 = interior point 12360 2 = exterior point 12361 3 = edge point 12362 4 = vertex point 12363 12364Syntax: 12365 LET <tag> = POINTS IN POLYGON <xval> <yval> <xpoly> <ypoly> 12366 <SUBSET/EXPCEPT/FOR qualification> 12367 where <xval> is a variable containing the x-coordinates of 12368 the data points being checked; 12369 <yval> is a variable containing the y-coordinates of 12370 the data points being checked; 12371 <xpoly> is a variable that will contain the x-coordinats 12372 of the polygon; 12373 <ypoly> is a variable that will contain the y-coordinats 12374 of the polygon; 12375 <tag> is a variable (of the same size as <xval> and <yval>) 12376 that specifies whether each point is an interior, 12377 exterior, edge, or vertex point; 12378 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 12379 12380Examples: 12381 LET TAG = POINTS IN POLYGON XVAL YVAL XPOLY YPOLY 12382 12383Note: 12384 Dataplot uses a Fortran translation of the C routine "InPoly1" 12385 algorithm given on page 244 of O'Rourke (see Reference section 12386 below). 12387 12388 This algorithm is based on counting the number of ray tracings. 12389 A complete description of the algorithm is given on pages 12390 239-245 of O'Rourke's book. 12391 12392 This algorithm works for both convex and non-convex polygons. 12393 12394Note: 12395 The points in the polygon are assumed to be sorted (i.e., 12396 contiguous rows define an edge). No check is made that these 12397 points in fact define a valid polygon. 12398 12399 The <xval> and <yval> points do not need to be in any specific 12400 order since they are tested independently of each other. 12401 12402Note: 12403 In deterining if a point is equal to a vertex point, Dataplot 12404 checks that the x-coordinate and the y-coordinate are within 12405 epsilon of each vertex where epsilon is set equal to 0.0000001. 12406 12407Default: 12408 None 12409 12410Synonyms: 12411 None 12412 12413Related Commands: 12414 CONVEX HULL = Compute the convex hull of a set of 12415 points. 12416 MINIMAL SPANNING TREE = Determine the minimal spanning tree. 12417 SPAINNING FOREST = Determine the spanning forest. 12418 12419References: 12420 O'Rourke (1998), "Computational Geometry in C", Second Edition, 12421 Cambridge Unversity Press, Chapter 7. 12422 12423Applications: 12424 Computational Geometry 12425 12426Implementation Date: 12427 2011/9 12428 12429Program: 12430 . Name: poly.dp 12431 . Purpose: Demonstrate "points in polygon" routine 12432 . Source: Data from O'Rourke (1998), "Computational Geometry in 12433 . C", Second Edition. 12434 . 12435 . Step 1: Read data 12436 . 12437 read xpoly ypoly 12438 0 0 12439 2 0 12440 2 2 12441 3 1 12442 4 2 12443 5 2 12444 3 3 12445 3 2 12446 2 4 12447 6 3 12448 7 4 12449 7 2 12450 8 5 12451 8 7 12452 7 7 12453 8 8 12454 5 9 12455 6 6 12456 5 7 12457 4 6 12458 4 8 12459 3 7 12460 2 7 12461 3 6 12462 4 4 12463 0 7 12464 2 3 12465 0 2 12466 end of data 12467 . 12468 read xval yval 12469 0 0 12470 1 0 12471 2 1 12472 1 2 12473 0 2 12474 6 2 12475 2 4 12476 5 4 12477 1 5 12478 3 5 12479 6 5 12480 7 6 12481 8 6 12482 1 7 12483 2 7 12484 3 7 12485 4 7 12486 4 8 12487 5 9 12488 end of data 12489 . 12490 . Step 2: Plot data 12491 . 12492 tic mark offset units screen 12493 tic mark offset 5 5 12494 pre-sort off 12495 line blank solid 12496 character circ blank 12497 character hw 0.5 0.375 12498 character fill on 12499 plot yval xval and 12500 plot ypoly xpoly 12501 set isubro popl 12502 cpu time 12503 let t1 = cputime 12504 let tag = point in polygon xval yval xpoly ypoly 12505 pause 12506 . 12507 line bl bl bl bl solid 12508 character circ circ circ circ blank 12509 character hw 0.5 0.375 all 12510 character fill on all 12511 char color blue red green cyan black 12512 plot yval xval subset tag = 1 and 12513 plot yval xval subset tag = 2 and 12514 plot yval xval subset tag = 3 and 12515 plot yval xval subset tag = 4 and 12516 plot ypoly xpoly 12517 12518-----POINT------------------------------------------------------- 12519 12520POINT 12521 12522Name: 12523 POINT 12524 12525Type: 12526 Diagrammatic Graphics Command 12527 12528Purpose: 12529 Draws a point at a position. 12530 12531Description: 12532 The coordinates define the (x,y) value of the position. 12533 12534Syntax: 12535 POINT <x> <y> 12536 where <x> is a decimal number or parameter in the range 0 to 100 12537 that specifies the horizontal coordinate; 12538 and <y> is a decimal number or parameter in the range 0 to 100 12539 that specifies the vertical coordinate. 12540 12541Examples: 12542 POINT 50 50 12543 POINT 20 80 12544 POINT 70 65.3 12545 12546Note: 12547 The keywords DATA and RELATIVE were added to the TRIANGLE 12548 command 7/1997. These keywords are independent and can 12549 be used separately or together. For example, 12550 TRIANGLE DATA, TRIANGLE RELATIVE, or TRIANGLE DATA RELATIVE. 12551 The word DATA should come before the word RELATIVE if both 12552 appear. 12553 12554 DATA means that the coordinates are specified in terms of 12555 the data units of the most recent plot rather than Dataplot 12556 0 to 100 screen units. 12557 12558 RELATIVE means that the coordinates of the first point 12559 are drawn in absolute coordinates an all subsequent points 12560 in the figure are relative to that first point. 12561 12562Default: 12563 None 12564 12565Synonyms: 12566 None 12567 12568Related Commands: 12569 CIRCLE = Draws a circle. 12570 ARROW = Draws an arrow. 12571 TRIANGLE = Draws a triangle. 12572 BOX = Draws a box. 12573 HEXAGON = Draws a hexagon. 12574 SEMI-CIRCLE = Draws a semi-circle. 12575 ARC = Draws an arc. 12576 ELLIPSE = Draws an ellipse. 12577 OVAL = Draws an oval. 12578 DIAMOND = Draws a diamond. 12579 DRAW = Draws a line. 12580 MOVE = Moves to a point. 12581 LINES = Sets the line type for figures and plot lines. 12582 LINE THICKNESSES = Sets the line thickness for figures and plot 12583 lines. 12584 LINE COLOR = Sets the line colors for figures and plot lines. 12585 CROSS-HAIR = Activates and reads the cross-hair. 12586 TEXT = Writes a text string. 12587 12588Applications: 12589 Presentation Graphics 12590 12591Implementation Date: 12592 Pre-1987 12593 12594Program: 12595 XX 12596 12597-----POIPDF (LET)-------------------------------- 12598 12599POIPDF 12600 12601Name: 12602 POIPDF (LET) 12603 12604Type: 12605 Library Function 12606 12607Purpose: 12608 Compute the Poisson probability density function. 12609 12610Description: 12611 The Poisson distribution is the distribution of the number of 12612 events in the interval (0,lambda) when the waiting time between 12613 events is exponentially distributed with mean 1 and standard 12614 deviation 1 (there are alternate interpretations as well). The 12615 Poisson distribution has the following probability mass 12616 function: 12617 12618 p(x,lambda) = exp(-lambda)*lambda**x/lambda! 12619 x = 0, 1, 2, ... 12620 12621 with lambda denoting the shape parameter. 12622 12623Syntax: 12624 LET <y> = POIPDF(<x>,<lambda>) <SUBSET/EXCEPT/FOR qualification> 12625 where <x> is a non-negative integer variable, number, or 12626 parameter; 12627 <lambda> is a number or parameter that specifies the shape 12628 parameter of the Poisson distribution; 12629 <y> is a variable or a parameter (depending on what <x> 12630 is) where the computed Poisson pdf value is stored; 12631 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 12632 12633Examples: 12634 LET A = POIPDF(3,0.5) 12635 LET X2 = POIPDF(X1,0.3) 12636 12637Note: 12638 For a number of commands utilizing the Poisson distribution, 12639 it is convenient to bin the data. There are two basic ways 12640 of binning the data. 12641 12642 1) For some commands (histograms, maximum likelihood 12643 estimation), bins with equal size widths are 12644 required. This can be accomplished with the 12645 following commands: 12646 12647 LET AMIN = MINIMUM Y 12648 LET AMAX = MAXIMUM Y 12649 LET AMIN2 = AMIN - 0.5 12650 LET AMAX2 = AMAX + 0.5 12651 CLASS MINIMUM AMIN2 12652 CLASS MAXIMUM AMAX2 12653 CLASS WIDTH 1 12654 LET Y2 X2 = BINNED 12655 12656 2) For some commands, unequal width bins may be 12657 helpful. In particular, for the chi-square goodness 12658 of fit, it is typically recommended that the minimum 12659 class frequency be at least 5. In this case, it may 12660 be helpful to combine small frequencies in the tails. 12661 Unequal class width bins can be created with the 12662 commands 12663 12664 LET MINSIZE = <value> 12665 LET Y3 XLOW XHIGH = INTEGER FREQUENCY TABLE Y 12666 12667 If you already have equal width bins data, you can 12668 use the commands 12669 12670 LET MINSIZE = <value> 12671 LET Y3 XLOW XHIGH = COMBINE FREQUENCY TABLE Y2 X2 12672 12673 The MINSIZE parameter defines the minimum class 12674 frequency. The default value is 5. 12675 12676Note: 12677 You can generate Poisson random numbers, probability 12678 plots, and chi-square goodness of fit tests with the 12679 following commands: 12680 12681 LET LAMBDA = <value> 12682 LET Y = POISSON RANDOM NUMBERS FOR I = 1 1 N 12683 12684 POISSON PROBABILITY PLOT Y 12685 POISSON PROBABILITY PLOT Y2 X2 12686 POISSON PROBABILITY PLOT Y3 XLOW XHIGH 12687 12688 POISSON CHI-SQUARE GOODNESS OF FIT Y 12689 POISSON CHI-SQUARE GOODNESS OF FIT Y2 X2 12690 POISSON CHI-SQUARE GOODNESS OF FIT Y3 XLOW XHIGH 12691 12692 To obtain the maximum likelihood estimates of lambda, 12693 enter the command 12694 12695 POISSON MAXIMUM LIKELIHOOD Y 12696 12697 The formula for the maximum likelihood estimate of 12698 lambda is: 12699 12700 lambdahat = xbar 12701 12702 with xbar denoting the sample mean. 12703 12704 You can generate the estimate of lambda based on the 12705 maximum ppcc value or the minimum chi-square goodness of 12706 fit with the commands 12707 12708 LET LAMBDA1 = <value> 12709 LET LAMBDA2 = <value> 12710 POISSON KS PLOT Y 12711 POISSON KS PLOT Y2 X2 12712 POISSON KS PLOT Y3 XLOW XHIGH 12713 POISSON PPCC PLOT Y 12714 POISSON PPCC PLOT Y2 X2 12715 POISSON PPCC PLOT Y3 XLOW XHIGH 12716 12717 The default values of lambda1 and lambda2 are 1 and 50, 12718 respectively. Due to the discrete nature of the percent 12719 point function for discrete distributions, the ppcc plot 12720 will not be smooth. For that reason, if there is sufficient 12721 sample size the KS PLOT (i.e., the minimum chi-square value) 12722 is typically preferred. However, it may sometimes be useful 12723 to perform one iteration of the PPCC PLOT to obtain a rough 12724 idea of an appropriate neighborhood for the shape parameter 12725 since the minimum chi-square statistic can generate extremely 12726 large values for non-optimal values of the shape parameters. 12727 Also, since the data is integer values, one of the binned 12728 forms is preferred for these commands. 12729 12730Note: 12731 Library functions are distinguished from let subcommands 12732 in the following ways. 12733 1) Functions enclose the input value in parenthesis. Let 12734 subcommands use spaces. 12735 2) Functions can accept (and return) either parameters 12736 (i.e., single values) or variables (i.e., an array of 12737 values) while let subcommands are specific in which they 12738 accept as input and what they return as output. 12739 3) Functions can accept expressions while let subcommands 12740 do not. For example, the following is legal: 12741 LET Y2 = ABS(Y1-INT(Y1)) 12742 For let subcommands, you typically have to do something 12743 like the following: 12744 LET YTEMP = Y**2 + 8 12745 LET A = SUM YTEMP 12746 12747Default: 12748 None 12749 12750Synonyms: 12751 None 12752 12753Related Commands: 12754 POICDF = Compute the Poisson cumulative distribution function. 12755 POIPPF = Compute the Poisson percent point function. 12756 BINCDF = Compute the binomial cumulative distribution function. 12757 BINPDF = Compute the binomial probability mass function. 12758 BINPPF = Compute the binomial percent point function. 12759 NBCDF = Compute the negative binomial cumulative distribution 12760 function. 12761 NBPDF = Compute the negative binomial probability mass 12762 function. 12763 NBPPF = Compute the negative binomial percent point function. 12764 GEOCDF = Compute the geometric cumulative distribution function. 12765 GEOPDF = Compute the geometric probability mass function. 12766 GEOPPF = Compute the geometric percent point function. 12767 12768Reference: 12769 Johnson, Kotz, and Kemp (1992), "Univariate Discrete 12770 Distributions", Second Edition, Wiley, chapter 4. 12771 12772 Evans, Hastings, and Peacock (2000), "Statistical 12773 Distributions", Third Edition, Wiley, pp. 155-160. 12774 12775Applications: 12776 Distributional Modeling 12777 12778Implementation Date: 12779 1994/4 12780 12781Program: 12782 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 12783 YLIMITS 0 0.2 12784 XLIMITS 0 50 12785 XTIC OFFSET 0.5 0.5 12786 LINE BLANK 12787 SPIKE ON 12788 SPIKE LINE DASH 12789 CHARACTER CIRCLE 12790 CHARACTER FILL ON 12791 CHARACTER SIZE 1.2 12792 TITLE AUTOMATIC 12793 X1LABEL NUMBER OF SUCCESSES 12794 Y1LABEL PROBABILITY 12795 TITLE AUTOMATIC; TITLE SIZE 3 12796 PLOT POIPDF(X,5) FOR X = 0 1 50 12797 PLOT POIPDF(X,15) FOR X = 0 1 50 12798 PLOT POIPDF(X,25) FOR X = 0 1 50 12799 PLOT POIPDF(X,35) FOR X = 0 1 50 12800 END OF MULTIPLOT 12801 12802-----POIPPF (LET)-------------------------------- 12803 12804POIPPF 12805 12806Name: 12807 POIPPF (LET) 12808 12809Type: 12810 Library Function 12811 12812Purpose: 12813 Compute the Poisson percent point function. 12814 12815Description: 12816 The Poisson distribution is the distribution of the number of 12817 events in the interval (0,lambda) when the waiting time between 12818 events is exponentially distributed with mean 1 and standard 12819 deviation 1 (there are alternate interpretations as well). The 12820 Poisson distribution has the following probability density 12821 function: 12822 p(x,lambda) = exp(-lambda)*lambda**x/lambda! 12823 where x is a non-negative integer. 12824 12825 The percent point function is the inverse of the cumulative 12826 distribution function. The cumulative distribution sums the 12827 probability from 0 to the given x value. The percent point 12828 function takes a cumulative probability value and computes the 12829 corresponding x value. The Poisson percent point function is 12830 computed using a normal approximation. 12831 12832 The input value is a real number between 0 and 1 (since it 12833 corresponds to a probability). 12834 12835Syntax: 12836 LET <y2> = POIPPF(<y1>,<lambda>) <SUBSET/EXCEPT/FOR qualification> 12837 where <y1> is a variable, a number, or a parameter in the range 0 12838 to 1; 12839 <y2> is a variable or a parameter (depending on what <y1> is) 12840 where the computed Poisson ppf value is stored; 12841 <lambda> is a number or parameter that specifies the shape 12842 parameter of the Poisson distribution; 12843 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 12844 12845Examples: 12846 LET A = POIPPF(0.9,5) 12847 LET X2 = POIPPF(X1,0.7) 12848 12849Note: 12850 Library functions are distinguished from let subcommands 12851 in the following ways. 12852 1) Functions enclose the input value in parenthesis. Let 12853 subcommands use spaces. 12854 2) Functions can accept (and return) either parameters 12855 (i.e., single values) or variables (i.e., an array of 12856 values) while let subcommands are specific in which they 12857 accept as input and what they return as output. 12858 3) Functions can accept expressions while let subcommands 12859 do not. For example, the following is legal: 12860 LET Y2 = ABS(Y1-INT(Y1)) 12861 For let subcommands, you typically have to do something 12862 like the following: 12863 LET YTEMP = Y**2 + 8 12864 LET A = SUM YTEMP 12865 12866Default: 12867 None 12868 12869Synonyms: 12870 None 12871 12872Related Commands: 12873 POICDF = Compute the Poisson cumulative distribution function. 12874 POIPDF = Compute the Poisson probability density function. 12875 BINCDF = Compute the binomial cumulative distribution function. 12876 BINPDF = Compute the binomial probability density function. 12877 BINPPF = Compute the binomial percent point function. 12878 NBCDF = Compute the negative binomial cumulative distribution 12879 function. 12880 NBPDF = Compute the negative binomial probability density 12881 function. 12882 NBPPF = Compute the negative binomial percent point function. 12883 GEOCDF = Compute the geometric cumulative distribution function. 12884 GEOPDF = Compute the geometric probability density function. 12885 GEOPPF = Compute the geometric percent point function. 12886 12887Reference: 12888 "Discrete Univariate Distributions", Johnson and Kotz, Houghton 12889 Mifflin, 1970 (chapter 4). 12890 12891Applications: 12892 Pre-1987 12893 12894Implementation Date: 12895 1994/4 12896 12897Program: 12898 MULTIPLOT 2 2 12899 MULTIPLOT CORNER COORDINATES 0 0 100 100 12900 YLIMITS 0 50 12901 XLIMITS 0 1 12902 MAJOR XTIC NUMBER 6 12903 MINOR XTIC NUMBER 1 12904 XTIC DECIMAL 1 12905 TITLE AUTOMATIC 12906 X1LABEL PROBABILITY 12907 Y1LABEL NUMBER OF SUCCESSES 12908 PLOT POIPPF(X,5) FOR X = 0.01 0.01 0.99 12909 PLOT POIPPF(X,15) FOR X = 0.01 0.01 0.99 12910 PLOT POIPPF(X,25) FOR X = 0.01 0.01 0.99 12911 PLOT POIPPF(X,35) FOR X = 0.01 0.01 0.99 12912 END OF MULTIPLOT 12913 12914-----POISSON DISPERSION TEST------------------------------------ 12915 12916POISSON DISPERSION TEST 12917 12918Name: 12919 POISSON DISPERSION TEST 12920 12921Type: 12922 Analysis Command 12923 12924Purpose: 12925 Perform a Poisson dispersion test for Poissonality. 12926 12927Description: 12928 The Poisson dispersion test is one of the most common tests to 12929 determine if a univariate data set follows a Poisson distribution. 12930 12931 The Poisson dispersion test statistic is defined as: 12932 12933 D = SUM[i=1 to N][(X(i) - XBAR)**2/XBAR] 12934 12935 with XBAR and N denoting the sample mean and the sample size, 12936 respectively. 12937 12938 Note that this test can be applied to either raw (ungrouped) data 12939 or to frequency (grouped) data. 12940 12941 This test follows an approximately chi-square distribution with 12942 N - 1 degrees of freedom. This is a two-tailed test. 12943 12944Syntax 1: 12945 POISSON DISPERSION TEST <y> <SUBSET/EXCEPT/FOR qualification> 12946 where <y> is the response variable; 12947 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 12948 12949 This syntax is used for the raw (ungrouped) data case. 12950 12951Syntax 2: 12952 POISSON DISPERSION TEST <y> <x> <SUBSET/EXCEPT/FOR qualification> 12953 where <y> is the variable containing the frequencies; 12954 <x> is the variable containing the class mid-points; 12955 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 12956 12957 This syntax is used for the grouped data case. 12958 12959Syntax 3: 12960 MULTIPLE POISSON DISPERSION TEST <y1> ... <yk> 12961 <SUBSET/EXCEPT/FOR qualification> 12962 where <y1> ... <yk> is a list of 1 to 30 response variables; 12963 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 12964 12965 This syntax performs a Poisson dispersion test on <y1>, then 12966 on <y2>, and so on. Up to 30 response variables may be specified. 12967 12968 Note that the syntax 12969 12970 MULTIPLE POISSON DISPERSION TEST Y1 TO Y4 12971 12972 is supported. This is equivalent to 12973 12974 MULTIPLE POISSON DISPERSION TEST Y1 Y2 Y3 Y4 12975 12976Syntax 4: 12977 REPLICATED POISSON DISPERSION TEST <y> <x1> ... <xk> 12978 <SUBSET/EXCEPT/FOR qualification> 12979 where <y> is the response variable; 12980 <x1> ... <xk> is a list of 1 to 6 group-id variables; 12981 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 12982 12983 This syntax peforms a cross-tabulation of <x1> ... <xk> and performs a 12984 Poisson dispersion test for each unique combination of cross-tabulated 12985 values. For example, if X1 has 3 levels and X2 has 2 levels, there 12986 will be a total of 6 Poisson dispersion tests performed. 12987 12988 Up to six group-id variables can be specified. 12989 12990 Note that the syntax 12991 12992 REPLICATED POISSON DISPERSION TEST Y X1 TO X4 12993 12994 is supported. This is equivalent to 12995 12996 REPLICATED POISSON DISPERSION TEST Y X1 X2 X3 X4 12997 12998Examples: 12999 POISSON DISPERSION TEST Y1 13000 POISSON DISPERSION TEST Y1 SUBSET TAG > 2 13001 MULTIPLE POISSON DISPERSION TEST Y1 TO Y10 13002 REPLICATED POISSON DISPERSION TEST Y X 13003 13004Note: 13005 Syntax 1 and Syntax 3 support matrix arguments. Syntax 3 and 13006 Syntax 4 support the TO syntax. 13007 13008 For Syntax 4 (the REPLICATED form), the variables must all have the 13009 same number of observations. 13010 13011Note: 13012 The following statistics are also supported: 13013 13014 LET A = POISSON DISPERSION TEST Y 13015 LET A = POISSON DISPERSION TEST CDF Y 13016 LET A = POISSON DISPERSION TEST PVALUE Y 13017 13018 LET A = GROUPED POISSON DISPERSION TEST Y X 13019 LET A = GROUPED POISSON DISPERSION TEST CDF Y X 13020 LET A = GROUPED POISSON DISPERSION TEST PVALUE Y X 13021 13022 In addition to the above LET command, built-in statistics are 13023 supported for about 17 different commands (enter HELP STATISTICS 13024 for details). 13025 13026Note: 13027 The POISSON DISPERSION TEST command automatically saves the following 13028 internal parameters: 13029 13030 STATVAL = the value of the test statistic 13031 STATCDF = the CDF of the test statistic 13032 PVALUE = the p-value for the two-sided test 13033 CUTLOW50 = the 50% lower tailed critical value 13034 CUTUPP50 = the 50% upper tailed critical value 13035 CUTLOW80 = the 80% lower tailed critical value 13036 CUTUPP80 = the 80% upper tailed critical value 13037 CUTLOW90 = the 90% lower tailed critical value 13038 CUTUPP90 = the 90% upper tailed critical value 13039 CUTLOW95 = the 95% lower tailed critical value 13040 CUTUPP95 = the 95% upper tailed critical value 13041 CUTLOW99 = the 99% lower tailed critical value 13042 CUTUPP99 = the 99% upper tailed critical value 13043 CUTLO999 = the 99.9% lower tailed critical value 13044 CUTUP999 = the 99.9% upper tailed critical value 13045 13046 If the MULTIPLE or REPLICATED option is used, these values will 13047 be written to the file "dpst1f.dat" instead. 13048 13049Default: 13050 None 13051 13052Synonyms: 13053 None 13054 13055Related Commands: 13056 POISSON PLOT = Generate a Poisson plot. 13057 GOODNESS OF FIT = Perform Anderson-Darling, Kolmogorov-Smirnov, 13058 Chi-Square, and PPCC goodness of fit tests. 13059 POIPDF = Compute the Poisson probability mass function. 13060 13061Reference: 13062 Spinelli and Stephens (1997), "Cramer-Von Mises Tests of Fit for the 13063 Poisson Distribution", Canadian Journal of Statistics, Vol. 25(2), 13064 pp. 257-267. 13065 13066 Kendell and Stuart (1979), "The Advanced Theory of Statistics: Volume 2", 13067 Fourth Edition, Griffin, London. 13068 13069Applications: 13070 Distributional Fitting 13071 13072Implementation Date: 13073 2013/11 13074 13075Program 1: 13076 LET LAMBDA = 25 13077 LET Y = POISSON RANDOM NUMBERS FOR I = 1 1 1000 13078 SET WRITE DECIMALS 4 13079 POISSON DISPERSION TEST Y 13080 13081Program 2: 13082 . Step 1: Read the data 13083 . 13084 . This data set is from: 13085 . 13086 . Spinelli and Stephens (1997), "Cramer-Von Mises Tests of Fit 13087 . for the Poisson Distribution", Canadian Journal of Statistics, 13088 . Vol. 25(2). 13089 . 13090 . Hoaglin (1980), "A Poissonness Plot", The American Statistician, 13091 . 34, pp. 146-149. 13092 . 13093 . Note that there is an error in one of the entries in the Spinelli 13094 . and Stephens (for cell 2, they give a value of 283 rather than the 13095 . value of 383, their computed statistics are consistent with using 13096 . the value 383). 13097 . 13098 read x2 y2 13099 0 57 13100 1 203 13101 2 383 13102 3 525 13103 4 532 13104 5 408 13105 6 273 13106 7 139 13107 8 45 13108 9 27 13109 10 10 13110 11 4 13111 12 0 13112 13 1 13113 14 1 13114 end of data 13115 . 13116 . Step 2: Perform the Poisson Dispersion test. 13117 . 13118 set write decimals 4 13119 poisson dispersion test y2 x2 13120 13121-----POISSON PLOT-------------------------------------- 13122 13123POISSON PLOT 13124 13125Name: 13126 POISSON PLOT 13127 13128Type: 13129 Graphics Command 13130 13131Purpose: 13132 Generates one of the following types of plots: 13133 13134 1) a Poisson plot 13135 2) a geometric plot 13136 3) a negative binomial plot 13137 4) a binomial plot 13138 5) a logarithmic series plot 13139 13140Description: 13141 These plots are used to determine if the specified 13142 distribution provides an appropriate distributiuonal 13143 model to a set of data. These are similar in concept 13144 to probability plots in that we generate a plot that 13145 should appear linear if the data are in fact fit well 13146 by the distribution. 13147 13148 The following table shows how these plots are constructed 13149 where x and n(x) denote the class value and the corresponding 13150 frequency. In all cases, the x-coordinate is x. 13151 13152 phi(n*(x)) 13153 Y-Axis Theoretical Theoretical 13154 Distribution Coordinate Slope Intercept 13155 ============================================================== 13156 Poisson LOG(x!*n*(x)/N) LOG(lambda) -lambda 13157 Geometric LOG(n*(x)/N) LOG(1-p) LOG(p) 13158 Negative Binomial LOG(n*(x)/ LOG(1-p) n*LOG(p) 13159 {N*(n+x-1 x)} 13160 Binomial LOG(n*(x)/ LOG(p/(1-p)) n*LOG(1-p) 13161 {N*(n+x x)} 13162 Logarithmic Series LOG(x*n*(x)/N) LOG(theta) -LOG(-LOG(1-theta)) 13163 13164 where 13165 p = probability of success parameter for the 13166 geometric, binomial, and negative binomial 13167 distributions. 13168 theta = the shape parameter for the logarithmic series 13169 distribution. 13170 n = the number of trials parameter for the binomial 13171 distribution. 13172 x = class value 13173 n*(x) = adjusted class frequency (defined below) 13174 13175 The theoretical slope parameter can be used to estimate 13176 the shape parameter of the distribution. 13177 13178 Hoaglin and Tukey (see References below) provides the 13179 derivations of why these plots should be linear if the specified 13180 distribution is appropriate. They also make the following 13181 suggestions for enhancing these plots: 13182 13183 1) A 95% confidence interval for each point on the plot 13184 is given as 13185 13186 phi(n*(x)) +/- h(x) 13187 13188 where 13189 13190 n*(x) = n(x) - 0.8*n(x)/N - 0.67 n(x) >= 2 13191 = 1/e n(x) = 1 13192 = undefined n(x) = 0 13193 13194 h(x) = 1.96*SQRT(1 - phat(x))/ 13195 SQRT{n(x) - (0.25*phat(x) +0.47)*SQRT(n(x))} 13196 13197 N = total sample size 13198 13199 phat(x) = n(k)/N 13200 13201 The rationale for this confidence interval is given in 13202 the Hoaglin and Tukey reference. 13203 13204 The n*(x) values are referred to as the adjusted 13205 frequencies. 13206 13207 2) These plots can be "leveled". By leveling, we convert 13208 the plot from interpretation of departures from a 13209 diagonal line to departures from a horizontal line. 13210 This may be an easier visual task. 13211 13212 To level the plot, we plot 13213 13214 phi'(n(x)) = phi(n(x)) - (intercept + slope*x) 13215 13216 where intercept and slope are taken from the columns 13217 "theoretical intercept" and "theoretical slope" in the 13218 table above. 13219 13220 Note that a preliminary estimate of the shape parameter 13221 for the distribution is required to compute the 13222 theoretical intercept and the theoretical slope. 13223 This is discussed further in a Note section below. 13224 13225Syntax 1: 13226 <dist> PLOT <y> <SUBSET/EXCEPT/FOR qualification> 13227 where <y> is a response variable; 13228 <dist> is one of the following: 13229 POISSON 13230 GEOMETRIC 13231 NEGATIVE BINOMIAL 13232 BINOMIAL 13233 LOGARITHMIC SERIES; 13234 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 13235 13236 This syntax is used for the case where you have raw data. 13237 Dataplot will automatically create the frequency table. 13238 13239Syntax 2: 13240 <dist> PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 13241 where <y> is a variable containing frequencies; 13242 <x> is a variable containing the class value; 13243 <dist> is one of the distributions listed above: 13244 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 13245 13246Examples: 13247 POISSON PLOT Y 13248 POISSON PLOT Y X 13249 GEOMETRIC PLOT Y 13250 GEOMETRIC PLOT Y X 13251 13252Note: 13253 For the leveled version of the plot, a preliminary estimate 13254 of the shape parameter(s) is required. 13255 13256 1) For the Poisson distribution, the maximum likelihood 13257 estimate of lambda is the sample mean. This is used 13258 as the prelimanary estimate of lambda in the leveled 13259 version of the plot. 13260 13261 2) For the binomial distribution, you need to specify 13262 the n parameter (the number of trials) by entering 13263 the following command before the BINOMIAL PLOT 13264 command: 13265 13266 LET N = <value> 13267 13268 The sample mean is then used as the estimate of the 13269 p (probability of success) parameter. This is the 13270 maximum likelihood estimate. 13271 13272 3) For the geometric distribution, the maximum likelihood 13273 estimate of the p (probability of success) parameter is 13274 13275 1/(xbar + 1) 13276 13277 where xbar is the sample mean. 13278 13279 4) For the negative binomial distribution, there are two 13280 parameters: p and k. For this plot, k is restricted to 13281 integer values. 13282 13283 You can either specify a value for k by entering 13284 the command 13285 13286 LET K = <value> 13287 13288 or you can let Dataplot estimate the value. 13289 13290 If k is not specified, the moment estimate of k is 13291 used: 13292 13293 kmom = xbar**2/(s**2 - xbar) 13294 13295 This estimate will be rounded to the nearest integer. 13296 13297 The maximum likelihood estimate of p is then 13298 13299 phat = k/(xbar + k) 13300 13301 If k >= 2, then the bias corrected estimate is used 13302 13303 phat = (k - 1)/(xbar + k - 1) 13304 13305 5) For the logarithmic series distribution, you can 13306 specify the desired value of theta by entering the 13307 command 13308 13309 LET THETA = <value> 13310 13311 You can obtain this estimate either by using 13312 maximum likelihood, the PPCC plot, or the KS plot. 13313 13314Note: 13315 The appearance of the plot can be controlled with 13316 the LINE and CHARACTER commands. Specifically, 13317 13318 trace 1 = phi(n(x)) versus x 13319 trace 2 = fitted line for phi(n(x)) versus x 13320 trace 3 = phi(n*(x)) versus x 13321 trace 4 = fitted line for phi(n*(x)) versus x 13322 trace 5 = lower confidence point 13323 trace 6 = upper confidence point 13324 trace 7 and above = line connecting the lower and upper 13325 confidence points 13326 13327 If you want to suppress any of these components, you can 13328 set both the CHARACTER and LINE settings to BLANK. The 13329 example programs below demonstrate the use of the LINE 13330 and CHARACTER commands to control the appearance of the plot. 13331 13332Note: 13333 By default, the unleveled plot is generated. To generate 13334 the leveled plot, enter the command 13335 13336 SET POISSON PLOT LEVEL ON 13337 13338 To reset the default, enter the command 13339 13340 SET POISSON PLOT LEVEL OFF 13341 13342 This command applies to all five of the plots described here, 13343 not just the Poisson plot. 13344 13345Note: 13346 The following internal parameters are saved by this plot: 13347 13348 All plots: 13349 PPA0 - the intercept of the fitted line (unadjusted 13350 frequencies) 13351 PPA1 - the slope of the fitted line (unadjusted 13352 frequencies) 13353 PPA0ADJU - the intercept of the fitted line (adjusted 13354 frequencies) 13355 PPA1 - the slope of the fitted line (adjusted 13356 frequencies) 13357 13358 Poisson plot: 13359 LAMBDAPP - the estimate of lambda based on the 13360 unadjusted frequencies 13361 LAMBDAPA - the estimate of lambda based on the 13362 adjusted frequencies 13363 13364 Binomial, negative binomial, geometric plot: 13365 PPP - the estimate of p based on the unadjusted 13366 frequencies 13367 PPPADJ - the estimate of p based on the adjusted 13368 frequencies 13369 13370 Logarithmic series plot: 13371 THETAPP - the estimate of theta based on the 13372 unadjusted frequencies 13373 THETAPPA - the estimate of theta based on the 13374 adjusted frequencies 13375 13376Default: 13377 The unleveled version of the plot is generated by default. 13378 13379Synonyms: 13380 None 13381 13382Related Commands: 13383 PROBABILITY PLOT = Generates a probability plot. 13384 PPCC PLOT = Generates a ppcc plot. 13385 KS PLOT = Generates a Kolmogorov-Smirnov (or 13386 chi-square) plot. 13387 ORD PLOT = Generate an Ord plot. 13388 HISTOGRAM = Generates a histogram. 13389 LINES = Sets the type for plot lines. 13390 CHARACTER = Sets the type for plot characters. 13391 13392References: 13393 Hoaglin (1980), "A Poissonness Plot", The American Statistician, 13394 34, pp. 146-149. 13395 13396 Hoaglin and Tukey (1985), "Checking The Shape of Discrete 13397 Distributions". In Hoaglin, Mosteller, and Tukey, editors, 13398 "Exploring Data Tables, Trends, and Shapes", chapter 9, 13399 John Wiley and Sons, New York. 13400 13401 Friendly (2000), "Visualizing Categorical Data", SAS Publishing, 13402 Cary, NC, pp. 49-56. 13403 13404Applications: 13405 Distributional Modeling 13406 13407Implementation Date: 13408 2007/5 13409 13410Program: 13411 . Following data from p. 51 of Friendly 13412 read x y 13413 0 109 13414 1 65 13415 2 22 13416 3 3 13417 4 1 13418 end of data 13419 . 13420 title case asis 13421 title offset 2 13422 label case asis 13423 x1label displacement 6 13424 title Poisson Plot 13425 x1label X 13426 y1label LOG(x!*n(x)/N) 13427 x3label 13428 . 13429 char blank all 13430 char fill off all 13431 char hw 1.5 1.2 all 13432 char color black all 13433 char circle blank circle blank circle circle 13434 char fill on off on 13435 char color blue black green 13436 line dotted all 13437 line blank solid blank solid blank blank 13438 line color black blue black green 13439 tic offset units screen 13440 tic offset 3 3 13441 . 13442 poisson plot y x 13443 . 13444 let lambml = weighted mean x y 13445 justification center 13446 move 50 8 13447 text Unadjusted: Intercept = ^ppa0, Slope = ^ppa1 13448 move 50 5 13449 text Adjusted: Intercept = ^ppa0adju, Slope = ^ppa1adju 13450 move 50 2 13451 text Lambda: ML = ^lambml, PP = ^lambdapp, PPadj = ^lambdapa 13452 13453-----POLYGON------------------------------------------------------- 13454 13455POLYGON 13456 13457Name: 13458 POLYGON 13459 13460Type: 13461 Diagrammatic Graphics Command 13462 13463Purpose: 13464 Draws a polygon. 13465 13466Description: 13467 The POLYGON command takes an array of x-coordinates and an 13468 array of y-coordinates and draws the polygon defined by these 13469 points. 13470 13471 Although Dataplot provides many specific geometric figures, the 13472 POLYGON command provides the most flexible option. That is, 13473 you can create an arbitrarily complex geometric figure to 13474 append to a plot. 13475 13476Syntax 1: 13477 POLYGON <x> <y> <SUBSET/EXCEPT/FOR qualification> 13478 where <x> is an array of x coordinates; 13479 <y> is an array of y coordinates; 13480 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 13481 rarely used in this context. 13482 13483 In this syntax, the coordinates are specified in absolute 13484 0 to 100 Dataplot screen units. 13485 13486Syntax 2: 13487 POLYGON DATA <x> <y> <SUBSET/EXCEPT/FOR qualification> 13488 where <x> is an array of x coordinates; 13489 <y> is an array of y coordinates; 13490 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 13491 rarely used in this context. 13492 13493 In this syntax, the coordinates are specified in absolute 13494 units of the most recent plot. 13495 13496Syntax 3: 13497 POLYGON RELATIVE <x> <y> <SUBSET/EXCEPT/FOR qualification> 13498 where <x> is an array of x coordinates; 13499 <y> is an array of y coordinates; 13500 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 13501 rarely used in this context. 13502 13503 In this syntax, the first coordinate is specified in absolute 13504 0 to 100 Dataplot screen units. Subsequent points are 13505 relative to the prior point (i.e., point 2 is relatvie to 13506 point 1, point 3 is relative to point 2, etc.) in Dataplot 13507 0 to 100 screen units. 13508 13509Syntax 4: 13510 POLYGON RELATIVE DATA <x> <y> <SUBSET/EXCEPT/FOR qualification> 13511 where <x> is an array of x coordinates; 13512 <y> is an array of y coordinates; 13513 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 13514 rarely used in this context. 13515 13516 In this syntax, the first coordinate is specified in absolute 13517 units of the most recent plot. Subsequent points are 13518 relative to the prior point (i.e., point 2 is relatvie to 13519 point 1, point 3 is relative to point 2, etc.) in units of 13520 the most recent plot. 13521 13522Examples: 13523 LET X = DATA 0.5 1.5 1.5 0.5 0.5 13524 LET Y = DATA 0 0 10 10 0 13525 POLYGON DATA X Y 13526 13527Note: 13528 The line style (i.e., SOLID, DASH), line color, and line thickness 13529 for drawing the border of the polygon are dictated by the first 13530 entry of the LINE, LINE COLOR, and LINE THICKNESS commands 13531 respectively. The attributes of the interior of the polygon 13532 are controlled by the various REGION attribute commands 13533 (e.g., REGION FILL, REGION FILL COLOR). 13534 13535Note: 13536 Dataplot will automatically check if the first point is equal 13537 to the last point. If not, Dataplot adds a point to close the 13538 polygon. 13539 13540Default: 13541 None 13542 13543Synonyms: 13544 None 13545 13546Related Commands: 13547 BOX = Draws a box. 13548 CIRCLE = Draws a circle. 13549 ARC = Draws an arc. 13550 DRAW = Draws a line. 13551 MOVE = Moves to a point. 13552 LINES = Sets the line type for figures and plot lines. 13553 LINE THICKNESSES = Sets the line thickness for figures and plot 13554 lines. 13555 LINE COLOR = Sets the line colors for figures and plot lines. 13556 CROSS-HAIR = Activates and reads the cross-hair. 13557 TEXT = Writes a text string. 13558 REGION FILL = Specifies the fill attribute of a region. 13559 13560Applications: 13561 Presentation Graphics 13562 13563Implementation Date: 13564 7/1997 13565 13566Program: 13567 SKIP 25 13568 READ TEXAS.DAT X Y 13569 . 13570 PLOT Y X 13571 . 13572 REGION FILL ON 13573 REGION FILL COLOR G90 13574 POLYGON DATA X Y 13575 13576-----POLYNOMIAL (LET)----------------------------------- 13577 13578POLYNOMIAL 13579 13580The following are DATAPLOT polynomial commands: 13581 POLYNOMIAL ADDITION = Carries out a polynomial addition. 13582 POLYNOMIAL SUBTRACTION = Carries out a polynomial subtraction. 13583 POLYNOMIAL MULTIPLICATION = Carries out a polynomial multiplication. 13584 POLYNOMIAL DIVISION = Carries out a polynomial division. 13585 POLYNOMIAL SQUARE = Carries out a polynomial square. 13586 POLYNOMIAL EVALUATION = Carries out a polynomial evaluation. 13587 13588-----POLYNOMIAL ADDITION (LET)----------------------------------- 13589 13590POLYNOMIAL ADDITION (LET) 13591 13592Name: 13593 POLYNOMIAL ADDITION (LET) 13594 13595Type: 13596 Subcommand under LET 13597 13598Purpose: 13599 Carry out the addition of 2 polynomials (with real coefficients). 13600 13601Syntax: 13602 LET <v3> = POLYNOMIAL ADDITION <v1> <v2> 13603 <SUBSET/EXCEPT/FOR/qualification> 13604 where <v1> is the variable whose elements are the ordered (real) 13605 coefficients of the first polynomial; 13606 <v2> is the variable whose elements are the ordered (real) 13607 coefficients of the second polynomial; 13608 <v3> is the variable whose elements are the ordered (real) 13609 coefficients of the resultant polynomial; 13610 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 13611 rarely used in this context. 13612 13613Examples: 13614 LET Y3 = POLYNOMIAL ADDITION Y1 Y2 13615 LET Y3 = POLYNOMIAL ADDITION Y1 Y2 SUBSET Y1 > 10 13616 LET Y3 = POLYNOMIAL ADDITION Y1 Y2 FOR I = 1 1 3 13617 13618Note: 13619 The ordering of the coefficients within a variable is as follows: 13620 element 1 is the coefficient of the constant term; 13621 element 2 is the coefficient of the linear term; 13622 element 3 is the coefficient of the quadratic term; 13623 element 4 is the coefficient of the cubic term; 13624 etc. 13625 Thus the polynomial 13626 4 + 11*x + 37*x**2 + 8*x**3 + 19*x**4 13627 can be stored in the variable Y with 5 elements (4 11 37 8 19) via: 13628 SERIAL READ Y 13629 4 11 37 8 19 13630 END OF DATA 13631 or 13632 LET Y = DATA 4 11 37 8 19 13633 13634Default: 13635 None 13636 13637Synonyms: 13638 None 13639 13640Related Commands: 13641 LET = Evaluates general functions. 13642 POLYNOMIAL SUBTRACTION = Carries out a polynomial subtraction. 13643 POLYNOMIAL MULTIPLICATION = Carries out a polynomial multiplication. 13644 POLYNOMIAL DIVISION = Carries out a polynomial division. 13645 POLYNOMIAL SQUARE = Carries out a polynomial square. 13646 POLYNOMIAL EVALUATION = Carries out a polynomial evaluation. 13647 COMPLEX ROOTS = Computes the roots of complex 13648 polynomial. 13649 PLOT = Plots data or functions 13650 COMPLEX ADDITION = Carries out a complex addition. 13651 VECTOR ADDITION = Carries out a vector addition. 13652 SET UNION = Carries out a set union. 13653 LOGICAL AND = Carries out a logical and. 13654 MATRIX ADDITION = Carries out a matrix addition. 13655 13656Applications: 13657 Mathematics 13658 13659Implementation Date: 13660 87/10 13661 13662Program: 13663 LET Y1 = DATA 4 11 37 8 19 13664 LET Y2 = DATA 1 2 1 13665 LET Y3 = POLYNOMIAL ADDITION Y1 Y2 13666 SET WRITE DECIMALS 0 13667 WRITE Y1 Y2 Y3 13668 13669-----POLYNOMIAL DEGREE------------------------------------------------- 13670 13671POLYNOMIAL DEGREE 13672 13673Name: 13674 POLYNOMIAL DEGREE 13675 13676Type: 13677 Support Command 13678 13679Purpose: 13680 Specifies the polynomial degree for certain variations of the 13681 SMOOTH, SPLINE FIT, and FIT commands. 13682 13683Description: 13684 The syntax for the SMOOTH, SPINE FIT, and FIT commands allows the 13685 analyst to embed the desired degree directly in the command, as a 13686 pre-word, as in 13687 CUBIC SMOOTH Y 13688 QUINTIC SPLINE FIT Y X K 13689 QUARTIC FIT Y X 13690 If the analyst chooses not to use such a pre-word, the degree 13691 information can be conveyed via the POLYNOMIAL DEGREE command, as 13692 in 13693 POLYNOMIAL DEGREE 3 13694 SMOOTH Y 13695 POLYNOMIAL DEGREE 5 13696 SPLINE FIT Y X K 13697 POLYNOMIAL DEGREE 4 13698 FIT Y X 13699 In practice, embedding degree information directly in the command 13700 is much more popular than using the POLYNOMIAL DEGREE command. 13701 13702Syntax: 13703 POLYNOMIAL DEGREE <n> 13704 where <n> is an integer number or parameter that is the desired 13705 degree of the polynomial in certain forms of the FIT, 13706 SPLINE FIT, and SMOOTH commands. 13707 13708Examples: 13709 POLYNOMIAL DEGREE 3 13710 POLYNOMIAL DEGREE 1 13711 13712Note: 13713 The POLYNOMIAL DEGREE command with no arguments reverts the 13714 polynomial degree to default. 13715 13716Default: 13717 For smoothing --1 (= linear); 13718 for spline fitting--3 (= cubic); 13719 for fitting --1 (= linear). 13720 13721Synonyms: 13722 None 13723 13724Related Commands: 13725 FIT = Carries out least squares fit. 13726 PRE-FIT = Carries out least squares pre-fit. 13727 SPLINE FIT = Carries out spline fit. 13728 SMOOTH = Carries out smoothing. 13729 FIT STANDARD DEVI = Set the minimum standard deviation for the 13730 fit command. 13731 WEIGHTS = Set weights for the fit command. 13732 FILTER WIDTH = Set the filter width for the SMOOTH command. 13733 KNOTS = Set the knots variable for the SPLINE FIT 13734 command. 13735 13736Applications: 13737 XX 13738 13739Implementation Date: 13740 XX 13741 13742Program: 13743 XX 13744 13745-----POLYNOMIAL DIVISION (LET)----------------------------------- 13746 13747POLYNOMIAL DIVISION (LET) 13748 13749Name: 13750 POLYNOMIAL DIVISION (LET) 13751 13752Type: 13753 Subcommand under LET 13754 13755Purpose: 13756 Carry out the division of 2 polynomials (with real coefficients). 13757 13758Syntax: 13759 LET <v3> <v4> = POLYNOMIAL DIVISION <v1> <v2> 13760 <SUBSET/EXCEPT/FOR/qualification> 13761 where <v1> is the variable whose elements are the ordered (real) 13762 coefficients of the first polynomial; 13763 <v2> is the variable whose elements are the ordered (real) 13764 coefficients of the second polynomial; 13765 <v3> is the variable whose elements are the ordered (real) 13766 coefficients of the resultant quotient polynomial; 13767 <v4> is the variable whose elements are the ordered (real) 13768 coefficients of the resultant remainder polynomial; 13769 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 13770 rarely used in this context. 13771 13772Examples: 13773 LET Y3 Y4 = POLYNOMIAL DIVISION Y1 Y2 13774 13775Note: 13776 The ordering of the coefficients within a variable is as follows: 13777 element 1 is the coefficient of the constant term; 13778 element 2 is the coefficient of the linear term; 13779 element 3 is the coefficient of the quadratic term; 13780 element 4 is the coefficient of the cubic term; 13781 etc. 13782 Thus the polynomial 13783 4 + 11*x + 37*x**2 + 8*x**3 + 19*x**4 13784 can be stored in the variable Y with 5 elements (4 11 37 8 19) via: 13785 SERIAL READ Y 13786 4 11 37 8 19 13787 END OF DATA 13788 or 13789 LET Y = DATA 4 11 37 8 19 13790 13791Default: 13792 None 13793 13794Synonyms: 13795 None 13796 13797Related Commands: 13798 LET = Evaluates general functions. 13799 POLYNOMIAL ADDITION = Carries out a polynomial addition. 13800 POLYNOMIAL SUBTRACTION = Carries out a polynomial subtraction. 13801 POLYNOMIAL MULTIPLICATION = Carries out a polynomial multiplication. 13802 POLYNOMIAL SQUARE = Carries out a polynomial square. 13803 POLYNOMIAL EVALUATION = Carries out a polynomial evaluation. 13804 COMPLEX DIVISION = Carries out complex division. 13805 COMPLEX ROOTS = Computes the roots of a complex 13806 polynomial. 13807 PLOT = Plots data or functions 13808 13809Applications: 13810 Mathematics 13811 13812Implementation Date: 13813 87/10 13814 13815Program: 13816 LET Y1 = DATA 1 -5 6 13817 LET Y2 = DATA 1 -2 13818 LET Y3 Y4 = POLYNOMIAL DIVISION Y1 Y2 13819 WRITE Y1 Y2 13820 WRITE Y3 13821 WRITE Y4 13822 13823-----POLYNOMIAL EVALUATION (LET)--------------------------------- 13824 13825POLYNOMIAL EVALUATION (LET) 13826 13827Name: 13828 POLYNOMIAL EVALUATION (LET) 13829 13830Type: 13831 Subcommand under LET 13832 13833Purpose: 13834 Carry out the evaluation of a polynomial (with real coefficients) 13835 for each point in a variable. 13836 13837Syntax: 13838 LET <v3> = POLYNOMIAL EVALUATION <v1> <v2> 13839 <SUBSET/EXCEPT/FOR/qualification> 13840 where <v1> is the variable whose elements are the ordered (real) 13841 coefficients of the polynomial; 13842 <v2> is the variable whose elements are the values at which 13843 the polynomial is to be evaluated; 13844 <v3> is the variable whose elements are the computed values of 13845 the polynomial; 13846 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 13847 rarely used in this context. 13848 13849Examples: 13850 LET Y = POLYNOMIAL EVALUATION C X 13851 LET Y = POLYNOMIAL EVALUATION C X SUBSET X > 10 13852 LET Y = POLYNOMIAL EVALUATION C X FOR I = 1 1 3 13853 13854Note: 13855 The ordering of the coefficients within a variable is as follows: 13856 element 1 is the coefficient of the constant term; 13857 element 2 is the coefficient of the linear term; 13858 element 3 is the coefficient of the quadratic term; 13859 element 4 is the coefficient of the cubic term; 13860 etc. 13861 Thus the polynomial 13862 4 + 11*x + 37*x**2 + 8*x**3 + 19*x**4 13863 can be stored in the variable Y with 5 elements (4 11 37 8 19) via: 13864 SERIAL READ Y 13865 4 11 37 8 19 13866 END OF DATA 13867 or 13868 LET Y = DATA 4 11 37 8 19 13869 13870Default: 13871 None 13872 13873Synonyms: 13874 None 13875 13876Related Commands: 13877 LET = Evaluates general functions. 13878 POLYNOMIAL ADDITION = Carries out a polynomial addition. 13879 POLYNOMIAL SUBTRACTION = Carries out a polynomial subtraction. 13880 POLYNOMIAL MULTIPLICATION = Carries out a polynomial multiplication. 13881 POLYNOMIAL DIVISION = Carries out a polynomial division. 13882 POLYNOMIAL SQUARE = Carries out a polynomial square. 13883 COMPLEX ROOTS = Computes the roots of a complex 13884 polynomial. 13885 PLOT = Plots data or functions 13886 13887Applications: 13888 Mathematics 13889 13890Implementation Date: 13891 87/10 13892 13893Program: 13894 . PURPOSE--DETERMINE THE COMPLEX ROOTS OF THE POLYNOMIAL 13895 . 1.2 + 3.55*X + 12.25*X**2 + 7.33*X**3 13896 . + 14.2377*X**4 -10.752*X**5 + 5.42*X**6 13897 . NOTE--FOR TESTING PURPOSES, THE ROOTS ARE 13898 . -0.1977768 -0.6085631 13899 . -0.1977768 0.6085631 13900 . -0.1802901 -0.3198090 13901 . -0.1802901 0.3198091 13902 . 1.369949 1.461156 13903 . 1.369949 -1.461156 13904 . 13905 . STEP 1--DEFINE THE COEFFICIENTS OF THE POLYNOMIAL 13906 LET P = DATA 1.2 3.55 12.25 7.33 14.2377 -10.752 5.42 13907 . STEP 2--DEFINE A SEQUENCE OF POINTS, EVALUATE THE POLYNOMIAL 13908 . AT THOSE POINTS, PLOT THE EVALUATED POLYNOMIAL. 13909 LET X = SEQUENCE -1 .1 1 13910 LET Y = POLYNOMIAL EVALUATION P X 13911 MULTIPLOT 2 1; MULTIPLOT CORNER COORDINATES 0 0 100 100 13912 TITLE ORIGINAL FUNCTION 13913 PLOT Y X 13914 . STEP 3--FIND THE COMPLEX ROOTS 13915 LET X2 Y2 = COMPLEX ROOTS P 13916 PRINT X2 Y2 13917 . STEP 4--PLOT THE COMPLEX ROOTS 13918 CHAR X 13919 LINES 13920 X1LABEL REAL COMPONENT 13921 Y1LABEL COMPLEX COMPONENT 13922 GRID ON 13923 TITLE ROOTS OF FUNCTION 13924 PLOT Y2 X2 13925 END OF MULTIPLOT 13926 13927-----POLYNOMIAL MULTIPLICATION (LET)----------------------------- 13928 13929POLYNOMIAL MULTIPLICATION (LET) 13930 13931Name: 13932 POLYNOMIAL MULTIPLICATION (LET) 13933 13934Type: 13935 Subcommand under LET 13936 13937Purpose: 13938 Carry out the multiplication of 2 polynomials (with real 13939 coefficients). 13940 13941Syntax: 13942 LET <v3> = POLYNOMIAL MULTIPLICATION <v1> <v2> 13943 <SUBSET/EXCEPT/FOR/qualification> 13944 where <v1> is the variable whose elements are the ordered (real) 13945 coefficients of the first polynomial; 13946 <v2> is the variable whose elements are the ordered (real) 13947 coefficients of the second polynomial; 13948 <v3> is the variable whose elements are the ordered (real) 13949 coefficients of the resultant polynomial; 13950 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 13951 rarely used in this context. 13952 13953Examples: 13954 LET Y3 = POLYNOMIAL MULTIPLICATION Y1 Y2 13955 LET Y3 = POLYNOMIAL MULTIPLICATION Y1 Y2 SUBSET Y1 > 7 13956 LET Y3 = POLYNOMIAL MULTIPLICATION Y1 Y2 FOR I = 1 1 3 13957 13958Note: 13959 The ordering of the coefficients within a variable is as follows: 13960 element 1 is the coefficient of the constant term; 13961 element 2 is the coefficient of the linear term; 13962 element 3 is the coefficient of the quadratic term; 13963 element 4 is the coefficient of the cubic term; 13964 etc. 13965 Thus the polynomial 13966 4 + 11*x + 37*x**2 + 8*x**3 + 19*x**4 13967 can be stored in the variable Y with 5 elements (4 11 37 8 19) via: 13968 SERIAL READ Y 13969 4 11 37 8 19 13970 END OF DATA 13971 or 13972 LET Y = DATA 4 11 37 8 19 13973 13974Default: 13975 None 13976 13977Synonyms: 13978 None 13979 13980Related Commands: 13981 LET = Evaluates general functions. 13982 POLYNOMIAL ADDITION = Carries out a polynomial addition. 13983 POLYNOMIAL SUBTRACTION = Carries out a polynomial subtraction. 13984 POLYNOMIAL DIVISION = Carries out a polynomial division. 13985 POLYNOMIAL SQUARE = Carries out a polynomial square. 13986 POLYNOMIAL EVALUATION = Carries out a polynomial evaluation. 13987 COMPLEX ROOTS = Computes the roots of a complex 13988 polynomial. 13989 PLOT = Plots data or functions 13990 COMPLEX MULTIPLICATION = Carries out a complex multiplication. 13991 VECTOR DOT PRODUCT = Computes the vector dot product. 13992 MATRIX MULTIPLICATION = Carries out a matrix multiplication. 13993 13994Applications: 13995 Mathematics 13996 13997Implementation Date: 13998 87/10 13999 14000Program: 14001 . PURPOSE--DETERMINE THE COMPLEX ROOTS OF A SUM OF 20 QUINTICS 14002 . WHERE THE K-TH QUINTIC IS OF THE FORM (1 + (1/K)*X)**5 14003 . NOTE--FOR TESTING PURPOSES-- 14004 . THE RESULTING POLYNOMIAL HAS COEFFICIENTS-- 14005 . 0.2000000E+02 14006 . 0.1798870E+02 14007 . 0.1596163E+02 14008 . 0.1200868E+02 14009 . 0.5411423E+01 14010 . 0.1036926E+01 14011 . WITH COMPLEX ROOTS-- 14012 . -0.2387324E+01 0.0000000E+00 (DOUBLE ROOT) 14013 . -0.1639799E+01 -0.1343364E+01 14014 . -0.1639799E+01 0.1343364E+01 14015 . 0.2241036E+00 -0.1322019E+01 14016 . 0.2241036E+00 0.1322019E+01 14017 . 14018 FEEDBACK OFF; DIMENSION 100 VARIABLES 14019 LET N = 20 14020 . STEP 1--DEFINE THE 20 MONOMIALS 14021 LOOP FOR K = 1 1 N 14022 LET M^K (1) = 1 14023 LET M^K (2) = 1/K 14024 END OF LOOP 14025 . STEP 2--DEFINE THE 20 POLYNOMIALS 14026 LOOP FOR K = 1 1 N 14027 LET P^K = POLYNOMIAL MULTIPLICATION M^K M^K 14028 LET P^K = POLYNOMIAL MULTIPLICATION P^K M^K 14029 LET P^K = POLYNOMIAL MULTIPLICATION P^K M^K 14030 LET P^K = POLYNOMIAL MULTIPLICATION P^K M^K 14031 END OF LOOP 14032 . STEP 3--COMPUTE THE SUM OF THE 20 POLYNOMIALS 14033 LET PSUM = DATA 0 0 0 0 14034 LOOP FOR K = 1 1 N 14035 LET PSUM = POLYNOMIAL ADDITION PSUM P^K 14036 END OF LOOP 14037 . STEP 4--PLOT THE FUNCTION 14038 . 14039 MULTIPLOT 2 1; MULTIPLOT CORNER COORDINATES 0 0 100 100 14040 LET X = SEQUENCE -5 .1 5 14041 LET Y = POLYNOMIAL EVALUATION PSUM X 14042 TITLE SUM OF POLYNOMIALS 14043 PLOT Y X 14044 . STEP 5--FIND THE COMPLEX ROOTS 14045 LET X2 Y2 = COMPLEX ROOTS PSUM 14046 . STEP 6--PLOT THE COMPLEX ROOTS 14047 CHAR X; LINES; GRID ON 14048 X1LABEL REAL COMPONENT; Y1LABEL COMPLEX COMPONENT; TITLE PLOT ROOTS 14049 PLOT Y2 X2 14050 END OF MULTIPLOT 14051 14052-----POLYNOMIAL SQUARE (LET)------------------------------------- 14053 14054POLYNOMIAL SQUARE (LET) 14055 14056Name: 14057 POLYNOMIAL SQUARE (LET) 14058 14059Type: 14060 Subcommand under LET 14061 14062Purpose: 14063 Carry out the squaring of a polynomial (with real coefficients). 14064 14065Syntax: 14066 LET <v2> = POLYNOMIAL SQUARE <v1> <SUBSET/EXCEPT/FOR/qualification> 14067 where <v1> is the variable whose elements are the ordered (real) 14068 coefficients of the polynomial to be squared; 14069 <v2> is the variable whose elements are the ordered (real) 14070 coefficients of the resultant polynomial; 14071 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 14072 rarely used in this context. 14073 14074Examples: 14075 LET Y2 = POLYNOMIAL SQUARE Y1 14076 LET Y2 = POLYNOMIAL SQUARE Y1 SUBSET Y1 > 10 14077 LET Y2 = POLYNOMIAL SQUARE Y1 FOR I = 1 1 3 14078 14079Note: 14080 The ordering of the coefficients within a variable is as follows: 14081 element 1 is the coefficient of the constant term; 14082 element 2 is the coefficient of the linear term; 14083 element 3 is the coefficient of the quadratic term; 14084 element 4 is the coefficient of the cubic term; 14085 etc. 14086 Thus the polynomial 14087 4 + 11*x + 37*x**2 + 8*x**3 + 19*x**4 14088 can be stored in the variable Y with 5 elements (4 11 37 8 19) via: 14089 SERIAL READ Y 14090 4 11 37 8 19 14091 END OF DATA 14092 or 14093 LET Y = DATA 4 11 37 8 19 14094 14095Default: 14096 None 14097 14098Synonyms: 14099 None 14100 14101Related Commands: 14102 LET = Evaluates general functions. 14103 POLYNOMIAL ADDITION = Carries out a polynomial addition. 14104 POLYNOMIAL SUBTRACTION = Carries out a polynomial subtraction. 14105 POLYNOMIAL MULTIPLICATION = Carries out a polynomial multiplication. 14106 POLYNOMIAL DIVISION = Carries out a polynomial division. 14107 POLYNOMIAL EVALUATION = Carries out a polynomial evaluation. 14108 COMPLEX ROOTS = Computes the roots of a complex 14109 polynomial. 14110 COMPLEX EXPONENTIATION = Carries out a complex exponentiation. 14111 PLOT = Plots data or functions 14112 14113Applications: 14114 Mathematics 14115 14116Implementation Date: 14117 87/10 14118 14119Program: 14120 LET Y1 = DATA 4 11 37 8 19 14121 LET Y2 = POLYNOMIAL SQUARE Y1 14122 SET WRITE DECIMALS 0 14123 WRITE Y1 Y2 14124 14125-----POLYNOMIAL SUBTRACTION (LET)-------------------------------- 14126 14127POLYNOMIAL SUBTRACTION (LET) 14128 14129Name: 14130 POLYNOMIAL SUBTRACTION (LET) 14131 14132Type: 14133 Subcommand under LET 14134 14135Purpose: 14136 Carry out the subtraction of 2 polynomials (with real coefficients). 14137 14138Syntax: 14139 LET <v3> = POLYNOMIAL SUBTRACTION <v1> <v2> 14140 <SUBSET/EXCEPT/FOR/qualification> 14141 where <v1> is the variable whose elements are the ordered (real) 14142 coefficients of the first polynomial; 14143 <v2> is the variable whose elements are the ordered (real) 14144 coefficients of the second polynomial; 14145 <v3> is the variable whose elements are the ordered (real) 14146 coefficients of the resultant polynomial; 14147 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 14148 rarely used in this context. 14149 14150Examples: 14151 LET Y3 = POLYNOMIAL SUBTRACTION Y1 Y2 14152 LET Y3 = POLYNOMIAL SUBTRACTION Y1 Y2 SUBSET Y1 > 10 14153 LET Y3 = POLYNOMIAL SUBTRACTION Y1 Y2 FOR I = 1 1 3 14154 14155Note: 14156 The ordering of the coefficients within a variable is as follows: 14157 element 1 is the coefficient of the constant term; 14158 element 2 is the coefficient of the linear term; 14159 element 3 is the coefficient of the quadratic term; 14160 element 4 is the coefficient of the cubic term; 14161 etc. 14162 Thus the polynomial 14163 4 + 11*x + 37*x**2 + 8*x**3 + 19*x**4 14164 can be stored in the variable Y with 5 elements (4 11 37 8 19) via: 14165 SERIAL READ Y 14166 4 11 37 8 19 14167 END OF DATA 14168 or 14169 LET Y = DATA 4 11 37 8 19 14170 14171Default: 14172 None 14173 14174Synonyms: 14175 None 14176 14177Related Commands: 14178 LET = Evaluates general functions. 14179 POLYNOMIAL ADDITION = Carries out a polynomial addition. 14180 POLYNOMIAL MULTIPLICATION = Carries out a polynomial multiplication. 14181 POLYNOMIAL DIVISION = Carries out a polynomial division. 14182 POLYNOMIAL SQUARE = Carries out a polynomial square. 14183 POLYNOMIAL EVALUATION = Carries out a polynomial evaluation. 14184 COMPLEX SUBTRACTION = Carries out a complex subtraction. 14185 VECTOR SUBTRACTION = Carries out a vector subtraction. 14186 SET INTERSECTION = Carries out a set intersection. 14187 LOGICAL OR = Carries out a logical or. 14188 MATRIX SUBTRACTION = Carries out a matrix subtraction. 14189 COMPLEX ROOTS = Computes the roots of a complex 14190 polynomial. 14191 PLOT = Plots data or functions 14192 14193Applications: 14194 Mathematics 14195 14196Implementation Date: 14197 87/10 14198 14199Program: 14200 LET Y1 = DATA 4 11 37 8 19 14201 LET Y2 = DATA 1 2 1 14202 LET Y3 = POLYNOMIAL SUBTRACTION Y1 Y2 14203 SET WRITE DECIMALS 0 14204 WRITE Y1 Y2 Y3 14205 14206-----POOLED VARIANCE-COVARIANCE MATRIX (LET)------------------------- 14207 14208POOLED VARIANCE-COVARIANCE MATRIX 14209 14210Name: 14211 POOLED VARIANCE-COVARIANCE MATRIX (LET) 14212 14213Type: 14214 Let Subcommand 14215 14216Purpose: 14217 Compute the pooled variance-covariance matrix of a matrix. 14218 14219Description: 14220 This command operates on a matrix (M) and a group id variable 14221 (TAG). The TAG variable has the same number of rows as the 14222 matrix M. The values of TAG are typically integers that 14223 identify the group to which the corresponding row of the 14224 matrix belongs. 14225 14226 The POOLED VARIANCE-COVARIANCE MATRIX command returns a matrix 14227 that contains a pooled variance-covariance matrix, which is 14228 defined as: 14229 14230 SPOOL = (1/SUM(N(i)-1)) * SUM((1/N(i)-1)*C(i))) 14231 14232 where N(i) is the number of elements in group i and C(i) 14233 is the variance-covariance matrix of the rows belonging to 14234 group i. 14235 14236Syntax 1: 14237 LET <mat2> = POOLED VARIANCE-COVARIANCE MATRIX <mat1> <tag> 14238 where <mat1> is a matrix for which the pooled covariance matrix 14239 is to be computed; 14240 <tag> is the group-id variable; 14241 and where <mat2> is a matrix where the resulting pooled 14242 covariance matrix is saved. 14243 14244Syntax 2: 14245 LET <mat3> = POOLED VARIANCE-COVARIANCE MATRIX <mat1> <mat2> 14246 where <mat1> is a matrix containing the data for group 1; 14247 <mat2> is a matrix containing the data for group 2; 14248 and where <mat3> is a matrix where the resulting pooled 14249 variance-covariance matrix is saved. 14250 14251 This syntax can be used for the case where there are 14252 exactly two groups. In this case, the data for each group 14253 is stored in a separate matrix and no group id variable 14254 is required. 14255 14256Examples: 14257 LET COV = POOLED VARIANCE-COVARIANCE MATRIX M TAG 14258 14259Note: 14260 Matrices are created with either the READ MATRIX command or the 14261 MATRIX DEFINITION command. Enter HELP MATRIX DEFINITION and HELP 14262 READ MATRIX for details. 14263 14264Default: 14265 None 14266 14267Synonyms: 14268 None 14269 14270Related Commands: 14271 VARIANCE-COVARIANCE MATRIX = Compute the variance-covariance 14272 matrix of a matrix. 14273 CORRELATION MATRIX = Compute the correlation matrix of 14274 a matrix. 14275 MATRIX GROUP SD = Compute the group means for a matrix. 14276 MATRIX GROUP SD = Compute the group standard deviations 14277 for a matrix. 14278 14279Reference: 14280 "Applied Multivariate Statistical Analysis", Third Edition, 14281 Johnson and Wichern, Prentice-Hall, 1992. 14282 14283Applications: 14284 Multivariate Analysis 14285 14286Implementation Date: 14287 1998/8 14288 14289Program: 14290 DIMENSION 50 COLUMNS 14291 SKIP 25 14292 READ IRIS.DAT Y1 Y2 Y3 Y4 TAG 14293 LET N = SIZE Y1 14294 LET M = MATRIX DEFINITION Y1 N 4 14295 LET Z = POOLED VARIANCE-COVARIANCE MATRIX M TAG 14296 14297-----POSITIONAL TABULATION-------------------------------------- 14298 14299POSITIONAL TABULATION 14300 14301Name: 14302 POSITIONAL TABULATION 14303 14304Type: 14305 Analysis Command 14306 14307Purpose: 14308 Generate a position tabulation for one of Dataplot's supported 14309 univariate statistics for either a list of variables or a list 14310 of matrices. 14311 14312Description: 14313 Dataplot typically computes statistic for the rows of a variable. 14314 However, there may be times where it is desirable to compute a 14315 statistic for each row of a list of variables. For example, given 14316 the variables A, B, C, and D where each variable has 5 rows, 14317 the POSITIONAL TABULATION MEAN command will print the means for 14318 14319 row 1: mean of A(1), B(1), C(1), D(1) 14320 row 2: mean of A(2), B(2), C(2), D(2) 14321 row 3: mean of A(3), B(3), C(3), D(3) 14322 row 4: mean of A(4), B(4), C(4), D(4) 14323 row 5: mean of A(5), B(5), C(5), D(5) 14324 14325 If you specify a list of matrices, then the statistic will be 14326 computed for each (i,j) position of the matrices. 14327 14328Syntax: 14329 POSITIONAL TABULATION <stat> <y1> ... <yk> 14330 <SUBSET/EXCEPT/FOR qualification> 14331 where <stat> is one of Dataplot's supported statistics; 14332 <y1> ... <yk> is a list of 1 to 30 response variables or 14333 matrices (with the same dimensions); 14334 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 14335 14336 The list of response variables must all be of the same type (i.e., 14337 either all variables or all matrices). They must also have the 14338 same dimension (if variables, all must have the same number of 14339 rows and if matrices, all must have the same number of rows and 14340 the same number of columns). 14341 14342Examples: 14343 POSITIONAL TABULATION MEAN Y1 TO Y5 14344 POSITIONAL TABULATION MEAN Y1 TO Y5 FOR I = 1 1 25 14345 14346Note: 14347 For a list of supported statistics, enter the command 14348 14349 HELP STATISTICS 14350 14351 Only statistics that operate on a single response are supported. 14352 14353Note: 14354 The output is also written to the file DPST1F.DAT. For example, 14355 you can do something like the following 14356 14357 POSITIONAL TABULATION MEAN A B C D 14358 SKIP 0 14359 READ DPST1F.DAT ROW COL YMEAN 14360 14361Note: 14362 To specify the number of digits to print to the right of the 14363 decimal point, enter the command (the default is exponential 14364 format) 14365 14366 SET WRITE DECIMALS <value> 14367 14368Default: 14369 None 14370 14371Synonyms: 14372 None 14373 14374Related Commands: 14375 CROSS TABULATE = Generates a cross tabulation for a specified 14376 statistic. 14377 MATRIX ROW STATISTIC = Generate row statistics for a matrix. 14378 STATISTIC PLOT = Generate a statistic versus subset plot. 14379 FLUCTUATION PLOT = Generate a fluctuation plot. 14380 TABULATION PLOT = Generate a tabulation plot. 14381 14382Applications: 14383 Exploratory Data Analysis 14384 14385Implementation Date: 14386 2011/9 14387 14388Program 1: 14389 let y1 = data 1 2 3 14390 let y2 = data 4 5 6 14391 let y3 = data 7 8 9 14392 . 14393 set write decimals 3 14394 positional tabulation mean y1 y2 y3 14395 . 14396 read dpst1f.dat row col ymean 14397 14398 Program 2: 14399 read matrix a 14400 1 2 3 14401 4 5 6 14402 7 8 9 14403 end of data 14404 . 14405 read matrix b 14406 11 21 31 14407 41 51 61 14408 71 81 91 14409 end of data 14410 . 14411 read matrix c 14412 101 102 103 14413 111 121 131 14414 141 151 161 14415 end of data 14416 . 14417 SET WRITE DECIMALS 1 14418 POSITIONAL TABULATION SUM A B C 14419 14420-----POSITIVE PREDICTIVE VALUE (LET)-------------------------------- 14421 14422POSITIVE PREDICTIVE VALUE 14423 14424Name: 14425 POSITIVE PREDICTIVE VALUE (LET) 14426 14427Type: 14428 Let Subcommand 14429 14430Purpose: 14431 Compute the positive predictive value between two 14432 binary variables. 14433 14434Description: 14435 Given two variables with n parired observations where each 14436 variable has exactly two possible outcomes, we can generate 14437 the following 2x2 table: 14438 14439 | Variable 2 | 14440 Variable 1 | Success Failure | Row Total 14441 ==================================================== 14442 Success | N11 N12 | N11 + N12 14443 Failure | N21 N22 | N21 + N22 14444 ==================================================== 14445 Column Total | N11+N21 N12+N22 | Total 14446 14447 The parameters N11, N12, N21, and N22 denote the counts 14448 for each category. 14449 14450 Success and failure can denote any binary response. 14451 Dataplot expects "success" to be coded as "1" and "failure" 14452 to be coded as "0". Some typical examples would be: 14453 14454 1) Variable 1 denotes whether or not a patient has a 14455 disease (1 denotes disease is present, 0 denotes 14456 disease not present). Variable 2 denotes the result 14457 of a test to detect the disease (1 denotes a positive 14458 result and 0 denotes a negative result). 14459 14460 2) Variable 1 denotes whether an object is present or 14461 not (1 denotes present, 0 denotes absent). Variable 2 14462 denotes a detection device (1 denotes object detected 14463 and 0 denotes object not detected). 14464 14465 In these examples, the "ground truth" is typically given 14466 as variable 1 while some estimator of the ground truth is 14467 given as variable 2. 14468 14469 The positive predictive value is then N11/(N11+N21). This 14470 is the conditional probability of variable 1 being true 14471 given that variable 2 is true. In the context of the first 14472 example above, this is the probability that the disease is 14473 present when there is a positive test result. 14474 14475 Fleiss and his co-authors recommend positive predictive value 14476 and negative predictive value as an alternative to false 14477 positive and false negative due to the fact that the 14478 definitions of false positive and false negative have 14479 been inconsistent in the literature. 14480 14481Syntax: 14482 LET <par> = POSITIVE PREDICTIVE VALUE <y1> <y2> 14483 <SUBSET/EXCEPT/FOR qualification> 14484 where <y1> is the first response variable; 14485 <y2> is the second response variable; 14486 <par> is a parameter where the computed positive 14487 predictive value is stored; 14488 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 14489 14490Examples: 14491 LET A = POSITIVE PREDICTIVE VALUE Y1 Y2 14492 LET A = POSITIVE PREDICTIVE VALUE Y1 Y2 SUBSET TAG > 2 14493 14494Note: 14495 The two variables must have the same number of elements. 14496 14497Note: 14498 There are two ways you can define the response variables: 14499 14500 1) Raw data - in this case, the variables contain 14501 0's and 1's. 14502 14503 If the data is not coded as 0's and 1's, Dataplot 14504 will check for the number of distinct values. If 14505 there are two distinct values, the minimum value 14506 is converted to 0's and the maximum value is 14507 converted to 1's. If there is a single distinct 14508 value, it is converted to 0's if it is less than 14509 0.5 and to 1's if it is greater than or equal to 14510 0.5. If there are more than two distinct values, 14511 an error is returned. 14512 14513 2) Summary data - if there are two observations, the 14514 data is assummed to be the 2x2 summary table. 14515 That is, 14516 14517 Y1(1) = N11 14518 Y1(2) = N21 14519 Y2(1) = N12 14520 Y2(2) = N22 14521 14522Note: 14523 The following additional commands are supported 14524 14525 TABULATE POSITIVE PREDICTIVE VALUE Y1 Y2 X 14526 CROSS TABULATE POSITIVE PREDICTIVE VALUE Y1 Y2 X1 X2 14527 14528 POSITIVE PREDICTIVE VALUE PLOT Y1 Y2 X 14529 CROSS TABULATE POSITIVE PREDICTIVE VALUE PLOT Y1 Y2 X1 X2 14530 14531 BOOTSTRAP POSITIVE PREDICTIVE VALUE PLOT Y1 Y2 14532 JACKNIFE POSITIVE PREDICTIVE VALUE PLOT Y1 Y2 14533 14534Default: 14535 None 14536 14537Synonyms: 14538 PPV is a synonym for POSITIVE PREDICTIVE VALUE. 14539 14540Related Commands: 14541 NEGATIVE PREDICTIVE VALUE = Compute the negative predictive 14542 value between two binary variables. 14543 TRUE POSITIVES = Compute the proportion of 14544 true positives. 14545 TRUE NEGATIVES = Compute the proportion of 14546 true negatives. 14547 FALSE POSITIVES = Compute the proportion of 14548 false positives. 14549 FALSE NEGATIVES = Compute the proportion of 14550 false negatives. 14551 TEST SENSITIVITY = Compute the test sensitivity. 14552 TEST SPECIFICITY = Compute the test specificity. 14553 ODDS RATIO = Compute the bias corrected 14554 log(odds ratio). 14555 ODDS RATIO STANDARD ERROR = Compute the standard error of the 14556 bias corrected log(odds ratio). 14557 RELATIVE RISK = Compute the relative risk. 14558 TABULATE = Compute a statistic for data with 14559 a single grouping variable. 14560 CROSS TABULATE = Compute a statistic for data with 14561 two grouping variables. 14562 STATISTIC PLOT = Generate a plot of a statistic for 14563 data with a single grouping 14564 variable. 14565 CROSS TABULATE PLOT = Generate a plot of a statistic for 14566 data with two grouping variables. 14567 BOOTSTRAP PLOT = Generate a bootstrap plot for a 14568 given statistic. 14569 14570Reference: 14571 Fleiss, Levin, and Paik (2003), "Statistical Methods for 14572 Rates and Proportions", Third Edition, Wiley, chapter 1. 14573 14574Applications: 14575 Categorical Data Analysis 14576 14577Implementation Date: 14578 2007/4 14579 14580Program: 14581 let n = 1 14582 . 14583 let p = 0.2 14584 let y1 = binomial rand numb for i = 1 1 100 14585 let p = 0.1 14586 let y2 = binomial rand numb for i = 1 1 100 14587 . 14588 let p = 0.4 14589 let y1 = binomial rand numb for i = 101 1 200 14590 let p = 0.08 14591 let y2 = binomial rand numb for i = 101 1 200 14592 . 14593 let p = 0.15 14594 let y1 = binomial rand numb for i = 201 1 300 14595 let p = 0.18 14596 let y2 = binomial rand numb for i = 201 1 300 14597 . 14598 let p = 0.6 14599 let y1 = binomial rand numb for i = 301 1 400 14600 let p = 0.45 14601 let y2 = binomial rand numb for i = 301 1 400 14602 . 14603 let p = 0.3 14604 let y1 = binomial rand numb for i = 401 1 500 14605 let p = 0.1 14606 let y2 = binomial rand numb for i = 401 1 500 14607 . 14608 let x = sequence 1 100 1 5 14609 . 14610 let a = positive predictive value y1 y2 subset x = 1 14611 tabulate positive predictive value y1 y2 x 14612 . 14613 label case asis 14614 xlimits 1 5 14615 major xtic mark number 5 14616 minor xtic mark number 0 14617 xtic mark offset 0.5 0.5 14618 ytic mark offset 0.05 0.05 14619 y1label Positive Predictive Value 14620 x1label Group ID 14621 character x blank 14622 line blank solid 14623 . 14624 positive predictive value plot y1 y2 x 14625 14626-----POSTSCRIPT------------------------------------------------------- 14627 14628POSTSCRIPT 14629 14630Name: 14631 POSTSCRIPT 14632 14633Type: 14634 Output Device Command 14635 14636Purpose: 14637 Direct graphical output to a POSTSCRIPT device. 14638 14639Description: 14640 Postscript is a device independent page description language 14641 supported by various vendors. Although Postscript is primarily 14642 used by printers, it can be used by other types of devices (e.g., 14643 film recorders) as well. Note that Postscript is a complete 14644 language as opposed to a simple device protocol. The Postscript 14645 file is an ASCII file containing Postscript commands. To render a 14646 Postscript file on a specific device, one of the following 14647 methods is used 14648 14649 1. A specific device may have built-in support for Postscript 14650 files. Typically, this is provided by a vendor written 14651 driver. In this case, the Postscript file can be sent 14652 directly to the device. 14653 14654 2. If the device does not support Postscript directly, 14655 a Postscript translator may be available that allows 14656 you to view or print the Postscript file on a non-Postscript 14657 device. One example of this is the ghostview/ghostscript 14658 software. Ghostscript is the underlying Postscript 14659 translator while Ghostview is a GUI program that 14660 allows you to view the Postscript file on the screeen 14661 and to print the Postscript file on a non-Postscript 14662 printer. Other translators/viewers are available. 14663 14664 Postscript is routinely supported in the Linux environment for 14665 printers. In the Windows environment, it is more common to use 14666 Ghostview (or some other Postscript translator) to send Postscript 14667 files to a printer. 14668 14669 Postscript is the most commonly used format in Dataplot for 14670 printing graphics. 14671 14672 Many word processing and page publishing programs import Postscript 14673 files thereby allowing graphics generated by other programs to be 14674 to be embedded with text. However, they normally require that the 14675 Postscript file be in a special format called encapsulated 14676 Postscript. The primary difference between encapsulated Postscript 14677 and standard Postscript is that encapsulated Postscript assumes that 14678 each graph is in a separate file while standard Postscript can 14679 contain multiple pages in the same file. In order to generate 14680 encapsulated Postscript in Dataplot, you would typically do something 14681 like the following 14682 14683 SET IPL1NA PLOT1.EPS 14684 DEVICE 2 POSTSCRIPT ENCAPSULATED 14685 ... Generate first plot .. 14686 DEVICE 2 CLOSE 14687 . 14688 SET IPL1NA PLOT2.EPS 14689 DEVICE 2 POSTSCRIPT ENCAPSULATED 14690 ... Generate second plot .. 14691 DEVICE 2 CLOSE 14692 14693 The SET IPL1NA command is used to give the plot file a unique name. 14694 This basic sequence can be repeated as often as needed. 14695 14696 Postscript is closely related to the Portable Document Format (PDF). 14697 PDF is essentially a binary form of Postscript. 14698 14699Syntax 1: 14700 POSTSCRIPT 14701 14702 This form designates device 1 (the terminal) as a Postscript 14703 device. 14704 14705Syntax 2: 14706 POSTSCRIPT ENCAPSULATED 14707 14708 This form designates device 1 (the terminal) as an encapsulated 14709 Postscript device. 14710 14711Syntax 3: 14712 DEVICE <1/2/3> POSTSCRIPT 14713 14714 This form designates one of DATAPLOT's 3 devices (it will typically 14715 be device 2) as a Postscript device. 14716 14717Syntax 4: 14718 DEVICE <1/2/3> POSTSCRIPT ENCAPSULATED 14719 14720 This form designates one of DATAPLOT's 3 devices (it will typically 14721 be device 2) as an encapsulated Postscript device. 14722 14723Examples: 14724 POSTSCRIPT 14725 DEVICE 2 POSTSCRIPT 14726 DEVICE 3 POSTSCRIPT 14727 DEVICE 2 POSTSCRIPT ENCAPSULATED 14728 14729Note: 14730 The Postscript driver can support either color or monochrome 14731 Postscript devices. The default is monochrome. Enter a DEVICE 14732 <num> COLOR ON command after the POSTSCRIPT command to get color. 14733 Postscript supports the full range of color and gray scale provided 14734 for in DATAPLOT. Enter HELP COLOR for a list of available colors 14735 and gray scales. Colors can have a different appearance on 14736 different Postscript devices. Specifically, Postscript color 14737 printers can come with 1 bit, 4 bits. or 8 bits for each of 3 14738 colors. The output quality will vary significantly depending on 14739 the number of bits used. 14740 14741 Monochrome Postscript devices do support gray scale. Be aware 14742 that they do it by "dithering" since each pixel is either on or 14743 off. Dithering means that gray scale is emulated by turning some 14744 proportion of neighboring pixels on or off to get the desired 14745 effect. 14746 14747 If you want to make color on the default, enter the command 14748 (you may want to put this in your DPLOGF.TEX startup file) 14749 14750 SET POSTSCRIPT COLOR DEFAULT 14751 14752Note: 14753 One of Postscript's strengths is the availability of scalable and 14754 rotatable typeset quality fonts. Postscript fonts (for hardware 14755 generated characters) can be specified with the following command: 14756 14757 SET POSTSCRIPT FONT <font id> 14758 14759 The available fonts (34 are currently supported) can be shown with 14760 the following command: 14761 14762 <a href="../ch7/postshow.pdf">POSTSCRIPT SHOW FONTS</a> 14763 14764 The default font is Helvetica Bold. 14765 14766Note: 14767 Postscript fonts are only used when hardware characters are 14768 generated. This means that Greek characters and other special 14769 symbols are not available with the Postscript fonts. The 14770 exception is that the SP(), CR(), LC(), and UC() options are 14771 supported for hardware fonts. 14772 14773 Greek characters (and a few other special symbols) can be generated 14774 by using the symbol font (SET POSTSCRIPT FONT SYMBOL). In this 14775 case, a Greek alpha is obtained by entering TEXT LC()A rather than 14776 TEXT LC()ALPH(). The limitation is that only one Postscript font 14777 can be active for a plot, so text strings that require a mixture of 14778 standard and Greek characters are not practical with this method. 14779 DATAPLOT does not support automatically switching to the symbol 14780 font when a Greek character (e.g., ALPH(), BETA()) is encountered 14781 in the text string. 14782 14783 At this time, if you have text strings which consist only of Greek 14784 characters you can use the symbol font. However, if your string is 14785 a mixture of standard and Greek characters, you need to use one of 14786 the software fonts. 14787 14788 NOTE 5/2009: 14789 14790 The Postscript device was upgraded to handle most of Dataplot's 14791 supported special characters. These special characters are 14792 mapped to the Postscript symbol font. There is not a 1-to-1 14793 correspondence between Dataplot's special characters and 14794 the symbols available in the Postscript symbol font. The 14795 supported symbols below are ones that are available in 14796 both the Dataplot special symbol set and the Postscript 14797 symbol font. Note that this means that you can mix these 14798 Greek characters and special symbols with regular text 14799 without setting the SYMBOL font. 14800 14801 Specifically, the following are supported: 14802 14803 i) subscripts and superscripts 14804 14805 ii) Greek characters 14806 14807 iii) A subset of the mathematical symbols and other special 14808 characters. The following is the list of Dataplot 14809 special characters that will be translated to 14810 equivalent characters in the Postscript symbol font: 14811 14812 INTE(), SUMM(), PROD(), INFI(), DOTP(), 14813 DEL(), DIVI(), LT(), GT(), LTEQ(), GTEQ(), 14814 NOT(), +-(), APPR(), TILD(), EQUI(), VARI(), 14815 CARA(), TIME(), PART(), RADI(), SUBS(), 14816 SUPE(), UNIO(), INTR(), ELEM(), THEX(), 14817 THFO(), RAPO(), LBRA(), RBRA(), LCBR(), 14818 RCBR(), LELB(), RELB(), RARR(), UARR(), 14819 DARR(), VBAR(), HBAR(), DEGR() 14820 14821 The full set of special symbols supported by Dataplot 14822 is documented in chapter 13 of Volume I of the 14823 Reference Manual 14824 14825 http://www.itl.nist.gov/div898/software/dataplot/ 14826 refman1/ch13/homepage.pdf 14827 14828Note: 14829 Postscript printers on most systems require that the first line 14830 start with a "%!". However, a few require that it start with 14831 " %!". The default in DATAPLOT is no leading space. If your 14832 system requires this (i.e, if the Postscript output is printed as 14833 text rather than a graph), enter the following command: 14834 14835 SET POSTSCRIPT SPACE ON 14836 14837 Note that while this was an issue with some early Postscript devices, 14838 with current Postscript devices this should no longer be an issue. 14839 14840Note: 14841 Landscape or portrait orientation can be set via the ORIENTATION 14842 command. It can be toggled as many times as desired in a 14843 DATAPLOT session. The default is landscape orientation. 14844 14845Note: 14846 The following SET commands can be used to specify the margins and 14847 resolution of the particular Postscript printer (these should 14848 normally not be required): 14849 14850 SET POSTSCRIPT PPI <number> sets the resolution (in points per 14851 inch). The default is 300. 14852 SET POSTSCRIPT [LANDSCAPE/PORTRAIT] LEFT MARGIN sets the 14853 left margin (in dots). The default is 50. 14854 SET POSTSCRIPT [LANDSCAPE/PORTRAIT] RIGHT MARGIN sets the 14855 right margin (in dots). The default is 50. 14856 SET POSTSCRIPT [LANDSCAPE/PORTRAIT] BOTTOM MARGIN sets the 14857 bottom margin (in dots). The default is 50. 14858 SET POSTSCRIPT [LANDSCAPE/PORTRAIT] TOP MARGIN sets the 14859 top margin (in dots). The default is 50. 14860 You can also use the WINDOW CORNER COORDINATES command to set the 14861 margin, but this affects all the active devices. 14862 14863Note: 14864 Display Postscript is a special version of Postscript for terminals 14865 and workstations. The standard Postscript driver does not work 14866 for these devices. Display Postscript does not currently seem 14867 to be of much interest. 14868 14869Note: 14870 Some tweaks were made to the Postscript device 1/2003. 14871 14872 1) Previously, Dataplot started a new page when the device 14873 was intialized. It also started a new page when the first 14874 plot was generated. This was to ensure that a fresh 14875 page was started if you were generating diagrammatic 14876 graphics before the first plot. However, it caused 14877 a blank page to be printed for most applications. 14878 Dataplot now automatically keeps track so that the first 14879 plot will not generate the unneeded page erase. 14880 14881 2) Previously, the LANDSCAPE WORDPERFECT orientation (this 14882 results in a landscape orientation on a portrait page) 14883 was supported for encapsulated Postscript, but not for 14884 regular Postscript. This orientation is now supported 14885 for regular Postscript. 14886 14887 3) Dataplot allows you to switch between the various 14888 orientations (LANDSCAPE, PORTRAIT, LANDSCAPE WORDPERFECT, 14889 SQUARE) when using Postscript. For this reason, it sets 14890 the bounding box for an 11x11 inch page. 14891 14892 The following command 14893 14894 SET POSTSCRIPT BOUNDING BOX <FIXED/FLOAT> 14895 14896 can be used to modify this behavior. If the value is 14897 FLOAT (the default), the bounding box is set for an 14898 11x11 inch page. If the value is set to FIXED, the 14899 bounding box will be set according to whatever the current 14900 orientation is when the device is initialized. However, 14901 you should not change the orientation if FIXED is used. 14902 14903 If you are simply using the Postscript output for printing, 14904 then you do not need to worry about this command. However, 14905 it may occasionally be useful if are importing the Postscript 14906 output into an external program. 14907 14908Note: 14909 In addition to Dataplot's native Postscript driver, you 14910 can also generate Postscript output using 14911 14912 DEVICE 2 LIBPLOT POSTSCRIPT 14913 DEVICE 2 CAIRO POSTSCRIPT 14914 14915 Libplot and Cairo are graphics libraries that support 14916 a number of different graphics devices. 14917 14918Default: 14919 Postscript is the default for the DEVICE 3 output. 14920 14921Synonyms: 14922 DEVICE 2 EPS is a synonym for DEVICE 2 POSTSCRIPT ENCAPSULATED 14923 SET POSTSCRIPT DEFAULT COLOR is a synonym for SET POSTSCRIPT 14924 COLOR DEFAULT 14925 14926DEVICE NOTES 14927 1) HARDWARE TEXT - Postscript hardware characters can be scaled to 14928 any size. Vertical strings are rotated 90 degrees. There are 14929 34 typeset fonts that can be selected. Postscript fonts are 14930 of publication quality. 14931 14932 2) COLOR - Postscript devices are treated as black and white by 14933 default (although they do support gray scale). To activate 14934 color, enter DEVICE 2 COLOR ON after the DEVICE 2 POSTSCRIPT 14935 command> Postscript supports the full range of DATAPLOT colors. 14936 The appearance of a specific color can vary depending on the 14937 device. 14938 14939 3) HARDWARE FILL - Area fills are generated in hardware. 14940 14941 4) DASH PATTERNS - The Postscript driver supports unique dash 14942 patterns for DASH, DOT, DASH2, DASH3, and DASH4. DASH5 is the 14943 same as DASH4. 14944 14945 5) LINE WIDTH - Thick lines are generated in hardware. 14946 14947 6) GRAPHICS INPUT - The CROSS-HAIR command is ignored for this 14948 device. 14949 14950Related Commands: 14951 CALCOMP = Direct graphical output to a Calcomp 14952 device. 14953 HPGL = Direct graphical output to an HPGL device. 14954 TEKTRONIX = Direct graphical output to a Tektronix 14955 device. 14956 X11 = Direct graphical output to an X11 device. 14957 DEVICE = Specify certain actions for the graphics 14958 output. 14959 SHOW COLOR = Show the available colors on the Postscript 14960 device. 14961 SET POSTSCRIPT CONVERT = Automatically convert Postscript output to 14962 a specified format when Postscript device 14963 is closed. 14964 PSVIEW = View the most recent plot in a Postscript 14965 viewer. 14966 14967Applications: 14968 Graphics Output 14969 14970Implementation Date: 14971 1989/02 14972 1989/06: Support for SET POSTSCRIPT FONT 14973 2003/01: Better handling of first page so a blank page will 14974 not be generated 14975 2003/01: Support for SET POSTSCRIPT BOUNDING BOX 14976 2003/01: LANDSCAPE WORDPERFECT orientation supported for 14977 regular Postscript 14978 2004/06: Support for SET POSTSCRIPT COLOR DEFAULT 14979 2009/05: Automatic support (i.e., SYMBOL font does not need to be 14980 set) for Greek characters and certain special symbols 14981 14982Program: 14983 DEVICE 2 POSTSCRIPT 14984 PLOT X**2 FOR X = 1 1 9 14985 DEVICE 2 CLOSE 14986 14987-----POSTSCRIPT BOUNDING BOX (SET)--------------------------------------- 14988 14989POSTSCRIPT BOUNDING BOX 14990 14991Name: 14992 POSTSCRIPT BOUNDING BOX (SET) 14993 14994Type: 14995 Set Subcommand 14996 14997Purpose: 14998 Specify whether the bounding box generated by Dataplot Postscript 14999 output will be "fixed" or "floating". 15000 15001Description: 15002 For Postscript output, Dataplot allows the orientation to be 15003 switched between landscape and portrait mode. For this reason, 15004 Dataplot sets the bounding box equivalent to an 11 inch x 11 inch 15005 page to accomodate either mode. 15006 15007 When importing Dataplot Postscript files into other programs, 15008 it may be prefferable to have the bounding box reflect either 15009 the landscape (i.e., 11 inch x 8.5 inch) or portrait (i.e., 15010 8.5 inch x 11 inch) orientation. 15011 15012 Setting this switch to FIXED will set the bounding box according 15013 to whatever orientation is in effect when the DEVICE 2 POSTSCRIPT 15014 command is entered. In this case, you should not change the 15015 orientation until a DEVICE 2 CLOSE command is entered. Setting 15016 this swith to FLOAT will use the default 11 inch x 11 inch 15017 bounding box (and you can change the orientation as often as you 15018 like). 15019 15020 If you are only interested in printing the Postscript file, you 15021 can ignore this command. If you intend to import the Postscript 15022 file into another program, it may be helpful to set the FIXED 15023 option. 15024 15025 This command does not apply to encapsulated Postscript files. 15026 Since encapsulated assumes that each graph will be in a separate 15027 file, it already sets the bounding box according to the orientation. 15028 15029Syntax: 15030 SET POSTSCRIPT BOUNDING BOX <FIXED/FLOAT> 15031 where FIXED specifies that the bounding box will be set using the 15032 current orientation and FLOAT sets the bounding box assuming 15033 that either landscape or portait orientation may be used. 15034 15035Examples: 15036 SET POSTRSCRIPT BOUNDING BOX FIXED 15037 SET POSTRSCRIPT BOUNDING BOX FLOAT 15038 15039Default: 15040 The default is FLOAT. 15041 15042Synonyms: 15043 None 15044 15045Related Commands: 15046 DEVICE xx POSTSCRIPT = Set the device to Postscript. 15047 ORIENTATION = Set the orientation of the plot. 15048 15049Applications: 15050 Graphics Output 15051 15052Implementation Date: 15053 2003/1 15054 15055Program: 15056 SET POSTSCRIPT BOUNDING BOX FIXED 15057 ORIENTATION LANDSCAPE 15058 DEVICE 2 POSTSCRIPT 15059 PLOT SIN(X) FOR X = -6 0.1 6 15060 DEVICE 2 CLOSE 15061 15062-----POSTSCRIPT CONVERT (SET)--------------------------------------- 15063 15064POSTSCRIPT CONVERT 15065 15066Name: 15067 POSTSCRIPT CONVERT (SET) 15068 15069Type: 15070 Set Subcommand 15071 15072Purpose: 15073 Specify that when a Postscript device is closed it will 15074 automatically be converted to the specified device. 15075 15076Description: 15077 It is often desirable to import Dataplot generated graphs 15078 into external programs. This includes word processors 15079 (e.g., Word, Word Perfect), presentation software (e.g., 15080 Power Point), image manipulation programs (e.g., gimp, 15081 pbm image conversion programs), image viewers (xv), web browsers, 15082 graphics editors (e.g., Photoshop, Corel Draw), and so on. 15083 15084 Most of these programs will accept Postscript or encapsulated 15085 Postscript as input. However, in some cases, non-Postscript 15086 formats are needed or preferred. For example, web browsers 15087 typically expect GIF, PNG, or JPEG images. Also, Dataplot 15088 does not generate the optional bit-map preview for encapsulated 15089 Postscript (although you can add one using Ghostview on Windows). 15090 Most programs do not actually convert Postscript files. Instead, 15091 they use the bit-map preview when displaying on non-Postscript 15092 devices and the original Postscript when displaying on Postscript 15093 devices. In these cases, it may be more convenient to import a 15094 JPEG version of the graph. 15095 15096 The SET POSTSCRIPT CONVERT command is used to specify one of the 15097 following devices: 15098 15099 1) JPEG 15100 2) PDF (Portable Document Format) 15101 3) TIFF (Ghostscript supports a number of tiff devices, Dataplot 15102 currently uses the "tifflzw" device) 15103 4) PBM (Portable Bit Map, supports black and white only) 15104 5) PGM (Portable Grey Map, supports greyscale, but not color) 15105 6) PPM (Portable Pix Map, supports color) 15106 7) PNM (Portable Any Map, covers PBM, PGM, PPM) 15107 15108 If one of these devices is set and a Postscript device is closed, 15109 then Dataplot invokes Ghostscript to convert the Postscript output 15110 to the specified device. The original Postscript file is preserved. 15111 The new file has the same name with the file extension replaced with 15112 "jpg", "pdf", "tif", "pbm", "pgm", "ppm", or "pnm" (depending on 15113 the selected device). 15114 15115 Note that Ghostscript supports conversion to a wide variety of 15116 output devices. The devices selected above were the ones that 15117 are the most useful in exporting Dataplot graphs to other software 15118 programs. Since our purpose for this command was to provide graphics 15119 formats suitable for input into other programs, we did not add support 15120 for the printer devices. If your main interest is simply in printing 15121 to a non-Postscript device, then run Ghostview after exiting Dataplot 15122 to print the Postscript file. 15123 15124 Between the original Postscript and the devices supported using the 15125 SET POSTSCRIPT CONVERT, it should be possible to import Dataplot 15126 graphics into most external programs. In particular, the JPEG and 15127 PBM formats (PBM, PGM, PPM, and PNM) are supported by most image 15128 conversion programs. 15129 15130 Alternatively, you can also use the "convert" program from the 15131 Image Magick software or the PS2PDF program (part of the Ghostscript 15132 installation). See the Note section below for details. 15133 15134Syntax 1: 15135 SET POSTSCRIPT CONVERT <device> 15136 where <device> is one of JPEG, PDF, TIFF, PBM, PGM, PPM, or PNM 15137 (any other choice is converted to NULL). 15138 15139Syntax 2: 15140 SET POSTSCRIPT CONVERT <program> 15141 where <program> is one of GHOSTSCRIPT, CONVERT, or PS2PDF. 15142 15143Syntax 3: 15144 SET POSTSCRIPT CONVERT <program> <device> 15145 where <program> is one of GHOSTSCRIPT, CONVERT, or PS2PDF; 15146 and <device> is one of JPEG, PDF, TIFF, PBM, PGM, PPM, or PNM 15147 (any other choice is converted to NULL). 15148 15149Examples: 15150 SET POSTRSCRIPT CONVERT PDF 15151 SET POSTRSCRIPT CONVERT JPEG 15152 SET POSTRSCRIPT CONVERT PPM 15153 15154Note: 15155 This command assumes that Ghostscript is installed on your local 15156 system. Currently, it is implemented on Unix (this includes Linux, 15157 Mac OSX, and FreeBSD) and Windows platforms. It can easily be 15158 extended to any platform (e.g., VAX VMS) to which Ghostscript has 15159 been ported. Contact Alan Heckert (alan.heckert@nist.gov) if 15160 you have a platform that you would like supported. 15161 15162 For Unix platforms, Ghostscript is launched with the command 15163 15164 gs 15165 15166 If gs is not in your default path, you can enter something like 15167 15168 set ghostscript path /usr/local/bin 15169 15170 On Windows platforms, Ghostscript is launched with 15171 15172 <ghostscript path>\GSWIN32C.EXE 15173 15174 where <ghostscript path> is the directory defined by the 15175 SET GHOSTSCRIPT PATH command. As of the 08/2019 version of 15176 Dataplot, the default path is 15177 15178 C:\Program Files\GS\GS9.27\BIN 15179 15180 If Ghostscript is installed in a different directory (typically the 15181 "GS9.27" will be different if you have installed a different version 15182 of Ghostscript), you can specify the correct directory with the command 15183 15184 SET GHOSTSCRIPT PATH <path-name> 15185 15186 Enter HELP GHOSTSCRIPT PATH for details. 15187 15188 If you have installed the 64-bit version of Ghostscript, enter the 15189 command 15190 15191 SET GHOSTSCRIPT VERSION 64 15192 15193 This will run the command GSWIN64C.EXE instead of GSWIN32C.EXE. 15194 15195 To reset the 32-bit version, enter 15196 15197 SET GHOSTSCRIPT VERSION 32 15198 15199 If you select the CONVERT option, you must have the Image Magick 15200 software installed on your local platform and the convert program 15201 should be in your default path. 15202 15203Note: 15204 If you use the GHOSTSCRIPT or PS2PDF option on Windows platforms, 15205 there are two addtional issues to consider. 15206 15207 1. Dataplot will typically try to run the underlying SYSTEM 15208 command in "hidden" mode. In "hidden" mode, the command 15209 prompt window will not pop up. 15210 15211 However, if either the program name or the file name 15212 contains spaces, the hidden mode cannot currently be 15213 used. In particular, the path name for the Ghostscript 15214 directory contains a space (i.e., the "Program Files") 15215 15216 One solution is to add the following directory to 15217 your default path 15218 15219 C:\Program Files\gs\gs9.27\bin 15220 15221 Change 9.27 to match the version of Ghostscript you have 15222 installed. Also, non-English systems will typically have a 15223 slightly different name for "Program Files". 15224 15225 2. For the PS2PDF option, the PS2PDF.BAT script is actually 15226 in the "lib" directory. In addition, the script calls 15227 the Ghostscript executable without a path name. So if 15228 you want to use PS2PDF, then the following directories 15229 need to be added to your default path 15230 15231 C:\Program Files\gs\gs9.27\bin 15232 C:\Program Files\gs\gs9.27\lib 15233 15234 To add directories to your default path, do the following 15235 15236 1. Bring up the Control Panel. 15237 2. Select "System and Security". 15238 3. Select "System". 15239 4. Select "Advanced System Settings". 15240 5. Select "Environment Variables". 15241 15242 Then use the "Enviroment Variables" menu to add the needed 15243 directories. 15244 15245Note: 15246 By default, the conversion is performed by Ghostscript. You can also 15247 specify the "convert" program that is part of the Image Magick software 15248 by entering the command 15249 15250 SET POSTSCRIPT CONVERT CONVERT 15251 15252 To reset the use of Ghostscript, enter 15253 15254 SET POSTSCRIPT CONVERT GHOSTSCRIPT 15255 15256 You can also specify the use of the ps2pdf program to perform the 15257 conversion. The ps2pdf program is a batch script file that is 15258 typically installed as part of the Ghostscript installation. Linux 15259 installations will typically have Ghostcript and ps2pdf installed. 15260 15261 The GHOSTSCRIPT option generates a Ghostscript command to perform the 15262 conversion, so the GHOSTSCRIPT and PS2PDF options perform essentially 15263 the same conversion. The advantage of the PS2PDF option is that it 15264 has a simpler syntax. The advantage of the GHOSTSCRIPT option is 15265 that it is not limited to converting the Postscript to PDF format 15266 (it also supports JPEG, TIFF, PBM, PBM, PGM, PPM, and PNM). 15267 15268 The SET GHOSTSCRIPT PATH applies to the PS2PDF option as well. 15269 15270Note: 15271 The converted image is created with a density of 72 dots per inch 15272 in both the horizontal and vertical directions. You can specify a 15273 different resolution with the commands 15274 15275 SET CONVERT DENSITY HORIZONTAL <value> 15276 SET CONVERT DENSITY VERTICAL <value> 15277 15278Note: 15279 When converting to an image format, you will typically want each 15280 graph in a separate file. You can do this as follows: 15281 15282 SET POSTSCRIPT CONVERT JPEG 15283 ORIENTATION LANDSCAPE WORDPERFECT 15284 SET IPL1NA PLOT1.PS 15285 DEVICE 2 POSTSCRIPT 15286 ... generate first plot ... 15287 DEVICE 2 CLOSE 15288 SET IPL1NA PLOT2.PS 15289 DEVICE 2 POSTSCRIPT 15290 ... generate second plot ... 15291 DEVICE 2 CLOSE 15292 15293 After these commands are run, you will have the Postscript files 15294 PLOT1.PS and PLOT2.PS. In addition, you will have the JPEG 15295 files PLOT1.jpg and PLOT2.jpg. 15296 15297 PDF may sometimes be the exception. Acroread (and other PDF 15298 viewers) can read PDF files with multiple graphs in them. 15299 15300Note: 15301 The CAPTURE HTML <file> command is used to generate Dataplot 15302 output to a web page. 15303 15304 If the PDF format is specified and the CAPTURE HTML command 15305 is activated, Dataplot will generate a link to the PDF file 15306 in the generated HTML code. Enter HELP CAPTURE for more 15307 information about the CAPTURE HTML option 15308 15309Note: 15310 On some platforms, Dataplot can generate PNG and JPEG image 15311 files directly. Enter HELP GD for details. 15312 15313Default: 15314 The default is device is NULL (i.e., no conversion is performed). 15315 15316Synonyms: 15317 SET OUTPUT DEVICE 15318 15319Related Commands: 15320 DEVICE xx POSTSCRIPT = Set the device to Postscript. 15321 POSTSCRIPT CONVERT = Specify the device that Postscript 15322 output will be converted to. 15323 PP = Print the current plot. 15324 SET GHOSTSCRIPT PATH = Set the directory where Ghostscript is 15325 installed. 15326 SET GHOSTVIEW PATH = Set the directory where Ghostview (and 15327 GSPRINT) is installed. 15328 SET GHOSTSCRIPT PRINTER = Use Ghostview as the default printer 15329 under Windows. 15330 GD = Specify the GD device for generating 15331 PNG and JPEG graphics. 15332 15333Applications: 15334 Graphics Output 15335 15336Implementation Date: 15337 2003/01 15338 2007/10: Added support for the "convert" program from ImageMagick 15339 2009/03: Added support for user specified density 15340 2019/08: Added support for the "ps2pdf" program 15341 15342Program: 15343 SET GHOSTSCRIPT PATH /usr/local/src/bin/ 15344 SET POSTSCRIPT CONVERT JPEG 15345 DEVICE 2 POSTSCRIPT 15346 PLOT SIN(X) FOR X = -6 0.1 6 15347 DEVICE 2 CLOSE 15348 SYSTEM xv dppl1f.jpg 15349 15350-----POSTSCRIPT DEFAULT COLOR (SET)---------------------------------- 15351 15352POSTSCRIPT DEFAULT COLOR 15353 15354Name: 15355 POSTSCRIPT DEFAULT COLOR (SET) 15356 15357Type: 15358 Set Subcommand 15359 15360Purpose: 15361 Specify whether Postscript devices default to black and white 15362 or to color. 15363 15364Description: 15365 Postscript devices can be either black and white or color. 15366 Since many Postscript printers are black and white, Dataplot 15367 initializes Postscript devices as black and white when the 15368 15369 DEVICE <1/2/3> POSTSCRIPT 15370 15371 command is entered. After entering this command, you can 15372 then specify that the Postscript device command is color by 15373 entering the command 15374 15375 DEVICE <1/2/3> COLOR ON 15376 15377 Although this works well enough for DEVICE 2 output, it is 15378 problematic for DEVICE 3 output. The DEVICE 3 output contains 15379 the most recent graph only (by default, in Postscript format). 15380 The PP command is used within Dataplot to print this DEVICE 3 15381 output on the default printer. Dataplot automatically 15382 opens and closes DEVICE 3 as needed without any explicit 15383 commands entered by the user. This makes it difficult to 15384 know the appropriate time to enter the DEVICE 3 COLOR ON 15385 command and cumbersome even if you can figure out when to 15386 enter the command. 15387 15388 For this reason, we have added the SET POSTSCRIPT DEFAULT COLOR 15389 command to specify whether the default for Postscript devices 15390 should be black and white or color. Although this command 15391 was motivated by the DEVICE 3 command, it applies to 15392 DEVICE 1 POSTSCRIPT and DEVICE 2 POSTSCRIPT commands as well. 15393 15394Syntax: 15395 SET POSTSCRIPT DEFAULT COLOR <ON/OFF> 15396 where <ON> specifies that Postscript devices will default 15397 to color and <OFF> specifies that they will default 15398 to black and white. 15399 15400Examples: 15401 SET POSTRSCRIPT DEFAULT COLOR ON 15402 SET POSTRSCRIPT DEFAULT COLOR OFF 15403 15404Default: 15405 The default is OFF (i.e., Postscript devices default to black 15406 and white). 15407 15408Synonyms: 15409 None 15410 15411Related Commands: 15412 DEVICE xx POSTSCRIPT = Set the device to Postscript. 15413 POSTSCRIPT CONVERT = Specify the device that Postscript 15414 output will be converted to. 15415 PP = Print the current plot. 15416 SET GHOSTSCRIPT PRINTER = Use Ghostview as the default printer 15417 under Windows. 15418 15419Applications: 15420 Graphics Output 15421 15422Implementation Date: 15423 2004/6 15424 15425Program: 15426 SET POSTSCRIPT DEFAULT COLOR ON 15427 DEVICE 2 POSTSCRIPT 15428 LINE COLOR BLUE 15429 PLOT SIN(X) FOR X = -6 0.1 6 15430 PP 15431 15432-----POSTSCRIPT SHOW FONTS----------------------------------------- 15433 15434POSTSCRIPT SHOW FONTS 15435 15436Name: 15437 POSTSCRIPT SHOW FONTS 15438 15439Type: 15440 Output Devices Command 15441 15442Purpose: 15443 List the available Postscript fonts and the commands to set the 15444 fonts. 15445 15446Description: 15447 DATAPLOT supports 34 Postscript fonts. The Postscript font is 15448 used whenever hardware characters are generated on a Postscript 15449 device. Postscript fonts are publication quality typeset fonts. 15450 This command is provided as a convenience to easily list the 15451 available fonts (and the command for setting it). 15452 15453 The sample output is as follows: 15454 15455 POSTSCRIPT FONT: Times-Roman 15456 SET POSTSCRIPT FONT TROM 15457 SET POSTSCRIPT TIMES ROMAN 15458 15459 The first line is the name of the font while the next two lines 15460 give the command for setting the font. 15461 15462Syntax: 15463 POSTSCRIPT SHOW FONTS 15464 15465Examples: 15466 POSTSCRIPT SHOW FONTS 15467 15468Default: 15469 None 15470 15471Synonyms: 15472 None 15473 15474Related Commands: 15475 SET POSTSCRIPT FONT = Specify the Postscript font to use. 15476 POSTSCRIPT = Direct graphical output to a Postscript 15477 device. 15478 15479Applications: 15480 XX 15481 15482Implementation Date: 15483 XX 15484 15485Program: 15486 POSTSCRIPT SHOW FONTS 15487 SET POSTSCRIPT FONT TROM 15488 15489-----POWCDF (LET)-------------------------------- 15490 15491POWCDF 15492 15493Name: 15494 POWCDF (LET) 15495 15496Type: 15497 Library Function 15498 15499Purpose: 15500 Compute the power function cumulative distribution function. 15501 15502Description: 15503 The cumulative distribution function of the standard 15504 power distribution is 15505 15506 F(x,c) = x**c 0 <= x <= 1; c > 0 15507 15508 The standard power distribution can be generalized with 15509 lower and upper bound parameters. If a and be denote the 15510 lower and upper bounds, then the location and scale 15511 parameters are: 15512 15513 location = a 15514 scale = b - a 15515 15516 The general form of the power distribution can then be 15517 found using the relation 15518 15519 F(x;c,a,b) = F((x-a)/(b-a);c,0,1) 15520 15521 If X has a Pareto distribution, then 1/X has a power 15522 distribution. The power distribution is also a special 15523 case of the beta distribution where the second shape 15524 parameter is equal to 1. 15525 15526Syntax: 15527 LET <y> = POWCDF(<x>,<c>,<a>,<b>) 15528 <SUBSET/EXCEPT/FOR qualification> 15529 where <x> is a number, parameter, or variable in the 15530 interval a to b; 15531 <c> is a number, parameter, or variable that specifies the 15532 shape parameter; 15533 <a> is a number, parameter, or variable that 15534 specifies the lower limit; 15535 <b> is a number, parameter, or variable that 15536 specifies the upper limit; 15537 <y> is a variable or a parameter (depending on what <x> is) 15538 where the computed power function cdf value is saved; 15539 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 15540 15541 If the <a> and <b> parameters are omitted, the default to 15542 0 and 1, respectively. 15543 15544Examples: 15545 LET A = POWCDF(3,1.5) 15546 LET X2 = POWCDF(X1,C) 15547 15548Note: 15549 Library functions are distinguished from let subcommands 15550 in the following ways. 15551 1) Functions enclose the input value in parenthesis. Let 15552 subcommands use spaces. 15553 2) Functions can accept (and return) either parameters 15554 (i.e., single values) or variables (i.e., an array of 15555 values) while let subcommands are specific in which they 15556 accept as input and what they return as output. 15557 3) Functions can accept expressions while let subcommands 15558 do not. For example, the following is legal: 15559 LET Y2 = ABS(Y1-INT(Y1)) 15560 For let subcommands, you typically have to do something 15561 like the following: 15562 LET YTEMP = Y**2 + 8 15563 LET A = SUM YTEMP 15564 15565Default: 15566 None 15567 15568Synonyms: 15569 None 15570 15571Related Commands: 15572 POWPDF = Compute the power function probability density function. 15573 POWPPF = Compute the power function percent point function. 15574 PARPDF = Compute the Pareto probability density function. 15575 BETPDF = Compute the beta probability density function. 15576 GEPPDF = Compute the generalized Pareto probability density 15577 function. 15578 EXPPDF = Compute the exponential probability density function. 15579 15580Reference: 15581 "Continuous Univariate Distributions", 2nd ed., Johnson, Kotz, and 15582 Balakrishnan, John Wiley and Sons, 1994 (page 607). 15583 15584 "Statistical Distributions", Third Edition, Evans, Hastings, 15585 and Peacock, John Wiley & Sons, 2000. 15586 15587Applications: 15588 Distributional Modeling 15589 15590Implementation Date: 15591 95/4 15592 15593Program: 15594 TITLE POWER FUNCTION CDF'S (0.1, 0.5, 1, 3, 10) 15595 PLOT POWCDF(X,0.1) FOR X = 0.01 0.01 1 AND 15596 PLOT POWCDF(X,0.5) FOR X = 0.01 0.01 1 AND 15597 PLOT POWCDF(X,1) FOR X = 0.01 0.01 1 AND 15598 PLOT POWCDF(X,3) FOR X = 0.01 0.01 1 AND 15599 PLOT POWCDF(X,10) FOR X = 0.01 0.01 1 15600 15601-----POWCHAZ (LET)-------------------------------- 15602 15603POWCHAZ 15604 15605Name: 15606 POWCHAZ (LET) 15607 15608Type: 15609 Library Function 15610 15611Purpose: 15612 Compute the power function cumulative hazard function. 15613 15614Description: 15615 The standard form of the cumulative hazard function is: 15616 15617 H(x,c) = -LOG(1-x**c) 0 <= x <= 1; c > 0 15618 15619 with c denoting the shape parameter. 15620 15621 The standard power distribution can be generalized with 15622 lower and upper bound parameters. If a and be denote the 15623 lower and upper bounds, then the location and scale 15624 parameters are: 15625 15626 location = a 15627 scale = b - a 15628 15629 The general form of the power distribution can then be 15630 found using the relation 15631 15632 H(x;c,a,b) = H((x-a)/(b-a);c,0,1) 15633 15634 If X has a Pareto distribution, then 1/X has a power 15635 distribution. The power distribution is also a special 15636 case of the beta distribution where the second shape 15637 parameter is equal to 1. 15638 15639Syntax: 15640 LET <y> = POWCHAZ(<x>,<c>,<a>,<b>) 15641 <SUBSET/EXCEPT/FOR qualification> 15642 where <x> is a number, parameter, or variable in the 15643 interval a to b; 15644 <c> is a number, parameter, or variable that specifies the 15645 shape parameter; 15646 <a> is a number, parameter, or variable that 15647 specifies the lower limit; 15648 <b> is a number, parameter, or variable that 15649 specifies the upper limit; 15650 <y> is a variable or a parameter (depending on what <x> is) 15651 where the computed power function cumulative hazard 15652 value is saved; 15653 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 15654 15655 If the <a> and <b> parameters are omitted, the default to 15656 0 and 1, respectively. 15657 15658Examples: 15659 LET A = POWCHAZ(3,1.5) 15660 LET X2 = POWCHAZ(X1,C) 15661 15662Note: 15663 Library functions are distinguished from let subcommands 15664 in the following ways. 15665 1) Functions enclose the input value in parenthesis. Let 15666 subcommands use spaces. 15667 2) Functions can accept (and return) either parameters 15668 (i.e., single values) or variables (i.e., an array of 15669 values) while let subcommands are specific in which they 15670 accept as input and what they return as output. 15671 3) Functions can accept expressions while let subcommands 15672 do not. For example, the following is legal: 15673 LET Y2 = ABS(Y1-INT(Y1)) 15674 For let subcommands, you typically have to do something 15675 like the following: 15676 LET YTEMP = Y**2 + 8 15677 LET A = SUM YTEMP 15678 15679Default: 15680 None 15681 15682Synonyms: 15683 None 15684 15685Related Commands: 15686 POWCDF = Compute the power function cumulative distribution 15687 function. 15688 POWHAZ = Compute the power function hazard function. 15689 POWPDF = Compute the power function probability density 15690 function. 15691 POWPPF = Compute the power function percent point function. 15692 PARPDF = Compute the Pareto probability density function. 15693 BETPDF = Compute the beta probability density function. 15694 GEPPDF = Compute the generalized Pareto probability density 15695 function. 15696 EXPPDF = Compute the exponential probability density function. 15697 15698Reference: 15699 "Continuous Univariate Distributions", 2nd ed., Johnson, Kotz, and 15700 Balakrishnan, John Wiley and Sons, 1994 (page 607). 15701 15702 "Statistical Distributions", Third Edition, Evans, Hastings, 15703 and Peacock, John Wiley & Sons, 2000. 15704 15705Applications: 15706 Distributional Modeling 15707 15708Implementation Date: 15709 2007/12 15710 15711Program: 15712 TITLE POWER FUNCTION CUMULATIVE HAZARD FUNCTIONS (0.1, 0.5, 1, 3, 10) 15713 PLOT POWCHAZ(X,0.1) FOR X = 0.01 0.01 0.99 AND 15714 PLOT POWCHAZ(X,0.5) FOR X = 0.01 0.01 0.99 AND 15715 PLOT POWCHAZ(X,1) FOR X = 0.01 0.01 0.99 AND 15716 PLOT POWCHAZ(X,2) FOR X = 0.01 0.01 0.99 AND 15717 PLOT POWCHAZ(X,5) FOR X = 0.01 0.01 0.99 15718 15719-----POWHAZ (LET)-------------------------------- 15720 15721POWHAZ 15722 15723Name: 15724 POWHAZ (LET) 15725 15726Type: 15727 Library Function 15728 15729Purpose: 15730 Compute the power function hazard function. 15731 15732Description: 15733 The standard form of the hazard function is: 15734 15735 h(x,c) = c*x**(c-1)/(1-x**c) 0 <= x < 1; c > 0 15736 15737 with c denoting the shape parameter. 15738 15739 The standard power distribution can be generalized with 15740 lower and upper bound parameters. If a and be denote the 15741 lower and upper bounds, then the location and scale 15742 parameters are: 15743 15744 location = a 15745 scale = b - a 15746 15747 The general form of the power distribution can then be 15748 found using the relation 15749 15750 h(x;c,a,b) = (1/(b-a))*h((x-a)/(b-a);c,0,1) 15751 15752 If X has a Pareto distribution, then 1/X has a power 15753 distribution. The power distribution is also a special 15754 case of the beta distribution where the second shape 15755 parameter is equal to 1. 15756 15757Syntax: 15758 LET <y> = POWHAZ(<x>,<c>,<a>,<b>) 15759 <SUBSET/EXCEPT/FOR qualification> 15760 where <x> is a number, parameter, or variable in the 15761 interval a to b; 15762 <c> is a number, parameter, or variable that specifies the 15763 shape parameter; 15764 <a> is a number, parameter, or variable that 15765 specifies the lower limit; 15766 <b> is a number, parameter, or variable that 15767 specifies the upper limit; 15768 <y> is a variable or a parameter (depending on what <x> is) 15769 where the computed power function hazard value is saved; 15770 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 15771 15772 If the <a> and <b> parameters are omitted, the default to 15773 0 and 1, respectively. 15774 15775 15776Examples: 15777 LET A = POWHAZ(3,1.5) 15778 LET X2 = POWHAZ(X1,C) 15779 15780Note: 15781 Library functions are distinguished from let subcommands 15782 in the following ways. 15783 1) Functions enclose the input value in parenthesis. Let 15784 subcommands use spaces. 15785 2) Functions can accept (and return) either parameters 15786 (i.e., single values) or variables (i.e., an array of 15787 values) while let subcommands are specific in which they 15788 accept as input and what they return as output. 15789 3) Functions can accept expressions while let subcommands 15790 do not. For example, the following is legal: 15791 LET Y2 = ABS(Y1-INT(Y1)) 15792 For let subcommands, you typically have to do something 15793 like the following: 15794 LET YTEMP = Y**2 + 8 15795 LET A = SUM YTEMP 15796 15797Default: 15798 None 15799 15800Synonyms: 15801 None 15802 15803Related Commands: 15804 POWCDF = Compute the power function cumulative distribution 15805 function. 15806 POWCHAZ = Compute the power function cumulative hazard 15807 function. 15808 POWPDF = Compute the power function probability density 15809 function. 15810 POWPPF = Compute the power function percent point function. 15811 PARPDF = Compute the Pareto probability density function. 15812 BETPDF = Compute the beta probability density function. 15813 GEPPDF = Compute the generalized Pareto probability density 15814 function. 15815 EXPPDF = Compute the exponential probability density function. 15816 15817Reference: 15818 "Continuous Univariate Distributions", 2nd ed., Johnson, Kotz, and 15819 Balakrishnan, John Wiley and Sons, 1994 (page 607). 15820 15821 "Statistical Distributions", Third Edition, Evans, Hastings, 15822 and Peacock, John Wiley & Sons, 2000. 15823 15824Applications: 15825 Distributional Modeling 15826 15827Implementation Date: 15828 2007/12 15829 15830Program: 15831 TITLE POWER FUNCTION HAZARD FUNCTIONS (0.1, 0.5, 1, 3, 10) 15832 PLOT POWHAZ(X,0.1) FOR X = 0.01 0.01 0.99 AND 15833 PLOT POWHAZ(X,0.5) FOR X = 0.01 0.01 0.99 AND 15834 PLOT POWHAZ(X,1) FOR X = 0.01 0.01 0.99 AND 15835 PLOT POWHAZ(X,2) FOR X = 0.01 0.01 0.99 AND 15836 PLOT POWHAZ(X,5) FOR X = 0.01 0.01 0.99 15837 15838-----POWER LAW RANDOM NUMBERS (LET)---------------------------------- 15839 15840POWER LAW RANDOM NUMBERS 15841 15842Name: 15843 POWER LAW RANDOM NUMBERS (LET) 15844 15845Type: 15846 Let Subcommand 15847 15848Purpose: 15849 Generate random failure times from a non-homogeneous 15850 Poisson process (NHPP) following a power law model. 15851 15852Description: 15853 If you have internet access, you can see a discussion of the 15854 NHPP Power Law model by entering the command: 15855 15856 WEB HANDBOOK NHPP POWER LAW 15857 15858 The non-homogeneous Poisson process power law model is: 15859 15860 M(t) = alpha*t**beta alpha, beta > 0 15861 15862 where M(t) is the expected number of failures at time 15863 t. The random failure times are generated from the 15864 formula for the interarrival times (i.e., the CDF for 15865 the waiting time for the next failure given a failure at 15866 time T): 15867 15868 F (t) = 1 - EXP(-ALPHA*[(T+t)**BETA-T**BETA] 15869 T 15870 15871Syntax: 15872 LET <y> = POWER LAW RANDUM NUMBERS FOR I = <start> <inc> <stop> 15873 where <start> is the starting row for the random numbers; 15874 <inc> is the increment for the random numbers; 15875 <stop> is the stopping row for the random numbers; 15876 <y> is a variable where the power law random numbers 15877 are saved. 15878 15879 Typically <start> and <inc> are 1 and <stop> is set to the 15880 number of random numbers to generate. If <start> and <inc> 15881 are not 1, then <y> will still contain <stop> elements, but 15882 the empty rows will be set to 0. 15883 15884 The alpha and beta parameters are specified with LET commands 15885 before entering the POWER LAW RANDOM NUMBERS command as 15886 demonstrated in the examples below. 15887 15888Examples: 15889 LET ALPHA = 2 15890 LET BETA = 3 15891 LET Y = POWER LAW RANDOM NUMBERS FOR I = 1 1 100 15892 15893 LET ALPHA = 1 15894 LET BETA = 2 15895 LET Y = POWER LAW RANDOM NUMBERS FOR I = 1 1 1000 15896 15897 LET ALPHA = 1 15898 LET BETA = 2 15899 LET Y = POWER LAW RANDOM NUMBERS FOR I = 2 5 100 15900 15901Default: 15902 None 15903 15904Synonyms: 15905 None 15906 15907Related Commands: 15908 RANDOM NUMBERS = Generate random numbers from various 15909 probability distributions. 15910 INTERARRIVAL TIME = Compute the interarrival times of a 15911 variable. 15912 DUANE PLOT = Generate a Duane plot. 15913 15914Applications: 15915 Reliability 15916 15917Implementation Date: 15918 1998/5 15919 15920Program: 15921 LET ALPHA = 2 15922 LET BETA = 3 15923 LET Y = POWER LAW RANDOM NUMBERS FOR I = 1 1 100 15924 X1LABEL ALPHA = ^ALPHA, BETA = ^BETA 15925 TITLE AUTOMATIC 15926 DUANE PLOT Y 15927 15928-----POWPDF (LET)-------------------------------- 15929 15930POWPDF 15931 15932Name: 15933 POWPDF (LET) 15934 15935Type: 15936 Library Function 15937 15938Purpose: 15939 Compute the power function probability density function. 15940 15941Description: 15942 The standard form of the probability density function is: 15943 15944 f(x,c) = c*x**(c-1) 0 <= x <= 1; c > 0 15945 15946 where c is a shape parameter. 15947 15948 The standard power distribution can be generalized with 15949 lower and upper bound parameters. If a and be denote the 15950 lower and upper bounds, then the location and scale 15951 parameters are: 15952 15953 location = a 15954 scale = b - a 15955 15956 The general form of the power distribution can then be 15957 found using the relation 15958 15959 f(x;c,a,b) = (1/(b-a))*f((x-a)/(b-a);c,0,1) 15960 15961 If X has a Pareto distribution, then 1/X has a power 15962 distribution. The power distribution is also a special 15963 case of the beta distribution where the second shape 15964 parameter is equal to 1. 15965 15966 15967Syntax: 15968 LET <y> = POWPDF(<x>,<c>,<a>,<b>) 15969 <SUBSET/EXCEPT/FOR qualification> 15970 where <x> is a number, parameter, or variable in the 15971 interval a to b; 15972 <c> is a number, parameter, or variable that specifies the 15973 shape parameter; 15974 <a> is a number, parameter, or variable that 15975 specifies the lower limit; 15976 <b> is a number, parameter, or variable that 15977 specifies the upper limit; 15978 <y> is a variable or a parameter (depending on what <x> is) 15979 where the computed power function pdf value is saved; 15980 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 15981 15982 If the <a> and <b> parameters are omitted, the default to 15983 0 and 1, respectively. 15984 15985 15986Examples: 15987 LET A = POWPDF(3,1.5) 15988 LET X2 = POWPDF(X1,C) 15989 15990Note: 15991 Library functions are distinguished from let subcommands 15992 in the following ways. 15993 1) Functions enclose the input value in parenthesis. Let 15994 subcommands use spaces. 15995 2) Functions can accept (and return) either parameters 15996 (i.e., single values) or variables (i.e., an array of 15997 values) while let subcommands are specific in which they 15998 accept as input and what they return as output. 15999 3) Functions can accept expressions while let subcommands 16000 do not. For example, the following is legal: 16001 LET Y2 = ABS(Y1-INT(Y1)) 16002 For let subcommands, you typically have to do something 16003 like the following: 16004 LET YTEMP = Y**2 + 8 16005 LET A = SUM YTEMP 16006 16007Default: 16008 None 16009 16010Synonyms: 16011 None 16012 16013Related Commands: 16014 POWCDF = Compute the power function cumulative distribution 16015 function. 16016 POWPPF = Compute the power function percent point function. 16017 PARPDF = Compute the Pareto probability density function. 16018 BETPDF = Compute the beta probability density function. 16019 GEPPDF = Compute the generalized Pareto probability density 16020 function. 16021 EXPPDF = Compute the exponential probability density function. 16022 16023Reference: 16024 "Continuous Univariate Distributions", 2nd ed., Johnson, Kotz, and 16025 Balakrishnan, John Wiley and Sons, 1994 (page 607). 16026 16027 "Statistical Distributions", Third Edition, Evans, Hastings, 16028 and Peacock, John Wiley & Sons, 2000. 16029 16030Applications: 16031 Distributional Modeling 16032 16033Implementation Date: 16034 95/4 16035 16036Program: 16037 TITLE POWER FUNCTION PDF'S (0.1, 0.5, 1, 3, 10) 16038 PLOT POWPDF(X,0.1) FOR X = 0.01 0.01 1 AND 16039 PLOT POWPDF(X,0.5) FOR X = 0.01 0.01 1 AND 16040 PLOT POWPDF(X,1) FOR X = 0.01 0.01 1 AND 16041 PLOT POWPDF(X,3) FOR X = 0.01 0.01 1 AND 16042 PLOT POWPDF(X,10) FOR X = 0.01 0.01 1 16043 16044-----POWPPF (LET)-------------------------------- 16045 16046POWPPF 16047 16048Name: 16049 POWPPF (LET) 16050 16051Type: 16052 Library Function 16053 16054Purpose: 16055 Compute the power function percent point function. 16056 16057Description: 16058 The standard form of the power function percent point 16059 function is 16060 16061 G(p;c) = p**(1/c) 0 <= p <= 1; c > 0 16062 16063 The standard power distribution can be generalized with 16064 lower and upper bound parameters. If a and be denote the 16065 lower and upper bounds, then the location and scale 16066 parameters are: 16067 16068 location = a 16069 scale = b - a 16070 16071 The general form of the power distribution can then be 16072 found using the relation 16073 16074 G(p;c,a,b) = loc + scale*G(p;c,0,1) 16075 16076 If X has a Pareto distribution, then 1/X has a power 16077 distribution. The power distribution is also a special 16078 case of the beta distribution where the second shape 16079 parameter is equal to 1. 16080 16081 16082Syntax: 16083 LET <y> = POWPPF(<p>,<c>,<a>,<b>) 16084 <SUBSET/EXCEPT/FOR qualification> 16085 where <p> is a number, parameter, or variable in the 16086 interval 0 to 1; 16087 <c> is a number, parameter, or variable that specifies the 16088 shape parameter; 16089 <a> is a number, parameter, or variable that 16090 specifies the lower limit; 16091 <b> is a number, parameter, or variable that 16092 specifies the upper limit; 16093 <y> is a variable or a parameter (depending on what <p> is) 16094 where the computed power function ppf value is saved; 16095 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 16096 16097 If the <a> and <b> parameters are omitted, the default to 16098 0 and 1, respectively. 16099 16100 16101Examples: 16102 LET A = POWPPF(0.9,3) 16103 LET X2 = POWPPF(X1,C) 16104 16105Note: 16106 Library functions are distinguished from let subcommands 16107 in the following ways. 16108 1) Functions enclose the input value in parenthesis. Let 16109 subcommands use spaces. 16110 2) Functions can accept (and return) either parameters 16111 (i.e., single values) or variables (i.e., an array of 16112 values) while let subcommands are specific in which they 16113 accept as input and what they return as output. 16114 3) Functions can accept expressions while let subcommands 16115 do not. For example, the following is legal: 16116 LET Y2 = ABS(Y1-INT(Y1)) 16117 For let subcommands, you typically have to do something 16118 like the following: 16119 LET YTEMP = Y**2 + 8 16120 LET A = SUM YTEMP 16121 16122Default: 16123 None 16124 16125Synonyms: 16126 None 16127 16128Related Commands: 16129 POWCDF = Compute the power function cumulative distribution 16130 function. 16131 POWPDF = Compute the power function probability density function. 16132 PARPDF = Compute the Pareto probability density function. 16133 BETPDF = Compute the beta probability density function. 16134 GEPPDF = Compute the generalized Pareto probability density 16135 function. 16136 EXPPDF = Compute the exponential probability density function. 16137 16138Reference: 16139 "Continuous Univariate Distributions", 2nd ed., Johnson, Kotz, and 16140 Balakrishnan, John Wiley and Sons, 1994 (page 607). 16141 16142 "Statistical Distributions", Third Edition, Evans, Hastings, 16143 and Peacock, John Wiley & Sons, 2000. 16144 16145Applications: 16146 Distributional Modeling 16147 16148Implementation Date: 16149 95/5 16150 16151Program: 16152 TITLE POWER FUNCTION PPF'S (0.5, 1, 3) 16153 LINE DASH SOLID DOT 16154 PLOT POWPPF(P,0.5) FOR P = 0 .01 1 AND 16155 PLOT POWPPF(P,1) FOR P = 0 .01 1 AND 16156 PLOT POWPPF(P,3) FOR P = 0 .01 1 16157 16158-----PP------------------------------------------------------- 16159 16160PP 16161 16162Name: 16163 PP 16164 16165Type: 16166 Support Command 16167 16168Purpose: 16169 Send the most recent plot to the printer. 16170 16171Description: 16172 DEVICE 3 (in file DPPL2F.DAT, name may vary on some systems) 16173 output is closed and re-opened at the beginning of a plot command, 16174 so only the most recent plot is in the graphics file. 16175 16176Syntax: 16177 PP 16178 16179Examples: 16180 PP 16181 16182Note: 16183 This command is operating system dependent. It is currently 16184 supported on the IBM PC and Unix (except Cray UNICOS). It has 16185 been coded (but not tested) for VAX/VMS. The primary requirement 16186 for supporting it on other systems is the ability to send a 16187 command to the operating system from a Fortran program. Contact 16188 your local site installer to see about adding this capability to 16189 your version if it does not currently work. 16190 16191Note: 16192 This command sends the file to the default printer. On the IBM PC, 16193 this is LPT1 (i.e., the printer connected to your PC). For Unix, 16194 enter the setenv PRINTER command before entering DATAPLOT. 16195 16196Note: 16197 By default, Postscript output is generated. To use another 16198 device, enter the following commands: 16199 DEVICE 3 CLOSE 16200 DEVICE 3 <device> <model> 16201 16202Note: 16203 When generating complex and time consuming plots, you may want to 16204 suppress the DEVICE 3 output. Enter the following commands to do 16205 this: 16206 DEVICE 3 CLOSE 16207 DEVICE 3 NULL 16208 16209Note: 16210 For Postscript devices, DATAPLOT normally generates a blank page 16211 before the first plot (to avoid problems if diagrammatic graphics 16212 are done before the first plot). This can be a bit of a nuisance 16213 for the PP command since only one plot is printed. The BLANK 16214 POSTSCRIPT command is used to control whether this blank page 16215 is generated (by default, is not for DEVICE 3). 16216 16217 This command does not affect Postscript output sent to device 16218 2 (use the PRE-ERASE OFF for a similar effect). 16219 16220Default: 16221 None 16222 16223Synonyms: 16224 ADD 16225 16226Related Commands: 16227 / PRINTER = Re-execute saved commands and send the output to the 16228 printer. 16229 / PSPRINTER = Re-execute saved commands and send the output to the 16230 printer in Postscript format. 16231 16232Applications: 16233 Printing 16234 16235Implementation Date: 16236 1992/07 16237 16238Program: 16239 PLOT X**2 FOR X = 1 1 9 16240 PP 16241 16242-----PPCC PLOT------------------------------------------------------- 16243 16244PPCC PLOT 16245 16246Name: 16247 ... PPCC PLOT 16248 ... KOLMOGOROV SMIRNOV PLOT 16249 ... ANDERSON DARLING PLOT 16250 ... CHI-SQUARE PLOT 16251 16252Type: 16253 Graphics Command 16254 16255Purpose: 16256 Generates a probability plot correlation coefficient (PPCC) 16257 plot. Alternatively, generate the plot based on other 16258 goodness of fit criterion. 16259 16260Description: 16261 A PPCC plot is a graphical data analysis technique for determining 16262 that member of the specified distributional family which provides 16263 a "best" distributional fit to the data. 16264 16265 The PPCC plot is based on the following two ideas: 16266 16267 1) The "straightness" of the probability plot is a good measure 16268 of distributional fit. That is, the "best" distributional 16269 fit is the one with the most linear probability plot. 16270 16271 2) The correlation coefficient of the points on the 16272 probabability plot is a good measure of the "straightness" 16273 (i.e., linearity) of the probability plot. 16274 16275 The PPCC plot is formed by selecting a value of the shape parameter, 16276 generating the probability plot (this probability plot is not 16277 actually graphed), and then computing the correlation coefficient 16278 of the resulting probability plot. The PPCC plot then consists of: 16279 16280 Vertical axis = probability plot correlation coefficient 16281 value for the given value of the shape parameter; 16282 Horizontal axis = distributional family parameter value (i.e., 16283 the value of the shape parameter. 16284 16285 The value of the distributional parameter (on the horizontal axis) 16286 which corresponds to the maximum of the PPCC plot curve (on the 16287 vertical axis) is, of course, of interest since it indicates the 16288 best-fit member of the family. 16289 16290 The PPCC PLOT has been extended to support the following 16291 additional goodness of fit statistics: 16292 16293 1) the Kolmogorov-Smirnov goodness of fit statistic; 16294 16295 2) the Anderson-Darling goodness of fit statistic; 16296 16297 3) the chi-square goodness of fit statistic. 16298 16299 For these alternative measures of goodness of fit, we follow a 16300 similar procedure. That is, we fix a value of the shape 16301 parameter, generate the corresponding probability plot in the 16302 background to obtain estimates for location and scale, and then 16303 compute the goodness of fit statistic based on these parameters. 16304 For these goodness of fit statistics, we are looking for the 16305 minimum value of the statistic rather than the maximum value of 16306 the statistic. 16307 16308 Some advantages of the PPCC plot as a fitting technique are: 16309 16310 1) The probability plot is invariant with respect to location 16311 and scale. This means that the fundamental linearity of the 16312 probability plot does not depend on the values of the 16313 location and shape parameters (i.e., we could plug-in 16314 any arbitrary values for them and the probability plot 16315 would still have the same linearity as measured by the 16316 ppcc statistic. The property follows from the fact that 16317 16318 G(p;loc,scale,shape) = loc + scale*G(p;0,1,shape) 16319 16320 where G denotes the percent point function of the 16321 specified distribution. So for the probability plot, 16322 using different values for loc and scale will change the 16323 scale on the x-axis, but not the linearity. 16324 16325 Once we determine the optimal value of the shape parameter 16326 from the PPCC plot, we can generate the corresponding 16327 probability plot. The intercept and slope of line fit to 16328 the probability provide valid estimates of location and 16329 scale (the Dataplot probability plot is designed in such a 16330 way that this is true). 16331 16332 Note: the Anderson-Darling, Kolmogorv-Smirnov, and 16333 chi-square variants are based on the cumulative 16334 distribution function and do not share this invariance 16335 property. However, we can still use the underlying 16336 probability plot to obtain estimates of location and 16337 scale for a given value of the shape parameter. 16338 16339 2) The probability plot, and thus the PPCC plot, only depends on 16340 the percent point function. That is, if we know how to 16341 compute the percent point function, we can use the 16342 PPCC plot/probability plot to estimate the parameters of 16343 the distribution. 16344 16345 The Anderson-Darling, Kolmogorov-Smirnov, and chi-square 16346 variants also depend on computing the cumulative 16347 distribution function. 16348 16349 3) The PPCC plot can show the sensitivity of the shape parameter. 16350 That is, it can show what neighborhood of the parameter 16351 estimate is likely to produce a reasonably straight 16352 probability plot. 16353 16354 4) The PPCC plot can be applied to binned data. 16355 16356 The chi-square variant can also be applied to binned data. 16357 Currently, the Anderson-Darling and Kolmogorov Smirnov 16358 variants cannot be applied to binned data. 16359 16360 5) The PPCC plot can be applied to censored data. 16361 16362 A censored PPCC plot is generated by finding the value 16363 of the shape parameter that results in the maximum 16364 correlation coefficient of the censored probability plot. 16365 For details on how the censored probablity plot is 16366 generated, enter the command 16367 16368 HELP PROBABILITY PLOT 16369 16370 The censoring variable should contain a 1 to indicate 16371 a failure time and a 0 to indicate a censoring time. 16372 The censored PPCC plot is not suppported for binned data. 16373 16374 The censoring option is not currently supported by the 16375 Anderson-Darling, Kolmogorov-Smirnov, and chi-square 16376 variants of the plot. 16377 16378 Some disadvantages of the PPCC plot as a fitting technique are: 16379 16380 1) The PPCC plot (and its variants) do not have the 16381 mathematical optimality properties that analytic 16382 methods such as maximum likelihood have. 16383 16384 2) If the percent point function is expensive to compute 16385 (e.g., if it involves the numerical inversion of a rather 16386 complicated cumulative distribution function), the ppcc 16387 plot can be slow to generate. These types of percent 16388 point functions may also have convergence problems. 16389 16390 In these cases, the SET PPCC PLOT DATA POINTS may be 16391 helpful in reducing the computational burden. See the 16392 Note section below. 16393 16394 2) The PPCC plot does not produce interval estimates for the 16395 parameters. 16396 16397 The bootstrap provides a method for generating these 16398 interval estimates. For details, enter 16399 16400 HELP DISTRIBUTIONAL BOOTSTRAP 16401 16402 3) Heavy-tailed distributions may have very high variability 16403 in the extremes of the data. This can sometimes lead to 16404 poor discrimination in the plot. 16405 16406 In our experience, the Anderson-Darling and 16407 Kolmogorov-Smirnov variants of the plot may perform better 16408 for these cases. 16409 16410 4) If a shape parameter behaves much like a scale or 16411 location parameter, the PPCC plot may not discriminate 16412 well. 16413 16414 The Anderson-Darling and Kolmogorov-Smirnov variants have 16415 the option of fixing the values of the location and scale 16416 parameters. This can sometimes be useful in these cases. 16417 16418 5) The PPCC plot does not generate smooth curves for discrete 16419 distributions due to the discreteness of the percent point 16420 function. For discrete distributions, the chi-square 16421 variant of the plot typically produces smoother plots. 16422 16423 6) The PPCC plot does not extend well to more than one 16424 shape parameter. 16425 16426 Dataplot has extended the PPCC plot to distributions with 16427 two shape parameters. Dataplot supports two formats for 16428 the PPCC plot with two shape parameters: 16429 16430 1) As in the one shape parameter case, the Y axis will 16431 contain the value of the correlation coefficient. The 16432 X axis will contain the value of the second shape 16433 parameter. Each value of the first shape parameter will 16434 be represented by a separate trace (i.e., curve) on the 16435 plot. 16436 16437 To change the order of the shape parameters in the 16438 above format, enter the command 16439 16440 SET PPCC PLOT AXIS ORDER REVERSE 16441 16442 To restore the default order, enter the command 16443 16444 SET PPCC PLOT AXIS ORDER DEFAULT 16445 16446 2) Alternatively, you can generate a 3D wireframe plot. 16447 16448 You can specify which format to use with the command 16449 16450 SET PPCC FORMAT <TRACE/3D> 16451 16452 The PPCC plot now supports two different types of grouping. 16453 16454 1) Some data sets are collected in binned format. That is, 16455 the values for the data are split into intervals and the 16456 number of occurences of the data within each interval are 16457 are counted. 16458 16459 Dataplot supports either equal sized bins (the bin 16460 variable contains the mid-point of the bin) or 16461 unequal size bins (two bin variables are specified: 16462 one contains the lower limit for the bins and the other 16463 contains the upper limits for the bins). 16464 16465 2) The PPCC plot also supports the case where there are 16466 multiple batches of data. In this case, a separate 16467 ppcc curve is drawn for each batch of data (for unbinned 16468 data a curve will also be drawn for the full data 16469 set). We refer to this as the "replication" case 16470 below. Replication can be used for either the raw data 16471 case or the binned data case. 16472 16473 This form is useful for the case where we want to 16474 know if different batches of data can be modeled 16475 with a common shape parameter. One example of this 16476 is accelerated testing where Weibull models should 16477 have a common shape parameter at different stress levels 16478 if a linear accelaraton model is valid. 16479 16480 PPCC plots are available for the following continuous distributional 16481 families (with the distributional parameter in parentheses) with one 16482 shape parameter: 16483 16484 1) Weibull (gamma) 16485 2) double weibull (gamma) 16486 3) inverted weibull (gamma) 16487 4) gamma (gamma) 16488 5) double gamma (gamma) 16489 6) log gamma (gamma) 16490 7) inverted gamma (gamma) 16491 8) Wald (gamma) 16492 9) fatigue life (gamma) 16493 10) Pareto (gamma) 16494 11) Pareto second kind (gamma) 16495 12) generalized Pareto (gamma) 16496 13) generalized half logistic (gamma) 16497 14) extreme value type 2 (gamma) 16498 15) generalized extreme value (gamma) 16499 16) extreme value (gamma, combines Weibull, 16500 extreme value type 2) 16501 17) geometric extreme exponential (gamma) 16502 18) Tukey lambda (lambda) 16503 19) skew normal (lambda) 16504 20) skew double exponential (lambda) 16505 21) t (nu) 16506 22) folded t (nu) 16507 23) chi-squared (nu) 16508 24) chi (nu) 16509 25) generalized logistic (alpha) 16510 26) generalized logistic type 2 (alpha) 16511 27) generalized logistic type 3 (alpha) 16512 28) generalized logistic type 5 (alpha) 16513 29) log double exponential (alpha) 16514 30) error (alpha) 16515 31) McLeish (alpha) 16516 32) lognormal (sd) 16517 33) power-normal (p) 16518 34) Von Mises (b) 16519 35) reciprocal (b) 16520 36) log-logistic (delta) 16521 37) wrapped cauchy (c) 16522 38) power function (c) 16523 39) Bradford (beta) 16524 40) Topp and Leone (beta) 16525 41) asymmetric double exponential (k) 16526 16527 PPCC plots are available for the following continuous distributional 16528 families (with the distributional parameter in parentheses) with two 16529 shape parameters: 16530 16531 1) inverse Gaussian (gamma, mu) 16532 2) reciprocal inverse gaussian (gamma, mu) 16533 3) generalized gamma (gamma, c) 16534 4) exponentiated Weibull (gamma, theta) 16535 5) exponential power (alpha, beta) 16536 6) beta (alpha, beta) 16537 7) inverted beta (alpha, beta) 16538 8) beta-normal (alpha, beta) 16539 9) asymmetric log double expo (alpha, beta) 16540 10) generalized Topp and Leone (alpha, beta) 16541 11) reflected gene Topp and Leone (alpha, beta) 16542 12) log beta (alpha, beta, assume 16543 c and d known) 16544 13) two-sided power (theta, n) 16545 14) Johnson SU (alpha1, alpha2) 16546 15) Johnson SB (alpha1, alpha2) 16547 16) alpha (alpha1, alpha2) 16548 17) Gompertz (c, b) 16549 18) g and h (g, h) 16550 19) F (nu1, nu2) 16551 20) log skew normal (lambda, sd) 16552 21) power lognormal (nu, sd) 16553 22) folded normal (mu, sd) 16554 23) folded Cauchy (loc, scale) 16555 24) skew t (nu, lambda) 16556 25) noncentral t (nu, lambda) 16557 26) noncentral chi-square (nu, lambda) 16558 27) truncated exponential (m, sd, assume truncation point, 16559 X0, is known) 16560 28) generalized Tukey-Lambda (lambda3, lambda4) 16561 29) Gompertz-Makeham (eta, zeta) 16562 30) generalized asymmetric Laplace (k, tau or mu, tau) 16563 31) generalized McLeish (alpha, a) 16564 32) trapezoid (b, c, assume a and d known) 16565 33) generalized logistic type 4 (p, q) 16566 16567 PPCC plots are available for the following discrete distributional 16568 families (with the distributional parameter in parentheses): 16569 16570 1) geometric (p) 16571 2) Yule (p) 16572 3) Poisson (lambda) 16573 4) binomial (p, assume n known) 16574 5) logarithmic series (theta) 16575 6) Consul (theta or m) 16576 7) zeta (alpha) 16577 8) Hermite (alpha, beta) 16578 9) beta geometric (alpha, beta) 16579 10) beta-binomial (alpha, beta assume n known) 16580 11) Katz (alpha, beta) 16581 12) negative binomial (k, p) 16582 13) zipf (alpha, n) 16583 14) discrete Weibull (beta, q) 16584 15) Borel-Tanner (lambda, k) 16585 16) Lagrange Poisson (lambda, theta) 16586 17) Polya-Aeppli (theta, p) 16587 18) lost games (p, n) 16588 19) generalized loga series (theta, beta) 16589 20) geeta (theta, beta or mu, beta) 16590 21) generalized lost games (p, a, assume j known) 16591 16592 The percent point function for the discrete distributions is a 16593 step function (since X is restricted to integer values). This can 16594 result in non-smooth ppcc and probability plots. For discrete 16595 distributions, the KS PLOT (which will plot the minimum value 16596 of chi-square statistic) is recommended over the PPCC PLOT as 16597 long as the sample size is reasonably large. 16598 16599Syntax 1: 16600 <family> PPCC PLOT <y> <SUBSET/EXCEPT/FOR/qualification> 16601 where <y> is the variable of raw data values under analysis; 16602 <family> is one of the distributions listed above: 16603 WEIBULL, DOUBLE WEIBULL, INVERTED WEIBULL, 16604 GAMMA, DOUBLE GAMMA, LOG GAMMA, INVERTED GAMMA, 16605 WALD, FATIGUE LIFE, PARETO, PARETO SECOND KIND, 16606 GENERALIZED PARETO, GENERALIZED HALF LOGISTIC, 16607 FRECHET (for extreme value type 2), 16608 GENERALIZED EXTREME VALUE, EXTREME VALUE, 16609 GEOMETRIC EXTREME EXPONENTIAL, 16610 TUKEY LAMBDA, SKEW NORMAL, T, FOLDED T, 16611 CHI-SQUARE, CHI, GENERALIZED LOGISTIC, 16612 LOG DOUBLE EXPONENTIAL, ERROR, LOGNORMAL, 16613 POWER NORMAL, VON MISES, RECIPROCAL, LOG LOGISTIC, 16614 WRAPPED CAUCHY, 16615 INVERSE GAUSSIAN, RECIPROCAL INVERSE GAUSSIAN, 16616 GENERALIZED GAMMA, EXPONENTIATED WEIBULL, 16617 EXPONENTIAL POWER, BETA, INVERTED BETA, 16618 TWO SIDED POWER, JOHNSON SU, JOHNSON SB, ALPHA, 16619 GOMPERTZ, G AND H, F, LOG SKEW NORMAL, 16620 POWER LOGNORMAL, FOLDED NORMAL, 16621 FOLDED CAUCHY, SKEW T, NONCENTRAL T, 16622 GEOMTRIC, YULE, POISSON, LOGARITHMIC SERIES, 16623 HERMITE, BETA BINOMIAL, NEGATIVE BINOMIAL, 16624 WARING 16625 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 16626 16627 This syntax is used for the raw data case. 16628 16629 Note that the response variable can also be a matrix. If a matrix 16630 name is encountered, a ppcc plot will be drawn for all the values 16631 in the matrix. 16632 16633 The syntax PPCC PLOT can be replaced with ANDERSON DARLING PLOT, 16634 KOLMOGOROV SMIRNOV PLOT, or CHI-SQUARE PLOT to generate the 16635 Anderson-Darling, Kolmogorov-Smirnov, and chi-square variants of 16636 the plot, respectively. 16637 16638Syntax 2: 16639 <family> PPCC PLOT <y> <x> <SUBSET/EXCEPT/FOR/qualification> 16640 where <y> is the variable of pre-computed frequencies; 16641 <x> is the variable of distinct values for the variable 16642 under analysis; 16643 <family> is one of the families listed above; 16644 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 16645 16646 This syntax is used for the binned data case where the bins 16647 are defined by the mid-points of each bin. 16648 16649 The syntax PPCC PLOT can be replaced with CHI-SQUARE PLOT to 16650 generate the chi-square variant of the plot. This syntax is 16651 not supported for the Anderson-Darling and Kolmogorov-Smirnov 16652 variants of the plot. 16653 16654Syntax 3: 16655 <family> PPCC PLOT <y> <xlow> <xhigh> 16656 <SUBSET/EXCEPT/FOR/qualification> 16657 where <y> is the variable of pre-computed frequencies; 16658 <xlow> is the variable containing the lower limits for the 16659 bins; 16660 <xhigh> is the variable containing the upper limits for the 16661 bins; 16662 <family> is one of the families listed above; 16663 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 16664 16665 This syntax is used for the binned data case where the bins 16666 are defined by the lower and upper limits of the bins (i.e., 16667 the bins can be of unequal width). 16668 16669 The syntax PPCC PLOT can be replaced with CHI-SQUARE PLOT to 16670 generate the chi-square variant of the plot. This syntax is 16671 not supported for the Anderson-Darling and Kolmogorov-Smirnov 16672 variants of the plot. 16673 16674Syntax 4: 16675 <family> CENSORED PPCC PLOT <y> <x> 16676 <SUBSET/EXCEPT/FOR/qualification> 16677 where <y> is the variable of raw data values under analysis; 16678 <x> is the censoring variabe; 16679 <family> is one of the distributions listed above; 16680 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 16681 16682 This syntax is used for the raw data case where there is 16683 censoring. A value of 1 indicates a failure time and a value 16684 of 0 indicates a censoring time. 16685 16686 Censoring is not supported for discrete disributions or grouped 16687 data. It is also not supported for the Anderson-Darling, 16688 Kolmogorov-Smirnov, and chi-square variants of the plot. 16689 16690Syntax 5: 16691 <family> CENSORED PPCC PLOT <y> <censor> <x> 16692 <SUBSET/EXCEPT/FOR/qualification> 16693 where <y> is the variable of pre-computed frequencies; 16694 <censor> is the censoring variabe; 16695 <x> is the variable of distinct values for the variable 16696 under analysis; 16697 <family> is one of the families listed above; 16698 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 16699 16700 This syntax is used for the case where we have frequency (binned) 16701 data with censoring. The bins are defined by their mid-points. 16702 When a particular bin has both censored and uncensored data, 16703 there will be 2 rows with the same value for <x>. 16704 16705 A value of 1 indicates a failure time and a value of 0 indicates 16706 a censoring time. 16707 16708 Censoring is not supported for discrete disributions or grouped 16709 data. It is also not supported for the Anderson-Darling, 16710 Kolmogorov-Smirnov, and chi-square variants of the plot. 16711 16712Syntax 6: 16713 <family> CENSORED PPCC PLOT <y> <censor> <xlow> <xhigh> 16714 <SUBSET/EXCEPT/FOR/qualification> 16715 where <y> is the variable of pre-computed frequencies; 16716 <censor> is the censoring variabe; 16717 <xlow> is the variable containing the lower limits for the 16718 bins; 16719 <xhigh> is the variable containing the upper limits for the 16720 bins; 16721 <family> is one of the families listed above; 16722 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 16723 16724 This syntax is used for the case where we have frequency (binned) 16725 data with censoring. The bins are defined by their lower and upper 16726 limits. This syntax allows bins with unequal widths. 16727 When a particular bin has both censored and uncensored data, 16728 there will be 2 rows with the same values for <xlow> and <xhigh>. 16729 16730 A value of 1 indicates a failure time and a value of 0 indicates 16731 a censoring time for the censoring variable. 16732 16733 Censoring is not supported for discrete disributions or grouped 16734 data. It is also not supported for the Anderson-Darling, 16735 Kolmogorov-Smirnov, and chi-square variants of the plot. 16736 16737Syntax 7: 16738 <family> REPLICATED PPCC PLOT <y> <x1> ... <xk> 16739 <SUBSET/EXCEPT/FOR/qualification> 16740 where <y> is the variable of raw data values under analysis; 16741 <x1> ... <xk> is a list of one to two group id variables; 16742 <family> is one of the distributions listed above; 16743 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 16744 16745 The group-id variables are cross-tabulated and a ppcc 16746 plot will be generated for each distinct combination of values 16747 for the group-id variables. These plots will be overlaid on the 16748 same plot. 16749 16750 The syntax PPCC PLOT can be replaced with ANDERSON DARLING PLOT, 16751 KOLMOGOROV SMIRNOV PLOT, or CHI-SQUARE PLOT to generate the 16752 Anderson-Darling, Kolmogorov-Smirnov, and chi-square variants of 16753 the plot, respectively. 16754 16755Syntax 8: 16756 <family> CENSORED REPLICATED PPCC PLOT <y> <x> <x1> .... <xk> 16757 <SUBSET/EXCEPT/FOR/qualification> 16758 where <y> is the variable of raw data values under analysis; 16759 <x> is the censoring variabe; 16760 <x1> ... <xk> is a list of one to two group id variables; 16761 <family> is one of the distributions listed above; 16762 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 16763 16764 The group-id variables are cross-tabulated and a ppcc 16765 plot will be generated for each distinct combination of values 16766 for the group-id variables. These plots will be overlaid on the 16767 same plot. 16768 16769 Censoring is not supported for discrete disributions or grouped 16770 data. It is also not supported for the Anderson-Darling, 16771 Kolmogorov-Smirnov, and chi-square variants of the plot. 16772 16773Syntax 9: 16774 <family> REPLICATED GROUPED PPCC PLOT <y> <x> <x1> ... <xk> 16775 <SUBSET/EXCEPT/FOR/qualification> 16776 where <y> is the variable of pre-computed frequencies; 16777 <x> is the variable of distinct values for the variable 16778 under analysis; 16779 <x1> ... <xk> is a list of one to two group id variables; 16780 <groupid> is a group id variable; 16781 <family> is one of the families listed above; 16782 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 16783 16784 This syntax is used for the binned data case where there are 16785 multiple batches of data. The bins are defined by the mid-points 16786 of each bin and there are multiple batches of data. 16787 16788 The syntax PPCC PLOT can be replaced with CHI-SQUARE PLOT to 16789 generate the chi-square variant of the plot. This syntax is 16790 not supported for the Anderson-Darling and Kolmogorov-Smirnov 16791 variants of the plot. 16792 16793Syntax 10: 16794 <family> REPLICATED UNEQUAL GROUPED PPCC PLOT 16795 <y> <xlow> <xhigh> <x1> ... <xk> 16796 <SUBSET/EXCEPT/FOR/qualification> 16797 where <y> is the variable of pre-computed frequencies; 16798 <xlow> is the variable containing the lower limits for the 16799 bins; 16800 <xhigh> is the variable containing the upper limits for the 16801 bins; 16802 <x1> ... <xk> is a list of one to two group id variables; 16803 <family> is one of the families listed above; 16804 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 16805 16806 This syntax is used for the binned data case where there are 16807 multiple batches of data. The bins are defined by the lower and 16808 upper limits of the bins (i.e., the bins can be of unequal width). 16809 16810 The syntax PPCC PLOT can be replaced with CHI-SQUARE PLOT to 16811 generate the chi-square variant of the plot. This syntax is 16812 not supported for the Anderson-Darling and Kolmogorov-Smirnov 16813 variants of the plot. 16814 16815Syntax 11: 16816 <family> MULTIPLE PPCC PLOT <y1> ... <yk> 16817 <SUBSET/EXCEPT/FOR/qualification> 16818 where <family> is one of the distributions listed above; 16819 <y1> ... <yk> is a list of response variables; 16820 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 16821 16822 Note that the response variables can also be matrices. If a 16823 matrix name is encountered, a ppcc plot will be drawn for 16824 all the values in the matrix. For multiple response variables, 16825 the ppcc plots will be overlaid on the same plot. 16826 16827 The syntax PPCC PLOT can be replaced with ANDERSON DARLING PLOT, 16828 KOLMOGOROV SMIRNOV PLOT, or CHI-SQUARE PLOT to generate the 16829 Anderson-Darling, Kolmogorov-Smirnov, and chi-square variants of 16830 the plot, respectively. 16831 16832Examples: 16833 LAMBDA PPCC PLOT X 16834 T PPCC PLOT X 16835 EXTREME VALUE TYPE 2 PPCC PLOT X 16836 POISSON PPCC PLOT X 16837 LAMBDA PPCC PLOT F X 16838 T PPCC PLOT F X 16839 EXTREME VALUE TYPE 2 PPCC PLOT F X 16840 POISSON PPCC PLOT F X 16841 16842Note: 16843 The PPCC is not the only goodness of fit criterion that 16844 can be used. The following additional options are available: 16845 16846 KOLMOGOROV-SMIRNOV PLOT (or KS PLOT) 16847 ANDERSON DARLING PLOT (or AD PLOT) 16848 CHI-SQUARE PLOT (or CHISQUARE PLOT) 16849 16850 Currently, these alternatives are limited to the uncensored 16851 case. In addition, the KS PLOT and AD PLOT are restricted to 16852 the raw data case and the CHI-SQUARE PLOT is restricted to 16853 the binned data case. 16854 16855 Note that the PPCC method is invariant to location and scale. 16856 This basically means that we can use the underlying probability 16857 plot to estimate the location and scale parameters. 16858 16859 These other methods are not invariant to location and scale. 16860 By default, we still use the estimates from the underlying 16861 probability plot to estimate location and scale. Although 16862 these estimates may not be "optimal", they should at least 16863 be reasonable. However, you can fix the estimates of location 16864 and scale by entering the commands 16865 16866 LET KSLOC = <value> 16867 LET KSSCALE = <value> 16868 16869 These apply to the Kolmogorov-Smirnov, Anderson-Darling, and 16870 chi-square variants of the plot. 16871 16872Note: 16873 For information on how the Kolmogorov-Smirnov, Anderson-Darling, 16874 and chi-square goodness of fit statistics are computed, enter 16875 16876 HELP GOODNESS OF FIT 16877 16878Note: 16879 The chi-square variant of the plot is most frequently used when the 16880 data are received in pre-binned form (for raw data, the PPCC, 16881 Anderson-Darling or Kolmogorov-Smirnov variants are typically 16882 preferred). However, you can use the chi-square test for raw data 16883 (you typically will want to have a reasonably large data set before 16884 doing this). For raw data, you can specify the binning with the 16885 commands CLASS WIDTH, CLASS LOWER, and CLASS UPPER. The default 16886 class width is 0.3 times the sample standard deviation. To 16887 specify other default algorithms, enter 16888 16889 HELP HISTOGRAM CLASS WIDTH 16890 16891 The chi-square test is sensitive to the choice of bins. There is no 16892 optimal choice for the bin width (since the optimal bin width 16893 depends on the distribution). Most reasonable choices should 16894 produce similar, but not identical, results. 16895 16896 For the chi-square approximation to be valid, the expected frequency 16897 should be at least 5. The chi-square approximation may not be valid 16898 for small samples, and if some of the counts are less than five, you 16899 may need to combine some bins in the tails. 16900 16901Note: 16902 The range of parameter is determined automatically. However, if 16903 you wish to restrict the range, you can specify the lower and upper 16904 limits by appending a 1 or 2 to the parameter name and assigning 16905 a value. For example, to restrict a Weibull ppcc plot to values 16906 0.5 and 20, do the following: 16907 16908 LET GAMMA1 = 0.5 16909 LET GAMMA2 = 20 16910 WEIBULL PPCC PLOT Y 16911 16912 A common use of this is to obtain a refinement of the estimate 16913 of the shape parameter. That is, an initial iteration (typically 16914 just the default values of the parameter) is used to identify 16915 the appropriate neighborhood of the optimal value of the shape 16916 parameter. Then a second iteration of the PPCC PLOT is generated 16917 with the parameter restricted to a much narrower range of values. 16918 Although this iteration can be repeated as many times as you 16919 like, for practical purposes a two iterations is typically sufficient. 16920 16921Note: 16922 The PPCC PLOT automatically saves several parameters. The MAXPPCC 16923 parameter contains the maximum correlation that was computed and 16924 the SHAPE parameter contains the value of the estimated 16925 distributional parameter (e.g., GAMMA for the Weibull distribution) 16926 that corresponds to MAXPPCC. 16927 16928 In the case of two shape parameters, these are saved as SHAPE1 and 16929 SHAPE2. 16930 16931Note: 16932 For the truncated exponential distribution, we assume that the 16933 truncation parameter, X0, is known. To set this value, enter 16934 16935 LET X0 = <value> 16936 16937 before generating the ppcc plot. 16938 16939 For the noncentral t and noncentral chi-square distributions, 16940 we can fix the value of the degrees of freedom parameter to a 16941 single value. In this case, the ppcc plot reverts to a 16942 one shape parameter plot. Enter the commands 16943 16944 LET NU1 = <value> 16945 LET NU2 = <value> 16946 16947 where <value> is the same for NU1 and NU2. 16948 16949Note: 16950 The SET MINMAX command can be used to specify a minimum or maximum 16951 Weibull distribution. A value of 1 specifies a maximum Weibull 16952 distribution and a value of 2 specifies a minimum Weibull 16953 distribution. 16954 16955Note: 16956 When the percent point function is expensive to compute, the 16957 PPCC plot can take a long time to generate. Two approaches 16958 to this are: 16959 16960 1) You can bin the data before generating the PPCC plot. 16961 16962 2) As an alternative to binning, you can use the command 16963 16964 SET PPCC PLOT DATA POINTS <value> 16965 16966 With this command, Dataplot will generate <value> equally 16967 spaced percentiles of the data. The PPCC plot is then 16968 generated on these percentiles. 16969 16970 If the number of data points in the response variable 16971 is less than <value>, then the full data set is used. 16972 16973 The minimum number for <value> is 25. Numbers in the 16974 range 50 to 200 are typically used. 16975 16976Note: 16977 In the one shape parameter case, 50 values of the shape 16978 parameter are used. For the two shape parameter case, the 16979 number of values used is dependent on the specific distribution. 16980 Typically, between 25 and 50 values are used in each direction. 16981 16982 You can modify the number values used for the shape parameters 16983 by entering the command 16984 16985 SET PPCC PLOT AXIS POINTS <val1> <val2> 16986 16987 where <val1> is the number of values for the first shape 16988 parameter and <val2> is the number of values for the second 16989 shape parameter. 16990 16991 There are two typical uses for this command: 16992 16993 1) For distributions with a fast percent point function 16994 (e.g., the Weibull), you can increase the number of values 16995 in order to generate a more accurate estimate. 16996 16997 2) For distributions with slow percent point functions, 16998 you might want to decrease the number of points in order 16999 to increase the speed of the PPCC plot. 17000 17001Note: 17002 For discrete distributions, the data will typically consist of 17003 integers. In this case, it is helpful to group the data based 17004 on these integer values. The following code shows the 17005 recommended way for doing this: 17006 17007 LET YLOW = MINIMUM Y 17008 LET YUPP = MAXIMUM Y 17009 LET YLOW = YLOW - 0.5 17010 CLASS LOWER YLOW 17011 LET YUPP = YUPP + 0.5 17012 CLASS UPPER YUPP 17013 CLASS WIDTH = 1 17014 LET Y2 X2 = BINNED Y 17015 LET LAMBDA = 4.2 17016 POISSON PPCC PLOT Y2 X2 17017 POISSON KS PLOT Y2 X2 17018 17019 This will center the bins around the integer values and will 17020 cover the first and last class. 17021 17022 In this case, the KS PLOT syntax will generate a plot that 17023 shows the minimum value of the chi-square statistic. It is 17024 usually recommended that the minimum bin size be at least 5 in 17025 order for the chi-square goodness of fit to generate accurate 17026 critical values. You can automatically combine bins with the 17027 command 17028 17029 LET MINSIZE = <value> 17030 LET Y3 XLOW XHIGH = COMBINE FREQUENCY TABLE Y2 X2 17031 17032Note: 17033 For the PPCC PLOT and the KS PLOT, the location and scale 17034 parameters are estimated via the probability plot. For 17035 long-tailed distributions, more accurate estimates may be 17036 obtained by applying a biweight fit of the probability plot. 17037 To specify this option, enter the command 17038 17039 SET PPCC PLOT LOCATION SCALE BIWEIGHT 17040 17041 To restore the use of the regular least squares estimates 17042 of location and scale, enter 17043 17044 SET PPCC PLOT LOCATION SCALE DEFAULT 17045 17046 This option is primarily for the KS PLOT. Since the 17047 PPCC PLOT is invariant to location and scale, we can 17048 simply wait to compute the biweight location and scale 17049 on the final probability plot. However, the KS PLOT is 17050 not invariant for location and scale and for long-tailed 17051 distributions this option can sometimes lead to improved 17052 estimates for the parameters. 17053 17054Note: 17055 The TO syntax is supported for the PPCC PLOT command. 17056 It is most useful for the MULTIPLE version of the command. 17057 17058Note: 17059 The chi-square variant of the plot can sometimes produce very 17060 large numbers. To improve the plot resolution for the smaller 17061 values of the chi-square statistic (which is the area of interest) 17062 you can provide a truncation value (i.e., values of the chi-square 17063 statistic greater than the truncation value will be set to the 17064 truncation value), enter the command 17065 17066 SET CHISQUARE LIMIT <value> 17067 17068Note: 17069 For the PPCC PLOT command, Dataplot fits a least squares line 17070 to the points on the underlying probability plot. For the 17071 AD PLOT, KS PLOT, and CHI-SQUARE PLOT variants, this least 17072 squares fit is used to obtain estimates for the location and 17073 scale parameters. 17074 17075 Alternatively, you can specify that Dataplot fit a robust regression 17076 using the biweight method by entering the command 17077 17078 SET PPCC PLOT LOCATION SCALE BIWEIGHT 17079 17080 To reset the default of non-robust least squares, enter 17081 17082 SET PPCC PLOT LOCATION SCALE DEFAULT 17083 17084 In our experience, this option can be useful for heavy tailed 17085 distributiuons such as the SLASH and CAUCHY distributions. 17086 17087Default: 17088 None 17089 17090Synonyms: 17091 AD PLOT is a synonym for ANDERSON DARLING PLOT 17092 KS PLOT is a synonym for KOLMOGOROV SMIRNOV PLOT 17093 17094 FRECHET and EV2 are synonyms for EXTREME VALUE TYPE 2. 17095 17096 LAMBDA PPCC PLOT and TUKEY PPCC PLOT are synonyms for TUKEY LAMBDA 17097 PPCC PLOT. 17098 17099 STUDENT T PPCC PLOT is a synonym for T PPCC PLOT. 17100 17101 The CHISQUARE term can be specified as CHISQUARE or CHI SQUARE. 17102 17103 FL PPCC PLOT, BRIN SAUNDERS PPCC PLOT, and SAUNDERS BRIN are 17104 synonyms for FATIGUE LIFE PPCC PLOT. 17105 17106 IG PPCC PLOT is a synonym for INVERSE GAUSSIAN PPCC PLOT. 17107 17108 RIG PPCC PLOT is a synonym for RECIPROCAL INVERSE GAUSSIAN PPCC 17109 PLOT. 17110 17111 GEP PPCC PLOT and GP PPCC PLOT are synonyums for GENERALIZED 17112 PARETO PLOT. 17113 17114 LOGNORMAL PPCC PLOT and LOG-NORMAL PPCC PLOT are synonyms for 17115 LOG NORMAL PPCC PLOT. 17116 17117 POWER LOG-NORMAL PPCC PLOT and POWER LOGNORMAL PPCC PLOT are 17118 synonyms for POWER LOG NORMAL PPCC PLOT. 17119 17120 VONMISES PPCC PLOT and VON-MISES PPCC PLOT are synonyms for 17121 VON MISES PPCC PLOT. 17122 17123 LOGLOGISTIC PPCC PLOT and LOG-LOGISTIC PPCC PLOT are synonyms for 17124 LOG LOGISTIC PPCC PLOT. 17125 17126 SKEW LAPLACE PPCC PLOT is a synonym for 17127 SKEW DOUBLE EXPONENTIAL PPCC PLOT. 17128 17129 ASYMMETRIC LAPLACE PPCC PLOT is a synonym for 17130 ASYMMETRIC DOUBLE EXPONENTIAL PPCC PLOT. 17131 17132Related Commands: 17133 PROBABILITY PLOT = Generates a probability plot. 17134 FREQUENCY PLOT = Generates a frequency plot. 17135 HISTOGRAM = Generates a histogram. 17136 PIE CHART = Generates a pie chart. 17137 PERCENT POINT PLOT = Generates a percent point plot. 17138 PLOT = Generates a data or function plot. 17139 17140Reference: 17141 James J. Filliben (1975), "The Probability Plot Correlation 17142 Coefficient Test for Normality," Technometric, Vol. 17, No. 1. 17143 17144Applications: 17145 Distributional Modeling 17146 17147Implementation Date: 17148 Pre-1987 17149 1990/5: Implemented IG, WALD, RIG, FL distributions. 17150 1993/12: Implemented GENERALIZED PARETO distribution. 17151 1995/5: Implemented LOGNORMAL, POWER NORMAL, POWER LOGNORMAL, 17152 POWER FUNCTION, CHI, VON MISES, and LOG LOGISTIC 17153 distributions implemented 95/5. 17154 2001/10: Implemented a number of 2 shape parameter distributions. 17155 2002/5: Implemented TWO-SIDED POWER distribution. 17156 2003/5: Implemented ERROR distribution. 17157 2004/1: Implemented FOLDED T, SKEWED T, SKEWED NORMAL, G AND H, 17158 INVERTED BETA distributions. 17159 2004/1: Support for additional two shape parameter distributions. 17160 2004/5: Added support for the SET PPCC FORMAT command 17161 2004/5: Fixed a number of bugs in various distributions. 17162 2004/5: Fixed a number of bugs in various distributions. 17163 2004/6: Implemented SKEW DOUBLE EXPONENTIAL, ASYMMETRIC DOUBLE 17164 EXPONENTIAL, MAXWELL 17165 2004/7: Implemented Meeker re-parametrization for GOMPERTZ MAKEHAM 17166 2004/9: Implemented GENERALIZED ASYMETRIC LAPLACE, BINOMIAL, 17167 MCLEISH, GENERALIZED MCLEISH 17168 2004/9: Implemented SET PPCC PLOT DATA POINTS 17169 2004/9: Implemented SET PPCC PLOT AXIS POINTS 17170 2004/9: Implemented SET PPCC PLOT AXIS ORDER 17171 2004/10: Implemented CENSORED case 17172 2005/5: Implemented REPLICATION case 17173 2005/5: Implemented binned case where bins are specified by 17174 the lower and upper limits (i.e., unequal width bins) 17175 2007/2: Implemented SET PPCC PLOT BIWEIGHT LOCATION SCALE 17176 2007/2: Implemented a additional distributions 17177 2009/10: Support for matrix arguments and TO syntax 17178 2009/10: Support for MULTIPLE and REPLICATION options 17179 2009/10: Support for ANDERSON DARLING variation 17180 17181Program 1: 17182 MULTIPLOT 2 2 17183 MULTIPLOT CORNER COORDINATES 0 0 100 100 17184 MULTIPLOT SCALE FACTOR 1.5 17185 TITLE AUTOMATIC 17186 X1LABEL THEORETICAL VALUE 17187 Y1LABEL DATA VALUE 17188 TITLE OFFSET 2 17189 X1LABEL DISPLACEMENT 10 17190 Y1LABEL DISPLACEMENT 14 17191 CHAR X 17192 LINE BLANK 17193 JUSTIFICATION RIGHT 17194 . 17195 LET LAMBDA = 1.5 17196 LET Y = TUKEY LAMBDA RANDOM NUMBERS FOR I = 1 1 100 17197 TUKEY LAMBDA PPCC PLOT Y 17198 MOVE 82 30 17199 TEXT LAMBDA = ^SHAPE 17200 MOVE 82 25 17201 TEXT PPCC = ^MAXPPCC 17202 . 17203 LET NU = 4 17204 LET Y = T RANDOM NUMBERS FOR I = 1 1 100 17205 T PPCC PLOT Y 17206 MOVE 82 30 17207 TEXT NU = ^SHAPE 17208 MOVE 82 25 17209 TEXT PPCC = ^MAXPPCC 17210 . 17211 LET GAMMA = 2.3 17212 LET Y = WALD RANDOM NUMBERS FOR I = 1 1 100 17213 WALD PPCC PLOT Y 17214 MOVE 82 30 17215 TEXT GAMMA = ^SHAPE 17216 MOVE 82 25 17217 TEXT PPCC = ^MAXPPCC 17218 . 17219 LET GAMMA = 1.6 17220 LET Y = WEIBULL RANDOM NUMBERS FOR I = 1 1 100 17221 SET PPCC PLOT AXIS POINTS 200 17222 LET GAMMA1 = 0.2 17223 LET GAMMA2 = 25 17224 LINE SOLID 17225 CHARACTER BLANK 17226 WEIBULL PPCC PLOT Y 17227 MOVE 82 30 17228 TEXT GAMMA = ^SHAPE 17229 MOVE 82 25 17230 TEXT PPCC = ^MAXPPCC 17231 . 17232 END OF MULTIPLOT 17233 17234Program 2: 17235 let gamma = 5.1 17236 let y = weibull rand numb for i = 1 1 200 17237 . 17238 let gamma1 = 0.5 17239 let gamma2 = 50 17240 set ppcc plot axis points 449 17241 . 17242 multiplot corner coordinates 2 2 98 98 17243 multiplot scale factor 2 17244 multiplot 2 2 17245 title automatic 17246 title offset 2 17247 justification center 17248 height 1.7 17249 tic mark offset units screen 17250 ytic mark offset 3 0 17251 . 17252 weibull ppcc plot y 17253 let shape = round(shape,1) 17254 let maxppcc2 = round(maxppcc,3) 17255 move 50 5 17256 text Shape: ^shape, Max PPCC: ^maxppcc2 17257 . 17258 weibull anderson darling plot y 17259 let shape = round(shape,1) 17260 let minad2 = round(minad,3) 17261 move 50 5 17262 text Shape: ^shape, Min AD: ^minad2 17263 . 17264 weibull ks plot y 17265 let shape = round(shape,1) 17266 let minks = round(minks,3) 17267 move 50 5 17268 text Shape: ^shape, Min KS: ^minks 17269 . 17270 set chisquare limit 100 17271 weibull chi-square plot y 17272 let shape = round(shape,1) 17273 let minchsq = round(minchisq,3) 17274 move 50 5 17275 text Shape: ^shape, Min Chi-Square: ^minchsq 17276 . 17277 end of multiplot 17278 17279-----PRECISION (LET)------------------------------ 17280 17281PRECISION 17282 17283Name: 17284 PRECISION (LET) 17285 17286Type: 17287 Let Subcommand 17288 17289Purpose: 17290 Compute the precision of a variable. 17291 17292Description: 17293 The sample precision is defined as the reciprocal of the sample 17294 variance. That is 17295 17296 Prec = (n-1)/SUM[i=1 to n][(X(i) - xbar)**2] 17297 17298 where n and xbar denote the sample size and the sample mean, 17299 respectively. 17300 17301 Note that high variance implies low precision while low variance 17302 implies high precision. 17303 17304 Some sources define the precision as the reciprocal of the standard 17305 deviation. 17306 17307Syntax 1: 17308 LET <par> = PRECISION <y> <SUBSET/EXCEPT/FOR qualification> 17309 where <y> is a response variable; 17310 <par> is a parameter where the precision value is saved; 17311 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 17312 17313Syntax 2: 17314 LET <par> = DIFFERENCE OF PRECISION <y1> <y2> 17315 <SUBSET/EXCEPT/FOR qualification> 17316 where <y1> is the first response variable; 17317 <y2> is the second response variable; 17318 <par> is a parameter where the difference of precision 17319 values is saved; 17320 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 17321 17322Examples: 17323 LET PREC = PRECISION Y1 17324 LET PREC = PRECISION Y1 SUBSET TAG > 2 17325 17326 LET DIFFPREC = DIFFERENCE OF PRECISION Y1 Y2 17327 17328Note: 17329 Dataplot statistics can be used in a number of commands. For 17330 details, enter 17331 17332 HELP STATISTICS 17333 17334Default: 17335 None 17336 17337Synonyms: 17338 None 17339 17340Related Commands: 17341 VARIANCE = Compute the variance of a variable. 17342 MEAN = Compute the mean of a variable. 17343 STANDARD DEVIATION = Compute the standard deviation of a 17344 variable. 17345 17346Applications: 17347 Data Analysis 17348 17349Implementation Date: 17350 2017/01 17351 2017/03: Added DIFFERENCE OF PRECISION 17352 17353Program 1: 17354 SKIP 25 17355 READ ZARR13.DAT Y 17356 LET P = PRECISION Y 17357 17358Program 2: 17359 . Step 1: Create the data 17360 . 17361 skip 25 17362 read gear.dat y x 17363 skip 0 17364 . 17365 char X 17366 line blank 17367 y1label Precision 17368 x1label Group 17369 x1tic mark offset 0.5 0.5 17370 label case asis 17371 title case asis 17372 title Precision of GEAR.DAT 17373 title offset 2 17374 . 17375 set statistic plot reference line average 17376 precision plot y x 17377 . 17378 set write decimals 5 17379 tabulate precision y x 17380 17381Program 3: 17382 SKIP 25 17383 READ IRIS.DAT Y1 TO Y4 X 17384 . 17385 LET A = DIFFERENCE OF PRECISION Y1 Y2 17386 SET WRITE DECIMALS 4 17387 TABULATE DIFFERENCE OF PRECISION Y1 Y2 X 17388 . 17389 XTIC OFFSET 0.2 0.2 17390 X1LABEL GROUP ID 17391 Y1LABEL DIFFERENCE OF PRECISION 17392 CHAR X 17393 LINE BLANK 17394 DIFFERENCE OF PRECISION PLOT Y1 Y2 X 17395 CHAR X ALL 17396 LINE BLANK ALL 17397 BOOTSTRAP DIFFERENCE OF PRECISION PLOT Y1 Y2 X 17398 17399-----PRED------------------------------------------------------- 17400 17401PRED 17402 17403Name: 17404 PRED 17405 17406Type: 17407 Keyword 17408 17409Purpose: 17410 An internal DATAPLOT variable into which the predicted values 17411 (i.e., "fitted values") are automatically placed whenever the FIT, 17412 PRE-FIT, SPLINE FIT, EXACT RATIONAL FIT, YATES ANALYSIS, LOWESS, 17413 SMOOTH, ANOVA, and MEDIAN POLISH commands are executed. 17414 17415Description: 17416 PRED can be used by the analyst in whatever fashion desired. A 17417 very common post-fit operation is to superimpose the predicted 17418 values atop the raw data as a visual check of model adequacy. This 17419 is usually done via 17420 CHARACTERS X BLANK 17421 LINES BLANK SOLID 17422 PLOT Y PRED VERSUS X 17423 17424Syntax: 17425 None 17426 17427Examples: 17428 WRITE X Y PRED RES 17429 PLOT Y PRED VERSUS X 17430 WRITE CALIB. X Y PRED RES 17431 LET PREDNEW = PRED 17432 17433Default: 17434 None 17435 17436Synonyms: 17437 None 17438 17439Related Commands: 17440 RES = A variable where residuals are stored. 17441 RESSD = A parameter where the residual standard 17442 deviation is stored. 17443 RESDF = A parameter where the residual degrees of 17444 freedom is stored. 17445 REPSD = A parameter where the replication standard 17446 deviation is stored. 17447 REPDF = A parameter where the replication degrees of 17448 freedom is stored. 17449 LOFCDF = A parameter where the lack of fit cdf is 17450 stored. 17451 FIT = Carries out a least squares linear or 17452 non-linear fit. 17453 EXACT RATIONAL FIT = Carries out an exact rational fit. 17454 PRE-FIT = Carries out a least squares pre-fit. 17455 SPLINE FIT = Carries out a spline fit. 17456 YATES ANALYSIS = Carries out an analysis of a Yates design. 17457 LOWESS = Carries out a locally weighted least squares 17458 fit. 17459 SMOOTH = Carries out a smoothing. 17460 ANOVA = Carries out an ANOVA. 17461 MEDIAN POLISH = Carries out a median polish. 17462 PLOT = Generates a data/function plot. 17463 17464Applications: 17465 Fitting 17466 17467Implementation Date: 17468 Pre-1987 17469 17470Program: 17471 SKIP 25 17472 READ BERGER1.DAT Y X 17473 CHARACTER X BLANK 17474 LINE BLANK SOLID 17475 PLOT Y PRED VS X 17476 17477-----PREDICTION BOUNDS-------------------------------------- 17478 17479PREDICTION BOUNDS 17480 17481Name: 17482 PREDICTION BOUNDS 17483 17484Type: 17485 Analysis Command 17486 17487Purpose: 17488 Generates prediction bounds for all m new observations given a 17489 previous sample. 17490 17491Description: 17492 Given a sample of n observations with mean xbar and standard 17493 deviation s, the two-sided prediction interval to contain all of 17494 m new indpendent, identically distributed observations is 17495 17496 xbar +/- r(1-alpha,m,n)*s 17497 17498 A conservative approximation for r(1-alpha,m,n) is 17499 17500 SQRT(1 + (1/n))*t(1-alpha/(2*m);n-1) 17501 17502 with t denoting the t percent point function. Dataplot uses the 17503 tabulated values given in Table A.13 of Hahn and Meeker when 17504 n and m are both less than or equal to 10. Otherwise, the 17505 approximation above is used. 17506 17507 The corresponding one-sided interval is 17508 17509 lower limit = xbar - r'(1-alpha,m,n)*s 17510 upper limit = xbar + r'(1-alpha,m,n)*s 17511 17512 A conservative approximation for r'(1-alpha,m,n) is 17513 17514 SQRT(1 + (1/n))*t(1-alpha/*m;n-1) 17515 17516 with t denoting the t percent point function. Dataplot uses the 17517 tabulated values given in Table A.14 of Hahn and Meeker when 17518 n and m are both less than or equal to 10. Otherwise, the 17519 approximation above is used. 17520 17521 In the formula above, the only value from the new observations is 17522 the sample size. That is, it can be applied before the new data is 17523 actually collected. The number of observations for the new sample 17524 is entered with the command 17525 17526 LET NNEW = <value> 17527 17528 If NNEW is not defined, then a value of 1 is used. 17529 17530 The difference between the PREDICTION BOUNDS command and the 17531 PREDICTION LIMITS command is that the PREDICTION LIMITS command 17532 generates a prediction interval for the mean of m new observations 17533 while the PREDICTION BOUNDS command generates a prediction interval 17534 to contain all of the new observations. 17535 17536 This prediction interval is based on the assumption that the 17537 underlying data is approximately normally distributed. Due to the 17538 central limit thereom, prediction limits for the mean are fairly 17539 robust against non-normality. However, the central limit thereom 17540 does not apply to prediction intervals to cover all of the new 17541 observations. So the PREDICTION BOUNDS command is much more 17542 sensitive to non-normality than is the PREDICTION LIMITS command. 17543 17544Syntax 1: 17545 <LOWER/UPPER> <LOGNORMAL/BOXCOX> PREDICTION BOUNDS <y> 17546 <SUBSET/EXCEPT/FOR qualification> 17547 where <y> is the response variable; 17548 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 17549 17550 If LOWER is specified, a one-sided lower prediction limit is 17551 returned. If UPPER is specified, a one-sided upper prediction 17552 limit is returned. If neither is specified, a two-sided limit 17553 is returned. 17554 17555 If the keyword LOGNORMAL is present, the log of the data will be 17556 taken, then the normal prediction bounds will be computed, and then 17557 the computed normal lower and upper limits will be exponentiated to 17558 obtain the lognormal prediction bounds. 17559 17560 Similarly, if the keyword BOXCOX is present, a Box-Cox transformation 17561 to normality will be applied to the data before computing the normal 17562 prediction bounds. The computed lower and upper limits will then 17563 be transformed back to the original scale. 17564 17565 This syntax supports matrix arguments for the response variable. 17566 17567Syntax 2: 17568 MULTIPLE <LOWER/UPPER> <LOGNORMAL/BOXCOX> PREDICTION BOUNDS 17569 <y1> ... <yk> <SUBSET/EXCEPT/FOR qualification> 17570 where <y1> .... <yk> is a list of 1 to 30 response variables; 17571 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 17572 17573 This syntax will generate a prediction interval for each of 17574 the response variables. 17575 17576 If LOWER is specified, a one-sided lower prediction limit is 17577 returned. If UPPER is specified, a one-sided upper prediction 17578 limit is returned. If neither is specified, a two-sided limit 17579 is returned. 17580 17581 If the keyword LOGNORMAL is present, the log of the data will be 17582 taken, then the normal prediction bounds will be computed, and then 17583 the computed normal lower and upper limits will be exponentiated to 17584 obtain the lognormal prediction bounds. 17585 17586 Similarly, if the keyword BOXCOX is present, a Box-Cox transformation 17587 to normality will be applied to the data before computing the normal 17588 prediction bounds. The computed lower and upper limits will then 17589 be transformed back to the original scale. 17590 17591 This syntax supports matrix arguments for the response variables. 17592 17593Syntax 3: 17594 REPLICATED <LOWER/UPPER> <LOGNORMAL/BOXCOX> PREDICTION BOUNDS 17595 <y> <x1> ... <xk> <SUBSET/EXCEPT/FOR qualification> 17596 where <y> is the response variable; 17597 <x1> .... <xk> is a list of 1 to 6 group-id variables; 17598 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 17599 17600 This syntax performs a cross-tabulation of the <x1> ... <xk> 17601 and generates a prediction interval for each unique combination 17602 of the cross-tabulated values. For example, if X1 has 3 levels 17603 and X2 has 2 levels, six prediction intervals will be generated. 17604 17605 If LOWER is specified, a one-sided lower prediction limit is 17606 returned. If UPPER is specified, a one-sided upper prediction 17607 limit is returned. If neither is specified, a two-sided limit 17608 is returned. 17609 17610 If the keyword LOGNORMAL is present, the log of the data will be 17611 taken, then the normal prediction bounds will be computed, and then 17612 the computed normal lower and upper limits will be exponentiated to 17613 obtain the lognormal prediction bounds. 17614 17615 Similarly, if the keyword BOXCOX is present, a Box-Cox transformation 17616 to normality will be applied to the data before computing the normal 17617 prediction bounds. The computed lower and upper limits will then 17618 be transformed back to the original scale. 17619 17620 This syntax does not support matrix arguments. 17621 17622Examples: 17623 PREDICTION BOUNDS Y1 17624 PREDICTION BOUNDS Y1 SUBSET TAG > 2 17625 MULTIPLE PREDICTION BOUNDS Y1 TO Y5 17626 REPLICATED PREDICTION BOUNDS Y X 17627 17628Note: 17629 A table of prediction limits is printed for alpha levels of 17630 50.0, 80.0, 90.0, 95.0, 99.0, and 99.9. 17631 17632Note: 17633 In addition to the PREDICTION BOUNDS command, the following 17634 commands can also be used: 17635 17636 LET ALPHA = 0.05 17637 LET NNEW = <value> 17638 17639 LET A = LOWER PREDICTION BOUNDS Y 17640 LET A = UPPPER PREDICTION BOUNDS Y 17641 LET A = ONE SIDED LOWER PREDICTION BOUNDS Y 17642 LET A = ONE SIDED UPPER PREDICTION BOUNDS Y 17643 17644 LET A = SUMMARY LOWER PREDICTION BOUNDS YMEAN YSD N 17645 LET A = SUMMARY UPPPER PREDICTION BOUNDS YMEAN YSD N 17646 LET A = SUMMARY ONE SIDED LOWER PREDICTION BOUNDS YMEAN YSD N 17647 LET A = SUMMARY ONE SIDED UPPER PREDICTION BOUNDS YMEAN YSD N 17648 17649 The first two commands specify the significance level and the number 17650 of new observations. The next four commands are used when you have 17651 raw data. The last four commands are used when only summary data 17652 (mean, standard deviation, sample size) is available. 17653 17654 In addition to the above LET command, built-in statistics are 17655 supported for about 20 different commands (enter HELP STATISTICS 17656 for details). 17657 17658Default: 17659 None 17660 17661Synonyms: 17662 None 17663 17664Related Commands: 17665 PREDICTION LIMITS = Generate prediction intervals for the mean 17666 of new observations. 17667 SD PREDICTION BOUNDS = Generate prediction limits for the 17668 standard deviation. 17669 CONFIDENCE LIMITS = Generate a confidence limit. 17670 TOLERANCE LIMITS = Generate a tolerance limit. 17671 17672Reference: 17673 Hahn and Meeker (1991), "Statistical Intervals: A Guide for 17674 Practitioners", Wiley, pp. 62-63. 17675 17676Applications: 17677 Confirmatory Data Analysis 17678 17679Implementation Date: 17680 2013/04 17681 2014/06: Support for LOGNORMAL and BOXCOX options 17682 17683Program 1: 17684 SKIP 25 17685 READ ZARR13.DAT Y 17686 SET WRITE DECIMALS 5 17687 LET NNEW = 5 17688 . 17689 PREDICTION BOUNDS Y 17690 LOWER PREDICTION BOUNDS Y 17691 UPPER PREDICTION BOUNDS Y 17692 17693Program 2: 17694 SKIP 25 17695 READ GEAR.DAT Y X 17696 SET WRITE DECIMALS 5 17697 LET NNEW = 5 17698 . 17699 REPLICATED PREDICTION BOUNDS Y X 17700 17701Program 3: 17702 . Following example from Hahn and Meeker's book. 17703 . 17704 let ymean = 50.10 17705 let ysd = 1.31 17706 let n1 = 5 17707 let nnew = 3 17708 let alpha = 0.05 17709 . 17710 set write decimals 5 17711 let slow1 = summary lower prediction bounds ymean ysd n1 17712 let supp1 = summary upper prediction bounds ymean ysd n1 17713 let slow2 = summary one sided lower prediction bounds ymean ysd n1 17714 let supp2 = summary one sided upper prediction bounds ymean ysd n1 17715 print slow1 supp1 slow2 supp2 17716 17717-----PREDICTION LIMITS-------------------------------------- 17718 17719PREDICTION LIMITS 17720 17721Name: 17722 PREDICTION LIMITS 17723 17724Type: 17725 Analysis Command 17726 17727Purpose: 17728 Generates a prediction interval for the mean of one or more 17729 new observations given a previous sample. 17730 17731Description: 17732 Given a sample of n observations with mean xbar and standard 17733 deviation s, the prediction interval to contain the mean 17734 of m new indpendent, identically distributed observations is 17735 17736 xbar +/- t(alpha/2,n-1)*s*SQRT((1/n) + (1/m)) 17737 17738 with t denoting the percent point function of the t distribution. 17739 17740 In this formula, the only value from the new observations is the 17741 sample size. That is, it can be applied before the new data is 17742 actually collected. The number of observations for the new sample 17743 is entered with the command 17744 17745 LET NNEW = <value> 17746 17747 If NNEW is not defined, then a value of 1 is used. 17748 17749 This prediction interval is based on the assumption that 17750 the underlying data is approximately normally distributed. 17751 However, this prediction interval is fairly robust against 17752 non-normality unless either the original sample size or the 17753 new sample is small or the departure from normality is severe 17754 (in particular, the data is not too skewed). Note that this 17755 includes the case of a prediction interval for a single future 17756 observation. 17757 17758Syntax 1: 17759 <LOWER/UPPER> <LOGNORMAL/BOXCOX> PREDICTION LIMITS <y> 17760 <SUBSET/EXCEPT/FOR qualification> 17761 where <y> is the response variable; 17762 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 17763 17764 If LOWER is specified, a one-sided lower prediction limit is 17765 returned. If UPPER is specified, a one-sided upper prediction 17766 limit is returned. If neither is specified, a two-sided limit 17767 is returned. 17768 17769 If the keyword LOGNORMAL is present, the log of the data will be 17770 taken, then the normal prediction limits will be computed, and then 17771 the computed normal lower and upper limits will be exponentiated to 17772 obtain the lognormal prediction limits. 17773 17774 Similarly, if the keyword BOXCOX is present, a Box-Cox transformation 17775 to normality will be applied to the data before computing the normal 17776 prediction limits. The computed lower and upper limits will then 17777 be transformed back to the original scale. 17778 17779 This syntax supports matrix arguments for the response variable. 17780 17781Syntax 2: 17782 MULTIPLE <LOWER/UPPER> <LOGNORMAL/BOXCOX> PREDICTION LIMITS 17783 <y1> ... <yk> 17784 <SUBSET/EXCEPT/FOR qualification> 17785 where <y1> .... <yk> is a list of 1 to 30 response variables; 17786 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 17787 17788 This syntax will generate a prediction interval for each of 17789 the response variables. 17790 17791 If LOWER is specified, a one-sided lower prediction limit is 17792 returned. If UPPER is specified, a one-sided upper prediction 17793 limit is returned. If neither is specified, a two-sided limit 17794 is returned. 17795 17796 If the keyword LOGNORMAL is present, the log of the data will be 17797 taken, then the normal prediction limits will be computed, and then 17798 the computed normal lower and upper limits will be exponentiated to 17799 obtain the lognormal prediction limits. 17800 17801 Similarly, if the keyword BOXCOX is present, a Box-Cox transformation 17802 to normality will be applied to the data before computing the normal 17803 prediction limits. The computed lower and upper limits will then 17804 be transformed back to the original scale. 17805 17806 This syntax supports matrix arguments for the response variables. 17807 17808Syntax 3: 17809 REPLICATED <LOWER/UPPER> <LOGNORMAL/BOXCOX> PREDICTION LIMITS 17810 <y> <x1> ... <xk> 17811 <SUBSET/EXCEPT/FOR qualification> 17812 where <y> is the response variable; 17813 <x1> .... <xk> is a list of 1 to 6 group-id variables; 17814 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 17815 17816 This syntax performs a cross-tabulation of the <x1> ... <xk> 17817 and generates a prediction interval for each unique combination 17818 of the cross-tabulated values. For example, if X1 has 3 levels 17819 and X2 has 2 levels, six prediction intervals will be generated. 17820 17821 If LOWER is specified, a one-sided lower prediction limit is 17822 returned. If UPPER is specified, a one-sided upper prediction 17823 limit is returned. If neither is specified, a two-sided limit 17824 is returned. 17825 17826 If the keyword LOGNORMAL is present, the log of the data will be 17827 taken, then the normal prediction limits will be computed, and then 17828 the computed normal lower and upper limits will be exponentiated to 17829 obtain the lognormal prediction limits. 17830 17831 Similarly, if the keyword BOXCOX is present, a Box-Cox transformation 17832 to normality will be applied to the data before computing the normal 17833 prediction limits. The computed lower and upper limits will then 17834 be transformed back to the original scale. 17835 17836 This syntax does not support matrix arguments. 17837 17838Examples: 17839 PREDICTION LIMITS Y1 17840 PREDICTION LIMITS Y1 SUBSET TAG > 2 17841 MULTIPLE PREDICTION LIMITS Y1 TO Y5 17842 REPLICATED PREDICTION LIMITS Y X 17843 LOGNORMAL PREDICTION LIMITS Y1 17844 17845Note: 17846 A table of prediction limits is printed for alpha levels of 17847 50.0, 80.0, 90.0, 95.0, 99.0, and 99.9. 17848 17849Note: 17850 In addition to the PREDICTION LIMIT command, the following 17851 commands can also be used: 17852 17853 LET ALPHA = 0.05 17854 LET NNEW = <value> 17855 17856 LET A = LOWER PREDICTION LIMIT Y 17857 LET A = UPPPER PREDICTION LIMIT Y 17858 LET A = ONE SIDED LOWER PREDICTION LIMIT Y 17859 LET A = ONE SIDED UPPER PREDICTION LIMIT Y 17860 17861 LET A = SUMMARY LOWER PREDICTION LIMIT YMEAN YSD N 17862 LET A = SUMMARY UPPPER PREDICTION LIMIT YMEAN YSD N 17863 LET A = SUMMARY ONE SIDED LOWER PREDICTION LIMIT YMEAN YSD N 17864 LET A = SUMMARY ONE SIDED UPPER PREDICTION LIMIT YMEAN YSD N 17865 17866 The first 2 commands specify the significance level and the number 17867 of new observations. The next 4 commands are used when you have raw 17868 data. The last 4 commands are used when only summary data (mean, 17869 standard deviation, sample size) is available. 17870 17871 In addition to the above LET command, built-in statistics are 17872 supported for about 20 different commands (enter HELP STATISTICS 17873 for details). 17874 17875Note: 17876 Prediction limits can also be generated for the case where the 17877 interval will contain ALL of the new points. Enter HELP PREDICTION 17878 BOUNDS for details. 17879 17880Note: 17881 The prediction limits described here are based on the assumption that 17882 the data follow an approximately normal distribution. If the data is 17883 not normally distributed, lognormal or Box-Cox transformations can be 17884 applied to make the data more closely approximate a normal 17885 distribution. The keywords LOGNORMAL and BOXCOX have been added to 17886 the command to allow these transformations to be applied automatically. 17887 17888 Note that if these options are used, the limits will be transformed 17889 back to the original scale for the data. 17890 17891Default: 17892 None 17893 17894Synonyms: 17895 PREDICTION INTERVALS is a synonym for PREDICTION LIMITS 17896 17897Related Commands: 17898 PREDICTION BOUNDS = Generate prediction bounds. 17899 SD PREDICTION LIMITS = Generate prediction limits for the 17900 standard deviation. 17901 CONFIDENCE LIMITS = Generate a confidence limit. 17902 TOLERANCE LIMITS = Generate a tolerance limit. 17903 17904Reference: 17905 Hahn and Meeker (1991), "Statistical Intervals: A Guide for 17906 Practitioners", Wiley, pp. 61-62. 17907 17908Applications: 17909 Confirmatory Data Analysis 17910 17911Implementation Date: 17912 2013/04 17913 2014/06: Support for LOGNORMAL and BOXCOX options 17914 17915Program 1: 17916 SKIP 25 17917 READ ZARR13.DAT Y 17918 SET WRITE DECIMALS 5 17919 LET NNEW = 5 17920 . 17921 PREDICTION LIMITS Y 17922 LOWER PREDICTION LIMITS Y 17923 UPPER PREDICTION LIMITS Y 17924 17925Program 2: 17926 SKIP 25 17927 READ GEAR.DAT Y X 17928 SET WRITE DECIMALS 5 17929 LET NNEW = 3 17930 . 17931 REPLICATED PREDICTION LIMITS Y X 17932 17933Program 3: 17934 . Following example from Hahn and Meeker's book. 17935 . 17936 let ymean = 50.10 17937 let ysd = 1.31 17938 let n1 = 5 17939 let nnew = 3 17940 let alpha = 0.05 17941 . 17942 set write decimals 5 17943 let slow1 = summary lower prediction limits ymean ysd n1 17944 let supp1 = summary upper prediction limits ymean ysd n1 17945 let slow2 = summary one sided lower prediction limits ymean ysd n1 17946 let supp2 = summary one sided upper prediction limits ymean ysd n1 17947 print slow1 supp1 slow2 supp2 17948 17949-----PRE-ERASE------------------------------------------------------- 17950 17951PRE-ERASE 17952 17953Name: 17954 PRE-ERASE 17955 17956Type: 17957 Plot Control Command 17958 17959Purpose: 17960 Specifies whether or not the screen should be automatically erased 17961 at the beginning of subsequent plots. 17962 17963Description: 17964 This command is typically used to overlay plots. The PLOT and 17965 3D-PLOT command can do this with the AND syntax. However, the AND 17966 syntax is not supported on any of the various other plot commands. 17967 The PRE-ERASE command can be used to overlay plots where the AND 17968 syntax is not allowed or is not convenient. 17969 17970Syntax: 17971 PRE-ERASE <ON or OFF> 17972 where ON specifies that the screen will be erased at the beginning 17973 of subsequent plots while OFF specifies that it will not. 17974 17975Examples: 17976 PRE-ERASE ON 17977 PRE-ERASE OFF 17978 PRE-ERASE 17979 17980Note: 17981 When overlaying plots, it is typically necessary to use the 17982 XLIMITS and YLIMITS commands to keep the axes on the same scales 17983 for all the overlaid plots. In addition, the frame, titles, 17984 labels, legends, etc. are redrawn with each subsequent plot. 17985 Although this does not cause any harm, it can be time consuming 17986 (particularly if a software font is in effect). You may want to 17987 shut these off after the original plot (e.g., TITLE ; FRAME OFF; 17988 LABEL ). 17989 17990Note: 17991 The PRE-ERASE command with no arguments reverts the setting to 17992 default. 17993 17994Default: 17995 The default is for plots to have automatic screen erasure (ON). 17996 17997Synonyms: 17998 None 17999 18000Related Commands: 18001 ERASE DELAY = Sets the delay after screen erasure. 18002 BELL = Sets the automatic bell switch for plots. 18003 HARDCOPY = Sets the automatic copy switch for plots. 18004 SEQUENCE = Sets the automatic sequence switch for plots. 18005 PLOT = Generates a data or function plot. 18006 RING = Rings the bell (immediately). 18007 ERASE = Erases the screen (immediately). 18008 COPY = Copies the screen (immediately). 18009 18010Applications: 18011 XX 18012 18013Implementation Date: 18014 XX 18015 18016Program: 18017 . PURPOSE--GENERATE A QUARTILE PLOT OF POINT BARROW FREON-11 DATA 18018 SKIP 50 18019 SET READ FORMAT 3F4.0,F5.0,F6.0,F3.0,2F9.0 18020 READ PBF11.DAT YEAR DAY BOT SD F11 FLAG WV CO2 18021 . 18022 RETAIN YEAR DAY BOT SD F11 WV CO2 FLAG SUBSET FLAG 0 18023 LET MONTH=INT(DAY/30.25)+1 18024 . 18025 TITLE QUARTILE PLOT 18026 XLIMITS 0 15 18027 YLIMITS 1 1.01 18028 CHARACTER U U 18029 LINE BLANK SOLID 18030 UPPER QUARTILE PLOT WV MONTH 18031 PRE-ERASE OFF 18032 CHARACTER L L 18033 LOWER QUARTILE PLOT WV MONTH 18034 18035-----PRE-FIT------------------------------------------------------- 18036 18037PRE-FIT 18038 18039Name: 18040 PRE-FIT 18041 18042Type: 18043 Analysis Command 18044 18045Purpose: 18046 Determines the "best fit" coefficients for a model, where the 18047 search is restricted to the points of a user-defined lattice. 18048 18049Description: 18050 The desired lattice is defined by the FOR statements at the end of 18051 the command. The"best fit" coefficients are determined by 18052 systematically evaluating the sum of squares surface at each of the 18053 points of the specified lattice of parameter values. The minimum 18054 point over the lattice is determined and noted, along with other 18055 extrema information. This command receives only light usage, 18056 typically in the following 2 contexts: 18057 1) immediately before the ... FIT command when the model is 18058 non-linear, when the starting values are unknown, and when the 18059 analyst is interested in gathering some preliminary information 18060 about the nature of the sum of squares surface. 18061 2) immediately after the ...FIT command when a least squares fit 18062 has been carried out, and the analyst is interested in examining 18063 the nature of the Lp surface (for p not = 2) in the vicinity of 18064 the least squares estimate. In this context, the FIT POWER 18065 command is also used. 18066 18067Syntax: 18068 PRE-FIT <y1> = <f> FOR <p> = <p1> <pinc> <p2> 18069 FOR <q> = <q1> <qinc> <q2> 18070 <additional optional FOR statements> 18071 where <y1> is the response (= dependent) variable; 18072 <f> is 18073 1) any general FORTRAN-like expression; or 18074 2) any function name that the user has already created 18075 via the LET FUNCTION command); 18076 <p> is the name of a parameter in the function; 18077 <p1> is a number or parameter that specifies the minimum 18078 value for the parameter; 18079 <pinc> is a number or parameter that specifies the increment 18080 for the parameter; 18081 <p2> is a number or parameter that specifies the maximum 18082 value for the parameter; 18083 <q> is the name of another parameter in the function; 18084 <q1> is a number or parameter that specifies the minimum 18085 value for the parameter; 18086 <qinc> is a number or parameter that specifies the increment 18087 for the parameter; 18088 <q2> is a number or parameter that specifies the maximum 18089 value for the parameter; 18090 and any additional FOR statments have a similar syntax. 18091 18092 All of the FOR statements should be on the same line. 18093 18094Examples: 18095 PRE-FIT Y=A+B*EXP(-C*X) FOR A=10 1 20 FOR B=50 10 100 ... 18096 FOR C = .1 .1 1 18097 PRE-FIT Y = A+EXP(C/X) FOR A = 1 2 10 FOR C = .5 .05 .6 18098 18099Default: 18100 None 18101 18102Synonyms: 18103 None 18104 18105Related Commands: 18106 PRED = A variable where predicted values are stored. 18107 RES = A variable where residuals are stored. 18108 RESSD = A parameter where the residual standard 18109 deviation is stored. 18110 RESDF = A parameter where the residual degrees of 18111 freedom is stored. 18112 REPSD = A parameter where the replication standard 18113 deviation is stored. 18114 REPDF = A parameter where the replication degrees of 18115 freedom is stored. 18116 LOFCDF = A parameter where the lack of fit cdf is 18117 stored. 18118 FIT = Carries out a least squares fit. 18119 EXACT RATIONAL FIT = Carries out an exact rational fit. 18120 SPLINE FIT = Carries out a spline fit. 18121 SMOOTH = Carries out a smoothing. 18122 ANOVA = Carries out an ANOVA. 18123 MEDIAN POLISH = Carries out a median polish. 18124 PLOT = Generates a data or function plot. 18125 18126Applications: 18127 Non-Linear Fitting 18128 18129Implementation Date: 18130 Pre-1987 18131 18132Program: 18133 XX 18134 18135-----PREPOST------------------------------------------------------- 18136 18137PREPOST 18138 18139Name: 18140 PREPOST 18141 18142Type: 18143 Output Device Command 18144 18145Purpose: 18146 The DEFINE PREPLOT command allows the analyst to specify a string 18147 that is sent to an output device at the beginning of a plot. The 18148 PREPOST command specifies the device that the DEFINE PREPLOT 18149 command applies to. 18150 18151Description: 18152 These commands are particularly useful for device emulators which 18153 often require escape codes to set the proper emulation mode. 18154 18155Syntax: 18156 PREPOST <device> 18157 where <device> specifies the graphics device that DEFINE PREPLOT 18158 applies to. 18159 18160Examples: 18161 PREPOST HP-GL 18162 PREPOST TEKTRONIX 4014 18163 18164Default: 18165 None 18166 18167Synonyms: 18168 None 18169 18170Related Commands: 18171 DEFINE PREPLOT = Define the preplot string. 18172 DEFINE POSTPLOT = Define the postplot string. 18173 18174Applications: 18175 XX 18176 18177Implementation Date: 18178 XX 18179 18180Program: 18181 . THE FOLLOWING SEQUENCE DEFINES CODES TO PUT A VT-240 IN 18182 . AND OUT OF TEKTRONIX 4014 MODE. 18183 DEFINE PREPLOT ESC [ ? 3 8 h 18184 DEFINE POSTPLOT ESC [ ? 3 8 l 18185 PREPOST TEKTRONIX 4014 18186 PLOT X**2 FOR X = 1 1 9 18187 18188-----PRE-SORT------------------------------------------------------- 18189 18190PRE-SORT 18191 18192Name: 18193 PRE-SORT 18194 18195Type: 18196 Plot Control Command 18197 18198Purpose: 18199 Specifies whether or not data to be plotted is pre-sorted by the 18200 horizontal axis variable. 18201 18202Description: 18203 By default, DATAPLOT pre-sorts the data before a plot according to 18204 the horizontal axis variable so that connected lines will look 18205 right. However, there are situations (e.g., drawing a map, 18206 plotting a trajectory) where it is necessary to plot the data in 18207 the order that they reside in the variables. The PRE-SORT command 18208 is used to specify this. 18209 18210Syntax: 18211 PRE-SORT <ON or OFF> 18212 where ON specifies that the data are pre-sorted while OFF specifies 18213 that they are not. 18214 18215Examples: 18216 PRE-SORT ON 18217 PRE-SORT OFF 18218 PRE-SORT 18219 18220Note: 18221 The PRE-SORT command with no arguments reverts the setting to 18222 default. 18223 18224Default: 18225 The default is for plots to pre-sort the data. 18226 18227Synonyms: 18228 None 18229 18230Related Commands: 18231 PLOT = Generates a data or function plot. 18232 18233Applications: 18234 XX 18235 18236Implementation Date: 18237 XX 18238 18239Program: 18240 PRE-SORT OFF 18241 FRAME OFF 18242 DEGREES 18243 LET THETA = SEQUENCE 0 10 1000 18244 LET R = 2*THETA 18245 LET Y = R*SIN(THETA) 18246 LET X = R*COS(THETA) 18247 TITLE A POLAR COORDINATE FUNCTION 18248 PLOT Y X 18249 18250-----PRIME NUMBERS (LET)---------------------------------------------- 18251 18252PRIME 18253 18254Name: 18255 PRIME NUMBERS (LET) 18256 18257Type: 18258 Let Subcommand 18259 18260Purpose: 18261 Compute prime numbers. 18262 18263Description: 18264 Prime numbers are integers that are only divisible by 1 and the 18265 number itself. 18266 18267Syntax: 18268 LET <resp> = PRIME NUMBERS FOR I = <start> <inc> <stop> 18269 where <resp> is a variable where the prime numbers are saved; 18270 <start> is the first row in <resp> where the pattern is saved 18271 (typically has a value of 1); 18272 <inc> is the row increment for saving values in <resp> 18273 (typically has a value of 1); and 18274 and <stop> is the last row in <resp> for saving values. 18275 18276 This syntax saves the first N (where N is determined by the values 18277 of <start>, <inc>, and <stop>) prime numbers in the variable <resp>. 18278 18279Examples: 18280 LET PRIME = PRIME NUMBERS FOR I = 1 1 100 18281 LET PRIME = PRIME NUMBERS FOR I = 1 1 10 18282 18283Default: 18284 None 18285 18286Synonyms: 18287 None 18288 18289Related Commands: 18290 SEQUENCE = Generate a sequence of numbers. 18291 PATTERN = Generate numbers with a specific pattern. 18292 FIBONNACCI NUMBERS = Generate Fibonnacci numbers. 18293 LOGISTIC NUMBERS = Generate numbers from a logistic sequence. 18294 CANTOR NUMBERS = Generate numbers from a Cantor set. 18295 DATA = Place numbers in a variable. 18296 18297Applications: 18298 XX 18299 18300Implementation Date: 18301 XX 18302 18303Program: 18304 LET PRIME = PRIME NUMBERS FOR I = 1 1 50 18305 PLOT PRIME 18306 18307-----PRINCIPAL COMPONENTS (LET)--------------------------------------- 18308 18309PRINCIPAL COMPONENTS 18310 18311Name: 18312 PRINCIPAL COMPONENTS (LET) 18313 18314Type: 18315 Let Subcommand 18316 18317Purpose: 18318 Find the principal components of a matrix. 18319 18320Description: 18321 Given a data matrix X with n cases and p variables (i.e., variables 18322 X1, X2, ... , Xp), a linear transformation to a new set of 18323 variables Y1, Y2, ... , Yp is calculated. That is, 18324 Y1 = a11X1 + a21X2 + ... + ap1Xp 18325 Y2 = a12X1 + a22X2 + ... + ap2Xp 18326 .... 18327 Yp = a1pX1 + a2pX2 + ... + appXp 18328 The Y variables are called the principal components and they have 18329 the following characteristics: 18330 1) The p principal components are uncorrelated. 18331 2) The first principal component explains the largest percentage 18332 of the variation in the original p-dimensional data set (and 18333 the second principal component explains the second largest 18334 percentage and so on). Typically the first few variables 18335 account for most of the variation while the remaining 18336 variables make a negligible contribution. 18337 18338 Principle components are used to reduce large dimensional data 18339 sets to data sets with a few dimensions that still retain most of 18340 the information in the original data matrix. That is, typically 18341 only the first few principal components are used. If the first 18342 few principal components do not account for most of the variation, 18343 there is little advantage to using them. By reducing the 18344 dimensionality of the original data, principal components can often 18345 simplify many analyses. The primary disadvantage of principal 18346 components is that interpretation can be more difficult since you 18347 are no longer working with the original variables. 18348 18349 Principle components reduce to the problem of finding the 18350 eigenvalues and eigenvectors of the covariance (or correlation 18351 matrix) of the data matrix. The ith row of the A matrix 18352 is the eigenvector corresponding to the ith eigenvalue of the 18353 covariance (or correlation) matrix. Also, the proportion of the 18354 variance in the original data matrix explained by the ith principal 18355 component is the ith eigenvalue divided by the sum of all p 18356 eigenvalues. Using the covariance matrix is preferred when the 18357 original data are reasonably comparable scales. If this is not 18358 the case, the correlation matrix is preferred. 18359 18360 DATAPLOT returns the principal components (i.e., the Y matrix), 18361 the eigenvectors (i.e., the A matrix), and the eigenvalues in 18362 separate steps. 18363 18364Syntax 1: 18365 LET <mat3> = PRINCIPAL COMPONENTS <mat1> 18366 <SUBSET/EXCEPT/FOR qualification> 18367 where <mat1> is the matrix for which the principal components are 18368 computed (it can be the original data matrix, a 18369 covariance matrix, or a correlation matrix); 18370 <mat3> is a p by p matrix where the principal components 18371 (i.e., the Y matrix) are saved (column 1 is the first 18372 principal component, column p is the pth principal 18373 component); 18374 and where the <SUBSET/EXCEPT/FOR qualification> is optional (and 18375 rarely used in this context). 18376 18377Syntax 2: 18378 LET <resp> = <id> PRINCIPAL COMPONENTS <mat1> 18379 <SUBSET/EXCEPT/FOR qualification> 18380 where <mat1> is the matrix for which the principal components are 18381 computed (it can be the original data matrix, a 18382 covariance matrix, or a correlation matrix); 18383 <id> identifies a specific principal component to be 18384 returned (FIRST, SECOND, THIRD, FOURTH, FIFTH, SIXTH, 18385 SEVENTH, EIGHTH, NINTH, TENTH); 18386 <resp> is a variable of length p where the specific 18387 principal component is saved; 18388 and where the <SUBSET/EXCEPT/FOR qualification> is optional (and 18389 rarely used in this context). 18390 18391Syntax 3: 18392 LET <resp> = PRINCIPAL COMPONENTS EIGENVALUES <mat1> 18393 <SUBSET/EXCEPT/FOR qualification> 18394 where <mat1> is the matrix for which the principal components are 18395 computed (it can be the original data matrix, a 18396 covariance matrix, or a correlation matrix); 18397 <resp> is a variable of length p where the eigenvalues of 18398 the covariance (or correlation) matrix are saved; 18399 and where the <SUBSET/EXCEPT/FOR qualification> is optional (and 18400 rarely used in this context). 18401 18402Syntax 4: 18403 LET <par> = <id> PRINCIPAL COMPONENTS EIGENVALUES <mat1> 18404 <SUBSET/EXCEPT/FOR qualification> 18405 where <mat1> is the matrix for which the principal components are 18406 computed (it can be the original data matrix, a 18407 covariance matrix, or a correlation matrix); 18408 <id> identifies a specific eigenvalue to be returned (FIRST, 18409 SECOND, THIRD, FOURTH, FIFTH, SIXTH, SEVENTH, EIGHTH, 18410 NINTH, TENTH); 18411 <par> is a parameter where the specific eigenvalue is saved; 18412 and where the <SUBSET/EXCEPT/FOR qualification> is optional (and 18413 rarely used in this context). 18414 18415Syntax: 5 18416 LET <mat3> = PRINCIPAL COMPONENTS EIGENVECTORS <mat1> 18417 <SUBSET/EXCEPT/FOR qualification> 18418 where <mat1> is the matrix for which the principal components are 18419 computed (it can be the original data matrix, a 18420 covariance matrix, or a correlation matrix); 18421 <mat3> is a p by p matrix where the eigenvectors of the 18422 covariance (or correlation) matrix (i.e., the A 18423 matrix) are saved; 18424 and where the <SUBSET/EXCEPT/FOR qualification> is optional (and 18425 rarely used in this context). 18426 18427Syntax: 6 18428 LET <resp> = <id> PRINCIPAL COMPONENTS EIGENVECTORS <mat1> 18429 <SUBSET/EXCEPT/FOR qualification> 18430 where <mat1> is the matrix for which the principal components are 18431 computed (it can be the original data matrix, a 18432 covariance matrix, or a correlation matrix); 18433 <id> identifies a specific eigenvector to be returned (FIRST, 18434 SECOND, THIRD, FOURTH, FIFTH, SIXTH, SEVENTH, EIGHTH, 18435 NINTH, TENTH); 18436 <resp> is a variable where the specific eigenvector is saved; 18437 and where the <SUBSET/EXCEPT/FOR qualification> is optional (and 18438 rarely used in this context). 18439 18440Examples: 18441 LET Y = PRINCIPAL COMPONENTS X 18442 LET E = PRINCIPAL COMPONENTS EIGENVALUES X 18443 LET A = PRINCIPAL COMPONENTS EIGENVECTORS X 18444 LET Y1 = FIRST PRINCIPAL COMPONENT X 18445 LET E1 = FIRST PRINCIPAL COMPONENT EIGENVALUE X 18446 LET A1 = FIRST PRINCIPAL COMPONENT EIGENVECTOR X 18447 18448Note: 18449 If the principal components are derived from the original data and 18450 the covariance matrix, the data matrix is scaled by subtracting 18451 the column mean before it is multiplied by the eigenvector matrix. 18452 That is, Y = A*(X-XBAR). 18453 18454Note: 18455 The PRINCIPAL COMPONENT TYPE command is used to specify whether 18456 the original matrix is a data matrix, a covariance matrix, or a 18457 correlation matrix. It also specifies whether the principal 18458 components are derived from the covariance or the correlation 18459 matrix. The default is an original data matrix with the 18460 principal components derived from the correlation matrix. 18461 18462Note: 18463 Principle components are sometimes used in regression problems 18464 to avoid multicolinearity problems while still maintaining most 18465 of the information in a large number of variables. This is 18466 demonstrated in the second program example. 18467 18468Note: 18469 Matrices are created with either the READ MATRIX command or the 18470 MATRIX DEFINITION command. Enter HELP MATRIX DEFINITION and HELP 18471 READ MATRIX for details. 18472 18473Note: 18474 The columns of a matrix are accessible as variables by appending an 18475 index to the matrix name. For example, the 4x4 matrix C has 18476 columns C1, C2, C3, and C4. These columns can be operated on like 18477 any other DATAPLOT variable. 18478 18479Note: 18480 The maximum size matrix that DATAPLOT can handle is set when 18481 DATAPLOT is built on a particular site. The default maximums are 18482 100 columns and 500 rows. Earlier versions may be 20 rows and 20 18483 columns or 100 rows and 100 columns. 18484 18485 If you have more than 500 rows in your input data, you can use the 18486 LOOP command to generate a covariance matrix and compute the 18487 principal components from this covariance matrix. 18488 18489Default: 18490 None 18491 18492Synonyms: 18493 None 18494 18495Related Commands: 18496 MATRIX ADDITION = Perform a matrix addition. 18497 MATRIX ADJOINT = Compute the adjoint matrix of a matrix. 18498 MATRIX COFACTOR = Compute a matrix cofactor. 18499 MATRIX DEFINITION = Set a matrix definition. 18500 MATRIX DETERMINANT = Compute a matrix determinant. 18501 MATRIX EIGENVALUES = Compute the matrix eigenvalues. 18502 MATRIX EIGENVECTORS = Compute the matrix eigenvectors. 18503 MATRIX EUCLID NORM = Compute the matrix Euclidean norm. 18504 MATRIX INVERSE = Compute a matrix inverse. 18505 MATRIX MINOR = Compute a matrix minor. 18506 MATRIX MULTIPLICAT = Perform a matrix multiplication. 18507 MATRIX NUMB OF COLU = Compute the number of columns in a matrix. 18508 MATRIX NUMB OF ROWS = Compute the number of rows in a matrix. 18509 MATRIX RANK = Compute the rank of a matrix. 18510 MATRIX SIMPLEX SOLU = Compute a matrix simplex solution. 18511 MATRIX SOLUTION = Solve a system of linear equations. 18512 MATRIX SPECTRAL NORM = Compute the matrix spectral norm. 18513 MATRIX SPECTRAL RADI = Compute the matrix spectral radius. 18514 MATRIX SUBMATRIX = Define a matrix submatrix. 18515 MATRIX SUBTRACTION = Perform a matrix subtraction. 18516 MATRIX TRACE = Compute a matrix trace. 18517 MATRIX TRANSPOSE = Compute a matrix transpose. 18518 CORRELATION MATRIX = Compute the correlation matrix of a matrix. 18519 VARIANCE-COVA MATRIX = Compute the variance-covariance matrix of a 18520 matrix. 18521 SINGULAR VALUES = Compute the singular values of a matrix. 18522 SINGULAR VALUE DECOM = Compute the singular value decomposition of 18523 a matrix. 18524 SINGULAR VALUE FACT = Compute the singular value factorization of 18525 a matrix. 18526 18527Reference: 18528 "Principle Components and Factor Analysis: Part I - Principle 18529 Components", Jackson, Journal of Quality Technology, October, 1980. 18530 18531 "Multivariate Statistical Methods", Morrison, McGraw-Hill, 1976. 18532 18533 "Graphical Exploratory Data Analysis", du Toit, Steyn, and Stumpf, 18534 Springer-Verlang, 1986. 18535 18536 "Applied Regression Analysis", Draper and Smith, John Wiley, 1981. 18537 18538Applications: 18539 Multivariate Analysis, Regression 18540 18541Implementation Date: 18542 87/10 18543 18544Program 1: 18545 . SOURCE: "GRAPHICAL EXPLORATORY DATA ANALYSIS", DU TOIT, ET AL 18546 . 28 STUDENTS FROM ABILITY TEST DATA SET (PAGE 6) 18547 DIMENSION 100 COLUMNS 18548 READ MATRIX X 18549 19 21 21 18 20 21 15 14 15 13 15 16 19 19 19 20 17 17 18550 21 20 15 24 22 18 11 18 16 19 14 17 21 15 17 18 18 19 18551 18 19 16 18 18 23 11 13 13 15 11 11 15 18 13 15 18 13 18552 18 23 10 18 16 16 11 9 8 15 6 9 12 16 8 13 9 15 18553 24 24 19 20 23 24 22 18 16 19 16 19 19 21 21 20 18 20 18554 19 19 23 21 23 23 9 8 13 15 20 15 17 12 20 16 16 21 18555 21 20 19 21 21 23 11 16 11 18 18 14 21 17 14 19 18 16 18556 21 20 21 20 16 22 7 11 17 16 8 10 13 17 16 17 15 11 18557 19 20 19 22 18 21 11 12 7 15 9 11 13 12 13 17 12 12 18558 19 23 22 22 16 25 12 15 16 19 15 10 15 20 18 18 17 13 18559 17 13 8 18 13 18 12 8 9 12 12 11 9 14 15 12 13 9 18560 21 22 22 15 23 23 16 12 16 15 13 14 19 17 16 18 19 18 18561 18 18 17 16 15 22 8 11 10 16 8 14 10 13 10 14 9 14 18562 13 18 21 16 17 15 11 12 11 9 11 11 16 18 14 13 15 18 18563 17 13 17 20 22 19 15 11 11 12 11 13 15 15 15 13 16 12 18564 18 12 9 9 15 17 9 5 3 12 7 7 12 10 10 13 10 12 18565 22 15 24 17 15 20 10 12 12 11 9 12 19 16 16 8 11 17 18566 18 17 18 18 13 18 14 12 15 11 10 9 21 14 12 15 11 13 18567 17 15 14 14 12 13 9 10 11 9 7 11 13 15 11 13 10 13 18568 16 20 17 13 15 16 10 16 12 10 7 13 12 18 13 18 10 15 18569 24 21 22 21 21 25 11 17 17 21 11 15 15 18 16 16 17 17 18570 23 23 21 22 16 21 10 18 16 14 14 13 17 21 19 16 17 19 18571 22 22 21 24 18 24 6 16 14 20 16 18 12 12 13 18 18 21 18572 22 17 19 19 21 20 17 15 9 13 16 17 18 11 13 16 19 14 18573 20 23 23 22 22 24 11 18 16 16 16 20 13 16 18 18 20 20 18574 22 17 21 17 17 22 10 14 16 16 13 8 13 18 21 12 13 15 18575 21 18 20 23 21 22 8 15 9 17 11 13 13 20 20 21 15 20 18576 21 22 19 20 18 17 11 15 12 14 11 10 11 13 14 14 15 14 18577 END OF DATA 18578 LET P = MATRIX NUMBER OF COLUMNS X 18579 PRINCIPAL COMPONENTS TYPE DATA COVARIANCE 18580 LET Y = PRINCIPAL COMPONENTS X 18581 LET A = PRINCIPAL COMPONENTS EIGENVECTORS X 18582 LET E = PRINCIPAL COMPONENTS EIGENVALUES X 18583 PRINT E 18584 LET ESUM = CUMULATIVE SUM E 18585 LET TEMP = ESUM(P) 18586 LET RATIO = 100*ESUM/TEMP 18587 . FORM CORR(Xi,Y1) = Ai1*SQRT(L1)/Si 18588 LOOP FOR K = 1 1 P 18589 LET TEMP = STANDARD DEVIATION X^K 18590 LET SD(K) = TEMP 18591 END OF LOOP 18592 LET TEMP = E(1) 18593 LET R1 = A1*SQRT(TEMP)/SD 18594 . FORM CORR(Xi,Y2) = Ai2*SQRT(L2)/Si 18595 LET TEMP = E(2) 18596 LET R2 = A2*SQRT(TEMP)/SD 18597 LINE BLANK ALL 18598 CHARACTER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 18599 LET TAG = SEQUENCE 1 1 P 18600 X1LABEL CORRELATION (XLC()I,UC()Y1) 18601 Y1LABEL CORRELATION (XLC()I,UC()Y2) 18602 LET TEMP = RATIO(1) 18603 LEGEND 1 PC 1 - ^TEMP % EXPLAINED 18604 LET TEMP = RATIO(2) 18605 LEGEND 2 PC 2 - ^TEMP % EXPLAINED 18606 PLOT R2 R1 TAG 18607 18608Program 2: 18609 . SOURCE: "APPLIED REGRESSION ANALYSIS", DRAPER AND SMITH. 18610 . HALD DATA (APPENDIX B) 18611 . PRINCIPAL COMPONENTS REGRESSION (CHAPTER 6-9 OF DRAPER, SMITH) 18612 . 18613 DIMENSION 100 COLUMNS 18614 READ X1 X2 X3 X4 Y 18615 7 26 6 60 78.5 18616 1 29 15 52 74.3 18617 11 56 8 20 104.3 18618 11 31 8 47 87.6 18619 7 52 6 33 95.9 18620 11 55 9 22 109.2 18621 3 71 17 6 102.7 18622 1 31 22 44 72.5 18623 2 54 18 22 93.1 18624 21 47 4 26 115.9 18625 1 40 23 34 83.8 18626 11 66 9 12 113.3 18627 10 68 8 12 109.4 18628 END OF DATA 18629 LET X = MATRIX DEFINITION X1 13 4 18630 LET CORR = CORRELATION MATRIX X 18631 PRINT CORR 18632 PRINCIPAL COMPONENT TYPE DATA CORRELATION 18633 LET W = PRINCIPAL COMPONENTS X 18634 LET E = PRINCIPAL COMPONENT EIGENVALUES X 18635 LET EVECT = PRINCIPAL COMPONENT EIGENVECTORS X 18636 LET RATIO = CUMULATIVE SUM E 18637 LET RATIO = RATIO/4. 18638 . 18639 PRINT E RATIO 18640 PRINT "EIGENVECTORS:"; PRINT EVECT 18641 PRINT "PRINCIPAL COMPONENTS:"; PRINT W 18642 FEEDBACK ON 18643 FIT Y W1 W2 18644 18645-----PRINCIPAL COMPONENTS TYPE---------------------------------------- 18646 18647PRINCIPAL COMPONENTS TYPE 18648 18649Name: 18650 PRINCIPAL COMPONENTS TYPE 18651 18652Type: 18653 Support Command 18654 18655Purpose: 18656 Specify the input format of the data for the PRINCIPAL COMPONENTS 18657 command. 18658 18659Description: 18660 See the documentation for the PRINCIPAL COMPONENTS command for a 18661 description of principal components. 18662 18663 Principle components reduce to the problem of finding the 18664 eigenvalues and eigenvectors of the covariance (or correlation 18665 matrix) of the data matrix. In addition, the data matrix can be 18666 raw data, a covariance matrix, or a correlation matrix. 18667 18668 The PRINCIPAL COMPONENTS TYPE command specifies two things. First, 18669 it specifies whether the data matrix is raw data, a covariance 18670 matrix, or a correlation matrix. Second, it specifies whether the 18671 principal components are calculated from the covariance or the 18672 correlation matrix. 18673 18674Syntax: 18675 PRINCIPAL COMPONENTS TYPE <key1> <key2> 18676 where <key1> is one of the following: 18677 DATA - original matrix is raw data 18678 COVARIANCE - original matrix is a covariance matrix 18679 CORRELATION - original matrix is a correlation matrix; 18680 and <key2> is one of the following: 18681 COVARIANCE - principal components computed from a 18682 covariance matrix 18683 CORRELATION - principal components computed from a 18684 correlation matrix. 18685 18686Examples: 18687 PRINCIPAL COMPONENTS TYPE DATA COVARIANCE 18688 PRINCIPAL COMPONENTS TYPE DATA CORRELATION 18689 PRINCIPAL COMPONENTS TYPE COVARIANCE COVARIANCE 18690 PRINCIPAL COMPONENTS TYPE COVARIANCE CORRELATION 18691 PRINCIPAL COMPONENTS TYPE CORRELATION CORRELATION 18692 18693Note: 18694 If the original data is a correlation matrix, principal components 18695 can only be computed from a correlation matrix. That is, the 18696 command PRINCIPAL COMPONENTS TYPE CORRELATION COVARIANCE is not 18697 supported. 18698 18699Default: 18700 The original matrix is raw data and the principal components are 18701 calculated from a covariance matrix. 18702 18703Synonyms: 18704 None 18705 18706Related Commands: 18707 CORRELATION MATRIX = Compute the correlation matrix of a matrix. 18708 VARIANCE-COVA MATRIX = Compute the variance-covariance matrix of a 18709 matrix. 18710 PRINCIPAL COMPONENTS = Compute principal components. 18711 18712Reference: 18713 "Principle Components and Factor Analysis: Part I - Principle 18714 Components", Jackson, Journal of Quality Technology, October, 1980. 18715 18716 "Multivariate Statistical Methods", Morrison, McGraw-Hill, 1976. 18717 18718Applications: 18719 Multivariate Analysis 18720 18721Implementation Date: 18722 87/10 18723 18724Program 1: 18725 . SOURCE: "GRAPHICAL EXPLORATORY DATA ANALYSIS", DU TOIT, ET AL 18726 . 28 STUDENTS FROM ABILITY TEST DATA SET (PAGE 6) 18727 DIMENSION 100 COLUMNS 18728 READ MATRIX X 18729 19 21 21 18 20 21 15 14 15 13 15 16 19 19 19 20 17 17 18730 21 20 15 24 22 18 11 18 16 19 14 17 21 15 17 18 18 19 18731 18 19 16 18 18 23 11 13 13 15 11 11 15 18 13 15 18 13 18732 18 23 10 18 16 16 11 9 8 15 6 9 12 16 8 13 9 15 18733 24 24 19 20 23 24 22 18 16 19 16 19 19 21 21 20 18 20 18734 19 19 23 21 23 23 9 8 13 15 20 15 17 12 20 16 16 21 18735 21 20 19 21 21 23 11 16 11 18 18 14 21 17 14 19 18 16 18736 21 20 21 20 16 22 7 11 17 16 8 10 13 17 16 17 15 11 18737 19 20 19 22 18 21 11 12 7 15 9 11 13 12 13 17 12 12 18738 19 23 22 22 16 25 12 15 16 19 15 10 15 20 18 18 17 13 18739 17 13 8 18 13 18 12 8 9 12 12 11 9 14 15 12 13 9 18740 21 22 22 15 23 23 16 12 16 15 13 14 19 17 16 18 19 18 18741 18 18 17 16 15 22 8 11 10 16 8 14 10 13 10 14 9 14 18742 13 18 21 16 17 15 11 12 11 9 11 11 16 18 14 13 15 18 18743 17 13 17 20 22 19 15 11 11 12 11 13 15 15 15 13 16 12 18744 18 12 9 9 15 17 9 5 3 12 7 7 12 10 10 13 10 12 18745 22 15 24 17 15 20 10 12 12 11 9 12 19 16 16 8 11 17 18746 18 17 18 18 13 18 14 12 15 11 10 9 21 14 12 15 11 13 18747 17 15 14 14 12 13 9 10 11 9 7 11 13 15 11 13 10 13 18748 16 20 17 13 15 16 10 16 12 10 7 13 12 18 13 18 10 15 18749 24 21 22 21 21 25 11 17 17 21 11 15 15 18 16 16 17 17 18750 23 23 21 22 16 21 10 18 16 14 14 13 17 21 19 16 17 19 18751 22 22 21 24 18 24 6 16 14 20 16 18 12 12 13 18 18 21 18752 22 17 19 19 21 20 17 15 9 13 16 17 18 11 13 16 19 14 18753 20 23 23 22 22 24 11 18 16 16 16 20 13 16 18 18 20 20 18754 22 17 21 17 17 22 10 14 16 16 13 8 13 18 21 12 13 15 18755 21 18 20 23 21 22 8 15 9 17 11 13 13 20 20 21 15 20 18756 21 22 19 20 18 17 11 15 12 14 11 10 11 13 14 14 15 14 18757 END OF DATA 18758 LET P = MATRIX NUMBER OF COLUMNS X 18759 PRINCIPAL COMPONENTS TYPE DATA COVARIANCE 18760 LET Y = PRINCIPAL COMPONENTS X 18761 LET A = PRINCIPAL COMPONENTS EIGENVECTORS X 18762 LET E = PRINCIPAL COMPONENTS EIGENVALUES X 18763 18764-----PRINTFILE-------------------------------------------------- 18765 18766PRINTFILE 18767 18768Name: 18769 PRINTFILE 18770 18771Type: 18772 Support Command 18773 18774Purpose: 18775 Print an ASCII file. 18776 18777Description: 18778 This is an operating system dependent command. 18779 18780 On Windows 7/8/10 platforms, the printing is invoked with the 18781 command 18782 18783 write.exe -p <filename> 18784 18785 This command uses WordPad to print the file. Note that Wordpad 18786 can print RTF formatted files and some Microsoft Word formatted 18787 files (this can depend on what versions of Word and WorPad you 18788 have installed). Currently, no provision is made for a non-default 18789 printer. 18790 18791 On Linux/Unix and MacOS platforms, the printing is invoked with 18792 the command 18793 18794 lpr <filename> 18795 18796 If you have specified the printer name with the SET PRINTER command, 18797 then the following command is used 18798 18799 lpr -P<printername> <filename> 18800 18801Syntax: 18802 PRINTFILE <file1> 18803 where <file1> is the name of the file to print. 18804 18805 In order to avoid conflict with the PRINT command, PRINTFILE cannot 18806 be abbreviated. Only the first 8 characters are evaluated, so a match 18807 up to PRINTFIL is succifient. 18808 18809Examples: 18810 PRINTFILE BERGER1.DAT 18811 18812Note: 18813 This command requires that the SYSTEM capability is supported. 18814 This should be the case for all currently supported platforms. 18815 18816Default: 18817 None 18818 18819Synonyms: 18820 None 18821 18822Related Commands: 18823 PP = Print the current plot to a Postscript printer. 18824 COPY = Copy a file to another file. 18825 LIST = Print the contents of the file. 18826 SEARCH = Search a file for a given string. 18827 EDIT = Edit a file. 18828 SYSTEM = Perform an operating system command. 18829 18830Applications: 18831 Interactive Usage 18832 18833Implementation Date: 18834 2019/03: 18835 18836Program: 18837 SKIP 25 18838 READ BERGER1.DAT Y X 18839 SET WRITE DECIMALS 4 18840 CPATURE BERGER1.OUT 18841 FIT Y X 18842 END OF CAPTURE 18843 PRINTFILE BERGER1.OUT 18844 18845-----PRINT------------------------------------------------------- 18846 18847PRINT 18848 18849Name: 18850 PRINT 18851 18852Type: 18853 Support Command 18854 18855Purpose: 18856 Writes variables (vectors), parameters (scalars), functions 18857 (including strings), and matrices to the screen or to a file. 18858 18859Syntax 1: 18860 PRINT <variable list> 18861 where <variable list> is a list of parameters, variables, strings, 18862 or matrices (separated by spaces). 18863 18864Syntax 2: 18865 PRINT <file name> <variable list> 18866 where <file name> specifies the name of the output file; 18867 and <variable list> is a list of parameters, variables, strings, 18868 or matrics (separated by spaces). 18869 18870 If the file name does not contain a period, place a period (no 18871 spaces) at the end of the file name. 18872 18873Examples: 18874 PRINT OUT. Y1 Y2 Y3 X 18875 PRINT DATA.SAVE X Y PRED RES 18876 PRINT X Y PRED RES 18877 18878Note: 18879 Numbers are written in exponential format by default. The analyst 18880 can specify a specific format with the SET WRITE FORMAT statement. 18881 The output file is rewound by default (that is, if the file 18882 already exists it is overwritten). Use the SET WRITE REWIND OFF 18883 command to allow multiple writes to the same file. The SET WRITE 18884 DECIMALS command can also be used to control the format of 18885 numbers. 18886 18887Note: 18888 DATAPLOT writes to an ASCII text file. No method of writing 18889 binary files is currently supported. 18890 18891Note: 18892 Literal text can be written by enclosing it in double quotes. For 18893 example, 18894 PRINT "Enter the value for X" 18895 18896Note: 18897 DATAPLOT has no restrictions on the file name other than it be a 18898 valid file name on the local operating system and that it contain 18899 a period "." in the file name itself or as a trailing character. 18900 DATAPLOT strips off trailing periods on those systems where it is 18901 appropriate to do so. On systems where trailing periods can be a 18902 valid file name (e.g., Unix), DATAPLOT opens the file with the 18903 trailing period. 18904 18905Note: 18906 File names are case sensitive on Unix file systems. For Unix, 18907 DATAPLOT opens the file as given. All other currently supported 18908 systems are not case sensitive regarding file names. 18909 18910 As a further caution for Unix hosts, certain expansion characters 18911 (specifically ~ to refer to your home directory) are interpreted 18912 by the shell and are not recognized by the Fortran compiler. These 18913 expansion characters are interpreted as literal characters and do 18914 not yield the intended file name. 18915 18916Default: 18917 XX 18918 18919Synonyms: 18920 WRITE is a synonym for PRINT. 18921 18922Related Commands: 18923 SET WRITE FORMAT = Define a Fortran like format for writing 18924 data. 18925 SET WRITE DECIMALS = Specify the number of digits to the right of 18926 the decimal point when printing numbers. 18927 SET WRITE REWIND = Specify if the output file is rewound 18928 before writing. 18929 READ = Read variables, parameters, strings, and 18930 matrices from a file. 18931 18932Applications: 18933 XX 18934 18935Implementation Date: 18936 XX 18937 18938Program: 18939 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 18940 LET Y2 = EXPONENTIAL RANDOM NUMBERS FOR I = 1 1 100 18941 LET Y3 = UNIFORM RANDOM NUMBERS FOR I = 1 1 100 18942 WRITE RANDOM.DAT Y1 Y2 Y3 18943 18944-----PRINTER (SET)-------------------------------------------------- 18945 18946PRINTER 18947 18948Name: 18949 PRINTER (SET) 18950 18951Type: 18952 Set Subcommand 18953 18954Purpose: 18955 This command sets the printer id for the PP command. 18956 18957Description: 18958 The PP command is used to send the most recent plot to 18959 the printer. 18960 18961 The PP command is operating system dependent. It is 18962 currently supported in the Unix and Windows 95/98/NT 18963 environments. 18964 18965 The PP command sends the graphics output to the default 18966 printer. Specifically, 18967 18968 1) On Unix, the PP command issues an "lpr dppl2f.dat" 18969 command. The default printer in Unix is set by the 18970 UNIX command "setenv PRINTER <printer-id>" for the 18971 c shell (other shells may have a slightly different 18972 way for defining the default printer). 18973 18974 2) On Windows 95/98/NT systems, the PP command issues the 18975 command "COPY DPPL2F.DAT PRN:". 18976 18977 On either system, it is sometimes desirable to override the 18978 default printer. The SET PRINTER command is used to override 18979 the default printer. If the command "SET PRINTER printer-id" 18980 is entered in Dataplot, then the PP command does the following: 18981 18982 1) On Unix, the PP command issues a 18983 "lpr -Pprinter-id dppl2f.dat" command. 18984 18985 2) On Windows 95/98/NT systems, the PP command issues the 18986 command "COPY DPPL2F.DAT printer-id". This is most often 18987 used to send the graphics output to a network printer 18988 rather than the local printer. 18989 18990 The printer-id will be specific to your local host. If 18991 you are unsure of the appropriate printer name, then contact 18992 your local system administrator for this information. 18993 18994Syntax: 18995 SET PRINTER <printer-id> 18996 where <printer-id> is the desired printer id. 18997 18998Examples: 18999 SET PRINTER lw7_duplex 19000 19001Default: 19002 For Unix, the default printer is set by the "setenv PRINTER" 19003 command when using the c shell. On Windows, the default 19004 printer is PRN:, i.e., the local printer. 19005 19006Synonyms: 19007 None 19008 19009Note: 19010 Dataplot has no way of determining if the given printer-id 19011 is valid on your system. 19012 19013Related Commands: 19014 PP = Print the current plot on the default printer. 19015 SYSTEM = Enter an operating system command within a 19016 Dataplot session. 19017 19018Applications: 19019 Interactive Usage 19020 19021Implementation Date: 19022 1998/5 19023 19024Program: 19025 SET PRINTER lw7 19026 PLOT X**2 FOR X = 1 1 9 19027 PP 19028 19029-----PRINTER TYPE------------------------------------------------ 19030 19031PRINTER TYPE 19032 19033Note: 19034 ******* This command is not yet operational ****** 19035 19036Name: 19037 PRINTER TYPE 19038 19039Type: 19040 Support Subcommand 19041 19042Purpose: 19043 Specifies whether the output from the / PRINTER command is 19044 generated as an ASCII text file or as a Postscript file. 19045 19046Description: 19047 The / command re-executes saved commands (see the documentation for 19048 the SAVE command for details). The / PRINTER command re-executes 19049 saved commands and also re-directs the output to the printer. The 19050 PRINTER TYPE command specifies whether this output is sent to the 19051 printer as a plain ASCII text file or is reformatted into a 19052 Postscript format. 19053 19054Syntax: 19055 PRINTER TYPE <ASCII/POSTSCRIPT> 19056 where ASCII specifies a plain ASCII text file and POSTSCRIPT 19057 specifies a Postscript formatted file. 19058 19059Examples: 19060 PRINTER TYPE ASCII 19061 PRINTER TYPE POSTSCRIPT 19062 19063Default: 19064 The output is sent as a plain ASCII text file. 19065 19066Synonyms: 19067 None 19068 19069Related Commands: 19070 / PRINTER = Re-executes saved commands and re-directs the 19071 output to a printer. 19072 SAVE = Specify commands to be saved for subsequent 19073 re-execution. 19074 19075Applications: 19076 XX 19077 19078Implementation Date: 19079 XX 19080 19081Program: 19082 XX 19083 19084-----PRINTING------------------------------------------------------- 19085 19086PRINTING 19087 19088Name: 19089 PRINTING 19090 19091Type: 19092 Support Command 19093 19094Purpose: 19095 Specifies whether the usual tabular output that is generated by 19096 most analysis category commands (FIT, SMOOTH, ANOVA, SUMMARY, 19097 etc.) should be printed or suppressed. 19098 19099Syntax: 19100 PRINTING <ON or OFF> 19101 where ON specifies that the output should be printed while OFF 19102 specifies that is should not be printed. 19103 19104Examples: 19105 PRINTING ON 19106 PRINTING OFF 19107 PRINTING 19108 19109Note: 19110 The PRINTING command with no arguments is equivalent to 19111 PRINTING ON. 19112 19113Default: 19114 At sign-on, the default is printing (i.e., ON). 19115 19116Synonyms: 19117 None 19118 19119Related Commands: 19120 ECHO = Allows/suppresses command echoing. 19121 FEEDBACK = Allows/suppresses feedback messages. 19122 PROMPT = Allows/suppresses the prompt character. 19123 SET = Sets the value of an internal variable (e.g., IPR). 19124 PROBE = Displays the value of an internal variable (e.g., 19125 IPR). 19126 19127Applications: 19128 Presentation 19129 19130Implementation Date: 19131 Pre-1987 19132 19133Program: 19134 XX 19135 19136-----PROBABILITY PLOT------------------------------------------------- 19137 19138PROBABILITY PLOT 19139 19140Name: 19141 ... PROBABILITY PLOT 19142 19143Type: 19144 Graphics Command 19145 19146Purpose: 19147 Generates a probability plot for one of 130+ distributions. 19148 19149Description: 19150 A probability plot is a graphical data analysis technique for 19151 determining how well the specified distribution fits the data 19152 set. Linearity in the probability plot is indicative of a good 19153 distributional fit. 19154 19155 The probability plot consists of: 19156 19157 Vertical axis = ordered observations; 19158 Horizontal axis = percent point function of the order 19159 statistic medians. 19160 19161 This is essentially a plot of the data percentiles versus 19162 the percentiles of the theoretical distribution. Dataplot 19163 computes the percent point function of the uniform order 19164 statistic medians to compute the percentiles of the theoretical 19165 distribution. 19166 19167 DATAPLOT has extensive probability plot capabilities (130+ 19168 distributions/distributional families are available). When 19169 distributional families are specified, the LET command is used 19170 before the PROBABILITY PLOT command to specify which member 19171 of the distributional family is desired. For example, 19172 19173 LET GAMMA = 5.3 19174 WEIBULL PROBABILITY PLOT Y 19175 19176 The name of the distributional parameter for families is given in 19177 the list below. 19178 19179 Probability plots serve two primary uses. 19180 19181 1) Distributional Modeling 19182 19183 The slope and intercept of the line fit to the probability 19184 plot are estimates for the location and scale parameters 19185 of the distribution. 19186 19187 The following provides one possible approach to 19188 distributional modeling. 19189 19190 a) If the distribution has one or two shape parameters, 19191 use the PPCC PLOT or KS PLOT to obtain estimates for 19192 the shape parameters (HELP PPCC PLOT or HELP KS PLOT for 19193 details). 19194 19195 b) Once the shape parameters (if any) have been estimated, 19196 generate the probability plot to obtain estimates for 19197 the location and scale parameters. 19198 19199 c) The bootstrap can be used to obtain confidence intervals 19200 for the distribution parameters and selected quantiles. 19201 Enter HELP DISTRIBUTIONAL BOOTSTRAP for details. 19202 19203 2) Goodness of Fit 19204 19205 The probability plot provides a graphical assessment of 19206 goodness of fit. The straighter the probability plot, 19207 the better the fit. One advantage of the graphical 19208 approach over quantitative measures (e.g., Kolmogorov-Smirnov 19209 test) is that it provides an indication of how the 19210 distribution is not a good fit. This can provide guidance 19211 to a better distributional model. 19212 19213 The correlation coefficient of the points on the probability 19214 plot provides a numerical measure of the straightness of 19215 the probability plot. Dataplot automatically saves this 19216 value in the internal parameter PPCC. The PPCC values 19217 provide a useful ranking measure when comparing different 19218 distributional models. 19219 19220Syntax 1: 19221 <dist> PROBABILITY PLOT <y> <SUBSET/EXCEPT/FOR/qualification> 19222 where <y> is a response variable of raw data values; 19223 <dist> is one of the following distributions: 19224 19225 Distributions with only location and scale parameters 19226 1) NORMAL 19227 2) HALFNORMAL 19228 3) SLASH 19229 4) COSINE 19230 5) LOGISTIC 19231 6) HALF LOGISTIC 19232 7) HYPERBOLIC SECANT 19233 8) CAUCHY 19234 9) HALF CAUCHY 19235 10) DOUBLE EXPONENTIAL 19236 11) EXPONENTIAL 19237 12) EXTREME VALUE TYPE 1 (or GUMBEL) 19238 13) UNIFORM 19239 14) SEMI-CIRCULAR 19240 15) ANGLIT 19241 16) ARCSIN 19242 17) RAYLEIGH 19243 19244 Distributions with one shape parameter 19245 1) MAXWELL (SIGMA) 19246 2) WEIBULL (GAMMA) 19247 3) DOUBLE WEIBULL (GAMMA) 19248 4) INVERTED WEIBULL (GAMMA) 19249 5) GAMMA (GAMMA) 19250 6) LOG GAMMA (GAMMA) 19251 7) DOUBLE GAMMA (GAMMA) 19252 8) INVERTED GAMMA (GAMMA) 19253 9) WALD (GAMMA) 19254 10) FATIGUE LIFE (GAMMA) 19255 11) EXTREME VALUE TYPE 2 (GAMMA) 19256 12) GENERALIZED EXTREME VALUE (GAMMA) 19257 13) PARETO (GAMMA) 19258 14) PARETO SECOND KIND (GAMMA) 19259 15) GENERALIZED PARETO (GAMMA) 19260 16) GENERALIZED HALF LOGISTIC (GAMMA) 19261 17) TUKEY LAMBDA (LAMBDA) 19262 18) SKEWED NORMAL (LAMBDA) 19263 19) SKEW DOUBLE EXPONENTIAL (LAMBDA) 19264 20) POISSON (LAMBDA) 19265 21) T (NU) 19266 22) FOLDED T (NU) 19267 23) CHI-SQUARED (NU) 19268 24) CHI (NU) 19269 25) LOGNORMAL (SD) 19270 26) LOG DOUBLE EXPONENTIAL (ALPHA) 19271 27) ERROR (ALPHA) 19272 28) GENERALIZED LOGISTIC (ALPHA) 19273 29) GENERALIZED LOGISTIC TYPE 2 (ALPHA) 19274 30) GENERALIZED LOGISTIC TYPE 3 (ALPHA) 19275 31) GENERALIZED LOGISTIC TYPE 5 (ALPHA) 19276 32) MCLEISH (ALPHA) 19277 33) ZETA (ALPHA) 19278 34) WRAPPED CAUCHY (C) 19279 35) POWER FUNCTION (C) 19280 36) TRIANGULAR (C) 19281 37) LOG LOGISTIC (DELTA) 19282 38) VON-MISES (B) 19283 39) DISCRETE UNIFORM (N) 19284 40) LEADS IN COIN TOSSING (N) 19285 41) GEOMETRIC (P) 19286 42) YULE (P) 19287 43) LOGARITHMIC SERIES (THETA) 19288 44) RECIPROCAL (B) 19289 45) BRADFORD (BETA) 19290 46) TOPP AND LEONE (BETA) 19291 47) ASYMMETRIC DOUBLE EXPO (K) 19292 48) CLASSICAL MATCHING (K) 19293 19294 Distributions with two shape parameter 19295 1) POWER-NORMAL (P, SD) 19296 2) POWER-LOGNORMAL (P, SD) 19297 3) FOLDED NORMAL (M, SD) 19298 4) FOLDED CAUCHY (M, SD) 19299 5) SKEWED T (LAMBDA, NU) 19300 6) NONCENTRAL T (NU, LAMBDA) 19301 7) NONCENTRAL CHISQUARE (NU, LAMBDA) 19302 8) LOG SKEWED NORMAL (LAMBDA, SD) 19303 9) BOREL TANNER (LAMBDA, K) 19304 10) LAGRANGE POISSON (LAMBDA, THETA) 19305 11) BETA (ALPHA, BETA) 19306 12) INVERTED BETA (ALPHA, BETA) 19307 13) BETA BINOMIAL (ALPHA, BETA) 19308 14) HERMITE (ALPHA, BETA) 19309 15) EXPONENTIAL POWER (ALPHA, BETA) 19310 16) BETA NORMAL (ALPHA, BETA) 19311 17) ASYMMETRIC LOG DOUBLE EXPO (ALPHA, BETA) 19312 18) BETA GEOMETRIC (ALPHA, BETA) 19313 19) ALPHA (ALPHA, BETA) 19314 20) KATZ (ALPHA, BETA) 19315 21) GENERALIZED TOPP AND LEONE (ALPHA, BETA) 19316 22) REFLECTED GENE TOPP LEONE (ALPHA, BETA) 19317 23) G AND H (G, H) 19318 24) JOHNSON SB (ALPHA1, ALPHA2) 19319 25) JOHNSON SU (ALPHA1, ALPHA2) 19320 26) EXPONENTIATED WEIBULL (GAMMA, THETA) 19321 27) GENERALIZED GAMMA (GAMMA, C) 19322 28) INVERSE GAUSSIAN (GAMMA, MU) 19323 29) RECIPROCAL INVERSE GAUSSIAN (GAMMA, MU) 19324 30) F (NU1, NU2) 19325 31) TWO-SIDED POWER (THETA, N) 19326 32) POLYA AEPPLI (THETA, P) 19327 33) GENERALIZED LOGA SERIES (THETA, BETA) 19328 34) GEETA (THETA, BETA or MU, BETA) 19329 35) CONSUL (THETA, BETA or MU, BETA) 19330 36) BINOMIAL (N, P) 19331 37) WARING (A, C) 19332 38) GOMPERTZ (C, B) 19333 39) GENERALIZED MCLEISH (ALPHA, A) 19334 40) ZIPF (ALPHA, N) 19335 41) NEGATIVE BINOMIAL (K, P) 19336 42) GENERALIZED LOGISTIC TYPE 4 (P, Q) 19337 43) LOST GAMES (P, R) 19338 44) DISCRETE WEIBULL (BETA, Q) 19339 45) CONSUL (THETA, M) 19340 19341 Distributions with three or more shape parameter 19342 1) LOG SKEWED T (LAMBDA, NU, SD) 19343 2) DOUBLY NONCENTRAL T (NU, LAMBDA1, LAMBDA2) 19344 3) NONCENTRAL F (NU1, NU2, LAMBDA) 19345 4) NONCENTRAL BETA (ALPHA, BETA, LAMBDA) 19346 5) TRUNCATED EXPONENTIAL (X0, M, SD) 19347 6) GENERALIZED EXPONENTIAL (LAMBDA1, LAMBDA2, S) 19348 7) GOMPERTZ-MAKEHAM (XI, LAMBDA, THETA) 19349 8) MIELKE BETA-KAPPA (BETA, THETA, K) 19350 9) HYPERGEOMETRIC (K, N, M) 19351 10) GENERALIZED INVERSE GAUSS (CHI, LAMBDA, THETA) 19352 11) BESSEL I (SIGMA1SQ, SIGMA2SQ, NU) 19353 (B, C, M) 19354 12) BESSEL K (SIGMA1SQ, SIGMA2SQ, NU) 19355 (B, C, M) 19356 13) WAKEBY (GAMMA, BETA, DELTA) 19357 14) BETA-NEGATIVE BINOMIAL (ALPHA, BETA, K) 19358 15) GENERALIZED NEGATIVE BINO (THETA, BETA, M) 19359 16) QUASI BINOMIAL TYPE I (P, M, PHI) 19360 17) GENERALIZED LOST GAMES (P, A, J) 19361 19362 18) DOUBLY NONCENTRAL F (NU1, NU2, LAMBDA1, LAMBDA2) 19363 19) TRUNCATED NORMAL (A, B, M, SD) 19364 20) TRAPEZOID (A, B, C, D) 19365 21) LOG BETA (ALPHA, BETA, C, D) 19366 22) TRUNCATED GENE NEGA BINO (THETA, BETA, M, N) 19367 19368 23) NORMAL MIXTURE (MU1, SD1, MU2, SD2, P) 19369 24) BI-WEIBULL (SCALE1, GAMMA1, LOC2, SCALE2, 19370 GAMMA2) 19371 19372 25) GENERALIZED TRAPEZOID (A, B, C, D, NU1, NU3, ALPHA) 19373 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 19374 19375 This syntax is used for the case where we have raw data. Note that 19376 the response variable can also be a matrix. If a matrix name is 19377 encountered, a probability plot will be drawn for all values in 19378 the matrix. 19379 19380Syntax 2: 19381 <dist> CENSORED PROBABILITY PLOT <y> <x> 19382 <SUBSET/EXCEPT/FOR/qualification> 19383 where <y> is the variable of raw data values under analysis; 19384 <x> is the censoring variable; 19385 <dist> is one of the distributions listed above; 19386 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 19387 19388 This syntax is used for the case where we have censored data. 19389 A value of 1 indicates a failure time and a value of 0 indicates 19390 a censoring time. 19391 19392 Censoring is not supported for discrete disributions or grouped data. 19393 19394Syntax 3: 19395 <dist> PROBABILITY PLOT <y> <x> 19396 <SUBSET/EXCEPT/FOR/qualification> 19397 where <y> is the variable of pre-computed frequencies; 19398 <x> is the variable of distinct values for the variable under 19399 analysis; 19400 <dist> is one of the distributions listed above; 19401 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 19402 19403 This syntax is used for the case where we have frequency 19404 (binned) data. The bins are defined by their mid-points. 19405 19406Syntax 4: 19407 <dist> CENSORED PROBABILITY PLOT <y> <censor> <x> 19408 <SUBSET/EXCEPT/FOR/qualification> 19409 where <y> is the variable of pre-computed frequencies; 19410 <censor> is a censoring variable; 19411 <x> is the variable of distinct values for the variable under 19412 analysis; 19413 <dist> is one of the distributions listed above; 19414 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 19415 19416 This syntax is used for the case where we have frequency (binned) 19417 data with censoring. The bins are defined by their mid-points. 19418 When a particular bin has both censored and uncensored data, 19419 there will be 2 rows with the same value for <x>. 19420 19421 A value of 1 indicates a failure time and a value of 0 indicates 19422 a censoring time for the censoring variable. 19423 19424 Censoring is not supported for discrete disributions or grouped data. 19425 19426Syntax 5: 19427 <dist> PROBABILITY PLOT <y> <xlow> <xhigh> 19428 <SUBSET/EXCEPT/FOR/qualification> 19429 where <y> is the variable of pre-computed frequencies; 19430 <xlow> is the variable containing the bin lower limit 19431 values; 19432 <xhigh> is the variable containing the bin upper limit 19433 values; 19434 <dist> is one of the distributions listed above; 19435 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 19436 19437 This syntax is used for the case where we have frequency 19438 (binned) data. The bins are defined by their lower and upper 19439 limits. This syntax allows bins with unequal widths. 19440 19441Syntax 6: 19442 <dist> CENSORED PROBABILITY PLOT <y> <censor> <xlow> <xhigh> 19443 <SUBSET/EXCEPT/FOR/qualification> 19444 where <y> is the variable of pre-computed frequencies; 19445 <censor> is a censoring variable; 19446 <xlow> is the variable containing the bin lower limit 19447 values; 19448 <xhigh> is the variable containing the bin upper limit 19449 values; 19450 <dist> is one of the distributions listed above; 19451 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 19452 19453 This syntax is used for the case where we have frequency (binned) 19454 data with censoring. The bins are defined by their lower and upper 19455 limits. This syntax allows bins with unequal widths. 19456 When a particular bin has both censored and uncensored data, 19457 there will be 2 rows with the same values for <xlow> and <xhigh>. 19458 19459 A value of 1 indicates a failure time and a value of 0 indicates 19460 a censoring time for the censoring variable. 19461 19462 Censoring is not supported for discrete disributions or grouped data. 19463 19464Syntax 7: 19465 <dist> MULTIPLE PROBABILITY PLOT <y1> ... <yk> 19466 <SUBSET/EXCEPT/FOR/qualification> 19467 where <y1> ... <yk> is a list of response variables; 19468 <dist> is one of the supported distributions (see syntax 1); 19469 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 19470 19471 Note that response variables can also be matrices. If a matrix 19472 name is encountered, a probability plot will be drawn for 19473 all the values in the matrix. For multiple response variables, 19474 the probability plots will be overlaid on the same plot. 19475 19476Syntax 8: 19477 <dist> REPLICATED PROBABILITY PLOT <y> <x1> ... <xk> 19478 <SUBSET/EXCEPT/FOR/qualification> 19479 where <y> is a response variable; 19480 <x1> .... <xk> is a list of one to six group-id variables; 19481 <dist> is one of the supported distributions (see syntax 1); 19482 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 19483 19484 The group-id variables are cross-tabulated and a probability 19485 plot will be generated for each distinct combination of values 19486 for the group-id variables. These plots will be overlaid on the 19487 same plot. 19488 19489Syntax 9: 19490 <dist> REPLICATED CENSORED PROBABILITY PLOT <y> <x> <x1> ... <xk> 19491 <SUBSET/EXCEPT/FOR/qualification> 19492 where <y> is a response variable; 19493 <x> is a censoring variable; 19494 <x2> is a group-id variable; 19495 <x1> .... <xk> is a list of one to six group-id variables; 19496 <dist> is one of the supported distributions (see syntax 1); 19497 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 19498 19499 The group-id variables are cross-tabulated and a probability 19500 plot will be generated for each distinct combination of values 19501 for the group-id variables. These plots will be overlaid on the 19502 same plot. 19503 19504 This syntax is used for the case where we have censored data 19505 in addition to replication. A value of 1 indicates a failure time 19506 and a value of 0 indicates a censoring time. 19507 19508 Censoring is not supported for discrete disributions or grouped data. 19509 19510Syntax 10: 19511 <dist> SUBSET PROBABILITY PLOT <y> <x1> ... <xk> 19512 <SUBSET/EXCEPT/FOR/qualification> 19513 where <y> is a response variable; 19514 <x1> ... <xk> is a list of one to two group-id variables; 19515 <dist> is one of the supported distributions (see syntax 1); 19516 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 19517 19518 The SUBSET option is similar to but distinct from the REPLICATED 19519 option. For the REPLICATED option, separate probability plots 19520 are generated for the distinct groups. For the SUBSET option, a 19521 single probability is generated. However, the different groups 19522 in the data can be drawn with separate attributes. 19523 19524Examples: 19525 NORMAL PROBABILITY PLOT X 19526 CAUCHY PROBABILITY PLOT X 19527 TUKEY LAMBDA PROBABILITY PLOT X 19528 LOGNORMAL PROBABILITY PLOT X 19529 WEIBULL PROBABILITY PLOT X 19530 EXTREME VALUE TYPE 1 PROBABILITY PLOT X 19531 POISSON PROBABILITY PLOT X 19532 NORMAL PROBABILITY PLOT F X 19533 CAUCHY PROBABILITY PLOT F X 19534 TUKEY LAMBDA PROBABILITY PLOT F X 19535 LOGNORMAL PROBABILITY PLOT F X 19536 WEIBULL PROBABILITY PLOT F X 19537 EXTREME VALUE TYPE 1 PROBABILITY PLOT F X 19538 POISSON PROBABILITY PLOT F X 19539 19540Note: 19541 The PROBABILITY PLOT command automatically saves the following 19542 parameters: 19543 19544 PPCC - the correlation coeffcient of the points on 19545 the probability plot 19546 PPA0 - the intercept of the line fitted to the probability 19547 plot (estimate of the location parameter) 19548 PPA1 - the slope of the line fitted to the probability 19549 plot (estimate of the scale parameter) 19550 SDPPA0 - the standard deviation of PPA0 19551 SDPPA1 - the standard deviation of PPA1 19552 PPRESSD - the residual standard deviation of the line fitted 19553 to the probability plot 19554 PPRESDF - the residual degrees of freedom of the line fitted 19555 to the probability plot 19556 PPA0BW - the intercept of the line fitted to the probability 19557 plot with biweight weighting of the residuals 19558 PPA1BW - the slope of the line fitted to the probability 19559 plot with biweight weighting of the residuals 19560 19561 The PPCC value provides a measure of the linearity of the 19562 probability plot. 19563 19564 The PPA0 and PPA1 provides estimates of the location and scale 19565 parameters. 19566 19567 For some distributions with heavy tails (e.g., Cauchy, slash), 19568 there can be extreme variability in the first few and last few 19569 points in the probability plot. This can distort the estimates 19570 of location and scale. Two iterations of biweight weighting of 19571 the residuals are applied to obtain PPA0BW and PPA1BW. In most 19572 cases, using PPA0 and PPA1 are preferred. However, in cases 19573 where there is extreme non-linearity in the tails, using 19574 PPA0BW and PPA1BW may be preferred as the location and scale 19575 estimates. 19576 19577Note: 19578 For uncensored data, Dataplot uses the uniform order statistic 19579 medians to determine the plotting positions. This needs to be 19580 modified somewhat for censored data. 19581 19582 For singly censored data (i.e., all the censored data have 19583 the same censoring time), we can use the N from the full sample 19584 to compute the uniform order statistics. However, we only plot 19585 the failure times. 19586 19587 An alternative that works with both singly and multiply (the 19588 censoring times are not necessarily the same) is to base the 19589 plotting positions on the Kaplan-Meier statistic. That is, 19590 19591 p(i) = ((n+0.7)/(n+0.4))*PRODUCT[k=1 to i][((n-k+0.7)/(n-k+1.7)] 19592 19593 with n denoting the full sample size. Again, only plotting 19594 positiions corresponding to failure times are plotted. 19595 The percent point function is computed on the p(i) values. 19596 19597 This method for censored probability plots is discussed in 19598 more detail on pp. 43-46 of the Bury book (see the References 19599 section below). 19600 19601 To specify which method to use, enter the command 19602 19603 SET CENSORED PROBABILITY PLOT 19604 <KAPLAN-MEIER/UNIFORM ORDER STATISTIC MEDIANS> 19605 19606Note: 19607 An alternative to binning data is to use the command 19608 19609 SET PROBABILITY PLOT DATA POINTS <value> 19610 19611 When this command is entered, Dataplot will compute <value> 19612 equally spaced percentiles and compute the probability plot 19613 on these percentiles. This option can be useful when generating 19614 probability plots on large data sets for distributions with 19615 expensive percent point functions. 19616 19617Note: 19618 For discrete distributions, the data will typicall consist of 19619 integers. In this case, it is helpful to group the data based 19620 on these integer values. The following code shows the 19621 recommended way for doing this: 19622 19623 LET YLOW = MINIMUM Y 19624 LET YUPP = MAXIMUM Y 19625 LET YLOW = YLOW - 0.5 19626 CLASS LOWER YLOW 19627 LET YUPP = YUPP + 0.5 19628 CLASS UPPER YUPP 19629 CLASS WIDTH = 1 19630 LET Y2 X2 = BINNED Y 19631 LET LAMBDA = 4.2 19632 POISSON PROBABILITY PLOT Y2 X2 19633 19634 This will center the bins around the integer values and will 19635 cover the first and last class. 19636 19637Note: 19638 By default, the theoretical distribution is plotted for the 19639 standard form (i.e., location = 0, scale = 1). The slope 19640 and intercept of the line fit to points on the probability 19641 plot provide estimates for the location and scale parameters. 19642 19643 However, if the location/scale parameters are estimated by 19644 some other method (e.g., maximum likelihood), it may be 19645 desirable to fix the location/scale parameters on the 19646 probability plot. To do this, enter the commands 19647 19648 LET PPLOC = <value> 19649 LET PPSCALE = <value> 19650 19651Note: 19652 The TO syntax is supported for the PROBABILITY PLOT command. 19653 It is most useful for the MULTIPLE version of the command. 19654 19655Default: 19656 None 19657 19658Synonyms: 19659 EV2 and FRECHET are synonyms for EXTREME VALUE TYPE 2. 19660 EV1 and GUMBEL are synonyms for EXTREME VALUE TYPE 1. 19661 FATIGUE LIFE is a synonym for FL. 19662 RECIPROCAL INVERSE GAUSSIAN is a synonym for RIG. 19663 IG is a synonym for INVERSE GAUSSIAN. 19664 SKEW LAPLACE is a synonym for SKEW DOUBLE EXPONENTIAL 19665 ASYMMETRIC LAPLACE is a synonym for ASYMMETRIC DOUBLE EXPONENTIAL 19666 HIGHLIGHT PROBABILITY PLOT is a synonym for SUBSET PROBABILITY PLOT 19667 19668Related Commands: 19669 FREQUENCY PLOT = Generates a frequency plot. 19670 HISTOGRAM = Generates a histogram. 19671 PIE CHART = Generates a pie chart. 19672 PERCENT POINT PLOT = Generates a percent point plot. 19673 PPCC PLOT = Generates probability plot correlation 19674 coefficient plot. 19675 PLOT = Generates a data or function plot. 19676 19677References: 19678 "The Probability Plot Correlation Coefficient Test for Normality", 19679 James J. Filliben, Technometrics, Vol. 17, No. 1, February 1975. 19680 19681 "Graphical Methods of Data Analysis", Chambers, Cleveland, Kleiner, 19682 and Tukey, Wadsworth, 1983. 19683 19684 "Statistical Distributions in Engineering", Karl Bury, Cambridge 19685 University Press, 1999. 19686 19687Applications: 19688 Distributional Analysis 19689 19690Implementation Date: 19691 Pre-1987 19692 1990/5: WALD, FL, RIG, INVERSE GAUSSIAN 19693 1993/12: GENERALIZED PARETO 19694 1994/9: DISCRETE UNIFORM, NON-CENTRAL T, 19695 NON-CENTRAL F, NON-CENTRAL CHI-SQUARE, 19696 NON-CENTRAL BETA, DOUBLY NON-CENTRAL T, 19697 DOUBLY NON-CENTRAL F, HYPERGEOMETRIC 19698 1994/10: VON-MISES 19699 1995/5: POWER LOGNORMAL, POWER NORMAL, COSINE, 19700 ALPHA, POWER FUNCTION, CHI, 19701 LOGARITHMIC SERIES, LOG LOGISTIC, 19702 GENERALIZED GAMMA, WARING 19703 1995/9: ANGLIT, ARCSIN, FOLDED NORMAL, TRUNCATED NORMAL 19704 1995/10: LOG GAMMA, HYPERBOLIC SECANT, GOMPERTZ 19705 1995/12: PARETO SECOND KIND, DOUBLE WEIBULL, 19706 WRAPPED UP CAUCHY, EXPONENTIATED WEIBULL, 19707 TRUNCATED EXPONENTIAL 19708 GENERALIZED LOGISTIC, EXPONENTIAL POWER 19709 1996/1: DOUBLE GAMMA, BETA-KAPPA, FOLDED CAUCHY 19710 1996/5: BETA BINOMIAL, GENERALIZED EXPONENTIAL 19711 1998/5: RECIPROCAL, NORMAL MIXTURE, INVERTED GAMMA 19712 2001/10: GENERALIZED LAMBDA, JOHNSON SU, 19713 JOHNSON SB, INVERTED WEIBULL, 19714 LOG DOUBLE EXPONENTIAL 19715 2002/5: TWO-SIDED POWER, BI-WEIBULL 19716 2003/5: ERROR 19717 2004/1: TRAPEZOID, GENERALIZED TRAPEZOID, FOLDED T, 19718 SKEWED T, SKEWED NORMAL, SLASH, INVERTED BETA, 19719 G AND H 19720 2004/5: Implemented the automatic computation of the 19721 biweight fit (PPA0BW and PPA1BW) 19722 2004/5: LOG SKEW NORMAL, LOG SKEW T, HERMITE, YULE 19723 2004/5: Fixed a number of bugs for various distributions 19724 2004/6: SKEW DOUBLE EXPONENTIAL, ASYMMETRIC DOUBLE EXPONENTIAL, 19725 MAXWELL, RAYLEIGH 19726 2004/8: Meeker reparameterization of GOMPERTZ MAKEHAM, 19727 GENERALIZED ASYMMETRIC LAPLACE, 19728 GENERALIZED INVERSE GAUSSIAN 19729 2004/9: MCLEISH, GENERALIZED MCLEISH, BESSEL I FUNCTION, 19730 BESSEL K FUNCTION 19731 2004/10: SET PROBABILITY DATA POINTS 19732 2004/10: Support for censored data 19733 2005/5: Support unequal bin widths for frequency data 19734 2009/9: Support for TO syntax and matrix arguments 19735 2009/9: Support for MULTIPLE and REPLICATION options 19736 2010/1: Support for HIGHLIGHT/SUBSET option 19737 19738Program: 19739 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 19740 TITLE AUTOMATIC; X1LABEL THEORETICAL VALUE; Y1LABEL DATA VALUE 19741 . 19742 LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 100 19743 NORMAL PROBABILITY PLOT Y 19744 . 19745 LET NU = 5 19746 LET Y = CHI-SQUARE RANDOM NUMBERS FOR I = 1 1 100 19747 CHI-SQUARE PROBABILITY PLOT Y 19748 . 19749 LET Y = EXPONENTIAL RANDOM NUMBERS FOR I = 1 1 100 19750 EXPONENTIAL PROBABILITY PLOT Y 19751 . 19752 LET Y = CAUCHY RANDOM NUMBERS FOR I = 1 1 1000 19753 LEGEND 1 CAUCHY RANDOM NUMBERS 19754 NORMAL PROBABILITY PLOT Y 19755 END OF MULTIPLOT 19756 19757-----PROBABILITY WEIGHTED MOMENTS (LET)---------------------------- 19758 19759PROBABILITY WEIGHTED MOMENTS 19760 19761Name: 19762 PROBABILITY WEIGHTED MOMENTS (LET) 19763 19764Type: 19765 Let Subcommand 19766 19767Purpose: 19768 Compute the probability weighted moments of a variable. 19769 19770Description: 19771 Given a random variable X with a cumulative distribution 19772 function F, the probability weighted moments are defined 19773 to be: 19774 19775 M(p,r,s) = E[X**p{F(X)}**r{1 - F(X)}**s] 19776 19777 Two special cases are 19778 19779 alpha(r) = M(1,0,r) = E[X{1 - F(X)}**r] 19780 beta(r) = M(1,r,0) = E[X{F(X)}**r] 19781 19782 For an ordered sample x(1:n) <= x(2:n) <= ... <= x(n:n), 19783 unbiased estimators of alpha(r) and beta(r) are: 19784 19785 a(r) = (1/n)*SUM[j=1 to n][(n-j)*(n-j-1)* ... *(n-j-r+1)/ 19786 ((n-1)*(n-2)* ... *(n-r))]*xj:n 19787 19788 b(r) = (1/n)*SUM[j=1 to n][(j-1)*(j-2)* ... *(j-r)/ 19789 ((n-1)*(n-2)* ,,,*(n-r))]*xj:n 19790 19791 The primary use of probability weighted moments (and the 19792 related L-moments) is in the estimation of parameters for 19793 a probability distribution. For a more detailed description 19794 of probability weighted moments and L-moments, see the papers 19795 listed in the References section below (in particular, the 19796 papers by Hoskings). Estimates based on probability 19797 weighted moments are often considered to be superior to 19798 standard moment-based estimates. They are sometimes used 19799 when maximum likelihood estimates are unavailable or 19800 difficult to compute. They may also be used as starting 19801 values for maximum likelihood estimates. Estimation methods 19802 based on probability weighted moments are discussed 19803 in the papers listed in the Reference section below 19804 (Dataplot generates L-moment based estimates for the 19805 maximum likelihood estimates for the generalized Pareto and 19806 the generalized extreme value distributions). 19807 19808Syntax 1: 19809 LET <y> = PROBABILITY WEIGHTED MOMENTS <x> <nmom> 19810 <SUBSET/EXCEPT/FOR qualification> 19811 where <x> is the response variable; 19812 <nmom> is the number of probability weighted moments 19813 that will be generated; 19814 <y> is a variable where the computed probability 19815 weighted moments are saved; 19816 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 19817 19818 This syntax computes the alpha probability weighted moments. 19819 19820Syntax 2: 19821 LET <y> = BETA PROBABILITY WEIGHTED MOMENTS <x> <nmom> 19822 <SUBSET/EXCEPT/FOR qualification> 19823 where <x> is the response variable; 19824 <nmom> is the number of probability weighted moments 19825 that will be generated; 19826 <y> is a variable where the computed probability 19827 weighted moments are saved; 19828 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 19829 19830 This syntax computes the beta probability weighted moments. 19831 19832Examples: 19833 LET PWM = PROBABILITY WEIGHTED MOMENTS Y 5 19834 LET PWM = PROBABILITY WEIGHTED MOMENTS Y 4 SUBSET Y > 0 19835 19836Note: 19837 Dataplot computes probability weighted moments using the 19838 SAMPWM routine written by Hoskings and documented in 19839 "Research Report: Fortran Routines for use with the Method 19840 of L-Moments" (see the Reference section below). 19841 19842 This routine is available from the statlib archive 19843 (http://lib.stat.cmu.edu/) at the following URL 19844 19845 http://lib.stat.cmu.edu/general/lmoments 19846 19847Note: 19848 L-moments are linear combinations of probability weighted 19849 moments and are frequently used in the application of probability 19850 weighted moments. 19851 19852Default: 19853 If the <nmom> parameter is omitted from the command, the 19854 first four sample probability weighted moments are computed. 19855 19856 By default, Dataplot computes the alpha probability weighted 19857 moments. 19858 19859Synonyms: 19860 None 19861 19862Related Commands: 19863 L MOMENTS = Compute the sample L-moments of a 19864 variable. 19865 MAXIMUM LIKELIHOOD = Compute maximum likelihood estimates for 19866 a probability distribution. 19867 19868References: 19869 "Research Report: Fortran Routines for use with the Method 19870 of L-Moments", J. R. M. Hosking, IBM Research Division, 19871 T. J. Watson Research Center, Yorktown Heights, NY 10598, 19872 6/2000. 19873 19874 "Probability Weighted Moments: Definition and Relation to 19875 Parameters of Several Distributions Expressable in Inverse 19876 Form", Greenwood, Landwehr, Matalas, and Wallis, Water 19877 Resources Research, 15, 1079, 1049-1054. 19878 19879 "Estimation of the Generalized Extreme Value Distribution 19880 by the Method of Probability-Weighte Moments", Hosking, 19881 Wallis, and Wood, Technometrics, 27, 1985, 251-261. 19882 19883 "Probability Weighted Moments Compared with Some Traditional 19884 Techniques in Estimating Gumbel Parameters and Quantiles", 19885 Landwehr, Matalas, Wallis, Water Resources Research, 19886 15, (1979a), 1055-1064. 19887 19888Applications: 19889 Distributional Modeling 19890 19891Implementation Date: 19892 2005/12 19893 19894Program: 19895 LET GAMMA = -0.3 19896 LET Y = GENERALIZED PARETO RANDOM NUMBERS FOR I = 1 1 100 19897 LET Y = 5*Y + 2 19898 LET PROBMOME = PROBABILITY WEIGHTED MOMENTS Y 19899 19900-----PROBE--------------------------------------------- 19901 19902PROBE 19903 19904Name: 19905 PROBE 19906 19907Type: 19908 Support Command 19909 19910Purpose: 19911 Dumps (prints out) the contents of certain internal underlying 19912 Fortran variables. 19913 19914Description: 19915 This command provides information which may assist in 19916 implementation and debugging. Hence it is normally only used by 19917 the service group which implements DATAPLOT on your computer. 19918 19919Syntax: 19920 PROBE <name> 19921 where <name> is the underlying Fortran variable to print. 19922 19923Examples: 19924 PROBE NUMCOL 19925 PROBE NUMNAM 19926 PROBE IBUGSU 19927 19928Note: 19929 The list of the variables that can probed is documented under 19930 the SET command. Enter HELP SET to examine the list. 19931 19932Note: 19933 The PROBE command is used to return the values of certain 19934 internal parameters and strings. This command was updated 19935 so that the returned value is automatically saved. If the 19936 returned value is an integer or real number, then the value 19937 is stored in the internal parameter PROBEVAL. If the 19938 returned value is a string, then the value is stored in the 19939 internal string PROBESTR. PROBESTR and PROBEVAL can then be 19940 used in the same way as other parameters and strings. 19941 19942 This feature is typically used in macros. For example, you 19943 might want to use the machine maximum value as a "missing 19944 value" indicator. A host independent way of using this value 19945 would now be: 19946 19947 PROBE CPUMAX 19948 LET MACHMAX = PROBVAL 19949 19950 You could then use the parameter MACHMAX wherever you wanted 19951 to define a missing value. 19952 19953 This feature was implemented 1998/8. 19954 19955Default: 19956 None 19957 19958Synonyms: 19959 None 19960 19961Related Commands: 19962 SET = Specify the value for an underlying Fortran variable. 19963 19964Applications: 19965 Implementation and debugging 19966 19967Implementation Date: 19968 Pre-1987 19969 19970Program: 19971 XX 19972 19973-----PROCESS ID--------------------------------------------------- 19974 19975PROCESS ID 19976 19977Name: 19978 PROCESS ID 19979 19980Type: 19981 Support Command 19982 19983Purpose: 19984 The PROCESS ID command returns the process id and stores it 19985 in the internal Dataplot parameter PID. 19986 19987Description: 19988 This command is compiler dependent. Dataplot currently 19989 supports this command on the following compilers/platforms: 19990 19991 1. INTEL Fortran compiler (Windows 2000/XP) 19992 2. g77 (Linux, cygwin, Sun Solaris) 19993 19994 The primary use of this command is to generate unique 19995 file names (for an example, see the Program example below). 19996 19997Syntax: 19998 PROCESS ID 19999 20000Example: 20001 PROCESS ID 20002 20003Default: 20004 None 20005 20006Synonyms: 20007 PID 20008 20009Related Commands: 20010 SYSTEM = Issue an operating system command. 20011 SLEEP = Pause for <n> seconds. 20012 CD = Change the current directory 20013 20014Applications: 20015 Utility Command 20016 20017Implementation Date: 20018 2006/3 20019 20020Program: 20021 LET STRING BASENAME = dppl1f.dat 20022 PROCESS ID 20023 LET STRING PLOTNAME = ^basename.^pid 20024 SET IPL1NA ^PLOTNAME 20025 DEVICE 2 POSTSCRIPT 20026 PLOT X**2 FOR X = 1 1 9 20027 DEVICE 2 CLOSE 20028 SYSTEM lpr ^PLOTNAME 20029 20030-----PRODUCT (LET)--------------------------------------------------- 20031 20032PRODUCT 20033 20034Name: 20035 PRODUCT (LET) 20036 20037Type: 20038 Let Subcommand 20039 20040Purpose: 20041 Compute the product of the elements in a variable. 20042 20043Syntax: 20044 LET <par> = PRODUCT <x1> <SUBSET/EXCEPT/FOR qualification> 20045 where <x1> is the variable for which the product will be computed; 20046 <par> is a parameter where the computed product is saved; 20047 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 20048 20049Examples: 20050 LET PROD = PRODUCT Y1 20051 LET PROD = PRODUCT Y1 SUBSET TAG > 2 20052 20053Default: 20054 None 20055 20056Synonyms: 20057 None 20058 20059Related Commands: 20060 SEQUENCE = Generate a sequence of numbers. 20061 PATTERN = Generate numbers with a specific pattern. 20062 SUM = Compute the sum of the elements in a variable. 20063 INTEGRAL = Compute the integral of the elements in a variable. 20064 PRODUCT PLOT = Generate a products (versus subsets) plot. 20065 20066Applications: 20067 Rare Usage 20068 20069Implementation Date: 20070 XX 20071 20072Program: 20073 . THIS EXAMPLE COMPUTES FACTORIALS 20074 LET N = 10 20075 LOOP FOR K = 1 1 N 20076 LET Y1 = SEQUENCE 1 1 K 20077 LET A = PRODUCT Y1 20078 PRINT K A 20079 END OF LOOP 20080 20081-----PRODUCT PLOT--------------------------------------------------- 20082 20083PRODUCT PLOT 20084 20085Name: 20086 PRODUCT PLOT 20087 20088Type: 20089 Graphics Command 20090 20091Purpose: 20092 Generates a product plot. 20093 20094Description: 20095 A product plot is a plot consisting of subsample products versus 20096 subsample index. The subsample product is the product of the data 20097 in the subsample. The product plot is used to answer the 20098 question-- "Does the subsample product change over different 20099 subsamples?". The plot consists of: 20100 Vertical axis = subsample product; 20101 Horizontal axis = subsample index. 20102 The PRODUCT PLOT yields 2 traces-- 20103 1. a subsample product trace; and 20104 2. a full-sample product reference line. 20105 Like usual, the appearance of these 2 traces is 20106 controlled by the first 2 settings of the LINES, 20107 CHARACTERS, SPIKES, BARS, and similar attributes. 20108 20109Syntax: 20110 PRODUCT PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 20111 where <y> is the response (= dependent) variable; 20112 <x> is the subsample identifier variable (this variable 20113 appears on the horizontal axis); 20114 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 20115 20116Examples: 20117 PRODUCT PLOT Y X 20118 PRODUCT PLOT Y X1 SUBSET X1 < 22 20119 20120Default: 20121 None 20122 20123Synonyms: 20124 None 20125 20126Related Commands: 20127 CHARACTERS = Sets the type for plot characters. 20128 LINES = Sets the type for plot lines. 20129 SUM PLOT = Generates a sum plot. 20130 PLOT = Generates a data or function plot. 20131 20132Applications: 20133 Rare Usage 20134 20135Implementation Date: 20136 88/9 20137 20138Program: 20139 LET Y = DATA 2 4 5 10 4 10 8 2 3 20140 LET X = DATA 1 1 1 2 2 3 3 3 3 20141 LINE BLANK DASH 20142 CHARACTER X BLANK 20143 XLIMITS 0.5 3.5 20144 YLIMITS 0 500 20145 Y1LABEL PRODUCT 20146 X1LABEL GROUP ID 20147 PRODUCT PLOT Y X 20148 20149-----PROFICIENCY TEST -------------------------------------------- 20150 20151PROFICIENCY TEST 20152 20153Name: 20154 PROFICIENCY TEST 20155 20156Type: 20157 Analysis Command 20158 20159Purpose: 20160 Generate the tables for either a one-sample or a two-sample 20161 proficiency test as defined by the ASTM E 2489 - 06 standard. 20162 20163Description: 20164 The following document 20165 20166 "Standard Practice for Statistical Analysis of One-Sample 20167 and Two-Sample Proficiency Testing Programs", ASTM 20168 International, 100 Barr Harbor Drive, PO BOX C700, 20169 West Conshohoceken, PA 19428-2959, USA. 20170 20171 describes a methodology for performing either a one-sample or 20172 a two-sample proficiency test. 20173 20174 Proficiency testing is the use of interlaboratory 20175 comparisons for the determination of laboratory testing 20176 or measurement performance. The methods in the E 2489- 06 20177 standard provide direction for assessing and categorizing 20178 the performances of individual laboratories based on the 20179 relative likelihood of occurence of their test results. 20180 20181 The standard recommends a minimum of 10 laboratories and states 20182 that it is desirable to have 30 or more participating 20183 laboratories. 20184 20185 Proficiency testing programs typically have a larger number 20186 of participants than an interlaboratory test. This results 20187 in a wider variation of test conditions, so a proficiency 20188 test can provide more information regarding the precision 20189 of test results that may be expected when a test method 20190 is used in the general testing community. 20191 20192 In this standard, the median is used as the consensus value. 20193 The measure of variablility is the interquartile range. In 20194 this standard, the interquartile range is defined as the difference 20195 between the upper hinge and the lower hinge (this is slightly 20196 different than the standard definition of the interquartile range 20197 as the difference between the 75th percentile and the 25th 20198 percentile). 20199 20200 The lower hinge is the median of the points less than or 20201 equal to the median and the upper hinge is the median of the 20202 points greater than or equal to the median. 20203 20204 The inner fence is the value equal to the upper (lower) 20205 hinge of the data set plus (upper) or minus (lower) 20206 1.5 times the interquartile range. 20207 20208 The outer fence is the value equal to the upper (lower) 20209 hinge of the data set plus (upper) or minus (lower) 20210 3.0 times the interquartile range. 20211 20212 A test result that is between the lower inner fence and 20213 upper inner fence is labeled as "typical". A test result 20214 that is between the inner and outer fence values is labeled 20215 as "unusual". A test result that is beyond the outer fence 20216 values is labeled as "extremely unusual". 20217 20218 These statistics are used because they are both simple and robust. 20219 Note that the above values are used in generating a box plot. 20220 20221Description of One-Sample Proficiency Test: 20222 The data consists of: 20223 20224 1. A response variable containing measurements on a sample 20225 2. A lab-id variable 20226 20227 For a one-sample proficiency analysis, each lab reports a 20228 single test result. 20229 20230 This E 2489 one-sample proficiency analysis generates the three 20231 tables documented in the above document: 20232 20233 1) The test results sorted by lab-id. 20234 20235 The purpose of this table is to make it easy to 20236 identify the results for a given laboratory. 20237 20238 2) The test results sorted in descending order with the 20239 median and lower and upper hinges marked. Each lab's 20240 result is categorized as "extremely unusual", "unusual", 20241 or typical. 20242 20243 The purpose of this table is to show the range and 20244 distribution of the test results. 20245 20246 3) The test results sorted in descending order (as in 20247 table 2). However, the data are divided into bins. 20248 20249 The purpose of this table is to show the range and 20250 distribution of the test results. 20251 20252 In addition to the tables, the standard also recommends 20253 complementing the tables with a dot plot. These are also 20254 known as dot diagrams or strip plots. In Dataplot, these are 20255 referred to as strip plots. Enter the command HELP STRIP PLOT 20256 for details on generating these plots in Dataplot. The first 20257 program example below demonstrates this plot. 20258 20259 A strip plot is an alternative to a histogram for displaying 20260 univariate data. The x-axis contains the value of the test result 20261 and the y-axis is simply a constant value. If two or more test 20262 results have the same value, the points are stacked vertically. 20263 You can draw the points are drawn as filled circles. Alternatively, 20264 you can draw the points drawn as the lab-id (this is useful for 20265 identifying outlying labs). 20266 20267 You can also generate the strip plot with the data divided 20268 into bins (you can specify the bin width and the starting 20269 and ending bin limits). In this form, the vertical axis 20270 will represent the number of occurences. This form 20271 of the strip plot is essentially a histogram. 20272 20273 Although the E 2489 - 06 standard does not explicitly talk about 20274 box plots, these can also be a useful complement to the tables since 20275 the box plot is a graphical representation of table 2. 20276 20277Description of Two-Sample Proficiency Test: 20278 The data consists of: 20279 20280 1. A response variable containing measurements on the 20281 first sample 20282 2. A response variable containing measurements on the 20283 second sample 20284 3. A lab-id variable 20285 20286 For a two-sample proficiency analysis, each lab reports exactly 20287 two test results (i.e., a single measurement on each sample). 20288 20289 The random error quantity is defined as 20290 20291 (X - Y) - (Xmed -Ymed) 20292 20293 where X and Y denote the test results for sample one and sample two, 20294 respectively, and Xmed and Ymed denote the medians of sample one and 20295 sample two, respectively. 20296 20297 This E 2489 two-sample proficiency analysis generates the three 20298 tables documented in the above document: 20299 20300 1) The test results for both samples sorted by lab-id. 20301 20302 The purpose of this table is to make it easy to 20303 identify the results for a given laboratory. 20304 20305 2) The test results sorted in descending order of the 20306 random error quantity with the median and lower and upper 20307 hinges marked. The random error quantity for each lab's 20308 result is categorized as "extremely unusual", "unusual", 20309 or "typical". 20310 20311 The purpose of this table is to show the range and 20312 distribution of the random error quantities. 20313 20314 3) The test results sorted in descending order of sample 20315 two with the median and lower and upper hinges marked. 20316 The test results for each sample are categorized as 20317 "extremely unusual", "unusual", or "typical". 20318 20319 The purpose of this table is to show the range and 20320 distribution of the test results for each sample. 20321 20322 The standard also recommends complementing the tables with a 20323 Youden plot. This is demonstrated in the second program 20324 example below. 20325 20326Syntax 1: 20327 ONE SAMPLE PROFICIENCY TEST <y> <labid> 20328 <SUBSET/EXCEPT/FOR qualification> 20329 where <y> is a response variable; 20330 <labid> is a lab id variable; 20331 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 20332 20333Syntax 2: 20334 TWO SAMPLE PROFICIENCY TEST <y1> <y2> <labid> 20335 <SUBSET/EXCEPT/FOR qualification> 20336 where <y1> is the first response variable; 20337 <y2> is the second response variable; 20338 <labid> is a lab id variable; 20339 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 20340 20341Examples: 20342 ONE SAMPLE PROFICIENCY TEST Y LABID 20343 TWO SAMPLE PROFICIENCY TEST Y1 Y2 LABID 20344 20345Note: 20346 You can use the CAPTURE HTML command to generate these tables in 20347 HTML format. You can use the CAPTURE LATEX command to generate 20348 these tables in Latex format. You can use the CAPTURE RTF command 20349 to generate these tables in Rich Text Format (RTF). 20350 20351Note: 20352 In table 2 of the one sample proficiency test, if multiple 20353 laboratories have the same value, only the first laboratory id is 20354 printed along with the number of occurrences of that value. 20355 20356 For the "Unusual" and "Extremely Unusual" categories, it may be 20357 desirable to print the individual laboratory id's in the table. 20358 20359 To specify that for both the "Unusual" and "Extremely Unusual" 20360 categories all laborotories will be identified, enter 20361 20362 SET ONE SAMPLE PROFICIENCY TEST IDENTIFY LAB UNUSUAL 20363 20364 To specify that for only the "Extremely Unusual" category all 20365 laborotories will be identified, enter 20366 20367 SET ONE SAMPLE PROFICIENCY TEST IDENTIFY LAB EXTREMELY UNUSUAL 20368 20369 To reset the default, enter 20370 20371 SET ONE SAMPLE PROFICIENCY TEST IDENTIFY LAB DEFAULT 20372 20373Default: 20374 None 20375 20376Synonyms: 20377 None 20378 20379Related Commands: 20380 E691 INTERLAB = Perform an E691 interlaboratory analysis. 20381 STRIP PLOT = Generate a strip plot. 20382 BOX PLOT = Generate a box plot. 20383 YOUDEN PLOT = Generate a Youden plot. 20384 CAPTURE HTML = Generate output in HTML format. 20385 CAPTURE LATEX = Generate output in Latek format. 20386 CAPTURE RTF = Generate output in RTF format. 20387 20388Reference: 20389 "Standard Practice for Statistical Analysis of One-Sample 20390 and Two-Sample Proficiency Testing Programs", ASTM 20391 International, 100 Barr Harbor Drive, PO BOX C700, 20392 West Conshohoceken, PA 19428-2959, USA. 20393 20394Applications: 20395 Interlaboratory Studies 20396 20397Implementation Date: 20398 2009/01 20399 2019/08: Added the SET ONE SAMPLE PROFICIENCY TEST IDENTIFY LAB 20400 command 20401 20402Program 1: 20403 . 20404 . Read the data 20405 . 20406 SKIP 25 20407 READ E2489A.DAT LABID Y 20408 . 20409 . Generate the tables to the screen 20410 . 20411 ONE SAMPLE PROFICIENCY TEST Y LABID 20412 . 20413 . Now generate the tables in RTF format (for import into Word) 20414 . 20415 CAPTURE RTF ONE.RTF 20416 ONE SAMPLE PROFICIENCY TEST Y LABID 20417 END OF CAPTURE 20418 . 20419 . Generate the strip plot for the raw (unbinned) data 20420 . 20421 LABEL CASE ASIS 20422 TITLE CASE ASIS 20423 TITLE OFFSET 2 20424 Y1LABEL Number of Occurences 20425 X1LABEL Data Values 20426 TITLE Dot Diagram for Original Data 20427 Y1TIC MARKS OFF 20428 Y1TIC MARK LABELS OFF 20429 Y2FRAME OFF 20430 X2FRAME OFF 20431 YLIMITS 0 2 20432 MAJOR YTIC MARK NUMBER 3 20433 MINOR YTIC MARK NUMBER 0 20434 SET STRIP PLOT STYLE STACK 20435 SET STRIP PLOT INCREMENT 0.1 20436 LET STRING SYMBL = CIRCLE 20437 IF SYMBL = CIRCLE 20438 CHARACTER CIRCLE ALL 20439 CHARACTER FILL ON ALL 20440 CHARACTER HW 1 0.75 ALL 20441 END OF IF 20442 IF SYMBL = LABID 20443 CHARACTER AUTOMATIC LABIDSRT 20444 END OF IF 20445 LINE BLANK ALL 20446 . 20447 STRIP PLOT Y 20448 . 20449 Y1TIC MARKS ON 20450 Y1TIC MARK LABELS ON 20451 . 20452 . Generate the strip plot for the binned data 20453 . 20454 CLASS LOWER 0.5 20455 CLASS UPPER 5 20456 CLASS WIDTH 0.1 20457 FRAME CORNER COORDINATES 15 40 85 70 20458 Y1LABEL Number of Occurences 20459 X1LABEL Data Values 20460 TITLE Dot Diagram for Binned Data 20461 Y2FRAME OFF 20462 X2FRAME OFF 20463 LET MAXFREQ = MAXIMUM Y2 20464 LET NUMTIC = MAXFREQ + 1 20465 YLIMITS 0 MAXFREQ 20466 MAJOR YTIC MARK NUMBER NUMTIC 20467 MINOR YTIC MARK NUMBER 0 20468 Y1TIC OFFSET 1 1 20469 SET STRIP PLOT STYLE STACK 20470 SET STRIP PLOT INCREMENT 1 20471 CHARACTER CIRCLE ALL 20472 CHARACTER FILL ON ALL 20473 CHARACTER HW 1 0.75 ALL 20474 LINE BLANK ALL 20475 Y1TIC OFFSET 0 0 20476 . 20477 STRIP PLOT Y2 X2 20478 . 20479 FRAME CORNER COORDINATES 20480 CHAR FILL OFF ALL 20481 CHAR BLANK ALL 20482 CHAR HW 20483 LINE SOLID ALL 20484 LIMITS 20485 FRAME ON 20486 MAJOR TIC MARK NUMBER 20487 MINOR TIC MARK NUMBER 20488 . 20489 . Now generate a box plot 20490 . 20491 Y1LABEL Test Results 20492 X1LABEL 20493 TITLE Box Plot for Proficiency Data 20494 XLIMITS 0 2 20495 XTIC MARKS OFF 20496 XTIC MARK LABELS OFF 20497 CHARACTER BOX PLOT 20498 LINE BOX PLOT 20499 FENCES ON 20500 . 20501 BOX PLOT Y 20502 XLIMITS 20503 X1TIC MARKS ON 20504 X1TIC MARK LABELS ON 20505 20506Program 2: 20507 . 20508 . Read the data 20509 . 20510 SKIP 25 20511 READ E2489B.DAT LABID Y1 Y2 20512 . 20513 . Generate the tables to the screen 20514 . 20515 TWO SAMPLE PROFICIENCY TEST Y1 Y2 LABID 20516 . 20517 . Now generate the tables in RTF format (for import into Word) 20518 . 20519 CAPTURE RTF TWO.RTF 20520 TWO SAMPLE PROFICIENCY TEST Y1 Y2 LABID 20521 END OF CAPTURE 20522 . 20523 . Generate the Youden plot 20524 . 20525 LET STRING SYMBL = LABID 20526 IF SYMBL = CIRCLE 20527 CHARACTER CIRCLE ALL 20528 CHARACTER FILL ON ALL 20529 CHARACTER HW 1 0.75 ALL 20530 END OF IF 20531 IF SYMBL = BOX 20532 CHARACTER BOX ALL 20533 CHARACTER FILL ON ALL 20534 CHARACTER HW 1 0.75 ALL 20535 END OF IF 20536 IF SYMBL = DIAMOND 20537 CHARACTER DIAMOND ALL 20538 CHARACTER FILL ON ALL 20539 CHARACTER HW 1 0.75 ALL 20540 END OF IF 20541 IF SYMBL = LABID 20542 LET LABIDSRT = LABID 20543 LET YSORT = SORTC Y LABIDSRT 20544 CHARACTER HW 2 1.50 ALL 20545 CHARACTER AUTOMATIC LABIDSRT 20546 END OF IF 20547 LINE BLANK ALL 20548 . 20549 LABEL CASE ASIS 20550 TITLE CASE ASIS 20551 TITLE OFFSET 2 20552 X1LABEL Test Results for Sample One 20553 Y1LABEL Test Results for Sample Two 20554 TITLE Youden Plot of Test Results 20555 . 20556 LIMITS 0 5 20557 TIC OFFSET UNITS DATA 20558 TIC MARK OFFSET 0 0.5 20559 . 20560 YOUDEN PLOT Y2 Y1 LABID 20561 . 20562 PROBE FX1MIN 20563 LET AX1 = PROBEVAL 20564 PROBE FX1MAX 20565 LET AX2 = PROBEVAL 20566 PROBE FY1MIN 20567 LET AY1 = PROBEVAL 20568 PROBE FY1MAX 20569 LET AY2 = PROBEVAL 20570 . 20571 LINE SOLID 20572 DRAWDATA AX1 MEDX AX2 MEDX 20573 DRAWDATA MEDY AY1 MEDY AY2 20574 LINE DASH 20575 DRAWDATA AX1 AY1 AX2 AY2 20576 LINE SOLID 20577 20578-----PROFILE PLOT------------------------------------------------ 20579 20580PROFILE PLOT 20581 20582Name: 20583 PROFILE PLOT 20584 20585Type: 20586 Graphics Command 20587 20588Purpose: 20589 Generates a profile plot. 20590 20591Description: 20592 A profile plot is a graphical data analysis technique for examining 20593 the relative behavior of all variables in a multivariate data set. 20594 The profile plot consists of a sequence of equi-spaced vertical 20595 spikes with each spike representing a different variable in the 20596 multivariate data set. An individual profile plot examines the 20597 behavior of all such variables but only for a specified subset of 20598 the data (e.g., looking at all the attributes of car performance, 20599 but only for a particular car, such as Chevrolet). The total length 20600 of a given spike is uniformly set to unity for sake of reference. 20601 The "data length" of a given spike is proportional to the magnitude 20602 of the variable for the subset relative to the maximum magnitude 20603 of the variable across all subsets. (Thus we are looking at the 20604 ratio of the "local" value of the variable to the "global" maximum 20605 of the variable.) An interconnecting line cutting across each spike 20606 at the "data length" gives the profile plot its unique appearance 20607 and name. 20608 20609Syntax: 20610 PROFILE PLOT <y1> <y2> ... <yk> <SUBSET/EXCEPT/FOR qualification> 20611 where <y1> ... <yk> are the response variables; 20612 and where the <SUBSET/EXCEPT/FOR qualification> must be given. It 20613 is not optional for this command as it is for most other 20614 DATAPLOT commands. 20615 20616Examples: 20617 PROFILE PLOT Y1 Y2 Y3 Y4 Y5 SUBSET AUTO 4 20618 PROFILE PLOT Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 SUBSET STATE 25 20619 20620Note: 20621 A few variations of the profile plot exist, all of which DATAPLOT 20622 can easily generate by judicious use of the components in the LINE, 20623 CHARACTER, SPIKE, and BAR commands (and their attribute setting 20624 commands). For example, suppose there are k variables in the 20625 profile plot (and so k spikes), then 20626 1) element 1 of LINES controls the appearance of the 20627 interconnecting line (this is usually SOLID); 20628 2) element 1 of SPIKE and SPIKE LINE controls the 20629 existence and appearance of the spikes from the base 20630 out to the interconnecting line (some analysts prefer 20631 this to be SOLID, others prefer this to be DOTTED). 20632 When using the SPIKE and SPIKE LINES commands in this context, note 20633 that both must be used if you want spikes to appear. The SPIKE 20634 (ON/OFF) command sets whether spikes will appear or not while the 20635 SPIKE LINES command sets the desired line type (SOLID, DOTTED, 20636 DASHED, etc.). Thus SPIKE ON and SPIKE LINES SOLID would for a 20637 profile plot turn the spikes on and set them to solid, respectively. 20638 20639Note: 20640 The generation of multiple profile plots per page is typical (one 20641 profile plot for each subset of interest). This is easily done in 20642 DATAPLOT by using the PROFILE PLOT command in conjunction with the 20643 MULTIPLOT and LOOP commands, as in the following which would 20644 generate 50 profile plots on the same page, where each profile plot 20645 would consist of 6 variables (spikes): 20646 MULTIPLOT 5 10 20647 LOOP FOR K = 1 1 50 20648 PROFILE PLOT Y1 Y2 Y3 Y4 Y5 Y6 SUBSET STATE K 20649 END OF LOOP 20650 20651Default: 20652 None 20653 20654Synonyms: 20655 None 20656 20657Related Commands: 20658 STAR PLOT = Generates a (multivariate) star plot. 20659 ANDREWS PLOT = Generates an Andrews (multivariate) plot. 20660 LINES = Sets the type for plot lines. 20661 SPIKES = Sets the type for plot spikes. 20662 MULTIPLOT = Allows multiple plots per page. 20663 LOOP = Starts a loop (iteration). 20664 END OF LOOP = Terminates a loop. 20665 ^ = Allows string and value substitution. 20666 20667Reference: 20668 "Graphical Methods of Data Analysis", Chambers, Cleveland, Kleiner, 20669 and Tukey. Wadsworth, 1983 (pp. 162-163). 20670 20671Applications: 20672 Multivariate Analysis 20673 20674Implementation Date: 20675 88/3 20676 20677Program: 20678 READ CITY Y1 TO Y6 20679 1 18 8 307 130 3504 12 20680 2 15 7 350 165 3693 11.5 20681 3 13 8 318 150 3436 11.0 20682 4 16 6 304 134 3433 111.6 20683 END OF DATA 20684 READ STRING S1 S2 S3 S4 20685 BOSTON PHILADELPHIA CHICAGO DENVER 20686 LINES SO DO DO DO DO DO DO BL BL BL BL BL BL 20687 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 20688 LOOP FOR K = 1 1 4 20689 XLABEL ^S^K 20690 PROFILE PLOT Y1 Y2 Y3 Y4 Y5 Y6 SUBSET CITY K 20691 END OF LOOP 20692 END OF MULTIPLOT 20693 20694-----SET PROMPT ADVANCE (SET)-------------------------------------------- 20695 20696PROMPT ADVANCE 20697 20698Name: 20699 SET PROMPT ADVANCE (SET) 20700 20701Type: 20702 Set Subcommand 20703 20704Purpose: 20705 Specify the name of the directory where DATAPLOT's auxiliary files 20706 are stored. 20707 20708Description: 20709 When expecting a new command, Dataplot writes a prompt character 20710 (by default, a ">"). With Fortran I/O, this write is automatically 20711 followed by a carriage return/line feed so that the input is actually 20712 entered on the next line. 20713 20714 Fortran 90 provides for an "ADVANCE" option for WRITE commands. 20715 Specifying an ADVANCE='NO' suppresses this carriage return/line feed 20716 so that the input is entered on the same line as the prompt. 20717 20718 Entering the command 20719 20720 SET PROMPT ADVANCE ON 20721 20722 will utilize this option to suppress the carriage return/line feed 20723 after printing the prompt character. 20724 20725 This feature is compiler dependent. Some Fortran compilers do not 20726 support the ADVANCE option when writing to standard output. 20727 Specifcally, the Intel Fortran compiler used for the Microsoft 20728 Windows implementation does not support this (note that earlier 20729 versions of this compiler did support support this). The gfortran 20730 compiler used for Linux/Unix and Mac OS X implementations does support 20731 this feature. 20732 20733Syntax: 20734 SET PROMPT ADVANCE <ON/OFF> 20735 where <ON> specifies that the carriage return/line feed will be 20736 suppressed while <OFF> specifies that it will not. 20737 20738Examples: 20739 SET PROMPT ADVANCE ON 20740 SET PROMPT ADVANCE OFF 20741 PROBE PROMPT ADVANCE 20742 20743Note: 20744 The SET PROMPT ADVANCE ON will be ignored when running the graphical 20745 user interface (GUI) is running. 20746 20747Default: 20748 OFF 20749 20750Synonyms: 20751 None 20752 20753Related Commands: 20754 PROMPT = Specify whether the prompt will be printed. 20755 20756Applications: 20757 Terminal usage 20758 20759Implementation Date: 20760 2009/07 20761 20762Program: 20763 SET PROMPT ADVANCE ON 20764 20765-----PROMPT------------------------------------------------------- 20766 20767PROMPT 20768 20769Name: 20770 PROMPT 20771 20772Type: 20773 Support Command 20774 20775Purpose: 20776 Specifies that after the execution of a command is completed, a 20777 prompt character will appear as an indication to the analyst to 20778 enter another command. 20779 20780Syntax: 20781 PROMPT <ON or OFF> 20782 where ON specifies that the prompt will appear after subsequent 20783 commands while OFF specifies that it will not. 20784 20785Examples: 20786 PROMPT ON 20787 PROMPT OFF 20788 PROMPT 20789 20790Note: 20791 The PROMPT command with no arguments is equivalent to PROMPT ON. 20792 20793Default: 20794 At sign-on, the default is a prompt (i.e., ON). 20795 20796Synonyms: 20797 None 20798 20799Related Commands: 20800 ECHO = Allows/suppresses command echoing. 20801 FEEDBACK = Allows/suppresses feedback messages. 20802 PRINTING = Allows/suppresses analysis output. 20803 SET = Sets the value of an internal variable (e.g., IPR). 20804 PROBE = Displays the value of an internal variable (e.g., IPR). 20805 20806Applications: 20807 XX 20808 20809Implementation Date: 20810 Pre-1987 20811 20812Program: 20813 XX 20814 20815-----PROPORTION CONFIDENCE LIMITS-------------------------------------- 20816 20817PROPORTION CONFIDENCE LIMITS 20818 20819Name: 20820 PROPORTION CONFIDENCE LIMITS 20821 20822Type: 20823 Analysis Command 20824 20825Purpose: 20826 Generates a confidence interval for proportions. 20827 20828Description: 20829 Given a set of N observations in a variable X, we can compute the 20830 proportion of successes. The PROPORTION CONFIDENCE LIMITS command 20831 computes a confidence interval for the proportion of successes. 20832 20833 In Dataplot, you define a success by entering the command 20834 20835 ANOP LIMITS <lower limit> <upper limit> 20836 20837 before entering the PROPORTION CONFIDENCE LIMITS command. That is, 20838 you specify the lower and upper values that define a success. Then 20839 the estimate for the proportion of successes is simply the number of 20840 points in the success region divided by the total number of points. 20841 In most applications, successes are defined by 1's and failures by 20842 0's. The default limits are 0.5 and 1.5, so if your data is defined 20843 by 0 and 1 values the ANOP LIMITS command can be omitted. 20844 20845 Several methods have been proposed for the confidence limits for a 20846 binomial proportion. The following methods are currently supported 20847 in Dataplot 20848 20849 NORMAL APPROXIMATION 20850 20851 The normal approximation interval is 20852 20853 phat +/- NORPPF(1 - alpha/2)*SQRT(phat*(1 - phat)/n) 20854 20855 where 20856 20857 X = the number of successes 20858 phat = X/n 20859 NORPPF = the percent point function of the normal distribution 20860 20861 Due to its simplicity, the method is commonly used. However, its 20862 use should be restricted to cases with relatively large sample sizes 20863 where phat is not near 0 or 1. 20864 20865 ADJUSTED WALD 20866 20867 The adjusted Wald interval is 20868 20869 p' +/- NORPPF(1-alpha/2)*SQRT(p'*(1-p'))/SQRT(n') 20870 20871 where 20872 20873 X' = X + NORPPF(1-alpha/2)**2/2 (X is the number of success) 20874 n' = n + NORPPF(1-alpha/2)**2 20875 p' = X'/n' 20876 NORPPF is the percent point function of the normal distribution 20877 20878 This method improves upon the normal approximation. 20879 20880 WILSON 20881 20882 This method was originally proposed by Wilson in 1927. Papers 20883 by Agresti and Coull and also by Brown, Cai and DasGupta 20884 recommended this interval and provided comparisons of this 20885 method to the adjusted Wald and other methods. 20886 20887 This method solves for the two values of p0 (say, 20888 p(upper) and p(lower) that result from setting z = z(alpha/2) 20889 and solving for p(0) = p(upper), and then setting 20890 z = -z(alpha/2) and solving for p(0) = p(lower) where 20891 z(alpha/2) denotes the variate value from the standard normal 20892 distribution such that the area to the right of the value is 20893 alpha/2. The solution for the two values of p(0) results in 20894 the following confidence intervals: 20895 20896 U. L. = {phat + z(alpha/2)**(2)/(2n) + 20897 z(alpha/2/(sqrt[(phat*(1-phat))/n + 20898 z(alpha/2)**(2)/(4n**2)]}/ 20899 {1 + z(alpha/2)**(2)/n} 20900 20901 L. L. = {phat + z(alpha/2)**(2)/(2n) - 20902 z(alpha/2/(sqrt[(phat*(1-phat))/n + 20903 z(alpha/2)**(2)/(4n**2)]}/ 20904 {1 + z(alpha/2)**(2)/n} 20905 20906 This approach can be justified on the grounds that it is the 20907 exact algebraic counterpart to the (large-sample) hypothesis test 20908 and is also supported by the research of Agresti and Coull. One 20909 advantage of this procedure is that its worth does not strongly 20910 depend upon the value of <i>n</i> and/or <i>p</i>, and indeed was 20911 recommended by Agresti and Coull for virtually all combinations of 20912 <i>n</i> and <i>p</i>. Simulations by Agresti and Coull and 20913 by Brown, Cai and DasGupta show that this method does a better 20914 job of maintaining the nomial coverage than does the adjusted 20915 Wald and normal approximation methods. Another advantage is 20916 that the limits are in the (0,1) interval. 20917 20918 JEFFREYS 20919 20920 The Jeffreys interval (the derivation for this interval is given in 20921 the Brown, Cai, DasGupta paper) is 20922 20923 LCL = BETPPF(alpha/2,X + 0.5) 20924 UCL = BETPPF(1 - alpha/2,n - X + 0.5) 20925 20926 where BETPPF is the percent point function of the beta distribution 20927 and X is the number of successes. 20928 20929 EXACT BINOMIAL (or CLOPPER-PEARSON) 20930 20931 Exact binomial intervals are obtained by 20932 20933 1) Solve the equation 20934 20935 BINCDF(x;p(u),N) = alpha/2 20936 20937 where BINCDF is the cumulative distribution function of the 20938 binomial distribution, x is the number of successes, and 20939 n is the number of trials. 20940 20941 2) Next solve the equation 20942 20943 BINCDF(x;p(l),n) = 1 - alpha/2 20944 20945 for p(l) to obtain the lower 100(1 - alpha)% limit for p. 20946 20947 Although this method is called "exact", it is not more 20948 accurate than the adjusted Wald or Wilson method. The 20949 "exact" terminology is based on the use of the binomial 20950 CDF function. However, since the binomial is a discrete 20951 distribution, the use of the CDF function does not 20952 result in "exact" 95% confidence intervals. The Agresti 20953 and Coull paper gives arguments to justify why the 20954 "approximate" Wilson and adjusted Wald methods can often be 20955 more accurate than the "exact" method. 20956 20957 To specify the method to use, enter the command 20958 20959 SET BINOMIAL METHOD <WILSON/ADJUSTED WALD/JEFFREYS/NORMAL/EXACT> 20960 20961 The default is the Wilson method. The Brown, Cai, and DasGupta paper 20962 studied the coverage properties of various methods. They specifically 20963 recommend the Wilson, the adjusted Wald, and the Jeffreys method as 20964 having the best coverage properties. Specifically, they recommend the 20965 Wilson and Jeffreys methods for n <= 40. For n > 40, these three 20966 methods have comparable performance. Although the normal 20967 approximation and exact binomial methods are not typically 20968 recommended, Dataplot provides them since they are still used in 20969 practice. 20970 20971 Dataplot computes this inverval for a number of different 20972 probability levels. 20973 20974Syntax: 20975 PROPORTION CONFIDENCE LIMITS <y> 20976 <SUBSET/EXCEPT/FOR qualification> 20977 where <y> is the response variable; 20978 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 20979 20980Examples: 20981 ANOP LIMITS 0.50 1.5 20982 PROPORTION CONFIDENCE LIMITS Y 20983 20984 SET BINOMIAL METHOD ADJUSTED WALD 20985 PROPORTION CONFIDENCE LIMITS Y SUBSET TAG = 1 TO 3 20986 20987Note: 20988 A table of confidence intervals is printed for alpha levels of 20989 50.0, 75.0, 90.0, 95.0, 99.0, 99.9, 99.99, and 99.999. The sample 20990 size, sample number of successes, and sample proportion of 20991 successes are also printed. 20992 20993Note: 20994 Prior versions of Dataplot used the following method for the 20995 confidence interval 20996 20997 (BINPPF(ALPHA/2,P,N)/N, BINPPF(1-ALPHA/2,P,N)/N) 20998 20999 where BINPPF is the percent point function of the binomial 21000 distribution. 21001 21002 This method is no longer supported. 21003 21004Default: 21005 None 21006 21007Synonyms: 21008 None 21009 21010Related Commands: 21011 AGRESTI COULL = Compute either the lower or upper 21012 confidence limit for either a one-sided or 21013 a two-sided binomial proportion of a 21014 variable (Wilson, adjusted Wald, or 21015 Jeffreys method). 21016 EXACT BINOMIAL = Compute either the lower or upper exact 21017 binomial confidence limit for either a 21018 one-sided or a two-sided binomial 21019 proportion of a variable. 21020 ANOP LIMITS = Specify success region for proportions. 21021 DIFFERENCE OF PROPORTION = Compute the confidence interval for 21022 CONFIDENCE LIMITS the difference of proportions. 21023 ANOP PLOT = Generate an analysis of proportions 21024 plot. 21025 CONFIDENCE LIMITS = Generate the confidence limits for 21026 the mean. 21027 21028Reference: 21029 Agresti, A. and Coull, B. A. (1998), "Approximate is better than 21030 "exact" for interval estimation of binomial proportions", 21031 The American Statistician, 52(2), 119-126. 21032 21033 Brown, L. D. Cai, T. T. and DasGupta, A. (2001), "Interval estimation 21034 for a binomial proportion," Statistical Science, 16(2), 101-133. 21035 21036 Wilson (1927), "Probable inference, the law of succession, and 21037 statistical inference," Journal of the American Statistical 21038 Association, Vol. 22, pp. 209-212. 21039 21040 "Statistical Methods", Eigth Edition, Snedecor and Cochran, 21041 1989, Iowa State University Press, pp. 121-124. 21042 21043 NIST/SEMATECH e-Handbook of Statistical Methods, 21044 http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm. 21045 21046Applications: 21047 Confirmatory Data Analysis 21048 21049Implementation Date: 21050 1999/05 21051 2017/11: Change method for determining the confidence interval 21052 21053Program: 21054 . Create a binary variable with 30 rows 21055 . with 8 successes. 21056 . 21057 let n = 30 21058 let nsuc = 8 21059 let y = 0 for i = 1 1 n 21060 let y = 1 for i = 1 1 nsuc 21061 . 21062 . Now do proportions confidence interval 21063 . 21064 set write decimals 6 21065 set binomial method wilson 21066 proportion confidence interval y 21067 set binomial method adjusted wald 21068 proportion confidence interval y 21069 set binomial method jeffreys 21070 proportion confidence interval y 21071 set binomial method exact 21072 proportion confidence interval y 21073 set binomial method normal 21074 proportion confidence interval y 21075 21076-----PROPORTION LIMITS-------------------------------------- 21077 21078PROPORTION LIMITS 21079 21080Name: 21081 PROPORTION LIMITS 21082 21083Type: 21084 Support Command 21085 21086Purpose: 21087 Define the upper and lower bounds for counting a response a success 21088 or failure in a subsequent analysis of proportions plot (values 21089 between these two numbers are counted as "successes" while values 21090 outside the two points are counted as "failures"). 21091 21092Syntax: 21093 PROPORTION LIMITS <lower> <upper> 21094 where <lower> is a decimal number or parameter that specifies the 21095 lower bound; 21096 and <upper> is a decimal number or parameter that specifies the 21097 upper bound. 21098 21099Examples: 21100 PROPORTION LIMITS 0.2 0.7 21101 PROPORTION LIMITS YLOW YHIGH 21102 21103 LET YLOW = Y(1) - 0.5 21104 LET YHIGH = Y(1) + 0.5 21105 PROPORTION LIMITS YLOW YHIGH 21106 21107Default: 21108 None 21109 21110Synonyms: 21111 ANOP LIMITS 21112 21113Related Commands: 21114 ANOP PLOT = Generate an analysis of proportions plot. 21115 21116Applications: 21117 Analysis of Proportions 21118 21119Implementation Date: 21120 XX 21121 21122Program: 21123 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 21124 LET TAG = PATTERN 1 2 3 4 5 FOR I = 1 1 100 21125 PROPORTION LIMITS 0.2 0.7 21126 CHARACTER CIRCLE BLANK 21127 LINE BLANK SOLID 21128 ANOP PLOT Y1 TAG 21129 21130-----PROPORTION PLOT--------------------------------------------------- 21131 21132PROPORTION PLOT 21133 21134Name: 21135 PROPORTION PLOT 21136 21137Type: 21138 Graphics Command 21139 21140Purpose: 21141 Generates a proportion plot. 21142 21143Description: 21144 A proportion plot is a plot consisting of subsample proportions 21145 versus subsample index. The subsample proportion is the percentage 21146 (0 to 100%) of the data in the subsample which falls in a 21147 pre-specified region of interest (see the PROPORTION LIMITS 21148 command). The proportion plot is used to answer the question-- 21149 "Does the proportion of data falling in a given region of interest 21150 change over different subsamples?". Note that the "region of 21151 interest" is frequently the upper or lower 10% of the data, the 21152 upper or lower 25% of the data, or some other extreme region of the 21153 data. The proportion plot consists of: 21154 Vertical axis = subsample proportion; 21155 Horizontal axis = subsample index. 21156 The PROPORTION PLOT yields 2 traces: 21157 1. a subsample proportion trace; and 21158 2. a full-sample proportion reference line. 21159 Like usual, the appearance of these 2 traces is 21160 controlled by the first 2 settings of the LINES, 21161 CHARACTERS, SPIKES, BARS, and similar attributes. 21162 21163Syntax: 21164 PROPORTION PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 21165 where <y> is the response (= dependent) variable; 21166 <x> is the subsample identifier variable (this variable 21167 appears on the horizontal axis); 21168 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 21169 21170Examples: 21171 PROPORTION PLOT Y X 21172 PROPORTION PLOT Y X1 21173 21174Default: 21175 None 21176 21177Synonyms: 21178 ANOP PLOT 21179 21180Related Commands: 21181 CHARACTERS = Sets the type for plot characters. 21182 LINES = Sets the type for plot lines. 21183 MEAN PLOT = Generates a mean plot. 21184 RANGE PLOT = Generates a range plot. 21185 UPPER QUARTILE PLOT= Generates an upper quartile plot 21186 LOWER QUARTILE PLOT= Generates a lower quartile plot 21187 BOX PLOT = Generates a box plot. 21188 XBAR CHART = Generates a xbar control chart. 21189 PLOT = Generates a data or function plot. 21190 21191Applications: 21192 Exploratory Data Analysis 21193 21194Implementation Date: 21195 88/9 21196 21197Program: 21198 LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 100 21199 LET X = SEQUENCE 1 10 1 10 21200 PROPORTION LIMITS 1 10000 21201 PROPORTION PLOT Y X 21202 21203-----PSEUDO INVERSE (LET)---------------------------------------- 21204 21205PSEUDO INVERSE 21206 21207Name: 21208 PSEUDO INVERSE (LET) 21209 21210Type: 21211 Let Subcommand 21212 21213Purpose: 21214 Compute the transpose of the Moore-Penrose pseudo inverse of a 21215 matrix. 21216 21217Description: 21218 If A is a square matrix of full rank, then the inverse of A 21219 exists (A is referred to as an invertible matrix) and 21220 21221 A*x = b 21222 21223 has the solution 21224 21225 x = A**(-1)*b 21226 21227 The Moore-Penrose pseudo inverse is a generalization of the 21228 matrix inverse when the matrix may not be invertible. If A is 21229 invertible, then the Moore-Penrose pseudo inverse is equal to 21230 the matrix inverse. However, the Moore-Penrose pseudo inverse 21231 is defined even when A is not invertible. 21232 21233 More formally, the Moore-Penrose pseudo inverse, A+, of an m-by-n 21234 matrix is defined by the unique n-by-m matrix satisfying the 21235 following four criteria (we are only considering the case where A 21236 consists of real numbers). 21237 21238 1) A*A+*A = A 21239 21240 2) A+*A*A+ = A+ 21241 21242 3) (A*A+)' = A*A+ 21243 21244 4) (A+*A)' = A+*A 21245 21246 If A is an mxn matrix where m > n and A is of full rank (= n), 21247 then 21248 21249 A+ = (A'*A)**(-1)*A' 21250 21251 and the solution of A*x = b is x = A+*b. In this case, the 21252 solution is not exact. It finds the solution that is 21253 closest in the least squares sense. 21254 21255Syntax: 21256 LET <mat2> = PSEUDO INVERSE <mat1> 21257 <SUBSET/EXCEPT/FOR qualification> 21258 where <mat1> is a matrix for which the pseudo inverse is to be 21259 computed; 21260 <mat2> is a matrix where the resulting transpose of the pseudo 21261 inverse is saved; 21262 and where the <SUBSET/EXCEPT/FOR qualification> is optional (and 21263 rarely used in this context). 21264 21265Examples: 21266 LET C = PSEUDO INVERSE A 21267 21268Note: 21269 The pseudo inverse is also referred to as the generalized 21270 inverse. 21271 21272Note: 21273 A pseudo inverse can be used for any operator pinv satisfying 21274 21275 M*pinv(M)*M = M 21276 21277 Dataplot specifically computes the Moore-Penrose pseudo inverse. 21278 Other formulations are not currently supported. 21279 21280Note: 21281 Dataplot computes the pseudo inverse using the MATMPI routine 21282 written by Charles Reeve while he was a member of the NIST 21283 Statistical Engineering Division. This routine is available at 21284 21285 http://www.itl.nist.gov/div898/software/reeves/homepage.htm 21286 21287 The MATMPI routine is based on the singular value decomposition. 21288 The singular value decomposition of A is 21289 21290 A=U*S*V' 21291 21292 where U and V are both nxn orthogonal matrices and S is an 21293 mxn diagonal matrix with singular values sigma(i) for 21294 i = 1, ..., n. Then 21295 21296 A+ = V*(S'*S)**(-1)*S'*U' 21297 21298 If the rank r of A is less than n, the inverse of S'*S does 21299 not exist and we use only the first r singular values. S 21300 is then a rxr matrix and U and V are shrunk accordingly. 21301 21302Note: 21303 Matrices are created with the READ MATRIX, CREATE MATRIX and 21304 MATRIX DEFINITION commands. 21305 21306Note: 21307 The columns of a matrix are accessible as variables by appending an 21308 index to the matrix name. For example, the 4x4 matrix C has 21309 columns C1, C2, C3, and C4. These columns can be operated on like 21310 any other DATAPLOT variable. 21311 21312Note: 21313 The maximum size matrix that DATAPLOT can handle is set when 21314 DATAPLOT is built on a particular site. Enter HELP DIMENSION 21315 and HELP MATRIX DIMENSION for details. 21316 21317Default: 21318 None 21319 21320Synonyms: 21321 None 21322 21323Related Commands: 21324 MATRIX INVERSE = Compute the inverse of a nxn matrix. 21325 MATRIX DEFINITION = Set a matrix definition. 21326 MATRIX DETERMINANT = Compute a matrix determinant. 21327 MATRIX EUCLID NORM = Compute the matrix Euclidean norm. 21328 MATRIX MULTIPLICAT = Perform a matrix multiplication. 21329 MATRIX SOLUTION = Solve a system of linear equations. 21330 MATRIX TRANSPOSE = Compute a matrix transpose. 21331 SINGULAR VALUE DECOM = Compute the singular value decomposition of 21332 a matrix. 21333 DIMENSION = Specify the maximum number of rows and 21334 columns in the internal Dataplot storage. 21335 MATRIX DIMENSION = Specify the row and column dimensions for 21336 matrix operations. 21337 21338Reference: 21339 Penrose (1956), "On Best Approximate Solution of Linear 21340 Matrix Equations", Proceedings of the Cambridge Philosophical 21341 Society, 52, pp. 17-19. 21342 21343 Dongarra, Bunch, Moler, Stewart (1979), "LINPACK User's Guide", 21344 Siam. 21345 21346Applications: 21347 Linear Algebra 21348 21349Implementation Date: 21350 2009/1 21351 21352Program: 21353 DIMENSION 100 COLUMNS 21354 READ MATRIX X 21355 16 16 19 21 21356 14 17 15 22 21357 24 23 21 24 21358 18 17 16 15 21359 18 11 9 18 21360 END OF DATA 21361 LET A = PSEUDO INVERSE X 21362 PRINT A 21363 21364-----PSIFN (LET)-------------------------------- 21365 21366PSIFN 21367 21368Name: 21369 PSIFN (LET) 21370 21371Type: 21372 Library Function 21373 21374Purpose: 21375 Compute the scaled kth derivative of the digamma (or psi) 21376 function. 21377 21378Description: 21379 The psifn function is defined as: 21380 psifn(x,k) = ((-1)**(K+1)/GAMMA(K+1))*PSI(X,K) 21381 where GAMMA is the gamma function and PSI(X,K) is the 21382 kth derivative of the digamma function. Enter 21383 HELP DIGAMMA for details on the digamma function. 21384 21385 Note that this is the kth derivative of the digamma 21386 function, not the log gamma function. That is, for k=1, the 21387 trigamma function is computed, not the digamma function. 21388 21389Syntax: 21390 LET <y> = PSIFN(<x>) <SUBSET/EXCEPT/FOR qualification> 21391 where <x> is a number, variable or a parameter; 21392 <y> is a variable or a parameter (depending on what <x> 21393 is) where the computed psifn values are stored; 21394 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 21395 21396Examples: 21397 LET A = PSIFN(1,2) 21398 LET X2 = PSIFN(X1,K) 21399 21400Note: 21401 DATAPLOT uses the routine PSIFN from the SLATEC Common Mathematical 21402 Library to compute this function. SLATEC is a large set of high 21403 quality, portable, public domain Fortran routines for various 21404 mathematical capabilities maintained by seven federal laboratories. 21405 21406Note: 21407 Library functions are distinguished from let subcommands 21408 in the following ways. 21409 1) Functions enclose the input value in parenthesis. Let 21410 subcommands use spaces. 21411 2) Functions can accept (and return) either parameters 21412 (i.e., single values) or variables (i.e., an array of 21413 values) while let subcommands are specific in which they 21414 accept as input and what they return as output. 21415 3) Functions can accept expressions while let subcommands 21416 do not. For example, the following is legal: 21417 LET Y2 = ABS(Y1-INT(Y1)) 21418 For let subcommands, you typically have to do something 21419 like the following: 21420 LET YTEMP = Y**2 + 8 21421 LET A = SUM YTEMP 21422 21423Default: 21424 None 21425 21426Synonyms: 21427 None 21428 21429Related Commands: 21430 GAMMA = Compute the gamma function. 21431 DIGAMMA = Compute the digamma function. 21432 LOGGAMMA = Compute the log (to base e) gamma function. 21433 GAMMAI = Compute the incomplete Gamma function. 21434 GAMMAIP = Compute an alternate form of the incomplete gamma 21435 function. 21436 GAMMAIC = Compute the complementary incomplete Gamma function. 21437 GAMMAR = Compute the reciprocal gamma function. 21438 TRICOMI = Compute Tricomi's incomplete gamma function. 21439 BETA = Compute the Beta function. 21440 21441Reference: 21442 "Handbook of Mathematical Functions, Applied Mathematics Series, 21443 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 21444 1964 (chapter 6). 21445 21446Applications: 21447 Special Functions 21448 21449Implementation Date: 21450 1998/5 21451 21452Program: 21453 YLIMITS 0 100 21454 MULTIPLOT 2 2 21455 MULTIPLOT CORNER COORDINATES 5 5 95 95 21456 TITLE AUTOMATIC 21457 PLOT PSIFN(X,1) FOR X = 0.1 0.1 3 21458 PLOT PSIFN(X,2) FOR X = 0.1 0.1 3 21459 PLOT PSIFN(X,3) FOR X = 0.1 0.1 3 21460 PLOT PSIFN(X,4) FOR X = 0.1 0.1 3 21461 END OF MULTIPLOT 21462 MOVE 50 97 21463 JUSTIFICATION CENTER 21464 TEXT SCALED PSI FUNCTIONS 21465 21466-----PSVIEW------------------------------------------------------- 21467 21468PSVIEW 21469 21470Name: 21471 PSVIEW 21472 21473Type: 21474 Support Command 21475 21476Purpose: 21477 View the most recent plot in a Postscript viewer. 21478 21479Description: 21480 DEVICE 3 (in file DPPL2F.DAT, the name may vary on some systems) 21481 output is closed and re-opened at the beginning of a plot command, 21482 so only the most recent plot is in the graphics file. 21483 21484 This command will view this Postscript file using a Postscript 21485 viewer. This command is currently supported for Windows and 21486 Unix/Linux systems. 21487 21488 For both Windows and Unix/Linux systems, the default viewer is 21489 ghostview. To specify a different viewer, enter the command 21490 21491 SET POSTSCRIPT VIEWER <viewer> 21492 21493 On Unix/Linux systems, <viewer> is case sensitive. 21494 21495 This command is useful when you want to view the Postscript 21496 version of the plot without leaving the Dataplot session. 21497 The Postscript version of the plot is typically of higher 21498 quality than the screen version of the plot. 21499 21500 The October, 2016 version of Dataplot made the following updates 21501 to this command. 21502 21503 1. You can now view the contents of the DEVICE 2 output (see 21504 Syntax 2 below). 21505 21506 2. You can view an arbitrary Postscript file (see Syntax 3 below). 21507 The December, 2019 version of Dataplot made the following updates 21508 to this command. 21509 21510 1. The default Postscript viewer for Linux is "xdg-open" and 21511 the default viewer for MacOS is "open". These applications 21512 will select the default Postscript viewer for files that 21513 have a ".ps" or ".eps" extension. You can use the 21514 SET POSTSCRIPT VIEWER command to request a specific 21515 Postscript viewer. 21516 21517 One issue is that the default names for DEVICE 2 and 21518 DEVICE 3 have a ".dat" extension rather than a ".ps" 21519 extension. For this reason, Dataplot added the command 21520 21521 SET BACKUP VIEWER <viewer> 21522 21523 The viewer specified by this command will be used when 21524 the given file name does not have a recognized extension. 21525 21526 2. You can now view PDF files. To specify the application 21527 that will be used to view the PDF file, enter the command 21528 21529 SET PDF VIEWER <viewer> 21530 21531 The PDF VIEWER will be used when the file has a 21532 ".pdf" extension. 21533 21534 The default viewer will be the Adobe Acrobat reader under 21535 Windows. For Linux systems, the default is to use "xdg-open" 21536 and for MacOS systems the default is to use "open". These 21537 applications will select the default PDF viewer for the 21538 local platform. 21539 21540 3. You can now view image files (e.g., PNG, JPG and GIF files). 21541 To specify the application that will be used to view the 21542 image file, enter the command 21543 21544 SET IMAGE VIEWER <viewer> 21545 21546 The IMAGE VIEWER will be used when the file has a 21547 ".png", ".jpg", ".jpeg", ".gif", ".tif",".tiff", 21548 ".bmp" or ".svg" extension. There are a large number of 21549 image file extensions. When an unrecognized file extension 21550 is found, Dataplot will use the viewer specified by the 21551 SET BACKUP VIEWER command. 21552 21553 For Windows, the default is to simply specify the file 21554 name and let the operating system select the appropriate 21555 application (this is determined by the "file association"). 21556 For Linux systems, the default is to use "xdg-open" and for 21557 MacOS systems the default is to use "open". These 21558 applications will select the default image viewer for the 21559 local platform based on the file extension. 21560 21561 4. This command will issue the following commands before 21562 invoking the viewer application 21563 21564 SET SYSTEM HIDDEN ON 21565 SET SYSTEM PERSIST OFF 21566 SET COMMAND LINE EXECUTE WAIT OFF 21567 21568 Enter HELP SYSTEM for details on the effect of these 21569 commands. These settings will be reset to their previous 21570 values after the viewer is invoked. 21571 21572 Although the default viewers will typically work well, you may 21573 prefer to specify the specific application to use. You can 21574 use the SET POSTSCRIPT VIEWER, SET PDF VIEWER, and SET IMAGE 21575 VIEWER commands to use specific applications rather than selecting 21576 system defaults (i.e., "xdg-open" or "open"). These commands can 21577 be added to your dplogf.tex file to make them your personal 21578 defaults. 21579 21580Syntax 1: 21581 PSVIEW 21582 21583 This syntax displays the most recent plot (i.e., the dppl2f.dat file). 21584 21585Syntax 2: 21586 PSVIEW DEVICE 2 21587 21588 This syntax displays the plots in the DEVICE 2 file (i.e., the 21589 dppl1f.dat file). 21590 21591Syntax 3: 21592 PSVIEW <file-name> 21593 21594 This syntax displays the plot or imgage specified by <file-name>. 21595 An appropriate viewer (Postscript, PDF, image) is selected based on 21596 the file name extension. Dataplot does not check for the existence 21597 of the file before invoking the application. 21598 21599Examples: 21600 SET POSTSCRIPT VIEWER evince 21601 PSVIEW 21602 21603 SET POSTSCRIPT VIEWER "C:\Program Files\GHOSTGUM\GSVIEW32.EXE" 21604 PSVIEW 21605 21606 PSVIEW DEVICE 2 21607 21608 PSVIEW PLOTS.PS 21609 PSVIEW PLOTS.PDF 21610 21611 SET IMAGE VIEWER gimp 21612 PSVIEW PLOTS.PNG 21613 21614Note: 21615 By default, the PSVIEW DEVICE 2 command will close the plot file 21616 before invoking the Postscript viewer. This is so that the last plot 21617 in the file is complete. However, this can be problematic if you 21618 want to generate additional plots. Specifically, you need to enter 21619 a DEVICE 2 POSTSCRIPT command to resume generating plots to this file. 21620 However, this new DEVICE 2 command will erase the files that previously 21621 existed in the file. 21622 21623 There are a several possible solutions to this. 21624 21625 You can request that the plot file not be close by entering the command 21626 21627 SET PSVIEW FILE CLOSE OFF 21628 21629 This will suppress closing the file. The disadvantage of this is that 21630 the last plot in the file may not be complete. A warning will be 21631 printed that the last file may not be complete. However, the 21632 advantage is that you can continue generating plots to the current 21633 plot file. 21634 21635 Alternatively, you can do something like 21636 21637 PSVIEW DEVICE 2 21638 SET IPL1NA PLOT_NEW.PS 21639 DEVICE 2 POSTSCRIPT 21640 21641 The SET IPL1NA command allows you to specify the name of the plot 21642 file (this should come before the DEVICE 2 POSTSCRIPT command). The 21643 advantage of this approach is that the last plot will be complete. 21644 The disadvantage is that you will create multiple plot files. 21645 21646Note: 21647 If a Dataplot command starts with a file name, Dataplot interprets 21648 this as a CALL command. For example, entering 21649 21650 test.dp 21651 21652 is equivalent to entering 21653 21654 call test.dp 21655 21656 Dataplot will now check the extension on the file name. 21657 Specifically if the file has a ".ps", ".PS", ".eps", ".EPS", ".jpg", 21658 ".JPG", ".jpeg", ".JPEG", ".png", ".PNG", ".gif", ".GIF", ".tif", 21659 ".TIF", ".tiff", or ".TIFF" extension, the following command will 21660 be executed 21661 21662 PSVIEW <file-name> 21663 21664 As discussed above, the appropriate viewer (Postscript, PDF or 21665 image) will be selected based on the file extension. 21666 21667Default: 21668 For Linux, the default viewer is "ghostview". For Windows, the 21669 default viewer is "C:\Program Files\GHOSTGUM\GSVIEW\GSVIEW32.EXE". 21670 21671Synonyms: 21672 SHOW is a synonym for PSVIEW 21673 21674Related Commands: 21675 PP = Print the most recent plot. 21676 SET IPL1NA = Specify the name of the plot file for DEVICE 2. 21677 SYSTEM = Invoke an operating system command. 21678 LIST = List the contents of a file. 21679 21680Applications: 21681 Interactive Usage 21682 21683Implementation Date: 21684 2011/09 21685 2016/10: Support for PSVIEW DEVICE 2 21686 2016/10: Support for arbitrary Postscript files 21687 2018/04: Added SHOW as a synonym 21688 2019/12: Support for PDF and image files 21689 21690Program 1: 21691 . Generate a plot and use the "evince" program (Linux) to view the 21692 . Postscript version of the graph. 21693 . 21694 SET POSTSCRIPT VIEWER evince 21695 PLOT X**2 FOR X = 1 1 9 21696 PSVIEW 21697 21698Program 2: 21699 device 2 postscript 21700 . 21701 char X 21702 line blank 21703 y1label Y 21704 x1label X 21705 title automatic 21706 title offset 2 21707 . 21708 plot x for x = 1 1 9 21709 plot x**2 for x = 1 1 9 21710 plot x**3 for x = 1 1 9 21711 . 21712 set psview file close off 21713 psview device 2 21714 . 21715 plot x**4 for x = 1 1 9 21716 21717-----PWD------------------------------------------------------- 21718 21719PWD 21720 21721Name: 21722 PWD 21723 21724Type: 21725 Support Command 21726 21727Purpose: 21728 This command returns the current working directory. 21729 21730Description: 21731 There are times when it is convenient to be able to retrieve 21732 the current working directory. The PWD command will print 21733 the current working directory. In addition, it will save 21734 the returned directory name in the string CURDIR. This 21735 string can be used to label plots. 21736 21737Syntax: 21738 PWD 21739 21740Examples: 21741 PWD 21742 21743Default: 21744 None 21745 21746Synonyms: 21747 GETCWD 21748 CURRENT DIRECTORY 21749 21750Note: 21751 If the name CURDIR has already been defined for a non-string 21752 (i.e., a parameter or a variable name), then the CURDIR string 21753 will not be created. 21754 21755Note: 21756 The returned working directory name will be truncated at 255 21757 characters (both in the printed feedback and for the CURDIR 21758 string). 21759 21760Note: 21761 The PWD command is implemented using the library function 21762 GETCWD. This is not part of the Fortran standard, so the 21763 PWD command may not be supported on all platforms. It should 21764 be available on Unix/Linux systems. It is also supported 21765 on Windows implementations built with the Intel compiler. 21766 21767Related Commands: 21768 CD = Change the current working directory. 21769 SYSTEM = Enter an operating system command within a 21770 Dataplot session. 21771 21772Applications: 21773 Interactive Usage 21774 21775Implementation Date: 21776 2011/1 21777 21778Program: 21779 PWD 21780 PRINT CURDIR 21781 21782-----PYRAMID------------------------------------------------------- 21783 21784PYRAMID 21785 21786Name: 21787 PYRAMID 21788 21789Type: 21790 Diagrammatic Graphics Command 21791 21792Purpose: 21793 Draws a pyramid. 21794 21795Description: 21796 The 3 pairs of coordinates define the (x,y) values for the 21797 vertices of the triangle that form the front of the pyramid. 21798 21799Syntax: 21800 PYRAMID <x1> <y1> <x2> <y2> <x3> <y3> 21801 where <x1> is a decimal number or parameter in the range 0 to 100 21802 that specifies the x coordinate for the first vertex; 21803 <y1> is a decimal number or parameter in the range 0 to 100 21804 that specifies the y coordinate for the first vertex; 21805 <x2> is a decimal number or parameter in the range 0 to 100 21806 that specifies the x coordinate for the second vertex; 21807 <y2> is a decimal number or parameter in the range 0 to 100 21808 that specifies the y coordinate for the second vertex; 21809 <x3> is a decimal number or parameter in the range 0 to 100 21810 that specifies the x coordinate for the third vertex; 21811 and <y3> is a decimal number or parameter in the range 0 to 100 21812 that specifies the y coordinate for the third vertex; 21813 21814Examples: 21815 PYRAMID 20 20 50 20 35 60 21816 21817Note: 21818 The line style (i.e., solid, dash), color, and thickness are 21819 controlled by the LINE, LINE COLOR, and LINE THICKNESS commands. 21820 The REGION FILL ON command can be used to generate solid filled 21821 pyramids. The REGION PATTERN can be used to do a hatch pattern 21822 fill. Other REGION commands can be used to control how the fill 21823 is done. 21824 21825Note: 21826 If you use a software font, pyramids can be embedded in text (e.g., 21827 the LEGEND or TEXT command) by entering the string PYRA(). 21828 Pyramids can also be used as plot characters (e.g., CHARACTERS 21829 PYRAMID), in which case the attributes are set with the various 21830 CHARACTER commands. 21831 21832Note: 21833 The keywords DATA and RELATIVE were added to the TRIANGLE 21834 command 7/1997. These keywords are independent and can 21835 be used separately or together. For example, 21836 TRIANGLE DATA, TRIANGLE RELATIVE, or TRIANGLE DATA RELATIVE. 21837 The word DATA should come before the word RELATIVE if both 21838 appear. 21839 21840 DATA means that the coordinates are specified in terms of 21841 the data units of the most recent plot rather than Dataplot 21842 0 to 100 screen units. 21843 21844 RELATIVE means that the coordinates of the first point 21845 are drawn in absolute coordinates an all subsequent points 21846 in the figure are relative to that first point. 21847 21848Default: 21849 None 21850 21851Synonyms: 21852 None 21853 21854Related Commands: 21855 POINT = Draws a point. 21856 ARROW = Draws an arrow. 21857 TRIANGLE = Draws a triangle. 21858 BOX = Draws a box. 21859 HEXAGON = Draws a hexagon. 21860 CIRCLE = Draws a circle. 21861 SEMI-CIRCLE = Draws a semi-circle. 21862 ARC = Draws an arc. 21863 ELLIPSE = Draws an ellipse. 21864 OVAL = Draws an oval. 21865 DIAMOND = Draws a diamond. 21866 CUBE = Draws a cube. 21867 DRAW = Draws a line. 21868 MOVE = Moves to a point. 21869 LINES = Sets the line type for figures and plot lines. 21870 LINE THICKNESSES = Sets the line thickness for figures and plot 21871 lines. 21872 LINE COLOR = Sets the line colors for figures and plot lines. 21873 CROSS-HAIR = Activates and reads the cross-hair. 21874 TEXT = Writes a text string. 21875 REGION FILL = Specifies whether a figure is filled or not. 21876 REGION PATTERN = Sets the type of fill pattern to use for 21877 figures. 21878 21879Applications: 21880 Presentation Graphics 21881 21882Implementation Date: 21883 Pre-1987 21884 21885Program: 21886 PYRAMID 10 10 20 10 15 20 21887 PYRAMID 60 10 80 3 65 30 21888 . 21889 THICKNESS 0.5 21890 PYRAMID 10 30 20 21 13 43 21891 THICKNESS 0.2 21892 . 21893 LINE DASH 21894 PYRAMID 10 50 20 50 15 60 21895 LINE SOLID 21896 . 21897 LINE COLOR G50 21898 THICKNESS 0.5 21899 PYRAMID 10 80 20 75 12 93 21900 THICKNESS 0.2 21901 LINE COLOR BLACK 21902 . 21903 REGION FILL ON 21904 PYRAMID 30 30 40 25 33 44 21905 REGION FILL COLOR G50 21906 PYRAMID 50 50 70 45 55 63 21907 REGION FILL COLOR BLACK 21908 REGION FILL ONTS 21909 PYRAMID 40 70 55 62 48 84 21910 REGION FILL ONF 21911 REGION PATTERN D1D2 21912 PYRAMID 85 10 95 3 88 19 21913 REGION PATTERN BLANK 21914 . 21915 FONT SIMPLEX; HEIGHT 6 21916 MOVE 40 85 21917 TEXT PYRA() DRAW A PYRAMID WITH THE TEXT COMMAND 21918 21919-----PYTHON MEAN (LET)---------------------------------- 21920 21921PYTHON MEAN 21922 21923Name: 21924 PYTHON MEAN (LET) 21925 21926Type: 21927 Let Subcommand 21928 21929Purpose: 21930 Compute the mean for a variable using Python. 21931 21932Description: 21933 This command is primarily a proof of concept command as the mean 21934 of a variable can be computed using the MEAN command. 21935 21936 This command works as follows: 21937 21938 1. It is assumed that Python and any needed Python packages 21939 (e.g., numpy) are already installed on the local platform. 21940 This specific command does not require any additional Python 21941 packages. 21942 21943 2. The Python script, mean.py, that computes the mean is stored in 21944 the "scripts" subdirectory of the Dataplot auxiliary files. 21945 21946 The default Linux/Unix location is "/usr/local/lib/dataplot" and 21947 the default Windows location is 21948 "C:\Program Files (x86)\NIST\DATAPLOT". However, the location on 21949 your local platform may vary. 21950 21951 3. The values for the variable for which the mean is to be computed 21952 are written to the file "dpst1f.dat" in the current directory. 21953 21954 4. The following command is executed 21955 21956 SYSTEM python <path>/script/mean.py > dpst2f.dat 21957 21958 with <path> denoting the the location of the Dataplot auxiliary 21959 files. The file "dpst2f.dat" will contain the computed mean 21960 value. 21961 21962 5. The computed mean will be saved in a user specified Dataplot 21963 parameter. 21964 21965 This initial PYTHON command was designed to create the basic structure 21966 for incorporating Python-based commands into Dataplot. It is 21967 anticipated that additional non-trivial Python-based commands will be 21968 added in subsequent Dataplot releases. 21969 21970Syntax: 21971 LET <par> = PYTHON MEAN <y> <SUBSET/EXCEPT/FOR qualification> 21972 where <y> is the response variable; 21973 <par> is a parameter where the computed mean is stored; 21974 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 21975 21976Examples: 21977 LET A = PYTHON MEAN Y1 21978 LET A = PYTHON MEAN Y1 SUBSET TAG > 2 21979 21980Note: 21981 If Python is not in your search path, you can use the command 21982 21983 SET PYTHON PATH <path> 21984 21985 to specify the directory where the Python executable is located. For 21986 example 21987 21988 SET PYTHON PATH /usr/local/bin 21989 21990Note: 21991 Both Python 2 and Python 3 are currently actively supported. If both 21992 Python 2 and Python 3 are installed on your local platform, you can 21993 use the following command to specify which version to run 21994 21995 SET PYTHON VERSION <2/3/DEFAULT> 21996 21997 Specifying "2" will run "python2", specifying "3" will run "python3" 21998 and specifying "DEFAULT" will run "python" (i.e., the default on your 21999 local platform). 22000 22001 The Dataplot written scripts will be written to the Python 3 22002 standard. However, if you only have Python 2 on your system, you can 22003 modify the "mean.py" script to be compatible with Python 2 (for this 22004 command, only the "print" commands should need to be changed). We do 22005 not anticipate providing both Python 2 and Python 3 versions of the 22006 scripts. 22007 22008Note: 22009 You can use the CAPTURE SCRIPT command to create Python scripts from 22010 within a Dataplot macro. You can then use the SYSTEM command to 22011 execute that script. That is, something like 22012 22013 CAPTURE SCRIPT file.py 22014 ... Python commands here ... 22015 END OF CAPTURE 22016 SYSTEM file.py 22017 22018Default: 22019 None 22020 22021Synonyms: 22022 None 22023 22024Related Commands: 22025 MEAN = Compute the mean of a variable. 22026 SYSTEM = Execute an operating system command. 22027 22028Applications: 22029 Data Analysis 22030 22031Implementation Date: 22032 2019/03 22033 22034Program: 22035 SKIP 25 22036 READ ZARR13.DAT Y 22037 LET YMEAN = PYTHON MEAN Y 22038 22039-----PYTHON------------------------------------------------------- 22040 22041PYTHON 22042 22043Name: 22044 PYTHON 22045 22046Type: 22047 Support Command 22048 22049Purpose: 22050 Run a Python script within a Dataplot session. 22051 22052Description: 22053 It may on occassion be useful to run a Python script within a Dataplot 22054 session. Dataplot assumes that Python is already installed on your 22055 local system. Also, any Python packages that your script needs should 22056 already be installed. Dataplot does not initiate an install of Python 22057 or of any Python packages if it not already installed. 22058 22059 If Python is not installed on your default path, you can specify it 22060 using the SET PYTHON PATH command. For example, the following is 22061 for the Anaconda installation of Python 3 under Windows (where 22062 Anaconda is installed for the single user heckert) 22063 22064 set python path c:\Users\heckert\AppData\Local\Continum\anaconda3\ 22065 22066 There are several different Python distributions. The appropriate 22067 Python path will depend on the specific distribution you used to 22068 install Python and whether you choose to install it for a single 22069 user or for all users. 22070 22071 If you need to specify that you want to run version 3 of Python, you 22072 can enter 22073 22074 set python version 3 22075 22076 If you need to specify that you want to run version 2 of Python, you 22077 can enter 22078 22079 set python version 2 22080 22081 On Windows platforms, the PYTHON command is equivalent to entering 22082 22083 set system persist off 22084 set system hidden on 22085 system <python-path>\python.exe <python-script-file> <arg-list> 22086 22087 Note that if either the Python path or the <python-script-file> 22088 contains spaces (and so will be quoted), then "set system hidden" will 22089 be set to "off". 22090 22091 On Linux platforms, the PYTHON command is equivalent to entering 22092 22093 system <python-path>/python <python-script-file> <arg-list> 22094 22095Syntax: 22096 PYTHON <script-file> <arg-list> 22097 where <script-file> contains the name of a file containing a Python 22098 script; 22099 and where <arg-list> is an optional list of arguments to the script. 22100 22101Examples: 22102 PYTHON plot.py 22103 22104Note: 22105 This command is host dependent. It has been tested on Windows 22106 and Linux systems. Note that the SYSTEM command must be activated 22107 for this command to work. 22108 22109Note: 22110 Dataplot does no error checking on the specified script file. It 22111 is passed as is to Python command. 22112 22113Note: 22114 The CAPTURE SCRIPT command can be used to generate the Python script 22115 within a Dataplot macro. This is demonstrated in the Program 22116 example below. 22117 22118Note: 22119 The name of the script file is case sensitive on Linux and MacOS 22120 systems. It is not case sensitive on Windows systems. 22121 22122 If Dataplot does not find the Python script file, it will search for 22123 it in the "scripts" sub-directory in the Dataplot auxiliary 22124 directory. Currently (2019/12), there are no Python scripts in that 22125 directory, although this may change in future releases of Dataplot. 22126 22127Default: 22128 None 22129 22130Synonyms: 22131 None 22132 22133Related Commands: 22134 SYSTEM = Issue an operating system command within Dataplot. 22135 RSCRIPT = Run a R script within Dataplot. 22136 CAPTURE SCRIPT = Create a script file within Dataplot. 22137 22138Applications: 22139 Run Python scripts 22140 22141Implementation Date: 22142 2019/12 22143 22144Program 1: 22145 . Step 1: Create the Python script using "capture script" 22146 . 22147 . This example is just meant to demostrate the 22148 . mechanics of calling Python scripts. 22149 . 22150 rm output.txt 22151 rm test.py 22152 . 22153 capture script test.py 22154 # Step 1: Open the output file 22155 # 22156 fout = open('output.txt', 'w') 22157 # 22158 # Step 2: Now write some output lines 22159 # 22160 line1 = "Line 1\n" 22161 line2 = "Line 2\n" 22162 line3 = "Line 3\n" 22163 fout.write(line1) 22164 fout.write(line2) 22165 fout.write(line3) 22166 # 22167 # Step 3: Now close the file 22168 # 22169 fout.close() 22170 # 22171 end of capture 22172 . 22173 list test.py 22174 pause 22175 . 22176 . Step 2: Determine if running on Windows or Linux and set 22177 . Python path and version 22178 . 22179 let computer = 1 22180 probe iopsy1 22181 if probeval = 1 22182 let computer = 2 22183 end of if 22184 . 22185 if computer = 1 22186 . Following should be modified for your system 22187 set python path c:\Users\heckert\AppData\Local\Continum\anaconda3\ 22188 set python version 3 22189 else 22190 . 22191 . On my CentOS Linux box, I need to do the following to invoke 22192 . version 3 of Python 22193 . 22194 . scl enable rh-python36 csh 22195 . 22196 set python version 3 22197 end of if 22198 . 22199 . Step 3: Run the Python script 22200 . 22201 python test.py 22202 . 22203 . Step 4: Display the results 22204 . 22205 list output.txt 22206 22207Program 2: 22208 . Purpose: Use Python script to extract Excel file to a CSV 22209 . file. From this, create a space separeated file with a 22210 . descriptive header for subsequent Dataplot use. Finally, 22211 . generate a Dataplot macro tha will read the space 22212 . delimited file. 22213 . 22214 . This macro demonstrates the use of the PYTHON and 22215 . the WRITE1 and WRITE2 commands. 22216 . extract the Excel file to a CSV file. 22217 . 22218 . Step 0: Define some basic strings and file names 22219 . 22220 probe path 22221 let string ipath = probestr 22222 probe iopsy1 22223 if probeval = 2 22224 let string islash = \ 22225 else 22226 let string islash = / 22227 end of if 22228 let string subdir = data 22229 let ipath = string concatenate ipath subdir 22230 . 22231 let string base = CORONA_VIRUS_COUNTRY_RANKINGS_042920 22232 let base = string concatenate ipath base 22233 let string ext1 = .CSV 22234 let string ext2 = .TXT 22235 let string ext3 = .DP 22236 let string ext4 = .XLSX 22237 let fname1 = string concatenate base ext1 22238 let fname2 = string concatenate base ext2 22239 let fname3 = string concatenate base ext3 22240 let fname4 = string concatenate base ext4 22241 . 22242 . Step 1: Use Python to create the CSV file 22243 . 22244 capture script read_corona.py 22245 # This Python script will read an Excel file and write the in 22246 # contents as a CSV file". This script is specific to the Corona 22247 # virus Excel file, so omit the error checking code. 22248 # 22249 # Step 1: Import needed packages 22250 # 22251 import pandas as pd 22252 from pandas import ExcelWriter 22253 from pandas import ExcelFile 22254 # 22255 # Step 2: Read the Corona virus Excel file file with Pandas 22256 # 22257 df = pd.read_excel("^fname4") 22258 22259 # 22260 # Step 3: Now use Pandas to write the Excel file 22261 df.to_csv("^fname1") 22262 # 22263 end of capture 22264 . 22265 . May need to use SET PYTHON PATH command 22266 . 22267 python read_corona.py 22268 . 22269 . Step 2: Read Original File 22270 . 22271 set convert character categorical 22272 set read delimiter , 22273 set read missing value -9999 22274 . 22275 skip 5 22276 read ^fname1 rowindex fileno country pop popurban medage areakm2 ... 22277 areami2 denstkm2 denstmi2 junk cumcases cumdeath 22278 skip 0 22279 delete rowindex junk 22280 . 22281 let ig = character code string country 22282 let ntemp = size cumdeath 22283 . 22284 . Step 2: Now create new output file 22285 . 22286 . First generate the header 22287 . 22288 write1 ^fname2 "Name: ^fname2" 22289 write1 ^fname2 "Description: Corona virus country rankings" 22290 write1 ^fname2 "Source: xxxx" 22291 write1 ^fname2 "Data: Column 1: Country" 22292 write1 ^fname2 " Column 2: Population (millions)" 22293 write1 ^fname2 " Column 3: Urban Population (millions)" 22294 write1 ^fname2 " Column 4: Median Age" 22295 write1 ^fname2 " Column 5: Area (1000 kilometers**2)" 22296 write1 ^fname2 " Column 6: Area (1000 miles**2)" 22297 write1 ^fname2 " Column 7: Population Density (1000 kilometers**2)" 22298 write1 ^fname2 " Column 8: Population Density (1000 miles**2)" 22299 write1 ^fname2 " Column 9: Cumulative Cases" 22300 write1 ^fname2 " Column 10: Cumulative Deaths" 22301 write1 ^fname2 " " 22302 write1 ^fname2 " " 22303 write1 ^fname2 " " 22304 write1 ^fname2 " " 22305 write1 ^fname2 " " 22306 write1 ^fname2 " " 22307 write1 ^fname2 " " 22308 write1 ^fname2 " " 22309 write1 ^fname2 " " 22310 write1 ^fname2 " " 22311 write1 ^fname2 "COUNTRY POP POPURBAN MEDAGE AREAKM2 AREAMI2 DENSTKM2 DENSTMI2 CUMCASES CUMDEATH" 22312 write1 ^fname2 "--------------------------------------------------------------------------------" 22313 . 22314 . Now write the data 22315 . 22316 set write format F5.0,3F10.1,4F10.0,2F12.0 22317 write1 ^fname2 country pop popurban medage areakm2 ... 22318 areami2 denstkm2 denstmi2 cumcases cumdeath 22319 set write format 22320 . 22321 . Step 3: Now create Dataplot macro to read the new file 22322 . 22323 write2 ^fname3 ". Name: ^fname3" 22324 write2 ^fname3 ". Purpose: Read ^fname2" 22325 write2 ^fname3 "." 22326 write2 ^fname3 "skip 25" 22327 write2 ^fname3 "set read format F5.0,3F10.1,4F10.0,2F12.0" 22328 write2 ^fname3 "read ^fname2 country pop popurban medage areakm2 areami2 denstkm2 denstmi2 cumcases cumdeath" 22329 write2 ^fname3 "skip 0" 22330 write2 ^fname3 "set read format" 22331 write2 ^fname3 "." 22332 loop for k = 1 1 ntemp 22333 write2 ^fname3 "let string cntry^k = ^ig^k" 22334 end of loop 22335 write2 ^fname3 "." 22336 . 22337 22338------------------------------------------------------------- 22339 22340 22341 22342 22343 22344 22345 22346 22347 22348 22349 22350 22351 22352 22353 22354 22355 22356 22357 22358 22359 22360 22361 22362 22363 22364 22365 22366 22367 22368 22369 22370 22371 22372 22373 22374 22375 22376 22377 22378 22379 22380 22381 22382 22383 22384 22385 22386 22387 22388 22389 22390 22391 22392 22393 22394 22395 22396 22397 22398 22399 22400------------------------- *Q* ZZZZZ-------------------- 22401 22402-----Q QUANTILE RANGE (LET)------------------------------- 22403 22404Q QUANTILE RANGE 22405 22406Name: 22407 Q QUANTILE RANGE (LET) 22408 22409Type: 22410 Let Subcommand 22411 22412Purpose: 22413 Compute the q quantile range for a variable. 22414 22415Description: 22416 The q quantile range is: 22417 22418 QQ = X(1-q) - X(q) 22419 22420 where q defines a quantile between 0 and 0.5 and X(q) 22421 denotes the q-th quantile of the data. 22422 22423 For example, if q = 0.20, then the q quantile range is 22424 the difference between the 80th and 20th quantiles of 22425 the data. The interquartile range is a special case of 22426 the q quantile range with q = 0.25. 22427 22428 The q quantile range is used as a robust measure of scale. 22429 22430 You can also compute the difference of the q quantile range 22431 for two response variables. 22432 22433Syntax 1: 22434 LET <par> = Q QUANTILE RANGE <y> 22435 <SUBSET/EXCEPT/FOR qualification> 22436 where <y> is the response variable; 22437 <par> is a parameter where the computed q quantile range 22438 is stored; 22439 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 22440 22441Examples: 22442 LET A = Q QUANTILE RANGE Y1 22443 LET A = Q QUANTILE RANGE Y1 SUBSET TAG > 2 22444 LET A = Q QUANTILE RANGE Y1 Y2 22445 22446Note: 22447 The desired quantile is specified with the following 22448 command 22449 22450 LET QUANT = <value> 22451 22452 If <value> is between 1 and 100, it is interpreted as as 22453 percentile (i.e., the quantile will be determined by 22454 dividing by 100). If <value> is between 0.5 and 1, 22455 then 1 - <value> will be used. If <value> is less than 22456 or equal to 0 or greater than or equal to 100, an error 22457 message will be printed. 22458 22459Note: 22460 Dataplot statistics can be used in a number of commands. For 22461 details, enter 22462 22463 HELP STATISTICS 22464 22465Default: 22466 None 22467 22468Synonyms: 22469 QQUANTILE RANGE is a synonym for Q QUANTILE RANGE. 22470 22471Related Commands: 22472 INTERQUARTILE RANGE = Compute the interquartile range of a 22473 variable. 22474 RANGE = Compute the range of a variable. 22475 QUANTILE = Compute a specified quantile of a 22476 variable. 22477 STANDARD DEVIATION = Compute the standard deviation of a 22478 variable. 22479 AVERAGE ABSOLUTE DEVIATION = Compute the average absolute 22480 deviation of a variable. 22481 MEDIAN ABSOLUTE DEVIATION = Compute the median absolute 22482 deviation of a variable. 22483 22484Reference: 22485 Rand Wilcox (1997), "Introduction to Robust Estimations and 22486 Hypothesis Testing," Academic Press, pp. 24-25. 22487 22488Applications: 22489 Robust Data Analysis 22490 22491Implementation Date: 22492 2012/9 22493 22494Program 1: 22495 LET Y1 = LOGISTIC RANDOM NUMBERS FOR I = 1 1 1000 22496 LET Y2 = DOUBLE EXPONENTIAL RANDOM NUMBERS FOR I = 1 1 1000 22497 LET Y3 = NORMAL RANDOM NUMBERS FOR I = 1 1 1000 22498 LET QUANT = 0.10 22499 LET A1 = Q QUANTILE RANGE Y1 22500 LET A2 = Q QUANTILE RANGE Y2 22501 LET A3 = Q QUANTILE RANGE Y3 22502 PRINT A1 A2 A3 22503 22504Program 2: 22505 SKIP 25 22506 READ GEAR.DAT DIAMETER BATCH 22507 TITLE AUTOMATIC 22508 TITLE CASE ASIS 22509 XLIMITS 1 10 22510 MAJOR XTIC MARK NUMBER 10 22511 MINOR XTIC MARK NUMBER 0 22512 XTIC OFFSET 1 1 22513 X1LABEL BATCH 22514 X2LABEL Q = 0.20 22515 Y1LABEL Q QUANTILE RANGE OF DIAMETER 22516 CHARACTER CIRCLE 22517 CHARACTER FILL ON 22518 CHARACTER HW 2 1.5 22519 LINE BLANK 22520 LET QUANT = 0.20 22521 Q QUANTILE RANGE PLOT DIAMETER BATCH 22522 22523-----QBICDF (LET)-------------------------------- 22524 22525QBICDF 22526 22527Name: 22528 QBICDF (LET) 22529 22530Type: 22531 Library Function 22532 22533Purpose: 22534 Compute the quasi-binomial type I cumulative distribution 22535 function. 22536 22537Description: 22538 The quasi-binomial type I distribution has the 22539 following probability mass function: 22540 22541 p(x;p,phi,m)= 22542 (m x)*p*(p+x*phi)**(x-1)*(1-p-x*phi)**(m-x) 22543 x = 0, 1, 2, 3, ,..., m; 22544 0 <= p <= 1; -p/m < phi < (1-p)/m 22545 22546 with p, phi, and m denoting the shape parameters and 22547 (a b} denoting the binomial coefficient: 22548 22549 (a b) = a!/(b!(a-b)!} 22550 22551 The cumulative distribution function is computed using 22552 the following recurrence relation given by Consul and 22553 Famoye: 22554 22555 p(x+1) = {(m-x)*(p+x*phi)/((x+1)*(1-p-x*phi))}* 22556 (1 + phi/(p+x*phi))**x* 22557 (1 - phi/(1-p-x*phi))**(m-x-1)*p(x) 22558 22559Syntax: 22560 LET <y> = QBICDF(<x>,<p>,<theta>,<beta>) 22561 <SUBSET/EXCEPT/FOR qualification> 22562 where <x> is a positive integer variable, number, or parameter; 22563 <p> is a number, parameter, or variable in the range 22564 (0,1) that specifies the first shape parameter; 22565 <phi> is a number, parameter, or variable that 22566 specifies the second shape parameter; 22567 <m> is a number, parameter, or variable that 22568 specifies the third shape parameter; 22569 <y> is a variable or a parameter (depending on what <x> 22570 is) where the computed quasi binomial type I 22571 cdf value is stored; 22572 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 22573 22574Examples: 22575 LET A = QBICDF(10,0.5,0.005,20) 22576 LET Y = QBICDF(X,0.7,0.01,20) 22577 PLOT QBICDF(X,0.3,0.005,20) FOR X = 0 1 20 22578 22579Note: 22580 Library functions are distinguished from let subcommands 22581 in the following ways. 22582 1) Functions enclose the input value in parenthesis. Let 22583 subcommands use spaces. 22584 2) Functions can accept (and return) either parameters 22585 (i.e., single values) or variables (i.e., an array of 22586 values) while let subcommands are specific in which they 22587 accept as input and what they return as output. 22588 3) Functions can accept expressions while let subcommands 22589 do not. For example, the following is legal: 22590 LET Y2 = ABS(Y1-INT(Y1)) 22591 For let subcommands, you typically have to do something 22592 like the following: 22593 LET YTEMP = Y**2 + 8 22594 LET A = SUM YTEMP 22595 22596Default: 22597 None 22598 22599Synonyms: 22600 None 22601 22602Related Commands: 22603 QBIPDF = Compute the quasi-binomial type I 22604 probability mass function. 22605 QBIPPF = Compute the quasi-binomial type I 22606 percent point function. 22607 BINPDF = Compute the binomial probability 22608 mass function. 22609 BBNPDF = Compute the beta-binomial 22610 probability mass function. 22611 NBPDF = Compute the negative binomial 22612 probability mass function. 22613 22614Reference: 22615 Consul and Famoye (2006), "Lagrangian Probability 22616 Distribution", Birkhauser, pp. 70-80. 22617 22618Applications: 22619 Distributional Modeling 22620 22621Implementation Date: 22622 2006/8 22623 22624Program: 22625 title size 3 22626 tic label size 3 22627 label size 3 22628 legend size 3 22629 height 3 22630 x1label displacement 12 22631 y1label displacement 15 22632 . 22633 multiplot corner coordinates 0 0 100 95 22634 multiplot scale factor 2 22635 label case asis 22636 title case asis 22637 case asis 22638 tic offset units screen 22639 tic offset 3 3 22640 title displacement 2 22641 y1label Probability 22642 x1label X 22643 . 22644 ylimits 0 1 22645 major ytic mark number 6 22646 minor ytic mark number 3 22647 xlimits 0 20 22648 line blank 22649 spike on 22650 . 22651 multiplot 2 2 22652 . 22653 title P = 0.3, Phi = 0.01, M = 20 22654 plot qbicdf(x,0.3,0.01,20) for x = 1 1 20 22655 . 22656 title P = 0.3, Phi = -0.01, M = 20 22657 let phi = -0.01 22658 plot qbicdf(x,0.3,phi,20) for x = 1 1 20 22659 . 22660 title P = 0.7, Phi = 0.01, M = 20 22661 plot qbicdf(x,0.7,0.01,20) for x = 1 1 20 22662 . 22663 title P = 0.7, Phi = -0.01, M = 20 22664 let phi = -0.01 22665 plot qbicdf(x,0.7,phi,20) for x = 1 1 20 22666 . 22667 end of multiplot 22668 . 22669 justification center 22670 move 50 97 22671 text Cumulative Distribution Functions for Quasi Binomial Type I 22672 22673-----QBIPDF (LET)-------------------------------- 22674 22675QBIPDF 22676 22677Name: 22678 QBIPDF (LET) 22679 22680Type: 22681 Library Function 22682 22683Purpose: 22684 Compute the quasi-binomial type I probability mass 22685 function. 22686 22687Description: 22688 The quasi-binomial type I distribution has the 22689 following probability mass function: 22690 22691 p(x;p,phi,m)= 22692 (m x)*p*(p+x*phi)**(x-1)*(1-p-x*phi)**(m-x) 22693 x = 0, 1, 2, 3, ,..., m; 22694 0 <= p <= 1; -p/m < phi < (1-p)/m 22695 22696 with p, phi, and m denoting the shape parameters and 22697 (a b} denoting the binomial coefficient: 22698 22699 (a b) = a!/(b!(a-b)!} 22700 22701 The quasi-binomial type I distribution is used to model 22702 Bernoulli trials. The parameter p denotes the initial 22703 probability of success, m denotes the number of Bernoulli 22704 trials, and phi denotes how the probability of success 22705 increases or decreases with the number of successes. 22706 Specificially, when phi = 0, the quasi-binomial type I 22707 distribution reduces to the binomial distribution. When 22708 phi <> 0, the probability of success in the xth trial 22709 becomes 22710 22711 p + x*phi 22712 22713Syntax: 22714 LET <y> = QBIPDF(<x>,<p>,<phi>,<m>) 22715 <SUBSET/EXCEPT/FOR qualification> 22716 where <x> is a positive integer variable, number, or parameter; 22717 <p> is a number, parameter, or variable in the range 22718 (0,1) that specifies the first shape parameter; 22719 <phi> is a number, parameter, or variable that 22720 specifies the second shape parameter; 22721 <m> is a number, parameter, or variable that 22722 specifies the third shape parameter; 22723 <y> is a variable or a parameter (depending on what <x> 22724 is) where the computed quasi binomial type I 22725 pdf value is stored; 22726 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 22727 22728Examples: 22729 LET A = QBIPDF(10,0.5,0.005,20) 22730 LET Y = QBIPDF(X,0.7,0.01,20) 22731 PLOT QBIPDF(X,0.3,0.005,20) FOR X = 0 1 20 22732 22733Note: 22734 For a number of commands utilizing the quasi-binomial type I 22735 distribution, it is convenient to bin the data. There are 22736 two basic ways of binning the data. 22737 22738 1) For some commands (histograms, maximum likelihood 22739 estimation), bins with equal size widths are 22740 required. This can be accomplished with the 22741 following commands: 22742 22743 LET AMIN = MINIMUM Y 22744 LET AMAX = MAXIMUM Y 22745 LET AMIN2 = AMIN - 0.5 22746 LET AMAX2 = AMAX + 0.5 22747 CLASS MINIMUM AMIN2 22748 CLASS MAXIMUM AMAX2 22749 CLASS WIDTH 1 22750 LET Y2 X2 = BINNED 22751 22752 2) For some commands, unequal width bins may be 22753 helpful. In particular, for the chi-square goodness 22754 of fit, it is typically recommended that the minimum 22755 class frequency be at least 5. In this case, it may 22756 be helpful to combine small frequencies in the tails. 22757 Unequal class width bins can be created with the 22758 commands 22759 22760 LET MINSIZE = <value> 22761 LET Y3 XLOW XHIGH = INTEGER FREQUENCY TABLE Y 22762 22763 If you already have equal width bins data, you can 22764 use the commands 22765 22766 LET MINSIZE = <value> 22767 LET Y3 XLOW XHIGH = COMBINE FREQUENCY TABLE Y2 X2 22768 22769 The MINSIZE parameter defines the minimum class 22770 frequency. The default value is 5. 22771 22772Note: 22773 You can generate quasi-binomial type I random numbers, 22774 probability plots, and chi-square goodness of fit 22775 tests with the following commands: 22776 22777 LET M = VALUE 22778 LET P = <value> 22779 LET PHI = <value> 22780 LET Y = QUASI BINOMIAL TYPE I RANDOM NUMBERS FOR I = 1 1 N 22781 22782 QUASI BINOMIAL TYPE I PROBABILITY PLOT Y 22783 QUASI BINOMIAL TYPE I PROBABILITY PLOT Y2 X2 22784 QUASI BINOMIAL TYPE I PROBABILITY PLOT Y3 XLOW XHIGH 22785 22786 QUASI BINOMIAL TYPE I CHI-SQUARE GOODNESS OF FIT Y 22787 QUASI BINOMIAL TYPE I CHI-SQUARE GOODNESS OF FIT Y2 X2 22788 QUASI BINOMIAL TYPE I CHI-SQUARE .. 22789 GOODNESS OF FIT Y3 XLOW XHIGH 22790 22791 In fitting the quasi-binomial type I distribution to data, 22792 we typically assume that the number of trials, m, is 22793 fixed and known and we then estimate p and phi. 22794 22795 To obtain the maximum likelihood estimates of p and phi, 22796 enter the command 22797 22798 QUASI BINOMIAL TYPE I MAXIMUM LIKELIHOOD Y 22799 QUASI BINOMIAL TYPE I MAXIMUM LIKELIHOOD Y2 X2 22800 22801 The maximum likelihood estimates are the solutions to the 22802 equations (for unbinned data): 22803 22804 SUM[i=1 to N][(m-X(i))/(1 - P - X(i)*PHI] - M*N = 0 22805 22806 SUM[i=1 to N][(X(i)*(X(i) - 1)/(p + X(i)*PHI) - 22807 SUM[i=1 to N][(M - X(i))/(1 - P - X(i)*PHI)] = 0 22808 22809 For binned data, the equations become 22810 22811 SUM[i=1 to k][n(i)*(i-1)*i/(p+i*phi)] - 22812 SUM[i=1 to k][n(i)*(m-1)*i/(1-p-i*phi)] = 0 22813 22814 (n/p) + SUM[i=1 to k][n(i)*(i-1)/(p+i*phi)] - 22815 SUM[i=1 to k][n(i)*(m-1)/(1-p-i*phi)] = 0 22816 22817 with k, n, and n(x) denoting the number of classes, the 22818 total sample size, and the frequency of the xth class, 22819 respectively. 22820 22821 These equations are known to have multiple solutions, 22822 so good starting values are required. By default, we use 22823 the starting values recommended by Consul and Famoye 22824 22825 p = 1 - (f0/n)**(1/m) 22826 phi = (1/(2*(m-2))*(-1 + 22827 SQRT(1 + 4*(m-2)*(-1+xbar/(m*p))/(m-1))) 22828 22829 with f0 denoting the frequency of the class x = 0 and 22830 xbar denoting the sample mean. 22831 22832 Alternatively, you can specify your own starting values 22833 by entering the commands 22834 22835 LET PSTART = <value> 22836 LET PHISTART = <value> 22837 22838 Consul and Famoye give formulas for the Fisher information 22839 matrix (the inverse of the parameter variance-covariance 22840 matrix). 22841 22842 You can generate estimates of p and phi based on the 22843 maximum ppcc value or the minimum chi-square goodness of fit 22844 with the commands 22845 22846 LET P1 = <value> 22847 LET P2 = <value> 22848 LET PHI1 = <value> 22849 LET PHI2 = <value> 22850 QUASI BINOMIAL TYPE I KS PLOT Y 22851 QUASI BINOMIAL TYPE I KS PLOT Y2 X2 22852 QUASI BINOMIAL TYPE I KS PLOT Y3 XLOW XHIGH 22853 QUASI BINOMIAL TYPE I PPCC PLOT Y 22854 QUASI BINOMIAL TYPE I PPCC PLOT Y2 X2 22855 QUASI BINOMIAL TYPE I PPCC PLOT Y3 XLOW XHIGH 22856 22857 The default values of p1 and p2 are 0.05 and 0.95, 22858 respectively. The default values for phi1 and phi2 are 22859 phi1 = -p1/m and phi2 = (1-p1)/m. Due to the discrete nature 22860 of the percent point function for discrete distributions, the 22861 ppcc plot will not be smooth. For that reason, if there is 22862 sufficient sample size the KS PLOT (i.e., the minimum 22863 chi-square value) is typically preferred. However, it may 22864 sometimes be useful to perform one iteration of the PPCC PLOT 22865 to obtain a rough idea of an appropriate neighborhood for the 22866 shape parameters since the minimum chi-square statistic can 22867 generate extremely large values for non-optimal values of the 22868 shape parameters. Also, since the data is integer values, one 22869 of the binned forms is preferred for these commands. 22870 22871Note: 22872 Library functions are distinguished from let subcommands 22873 in the following ways. 22874 1) Functions enclose the input value in parenthesis. Let 22875 subcommands use spaces. 22876 2) Functions can accept (and return) either parameters 22877 (i.e., single values) or variables (i.e., an array of 22878 values) while let subcommands are specific in which they 22879 accept as input and what they return as output. 22880 3) Functions can accept expressions while let subcommands 22881 do not. For example, the following is legal: 22882 LET Y2 = ABS(Y1-INT(Y1)) 22883 For let subcommands, you typically have to do something 22884 like the following: 22885 LET YTEMP = Y**2 + 8 22886 LET A = SUM YTEMP 22887 22888Default: 22889 None 22890 22891Synonyms: 22892 None 22893 22894Related Commands: 22895 QBICDF = Compute the quasi-binomial type I 22896 cumulative distribution function. 22897 QBIPPF = Compute the quasi-binomial type I 22898 percent point function. 22899 BINPDF = Compute the binomial probability 22900 mass function. 22901 BBNPDF = Compute the beta-binomial 22902 probability mass function. 22903 NBPDF = Compute the negative binomial 22904 probability mass function. 22905 INTEGER FREQUENCY TABLE = Generate a frequency table at 22906 integer values with unequal bins. 22907 COMBINE FREQUENCY TABLE = Convert an equal width frequency 22908 table to an unequal width frequency 22909 table. 22910 KS PLOT = Generate a minimum chi-square plot. 22911 PPCC PLOT = Generate a ppcc plot. 22912 PROBABILITY PLOT = Generate a probability plot. 22913 MAXIMUM LIKELIHOOD = Perform maximum likelihood 22914 estimation for a distribution. 22915 22916Reference: 22917 Consul and Famoye (2006), "Lagrangian Probability 22918 Distribution", Birkhauser, pp. 70-80. 22919 22920Applications: 22921 Distributional Modeling 22922 22923Implementation Date: 22924 2006/8 22925 22926Program 1: 22927 title size 3 22928 tic label size 3 22929 label size 3 22930 legend size 3 22931 height 3 22932 x1label displacement 12 22933 y1label displacement 15 22934 . 22935 multiplot corner coordinates 0 0 100 95 22936 multiplot scale factor 2 22937 label case asis 22938 title case asis 22939 case asis 22940 tic offset units screen 22941 tic offset 3 3 22942 title displacement 2 22943 y1label Probability Mass 22944 x1label X 22945 . 22946 ylimits 0 1 22947 major ytic mark number 6 22948 minor ytic mark number 3 22949 xlimits 0 20 22950 line blank 22951 spike on 22952 . 22953 multiplot 2 2 22954 . 22955 title P = 0.3, Phi = 0.01, M = 20 22956 plot qbipdf(x,0.3,0.01,20) for x = 1 1 20 22957 . 22958 title P = 0.3, Phi = -0.01, M = 20 22959 let phi = -0.01 22960 plot qbipdf(x,0.3,phi,20) for x = 1 1 20 22961 . 22962 title P = 0.7, Phi = 0.01, M = 20 22963 plot qbipdf(x,0.7,0.01,20) for x = 1 1 20 22964 . 22965 title P = 0.7, Phi = -0.01, M = 20 22966 let phi = -0.01 22967 plot qbipdf(x,0.7,phi,20) for x = 1 1 20 22968 . 22969 end of multiplot 22970 . 22971 justification center 22972 move 50 97 22973 text Probability Mass Functions for Quasi Binomial Type I 22974 22975Program 2: 22976 let p = 0.7 22977 let phi = 0.01 22978 let m = 20 22979 let psave = p 22980 let phisave = phi 22981 let y = quasi binomial type I rand numb for i = 1 1 500 22982 . 22983 let y3 xlow xhigh = integer frequency table y 22984 class lower -0.5 22985 class width 1 22986 class upper 20.5 22987 let y2 x2 = binned y 22988 . 22989 relative hist y2 x2 22990 limits freeze 22991 pre-erase off 22992 line color blue 22993 plot qbipdf(x,p,phi,m) for x = 0 1 20 22994 limits 22995 pre-erase on 22996 line color black 22997 . 22998 quasi binomial type I mle y 22999 let p = pml 23000 let phi = phiml 23001 . 23002 quasi binomial type I chi-square goodness of fit y3 xlow xhigh 23003 . 23004 char x 23005 line bl 23006 quasi binomial type I probability plot y3 xlow xhigh 23007 . 23008 char bl 23009 line so 23010 let p1 = 0.5 23011 let p2 = 0.9 23012 let a1 = (1 - p1)/m 23013 let a2 = (1 - p2)/m 23014 let phi1 = 0 23015 let phi2 = max(a1,a2) 23016 quasi binomial type I ks plot y3 xlow xhigh 23017 let p = shape1 23018 let phi = shape2 23019 quasi binomial type I chi-square goodness of fit y3 xlow xhigh 23020 23021-----QBIPPF (LET)-------------------------------- 23022 23023QBIPPF 23024 23025Name: 23026 QBIPPF (LET) 23027 23028Type: 23029 Library Function 23030 23031Purpose: 23032 Compute the quasi-binomial type I percent point function. 23033 23034Description: 23035 The quasi-binomial type I distribution has the 23036 following probability mass function: 23037 23038 p(x;p,phi,m)= 23039 (m x)*p*(p+x*phi)**(x-1)*(1-p-x*phi)**(m-x) 23040 x = 0, 1, 2, 3, ,..., m; 23041 0 <= p <= 1; -p/m < phi < (1-p)/m 23042 23043 with p, phi, and m denoting the shape parameters and 23044 (a b} denoting the binomial coefficient: 23045 23046 (a b) = a!/(b!(a-b)!} 23047 23048 The cumulative distribution function is computed using 23049 the following recurrence relation given by Consul and 23050 Famoye: 23051 23052 p(x+1) = {(m-x)*(p+x*phi)/((x+1)*(1-p-x*phi))}* 23053 (1 + phi/(p+x*phi))**x* 23054 (1 - phi/(1-p-x*phi))**(m-x-1)*p(x) 23055 23056 The percent point function is computed by summing the 23057 cumulative distribution function until the appropriate 23058 probability is obtained. 23059 23060Syntax: 23061 LET <y> = QBIPPF(<x>,<p>,<phi>,<m>) 23062 <SUBSET/EXCEPT/FOR qualification> 23063 where <x> is a positive integer variable, number, or parameter 23064 in the interval (0,1); 23065 <p> is a number, parameter, or variable in the range 23066 (0,1) that specifies the first shape parameter; 23067 <phi> is a number, parameter, or variable that 23068 specifies the second shape parameter; 23069 <m> is a number, parameter, or variable that 23070 specifies the third shape parameter; 23071 <y> is a variable or a parameter (depending on what <x> 23072 is) where the computed quasi binomial type I 23073 ppf value is stored; 23074 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 23075 23076Examples: 23077 LET A = QBIPPF(0.95,0.5,0.005,20) 23078 LET Y = QBIPPF(P,0.7,0.01,20) 23079 PLOT QBIPPF(P,0.3,0.005,20) FOR P = 0 0.01 1 23080 23081Note: 23082 Library functions are distinguished from let subcommands 23083 in the following ways. 23084 1) Functions enclose the input value in parenthesis. Let 23085 subcommands use spaces. 23086 2) Functions can accept (and return) either parameters 23087 (i.e., single values) or variables (i.e., an array of 23088 values) while let subcommands are specific in which they 23089 accept as input and what they return as output. 23090 3) Functions can accept expressions while let subcommands 23091 do not. For example, the following is legal: 23092 LET Y2 = ABS(Y1-INT(Y1)) 23093 For let subcommands, you typically have to do something 23094 like the following: 23095 LET YTEMP = Y**2 + 8 23096 LET A = SUM YTEMP 23097 23098Default: 23099 None 23100 23101Synonyms: 23102 None 23103 23104Related Commands: 23105 QBICDF = Compute the quasi-binomial type I 23106 cumulative distribution function. 23107 QBIPDF = Compute the quasi-binomial type I 23108 probability mass function. 23109 BINPDF = Compute the binomial probability 23110 mass function. 23111 BBNPDF = Compute the beta-binomial 23112 probability mass function. 23113 NBPDF = Compute the negative binomial 23114 probability mass function. 23115 23116Reference: 23117 Consul and Famoye (2006), "Lagrangian Probability 23118 Distribution", Birkhauser, pp. 70-80. 23119 23120Applications: 23121 Distributional Modeling 23122 23123Implementation Date: 23124 2006/8 23125 23126Program: 23127 title size 3 23128 tic label size 3 23129 label size 3 23130 legend size 3 23131 height 3 23132 x1label displacement 12 23133 y1label displacement 15 23134 . 23135 multiplot corner coordinates 0 0 100 95 23136 multiplot scale factor 2 23137 label case asis 23138 title case asis 23139 case asis 23140 tic offset units screen 23141 tic offset 3 3 23142 title displacement 2 23143 x1label Probability 23144 y1label X 23145 . 23146 xlimits 0 1 23147 major xtic mark number 6 23148 minor xtic mark number 3 23149 . 23150 multiplot 2 2 23151 . 23152 title P = 0.3, Phi = 0.01, M = 20 23153 plot qbippf(x,0.3,0.01,20) for x = 0 0.01 1 23154 . 23155 title P = 0.3, Phi = -0.01, M = 20 23156 let phi = -0.01 23157 plot qbippf(x,0.3,phi,20) for x = 0 0.01 1 23158 . 23159 title P = 0.7, Phi = 0.01, M = 20 23160 plot qbippf(x,0.7,0.01,20) for x = 0 0.01 1 23161 . 23162 title P = 0.7, Phi = -0.01, M = 20 23163 let phi = -0.01 23164 plot qbippf(x,0.7,phi,20) for x = 0 0.01 1 23165 . 23166 end of multiplot 23167 . 23168 justification center 23169 move 50 97 23170 text Percent Point Functions for Quasi Binomial Type I 23171 23172-----QMS------------------------------------------------------- 23173 23174QMS 23175 23176Name: 23177 QMS 23178 23179Type: 23180 Output Device Command 23181 23182Purpose: 23183 Direct graphical output to a QMS laser printer using the QUIC 23184 protocol. 23185 23186Syntax 1: 23187 QMS 23188 23189 This form directs the QMS output to the terminal screen. 23190 23191Syntax 2: 23192 DEVICE <1/2/3> QMS 23193 23194 This form designates one of DATAPLOT's 3 devices (it will 23195 typically be device 2) to be a QMS device. 23196 23197Examples: 23198 QMS 23199 DEVICE 2 QMS 23200 DEVICE 3 QMS 23201 23202Note: 23203 QMS fonts (for hardware generated characters) can be specified 23204 with the following command: 23205 SET QMS FONT <font id> 23206 where <font id> is one of the following: 23207 10 - EDP font 23208 104 - Standard Roman Medium 23209 124 - Standard Roman Bold 23210 144 - Standard Roman Italic 23211 16 - Simplex Roman 23212 204 - Apollo Medium 23213 328 - Complex Roman Bold 23214 404 - Q-Typewriter 23215 444 - Q-Typewriter Italic 23216 532 - Union 23217 521 - Tektronix small 23218 522 - Tektronix medium 23219 523 - Tektronix large 23220 524 - Tektronix largest 23221 904 - Q-Gothic 23222 924 - Q-Gothic Italic 23223 536 - Q-Greek 23224 517 - Q-Greek 23225 664 - Special Math 23226 Fonts 10, 104, 124, 144, 16, 204, 328, 404, and 444 are supported 23227 on all QMS printers using QUIC. The others are downloadable fonts 23228 that may or may not be available on a given QMS. Additional 23229 information on QMS fonts can be found in the QMS Programmer's 23230 Manual for Quic. In addition the following SET commands can be 23231 used to specify the margins and resolution of the particular QMS 23232 printer (these should normally not be required): 23233 SET QMS PPI <number> sets the resolution (in points per inch). 23234 The default is 300. 23235 SET QMS [LANDSCAPE/PORTRAIT] LEFT MARGIN sets the left 23236 margin (in dots). 23237 SET QMS [LANDSCAPE/PORTRAIT] RIGHT MARGIN sets the right 23238 margin (in dots). 23239 SET QMS [LANDSCAPE/PORTRAIT] BOTTOM MARGIN sets the bottom 23240 margin (in dots). 23241 SET QMS [LANDSCAPE/PORTRAIT] TOP MARGIN sets the top 23242 margin (in dots). 23243 23244Default: 23245 Off 23246 23247Synonyms: 23248 QUIC 23249DEVICE NOTES 23250 1) HARDWARE TEXT - QMS provides numerous hardware fonts. QMS fonts 23251 are fixed size and orientation fonts. Several are typeset 23252 quality fonts. 23253 2) COLOR - This device does not support color or gray scale. 23254 3) HARDWARE FILL - All area fills in software (although QMS 23255 provides a hardware fill, it is not reliable). 23256 4) DASH PATTERNS - Each dash specification generates a different 23257 type of dash pattern. 23258 5) LINE WIDTH - The QMS performs line width in hardware. 23259 6) GRAPHICS INPUT - The CROSS-HAIR command is ignored for this 23260 device. 23261 23262Related Commands: 23263 POSTSCRIPT = Direct graphical output to a Postscript 23264 device. 23265 CALCOMP = Direct graphical output to a Calcomp device. 23266 HPGL = Direct graphical output to an HPGL device. 23267 TEKTRONIX = Direct graphical output to a Tektronix device. 23268 X11 = Direct graphical output to an X11 device. 23269 DEVICE = Specify certain actions for the graphics 23270 output. 23271 SET QMS FONT = Specify the font to use on the QMS device. 23272 SET QMS PPI = Set the resolution of the QMS device. 23273 SET QMS ... MARGIN = Set the margin for the QMS device. 23274 23275Applications: 23276 XX 23277 23278Implementation Date: 23279 89/2 23280 23281Program: 23282 XX 23283 23284-----QN SCALE (LET)------------------------------- 23285 23286QN SCALE 23287 23288Name: 23289 QN SCALE (LET) 23290 23291Type: 23292 Let Subcommand 23293 23294Purpose: 23295 Compute the Qn scale estimate for a variable. 23296 23297Description: 23298 Mosteller and Tukey (see Reference section below) define 23299 two types of robustness: 23300 23301 1) resistance means that changing a small part, even by a 23302 large amount, of the data does not cause a large change 23303 in the estimate 23304 23305 2) robustness of efficiency means that the statistic has 23306 high efficiency in a variety of situations rather than 23307 in any one situation. Efficiency means that the estimate 23308 is close to optimal estimate given that we know what 23309 distribution that the data comes from. A useful measure 23310 of efficiency is: 23311 23312 Efficiency = (lowest variance feasible)/ 23313 (actual variance) 23314 23315 Many statistics have one of these properties. However, 23316 it can be difficult to find statistics that are both 23317 resistant and have robustness of efficiency. 23318 23319 The most common estimate of scale, the standard deviation, 23320 is the most efficient estimate of scale if the data come from 23321 a normal distribution. However, the standard deviation is 23322 not robust in the sense that changing even one value can 23323 dramatically change the computed value of the standard deviation 23324 (i.e., poor resistance). In addition, it does not have 23325 robustness of efficiency for non-normal data. 23326 23327 The median absolute deviation (MAD) and interquartile range are 23328 the two most commonly used robust alternatives to the standard 23329 deviation. The MAD in particular is a very robust scale 23330 estimator. However, the MAD has the following limitations: 23331 23332 1) It does not have particularly high efficiency for 23333 data that is in fact normal (37%). In comparison, the 23334 median has 64% efficiency for normal data. 23335 23336 2) The MAD statistic also has an implicit assumption of 23337 symmetry. That is, it measures the distance from a 23338 measure of central location (the median). 23339 23340 Rousseeuw and Croux proposed the Qn estimate of scale as an 23341 alternative to the MAD. It shares desirable robustness 23342 properties with MAD (50% breakdown point, bounded influence 23343 function). In addition, it has significantly better normal 23344 efficiency (82%) and it does not depend on symmetry. 23345 23346 The Qn scale estimate is motivated by the Hodges-Lehmann 23347 estimate of location: 23348 23349 HL = MEDIAN{(x(i) + x(j))/2; i < j} 23350 23351 An analogous scale estimate can be obtained by replacing 23352 pairwise averages with pairwised distances: 23353 23354 MEDIAN{|x(i) - x(j)|; i < j} 23355 23356 This estimate has high efficiency for normal data (86%), 23357 but a breakdown point of only 29%. Rousseeuw and Croux 23358 proposed the following variation of this statistic: 23359 23360 Qn = d{|x(i) - x(j)|; i < j}(k) 23361 23362 where d is a constant factor and k = (h choose 2) which is 23363 approximately (n choose 2)/4. The value of h is [n/2]+1 23364 (i.e., roughly half the number of obserations). In words, 23365 we take kth order statistic of the (n choose 2) interpoint 23366 distances. The value of d is choosen to make Qn a 23367 consistent estimator of scale. We use the value 2.2219 23368 since this is the value that makes Qn a consistent estimator 23369 for normal data. 23370 23371 The Rousseeuw and Croux article (see the Reference section 23372 below) discusses the properties of the Qn estimate in 23373 detail. 23374 23375Syntax: 23376 LET <par> = QN SCALE <y> <SUBSET/EXCEPT/FOR qualification> 23377 where <y> is the response variable; 23378 <par> is a parameter where the computed Qn estimate is 23379 stored; 23380 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 23381 23382Examples: 23383 LET A = QN SCALE Y1 23384 LET A = QN SCALE Y1 SUBSET TAG > 2 23385 23386Note: 23387 Dataplot uses code provided by Rousseeuw and Croux to compute 23388 the Qn estimate. This algorithm uses an efficient computational 23389 method for computing Qn. 23390 23391Note: 23392 The Rousseeuw and Croux article also proposes the Sn scale 23393 estimate. The article discusses the properties of both 23394 estimators in detail. 23395 23396Note: 23397 In addition, the Qn statistic is supported for the following 23398 plots and commands 23399 23400 QN SCALE PLOT Y X 23401 CROSS TABULATE QN SCALE PLOT Y X1 X2 23402 BOOTSTRAP QN SCALE PLOT Y 23403 JACKNIFE QN SCALE PLOT Y 23404 DEX QN SCALE PLOT Y X1 ... XK 23405 QN SCALE BLOCK PLOT Y X1 ... XK 23406 QN SCALE INFLUENCE CURVE Y 23407 QN SCALE INTERACTION PLOT Y X1 X2 23408 23409 TABULATE QN SCALE Y X 23410 CROSS TABULATE SN Y X1 X2 23411 LET Z = CROSS TABULATE QN SCALE Y X1 X2 23412 LET Y = MATRIX COLUMN QN SCALE M 23413 LET Y = MATRIX ROW QN SCALE M 23414 23415 23416Default: 23417 None 23418 23419Synonyms: 23420 None 23421 23422Related Commands: 23423 SN SCALE = Compute the Sn scale estimate of a 23424 variable. 23425 MEDIAN ABSOLUTE DEVIATION = Compute the median absolute 23426 deviation of a variable. 23427 INTERQUARTILE RANGE = Compute the interquartile range of 23428 a variable. 23429 STANDARD DEVIATION = Compute the standard deviation of a 23430 variable. 23431 DIFFERENCE OF SN = Compute the difference of the Sn 23432 scale estimates between two variables. 23433 STATISTIC PLOT = Generate a statistic versus subset 23434 plot. 23435 CROSS TABULATE PLOT = Generate a statistic versus subset 23436 plot (two subset variables). 23437 BOOTSTRAP PLOT = Generate a bootstrap plot for a 23438 statistic. 23439 23440Reference: 23441 "Alternatives to the Median Absolute Deviation", 23442 Peter J. Rousseuw and Christophe Croux, Journal of the American 23443 Statistical Association, December, 1993, Vol. 88, No. 424, 23444 pp. 1273-1283. 23445 23446 "Data Analysis and Regression: A Second Course in Statistics", 23447 Mosteller and Tukey, Addison-Wesley, 1977, pp. 203-209. 23448 23449Applications: 23450 Data Analysis 23451 23452Implementation Date: 23453 2003/4 23454 23455Program: 23456 MULTIPLOT 2 2 23457 MULTIPLOT CORNER COORDINATES 0 0 100 100 23458 MULTIPLOT SCALE FACTOR 2 23459 X1LABEL DISPLACEMENT 12 23460 . 23461 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 200 23462 LET SIGMA = 1 23463 LET Y2 = LOGNORMAL RANDOM NUMBERS FOR I = 1 1 200 23464 . 23465 BOOTSTRAP SAMPLES 500 23466 BOOTSTRAP QN SCALE PLOT Y1 23467 X1LABEL B025 = ^B025, B975=^B975 23468 HISTOGRAM YPLOT 23469 X1LABEL 23470 . 23471 BOOTSTRAP QN SCALE PLOT Y2 23472 X1LABEL B025 = ^B025, B975=^B975 23473 HISTOGRAM YPLOT 23474 . 23475 END OF MULTIPLOT 23476 JUSTIFICATION CENTER 23477 MOVE 50 96 23478 TEXT QN SCALE BOOTSTRAP: NORMAL 23479 MOVE 50 46 23480 TEXT QN SCALE BOOTSTRAP: LOGNORMAL 23481 23482-----QUADE TEST----------------------------------------- 23483 23484QUADE TEST 23485 23486Name: 23487 QUADE TEST 23488 23489Type: 23490 Analysis Command 23491 23492Purpose: 23493 Perform a Quade test that k treatments have identical effects. 23494 23495Description: 23496 The Quade test is a non-parametric test for analyzing randomized 23497 complete block designs. 23498 23499 The Quade test assumes that there are k experimental 23500 treatments (k >= 2). The observations are arranged in 23501 b blocks, that is 23502 23503 Treatment 23504 Block 1 2 ... k 23505 1 X11 X12 ... X1k 23506 2 X21 X22 ... X2k 23507 3 X31 X32 ... X3k 23508 ... ... ... ... ... 23509 b Xb1 Xb2 ... Xbk 23510 23511 Let R(Xij) be the rank assigned to Xij within block i (i.e., 23512 ranks within a given row). Average ranks are used in the case 23513 of ties. 23514 23515 Compute the range in each block (the maximum value - the minimum 23516 value for the original data) and then rank these: 23517 23518 Q(i) = rank of the range for the i-th block 23519 23520 Then let 23521 23522 S(ij) = Q(i)*[R(X(ij)) - (k+1)/2] 23523 23524 and 23525 23526 S(j) = SUM[i=1 to b][S(ij)] j = 1, 2, ..., k 23527 23528 Then the Quade test is 23529 23530 H0: The treatment effects have identical effects 23531 HA: At least one treatment is different from at least 23532 one other treatment 23533 Test Statistic: 23534 23535 T3 = (b-1)*B/(A2 - B) 23536 23537 where 23538 23539 A2 = SUM[i=1 to b][SUM[j=1 to k][S(ij)**2]] 23540 23541 B = (1/b)*SUM[j=1 to k][S(j)**2] 23542 23543 The T3 statistic is equivalent to performing a two-way 23544 analysis of variance of the S(ij). The A2 term is equivalent 23545 to the total sum of squares and B is equivalent to the 23546 treatment sum of squares. 23547 Significance Level: ALPHA 23548 Critical Region: 23549 The critical region can be approximated with an F 23550 distribution: 23551 23552 T3 > FPPF(ALPHA,k-1,(b-1)*(k-1)) where FPPF is the F 23553 percent point function. 23554 23555 Conclusion: Reject the null hypothesis if the test 23556 statistic is in the critical region. 23557 23558 If the hypothesis of identical treatment effects is rejected, 23559 it is often desirable to determine which treatments are 23560 different (i.e., multiple comparisons). Treatments i and j 23561 are considered different if 23562 23563 |S(i) - S(j)| > TPPF(1-alpha/2,(k-1)*(b-1))* 23564 SQRT[2*b*(A2 - B)/((b-1)*(k-1))] 23565 23566 This is equivalent to the Fisher least significant difference 23567 computed on the S(ij) rather than the data. 23568 23569Syntax: 23570 QUADE TEST <y> <block> <treat> 23571 <SUBSET/EXCEPT/FOR qualification> 23572 where <y> is the response variable; 23573 <block> is a variable that identifies the block; 23574 <treat> is a variable that identifies the treatment; 23575 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 23576 23577Examples: 23578 QUADE TEST Y BLOCK TREATMENT 23579 QUADE TEST Y X1 X2 23580 QUADE TEST Y BLOCK TREATMENT SUBSET BLOCK > 2 23581 23582Note: 23583 In Dataplot, the variables should be given as: 23584 23585 Y BLOCK TREAT 23586 X11 1 1 23587 X12 1 2 23588 ... 1 ... 23589 X1k 1 k 23590 X21 2 1 23591 X22 2 2 23592 ... 2 ... 23593 X2k 2 k 23594 23595 ... ... ... 23596 23597 23598 Xb1 b 1 23599 Xb2 b 2 23600 ... b ... 23601 Xb3 b k 23602 23603 If your data are in a format similar to that given in the 23604 DESCRIPTION section (i.e., you have colums Y1 to Yk, each 23605 with b rows), you can convert it to the format required by 23606 Dataplot with the commands: 23607 23608 LET NBLOCK = SIZE Y1 23609 LET BLOCKID = SEQUENCE 1 1 NBLOCK 23610 LET Y BLOCK TREAT = REPLICATED STACK Y1 Y2 Y3 Y4 Y5 BLOCKID 23611 QUADE TEST Y BLOCK TREAT 23612 23613Note: 23614 The response, ranked response, block, and treatment are 23615 written to the file dpst1f.dat in the current directory. 23616 23617 The treatment ranks and multiple comparisons are written to 23618 the file dpst2f.dat in the current directory. Comparisons 23619 that are statistically significant at the 95% level are 23620 flagged with a single asterisk while comparisons that are 23621 statistically significant at the 99% level are flagged with 23622 two asterisks. 23623 23624Note: 23625 The Quade test is based on the following assumptions: 23626 23627 1) The b rows are mutually independent. That means that 23628 the results within one block (row) do not affect 23629 the results within other blocks. 23630 23631 2) The data can be meaningfully ranked. 23632 23633 3) The data have at least interval scale so that the sample 23634 range may be determined within each block. 23635 23636Note: 23637 The following statistics are also supported: 23638 23639 LET A = QUADE TEST Y X1 X2 23640 LET A = QUADE TEST CDF Y X1 X2 23641 LET A = QUADE TEST PVALUE Y X1 X2 23642 23643 Enter HELP STATISTICS to see what commands can use these 23644 statistics. 23645 23646Note: 23647 The Quade test is similar to the Friedman test. A few distinctions: 23648 23649 1) For k = 2, the Friedman test is equivalent to a sign test while 23650 the Quade test is equivalent to a signed rank test. 23651 23652 2) According to Conover, the Quade test is typically more powerful 23653 for k < 5 while the Friedman test tends to become more powerful 23654 for k >= 5. 23655 23656 3) The Friedman test only requires ordinal scale data (i.e., the 23657 data can be ranked) while the Quade test requires at least 23658 interval scale data (the range within a block can be computed). 23659 23660Default: 23661 None 23662 23663Synonyms: 23664 None 23665 23666Related Commands: 23667 FRIEDMAN = Perform a Friedman test. 23668 ANOVA = Perform an analysis of variance. 23669 DURBIN = Perform a Durbin test for two-way 23670 incomplete balanced block designs. 23671 COCHRAN = Perform a Cochran test for two-way 23672 complete block designs (binary data). 23673 KRUSKAL WALLIS = Perform a Kruskall Wallis test. 23674 SIGN TEST = Perform a sign test. 23675 MEDIAN POLISH = Carries out a robust ANOVA. 23676 T TEST = Carries out a t test. 23677 RANK SUM TEST = Perform a rank sum test. 23678 SIGNED RANK TEST = Perform a signed rank test. 23679 DEX ... PLOT = Generates a dex plot for a statistic. 23680 23681Reference: 23682 W. J. Conover, (1999). "Practical Nonparameteric Statistics", 23683 Third Edition, Wiley, pp. 373-380. 23684 23685Applications: 23686 Analysis of Variance 23687 23688Implementation Date: 23689 2011/7 23690 23691Program: 23692 SKIP 25 23693 READ QUADE2.DAT Y X1 X2 23694 SET WRITE DECIMALS 5 23695 . 23696 LET A1 = QUADE TEST Y X1 X2 23697 LET A2 = QUADE TEST CDF Y X1 X2 23698 LET A3 = QUADE TEST PVALUE Y X1 X2 23699 PRINT A1 A2 A3 23700 . 23701 QUADE TEST Y X1 X2 23702 23703-----QUADRATIC FORM (LET)---------------------------------------- 23704 23705QUADRATIC FORM 23706 23707Name: 23708 QUADRATIC FORM (LET) 23709 23710Type: 23711 Let Subcommand 23712 23713Purpose: 23714 Compute the quadratic form of a matrix and a vector. 23715 23716Description: 23717 The quadratic form of a matrix M and a vector X is defined as: 23718 23719 A=X'MX 23720 23721 where X' is the transpose of X. If the vector X has n 23722 rows, then M must be an nxn matrix. 23723 23724 Quadratic forms are common in statistics, particularly in 23725 linear models and multivariate analysis. In Dataplot 23726 applications, the QUADRATIC FORM command is most typically 23727 used as an intermediate calculation in a larger macro. 23728 23729Syntax: 23730 LET <mat2> = QUADRATIC FORM <mat1> <x> 23731 where <mat1> is a matrix for which the quadratic form is to 23732 be computed; 23733 <x> is a vector for which the quadratic form is to 23734 be computed; 23735 and where <mat2> is a matrix where the resulting quadratic 23736 form is saved. 23737 23738Examples: 23739 LET A = QUADRATIC FORM M X 23740 23741Note: 23742 Matrices are created with either the READ MATRIX command or the 23743 MATRIX DEFINITION command. Enter HELP MATRIX DEFINITION and HELP 23744 READ MATRIX for details. 23745 23746Default: 23747 None 23748 23749Synonyms: 23750 None 23751 23752Related Commands: 23753 READ MATRIX = Read a matrix. 23754 MATRIX COLUMN DIMENSION = Dimension maximum number of columns 23755 for Dataplot matrices. 23756 23757 MATRIX MEAN = Compute the overall mean for a matrix. 23758 MATRIX COLUMN STATISTIC = Compute column statistics for a 23759 matrix. 23760 MATRIX ROW STATISTIC = Compute row statistics for a matrix. 23761 LINEAR COMBINATION = Compute a linear combination of a 23762 matrix and a vector. 23763 23764Reference: 23765 Any standard text on linear algebra. 23766 23767Applications: 23768 Multivariate Analysis 23769 23770Implementation Date: 23771 1998/8 23772 23773Program: 23774 . Perform a Fisher's dsicriminant analysis on Iris data. 23775 . 23776 . READ DATA, 3 GROUPS (N1=N2=N3=3), 2 VARIABLES 23777 FEEDBACK OFF 23778 DIMENSION 200 COLUMNS 23779 SKIP 25 23780 READ IRIS.DAT SEPLENG SEPWIDTH PETLENG PETWIDTH TAG 23781 SKIP 0 23782 LET NTOT = SIZE SEPLENG 23783 LET X = MATRIX DEFINITION SEPLENG NTOT 4 23784 LET P = MATRIX NUMBER OF COLUMNS X 23785 . 23786 LET GROUPID = DISTINCT TAG 23787 LET NG = SIZE GROUPID 23788 LET XMGRAND = MATRIX COLUMN MEANS X 23789 . 23790 . CALCULATE B0 = SUM (I=1,NG) (XBARi - XBARALL)(XBARi-XBARALL)' 23791 . 23792 LET DIAG = 0 FOR I = 1 1 P 23793 LET B0 = DIAGONAL MATRIX DIAG 23794 . 23795 LOOP FOR K = 1 1 NG 23796 LET N^K = SIZE TAG SUBSET TAG = K 23797 LET XMEANI = MATRIX COLUMN MEANS X SUBSET TAG = K 23798 LET XMEANI= XMEANI - XMGRAND 23799 LET B0TEMP = VECTOR TIMES TRANSPOSE XMEANI 23800 LET B0 = MATRIX ADDITION B0 B0TEMP 23801 END OF LOOP 23802 . 23803 . CALCULATE Spooled = (N1-1)S1 + .. + (Ng-1)Sg)/(N1+ .. + Ng - g) 23804 LET SPOOL = POOLED VARIANCE-COVARIANCE MATRIX X TAG 23805 LET DENOM = NTOT - NG 23806 LET WINVB = MATRIX MULTIPLICATION SPOOL DENOM 23807 LET WINVB = MATRIX INVERSE WINVB 23808 LET WINVB = MATRIX MULTIPLICATION WINVB B0 23809 . 23810 . COMPUTE EIGENVALUES AND SORT IN DECREASING ORDER 23811 . COMPUTE EIGENVECTORS, ONLY KEEP REAL COMPONENT, SORT 23812 . 23813 LET E = MATRIX EIGENVALUES WINVB 23814 LET EV = MATRIX EIGENVECTORS WINVB 23815 LET INDX = SEQUENCE 1 1 P 23816 RETAIN E FOR I = 1 1 P 23817 LET ESORT = SORTC E INDX 23818 LET REVERSE = SEQUENCE P 1 1 23819 LET REVERSE = SORTC REVERSE ESORT INDX 23820 LET EVECT = DIAGONAL MATRIX DIAG 23821 . NORMALIZE L'SpooledL =1 23822 . DIST = L'SpooledL, MULTIPLY EIGENVECTOR BY 1/SQRT(DIST) 23823 LOOP FOR K = 1 1 P 23824 LET LTAG = INDX(K) 23825 RETAIN EV^K FOR I = 1 1 P 23826 LET EVECT^LTAG = EV^K 23827 LET DIST = QUADRATIC FORM SPOOL EVECT^LTAG 23828 LET EVECT^LTAG = (1/SQRT(DIST))*EVECT^LTAG 23829 END OF LOOP 23830 . PLOT FIRST 2 DISCRIMINANTS 23831 LET ZY = LINEAR COMBINATION X EVECT1 23832 LET ZX = LINEAR COMBINATION X EVECT2 23833 DEVICE 1 OFF 23834 MEAN PLOT ZY TAG 23835 LET GMEANY = YPLOT 23836 MEAN PLOT ZX TAG 23837 LET GMEANX = YPLOT 23838 RETAIN GMEANX GMEANY SUBSET TAGPLOT = 1 23839 DEVICE 1 ON 23840 Y1LABEL FIRST DISCRIMINANT 23841 X1LABEL SECOND DISCRIMINANT 23842 CHARACTER CIRCLE SQUARE TRIANGLE 23843 LINE BLANK ALL 23844 LEGEND 1 CIRC() - SPECIES 1 23845 LEGEND 2 SQUA() - SPECIES 2 23846 LEGEND 3 TRIA() - SPECIES 3 23847 LEGEND FONT DUPLEX 23848 LEGEND SIZE 1.2 23849 TITLE PLOT FIRST 2 DISCRIMINANT FUNCTIONS 23850 PLOT ZY ZX TAG 23851 PRINT "FISHER's DISCRIMINANT ANALYSIS" 23852 PRINT " " 23853 PRINT " " 23854 PRINT "B0 MATRIX (= between group sums of cross-products):" 23855 PRINT B0 23856 PRINT " " 23857 PRINT " " 23858 PRINT "POOLED VARIANCE-COVARIANCE MATRIX:" 23859 PRINT SPOOL 23860 PRINT " " 23861 PRINT " " 23862 PRINT "EIGENVALUES:" 23863 PRINT ESORT 23864 PRINT " " 23865 PRINT " " 23866 PRINT "COLUMNS ARE THE DISCRIMINANT FUNCTIONS:" 23867 PRINT EVECT 23868 PRINT " " 23869 PRINT " " 23870 PRINT "GROUP MEANS:" 23871 PRINT GMEANX GMEANY 23872 23873-----QUANTILE (LET)----------------------------------------- 23874 23875QUANTILE 23876 23877Name: 23878 QUANTILE (LET) 23879 23880Type: 23881 Let Subcommand 23882 23883Purpose: 23884 Compute a user specified quantile for a variable. 23885 23886Description: 23887 The qth quantile of a data set is defined as that value 23888 where a q fraction of the data is below that value and (1-q) 23889 fraction of the data is above that value. For example, the 23890 0.5 quantile is the median. 23891 23892 Dataplot supports two methods for computing the quantile. 23893 23894 The first method is based on the order statistic. The 23895 formula is: 23896 23897 X(q) = (1 - r)*X(NI1) + r*X(NI2) 23898 23899 where 23900 23901 X are the observations sorted in ascending order 23902 NI1 = INT(Q*(N+1)) 23903 NI2 = NI1 + 1 23904 r = Q*(N+1) - INT(Q*(N+1)) 23905 23906 If q is < 1/(N+1), then X(1) is returned. If q > N/(N+1), then X(N) 23907 is returned. 23908 23909 An alternative method is called the Herrell-Davis 23910 estimate. This method attempts to provide a lower standard 23911 error for X(q) by utilizing all the order statistics rather 23912 than a single (or a weighted average of two) order statistic. 23913 Note that there are cases where the Herrell-Davis has a 23914 substantially smaller standard error than the order statistic 23915 method. However, there are also cases where the reverse is 23916 true. 23917 23918 To compute the Herrell-Davis estimate, do the following: 23919 23920 1. Sort the X in ascending order. 23921 23922 2. A = (N+1)*q - 1 23923 23924 3. B = (N+1)*(1-q) - 1 23925 23926 4. W(i) = BETCDF(i/n, A, B) - BETCDF((i-1)/n, A, B) 23927 23928 where BETCDF is the beta cumulative distribution 23929 function with shape parameters A and B. 23930 23931 5. X(q) = SUM[i=1 to n][W(i)*X(i)] 23932 23933 Note: The computations for A and B were modifed 2/2003 to: 23934 23935 A = (N+1)*q 23936 B = (N+1)*(1-q) 23937 23938 The original form was from the text in the Wilcox book. However, 23939 checking his S+ macros and verifying against the original 23940 Herrell and Davis article indicated that the new formulas are 23941 the correct ones. 23942 23943Syntax: 23944 LET <par> = <quan> QUANTILE <y> 23945 <SUBSET/EXCEPT/FOR qualification> 23946 where <y> is the response variable; 23947 <quan> is a number or parameter in the range (0,1) that 23948 specifies the desired quantile; 23949 <par> is a parameter where the computed quantile 23950 is stored; 23951 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 23952 23953Examples: 23954 LET A = 0.20 QUANTILE Y 23955 23956 LET XQ = 0.50 23957 LET A = XQ QUANTILE Y SUBSET TAG > 2 23958 23959Note: 23960 The PERCENTILE command is equivalent to the QUANTILE command 23961 using the order statistic method. The only difference is 23962 that the requested percentile is given as a percentage 23963 between 0 and 100% rather than as a fraction. 23964 23965Note: 23966 Note that there are a number of other ways of calculating percentiles 23967 in common use. Hyndman and Fan (1996) in an American Statistician 23968 article evaluated nine different methods (we will refer to these as R1 23969 through R9) for computing percentiles relative to six desirable 23970 properties. Their goal was to advocate a "standard" definition for 23971 percentiles that would be implemented in statistical software. Although 23972 this has not in fact happened, the article does provide a useful 23973 summary and evaluation of various methods for computing percentiles. 23974 Most statistical and spreadsheet software use one of the methods 23975 described in Hyndman and Fan. 23976 23977 The default method used by Dataplot described above is equivalent 23978 to method R6 of Hyndman and Fan. 23979 23980 The method advocated by Hyndman and Fan is R8. For the R8 method, 23981 23982 X(q) = X(NI1) + r*(X(NI2) - X(NI1)) 23983 23984 where 23985 23986 X are the observations sorted in ascending order 23987 NI1 = INT(Q*(N+(1/3)) + (1/3)) 23988 NI2 = NI1 + 1 23989 r = Q*(N+1) - INT(Q*(N+1)) 23990 23991 If q ≤ (2/3)/(N+(1/3)) the minimum value will be returned and if 23992 q ≥ (N-(1/3))/(N+(1/3)) the maximum value will be returned. 23993 23994 Method R7 (this is the default method in R and Excel) is calculated by 23995 23996 X(q) = X(NI1) + r*(X(NI2) - X(NI1)) 23997 23998 where 23999 24000 X are the observations sorted in ascending order 24001 NI1 = INT(Q*(N-1) + 1) 24002 NI2 = NI1 + 1 24003 r = Q*(N+1) - INT(Q*(N+1)) 24004 24005 If q = 1, then X(N) is returned. 24006 24007 The R6, R7, and R8 methods give fairly similar, but not exactly the 24008 same (particularly for small samples), results. For most purposes, 24009 any of these three methods should be acceptable. 24010 24011Note: 24012 The following command is used to determine which method 24013 is used to compute the quantile: 24014 24015 SET QUANTILE METHOD <ORDER/HERRELL-DAVIS/R6/R7/R8> 24016 24017 R6 is equivalent to ORDER. ORDER is the default. 24018 24019Note: 24020 Dataplot statistics can be used in 20+ commands. For details, enter 24021 24022 HELP STATISTICS 24023 24024 When using these commands, the specific quantile to compute is 24025 specified by entering the following command (before the plot command): 24026 24027 LET XQ = <value> 24028 24029 where <value> is a number in the interval (0,1) that specifies 24030 the desired quantile. 24031 24032Default: 24033 The default is to use the order statistic method to 24034 compute the quantile. 24035 24036Synonyms: 24037 None 24038 24039Related Commands: 24040 PERCENTILE = Compute a percentile of a variable. 24041 MEDIAN = Compute the median of a variable. 24042 LOWER QUARTILE = Compute the lower quartile of a 24043 variable. 24044 UPPER QUARTILE = Compute the upper quartile of a 24045 variable. 24046 FIRST DECILE = Compute the first decile (the 10th 24047 quantile) of a variable. 24048 STATISTIC PLOT = Generate a statistic versus subset 24049 plot for numerous statistics. 24050 CROSS TABULATE PLOT = Generate a statistic versus subset 24051 plot (two group variables) for a 24052 given statistics. 24053 BOOTSTRAP PLOT = Generate a bootstrap plot for a 24054 given statistic. 24055 24056References: 24057 Hyndman and Fan (November 1996), "Sample Quantiles in Statistical 24058 Packages", The American Statistician, Vol. 50, No. 4, pp. 361-365. 24059 24060 Rand Wilcox (1997), "Introduction to Robust Estimation and Hypothesis 24061 Testing", Academic Press. 24062 24063 Frank Herrell and C. E. Davis, (1982), "A New Distribution-Free Quantile 24064 Estimator", Biometrika, 69(3), 635-640. 24065 24066Applications: 24067 Data Analysis 24068 24069Implementation Date: 24070 2002/07 24071 2003/02: Correction in Herrell-Davis formulation. 24072 2015/02: Support for R7 and R8 methods 24073 24074Program 1: 24075 LET Y1 = LOGISTIC RANDOM NUMBERS FOR I = 1 1 100 24076 LET Q05A = 0.05 QUANTILE Y1 24077 LET Q95A = 0.95 QUANTILE Y1 24078 SET QUANTILE METHOD HERRELL DAVIS 24079 LET Q05B = 0.05 QUANTILE Y1 24080 LET Q95B = 0.95 QUANTILE Y1 24081 LET Q95B = XQ QUANTILE Y1 24082 LET Q05A = ROUND(Q05A,4) 24083 LET Q95A = ROUND(Q95A,4) 24084 LET Q05B = ROUND(Q05B,4) 24085 LET Q95B = ROUND(Q95B,4) 24086 PRINT "R6 METHOD: 0.05 Quantile = ^Q05A" 24087 PRINT "R6 METHOD: 0.95 Quantile = ^Q95A" 24088 PRINT "HD METHOD: 0.05 Quantile = ^Q05B" 24089 PRINT "HD METHOD: 0.95 Quantile = ^Q95B" 24090 24091Program 2: 24092 . Step 1: Read the data 24093 . 24094 read y 24095 95.1772 24096 95.1567 24097 95.1937 24098 95.1959 24099 95.1442 24100 95.0610 24101 95.1591 24102 95.1195 24103 95.1065 24104 95.0925 24105 95.1990 24106 95.1682 24107 end of data 24108 . 24109 . Step 2: Compute the quantiles using different methods 24110 . 24111 let xq = 0.90 24112 . 24113 let xqr6 = quantile y 24114 let xpr6 = round(xpr6,4) 24115 . 24116 set quantile method r7 24117 let xqr7 = quantile y 24118 let xqr7 = round(xqr7,4) 24119 . 24120 set quantile method r8 24121 let xqr8 = quantile y 24122 let xqr8 = round(xqr8,4) 24123 . 24124 . Step 3: Print the results 24125 . 24126 print "Quantile with R6 method: ^xqr6" 24127 print "Quantile with R7 method: ^xqr7" 24128 print "Quantile with R8 method: ^xqr8" 24129 24130-----QUANTILE-QUANTILE PLOT-------------------------------------- 24131 24132QUANTILE QUANTILE PLOT 24133 24134Name: 24135 QUANTILE-QUANTILE PLOT 24136 24137Type: 24138 Graphics Command 24139 24140Purpose: 24141 Generates a quantile-quantile plot. 24142 24143Description: 24144 A quantile-quantile plot (or q-q plot) is a graphical data analysis 24145 technique for comparing the distributions of 2 data sets. The 24146 quantile-quantile plot is a graphical alternative for the various 24147 classical 2-sample tests (e.g., t for location, F for dispersion). 24148 The plot consists of the following: 24149 24150 Vertical axis = estimated quantiles from data set 1; 24151 Horizontal axis = estimated quantiles from data set 2. 24152 24153 The "quantiles" of a distribution are the distribution's "percent 24154 points" (e.g., .5 quantile = 50% point = median). The advantage of 24155 the quantile-quantile plot is 2-fold: 24156 24157 1) the sample sizes do not need to be identical; 24158 2) many distributional aspects can be simultaneously tested. 24159 For example, shifts in location, shifts in dispersion, 24160 changes in symmetry/skewness, outliers, etc. 24161 24162 The quantile-quantile plot has 3 components: 24163 24164 1) the quantile points themselves; 24165 2) a 45 degree reference line. 24166 3) a least squares line fit to the quantile points. 24167 24168 If the two data sets come from similar distributions, then the 24169 points of the q-q plot should lie along the 45 degree reference 24170 line. 24171 24172 Like usual, the appearance of these 2 components is controlled by 24173 the first 2 settings of the CHARACTERS and LINES commands. It is 24174 typical for the quantile points to be represented as, say, X's with 24175 no connecting line, and the reference line to have no plot 24176 characters but to be solid. This is demonstrated in the sample 24177 program below. 24178 24179Syntax 1: 24180 QUANTILE-QUANTILE PLOT <y1> <y2> <SUBSET/EXCEPT/FOR qualification> 24181 where <y1> is the first response variable; 24182 <y2> is the second response variable; 24183 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 24184 24185Syntax 2: 24186 HIGHLIGHT QUANTILE-QUANTILE PLOT <y1> <y2> <tag> 24187 <SUBSET/EXCEPT/FOR qualification> 24188 where <y1> is the first response variable; 24189 <y2> is the second response variable; 24190 <tag> is a group-id variable that defines the highlighting; 24191 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 24192 24193 This syntax can be used to plot different plot points with 24194 different attributes. For example, it can used to highlight 24195 groups in the data or to emphasize the extremes. 24196 24197Examples: 24198 QUANTILE-QUANTILE PLOT Y1 Y2 24199 QUANTILE-QUANTILE PLOT RUN1 RUN2 24200 QUANTILE-QUANTILE PLOT BATCH1 BATCH2 24201 QUANTILE-QUANTILE PLOT Y1 Y2 SUBSET AUTO 4 24202 QUANTILE-QUANTILE PLOT Y1 Y2 SUBSET STATE 25 24203 24204Note: 24205 One of the distributions can be a theoretical distribution. For 24206 example, the following program generates a quantile-quantile plot 24207 of a data set against a normal distribution (this is called a 24208 normal quantile plot). 24209 24210 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 24211 LET X = SEQUENCE .01 .01 .99 24212 LET Y2 = NORPPF(X) 24213 QUANTILE-QUANTILE PLOT Y1 Y2 24214 24215 This same technique can be used other distributions (use the proper 24216 PPF function). This is also fairly close to what a probability 24217 plot does (DATAPLOT has a PROBABILITY PLOT command for over 25 24218 distributions). 24219 24220Note: 24221 For large data sets, it may be impractical to generate the plot for 24222 each individual point. As an alternative, you can generate the plot 24223 for a user specified number of quantiles. To do this, enter the 24224 command 24225 24226 SET QUANTILE QUANTILE PLOT NUMBER OF PERCENTILES <value> 24227 24228 where <value> specifies the desired number of quantiles. This is 24229 demonstrated in the Program 2 example below. 24230 24231Note: 24232 If the two data sets have similar distribution, then the points on 24233 the plot should fall along the 45 degree reference line. For 24234 example, if you enter a QUANTILE QUANTILE PLOT Y Y command, then the 24235 points will lie exactly on the reference line. This means that if 24236 a line is fit to the points on the plot and the two data sets come 24237 from similar distributions, then the itercept and the slope of the 24238 fitted line should be close to zero and one, respectively. In 24239 addition, the correlation coefficient of the fitted line should be 24240 close to one. 24241 24242 The parameters containing the intercept, slope, and correlation 24243 coefficient are automatically saved in the parameters PPA0, PPA1, 24244 and PPCC, respectively. This can be useful in labeling q-q plots. 24245 24246Note: 24247 If you have more than two data sets, you can generate a matrix plot 24248 of the pairwise q-q plots with the SCATTER PLOT MATRIX command. This 24249 is demonstrated in the Program 3 example. 24250 24251Default: 24252 None 24253 24254Synonyms: 24255 None 24256 24257Related Commands: 24258 TUKEY MEAN DIFFERENCE PLOT = Generates a Tukey mean difference plot. 24259 BOX PLOT = Generates a box plot. 24260 PLOT = Generates a data or function plot. 24261 BIHISTOGRAM = Generates a bihistogram. 24262 PROBABILITY PLOT = Generates a probability plot. 24263 PERCENTILE PLOT = Generates a percentile plot. 24264 T-TEST = Carries out a 2-sample t test. 24265 ANOVA = Carries out an ANOVA. 24266 MULTIPLOT = Allows multiple plots per page. 24267 CHARACTERS = Sets the type for plot characters. 24268 LINES = Sets the type for plot lines. 24269 24270Reference: 24271 Chambers, Cleveland, Kleiner, and Tukey (1983), "Graphical Methods 24272 of Data Analysis", Wadsworth, pp. 48-57. 24273 24274Applications: 24275 Exploratory Data Analysis 24276 24277Implementation Date: 24278 1988/03 24279 2011/02: Support for highlight option 24280 2016/06: Support for SET QUANTILE QUANTILE PLOT NUMBER OF PERCENTILES 24281 2016/06: Generate a fitted line to the quantile points 24282 2016/06: Automatically save PPA0, PPA1, and PPCC 24283 24284Program 1: 24285 SKIP 25 24286 READ AUTO83B.DAT Y1 Y2 24287 DELETE Y2 SUBSET Y2 < 0 24288 . 24289 LINE BLANK SOLID DASHED 24290 CHARACTER CIRCLE BLANK BLANK 24291 CHARACTER FILL ON OFF OFF 24292 CHARACTER HW 0.5 0.375 24293 TITLE AUTOMATIC 24294 TITLE OFFSET 2 24295 LABEL CASE ASIS 24296 Y1LABEL MPG for US Cars 24297 X1LABEL MPG for Japanese Cars 24298 . 24299 QUANTILE-QUANTILE PLOT Y1 Y2 24300 . 24301 LET PPA0 = ROUND(PPA0,3) 24302 LET PPA1 = ROUND(PPA1,3) 24303 LET PPCC = ROUND(PPCC,3) 24304 JUSTIFICATION LEFT 24305 MOVE 20 87; TEXT A0: ^PPA0 24306 MOVE 20 85; TEXT A1: ^PPA1 24307 MOVE 20 83; TEXT PPCC: ^PPCC 24308 24309Program 2: 24310 LET Y1 = NORMAL RANDOM NUMBER FOR I = 1 1 1000000 24311 LET Y2 = DOUBLE EXPONENTIAL RANDOM NUMBER FOR I = 1 1 1000000 24312 . 24313 LINE BLANK SOLID DASH 24314 CHARACTER CIRCLE BLANK BLANK 24315 CHARACTER FILL ON OFF 24316 CHARACTER HW 0.5 0.375 24317 TITLE AUTOMATIC 24318 TITLE OFFSET 2 24319 LABEL CASE ASIS 24320 Y1LABEL Normal Random Numbers 24321 X1LABEL Double Exponential Random Numbers 24322 . 24323 SET QUANTILE QUANTILE PLOT NUMBER OF PERCENTILES 1000 24324 QUANTILE-QUANTILE PLOT Y1 Y2 24325 . 24326 LET PPA0 = ROUND(PPA),3) 24327 LET PPA1 = ROUND(PPA1,3) 24328 LET PPCC = ROUND(PPCC,3) 24329 JUSTIFICATION LEFT 24330 MOVE 20 87; TEXT A0: ^PPA0 24331 MOVE 20 85; TEXT A1: ^PPA1 24332 MOVE 20 83; TEXT PPCC: ^PPCC 24333 24334Program 3: 24335 SKIP 25 24336 READ AUTO83B.DAT Y1 Y2 24337 DELETE Y2 SUBSET Y2 < 0 24338 . 24339 LINE BLANK BLANK SOLID DASH 24340 CHARACTER CIRCLE CIRCLE BLANK BLANK 24341 CHARACTER FILL ON ON 24342 CHARACTER HW 0.5 0.375 ALL 24343 CHARACTER COLOR BLACK RED 24344 TITLE AUTOMATIC 24345 TITLE OFFSET 2 24346 . 24347 LET N2 = SIZE Y2 24348 LET TAG = 1 FOR I = 1 1 N2 24349 LET TAG = 2 SUBSET Y2 > 32 24350 . 24351 HIGHLIGHT QUANTILE QUANTILE PLOT Y2 Y1 TAG 24352 24353Program 4: 24354 . Step 1: Read the data 24355 . 24356 skip 25 24357 read exp.dat y1 24358 read weibbury.dat y2 24359 read gamma.dat y3 24360 read frechet.dat y4 24361 skip 0 24362 . 24363 variable label y1 exp.dat 24364 variable label y2 weibbury.dat 24365 variable label y3 gamma.dat 24366 variable label y4 frechet.dat 24367 . 24368 . Step 2: Set some plot control features 24369 . 24370 case asis 24371 label case asis 24372 title case asis 24373 title offset 2 24374 tic mark offset units screen 24375 tic mark offset 5 5 24376 multiplot scale factor 4 24377 multiplot corner coordinates 10 10 90 90 24378 . 24379 line blank solid blank blank 24380 character circle blank blank blank 24381 character fill on 24382 character hw 0.5 0.375 all 24383 . 24384 . Step 3: Scatter plot matrix of quantile-quantile plot 24385 . 24386 label displacement 18 24387 set scatter plot matrix type quantile quantile 24388 scatter plot matrix y1 y2 y3 y4 24389 . 24390 justification center 24391 move 50 97 24392 text Quantile-Quantile Plots of Four Data Sets 24393 24394-----QUANTILE STANDARD ERROR (LET)------------------------------------ 24395 24396QUANTILE STANDARD ERROR 24397 24398Name: 24399 QUANTILE STANDARD ERROR (LET) 24400 24401Type: 24402 Let Subcommand 24403 24404Purpose: 24405 Compute the standard error for a user specified quantile for 24406 a variable. 24407 24408Description: 24409 The qth quantile of a data set is defined as that value 24410 where a q fraction of the data is below that value and (1-q) 24411 fraction of the data is above that value. For example, the 24412 0.5 quantile is the median. 24413 24414 Dataplot supports two methods for computing the quantile. 24415 The first method is the conventional method based on the order 24416 statistic. The second method, called the Herrell-Davis method, 24417 is based on using all the order statistics. The standard error 24418 methods given here only apply to the first method. 24419 24420 Two methods for obtaining the standard errors for the quantiles 24421 are supported. 24422 24423 The first method, called the Maritz-Jarrett method, is computed 24424 for the variable X and the desired quantile q as follows: 24425 24426 1. Sort the X in ascending order. 24427 24428 2. Let m = [q**n + 0.5] 24429 24430 3. A = m - 1 24431 24432 4. B = n - m 24433 24434 5. W(i) = BETCDF(i/n, A, B) - BETCDF((i-1)/n, A, B) 24435 24436 where BETCDF is the beta cumulative distribution 24437 function with shape parameters A and B. 24438 24439 6. C(k) = SUM[i=1 to n][W(i)*X(i)**k] 24440 24441 7. MJ = SQRT(C(2) - C(1)**2) 24442 24443 The second method, based on the kernel density, is computed for 24444 a variable X as follows: 24445 24446 1. Let h = 1.2*(Xhat(0.75) - Xhat(0.25))/n**(1/5). Xhat is 24447 the estimated quantile. 24448 24449 2. Compute the number of observations of X contained in the 24450 interval X +/- h. Call this NINT. 24451 24452 3. fhat(x) = NINT/(2*n*h) 24453 24454 4. The stanard error of Xhat(q) = 1/[2*SQRT(n)*fhat(Xhat(q))] 24455 24456Syntax: 24457 LET <par> = <quant> QUANTILE STANDARD ERROR <y> 24458 <SUBSET/EXCEPT/FOR qualification> 24459 where <y> is the response variable; 24460 <quant> is a number or parameter in the range (0.1) that 24461 specifies the desired quantile; 24462 <par> is a parameter where the computed quantile standard 24463 error is stored; 24464 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 24465 24466 In order to specify the desired quantile, enter the command 24467 24468 LET XQ = <value> 24469 24470 where <value> is a number in the interval (0,1). 24471 24472Examples: 24473 SET QUANTILE STANDARD ERROR MARITZ-JARRETT 24474 LET A = 0.20 QUANTILE STANDARD ERROR Y 24475 24476 SET QUANTILE STANDARD ERROR KERNEL DENSITY 24477 LET XQ = 0.20 24478 LET A = XQ QUANTILE STANDARD ERROR Y 24479 24480 SET QUANTILE STANDARD ERROR KERNEL DENSITY 24481 LET XQ = 0.20 24482 LET A = XQ QUANTILE STANDARD ERROR Y SUBSET TAG > 1 24483 24484Note: 24485 The following command is used to determine which method 24486 is used to compute the quantile standard error: 24487 24488 SET QUANTILE STANDARD ERROR <KERNEL DENSITY/MARITZ JARRETT> 24489 24490Note: 24491 Dataplot statistics can be used in 20+ commands. For details, enter 24492 24493 HELP STATISTICS 24494 24495 The specific quantile for which the standard error is to be 24496 computed is specified by entering the following command (before 24497 the plot command): 24498 24499 LET XQ = <value> 24500 24501 where <value> is a number in the interval (0,1) that specifies 24502 the desired quantile. 24503 24504Note: 24505 To obtain standard errors and confidence limits for the 24506 Herrell-Davis method, use the BOOTSTRAP PLOT command. For 24507 example, 24508 24509 LET XQ = 0.95 24510 SET QUANTILE METHOD HERRELL DAVIS 24511 BOOTSTRAP SAMPLES 500 24512 BOOTSTRAP QUANTILE STANDARD ERROR PLOT Y 24513 LET LCL = B025 24514 LET UCL = B975 24515 24516 The bootstrap method can also be applied to quantile estimated 24517 using the order statistic method. 24518 24519Default: 24520 The default is to use the Maritz-Jarrett method to 24521 compute the quantile standard error. 24522 24523Synonyms: 24524 None 24525 24526Related Commands: 24527 QUANTILE = Compute a quantile of a variable. 24528 MEDIAN = Compute the median of a variable. 24529 LOWER QUARTILE = Compute the lower quartile of a 24530 variable. 24531 UPPER QUARTILE = Compute the upper quartile of a 24532 variable. 24533 FIRST DECILE = Compute the first decile (the 10th 24534 quantile) of a variable. 24535 STATISTIC PLOT = Generate a statistic versus subset 24536 plot for numerous statistics. 24537 CROSS TABULATE PLOT = Generate a statistic versus subset 24538 plot (two group variables) for a 24539 given statistics. 24540 BOOTSTRAP PLOT = Generate a bootstrap plot for a 24541 given statistic. 24542 INFLUENCE CURVE = Generate an influence curve for a 24543 given statistic. 24544 DEX PLOT = Generate a dex plot for a given 24545 statistic. 24546 INTERACTION STATISTIC PLOT = Generate a dex plot for a given 24547 statistic. 24548 24549Reference: 24550 Rand Wilcox (1997), "Introduction to Robust Estimation and Hypothesis 24551 Testing", Academic Press. 24552 24553 Frank Herrell and C. E. Davis, (1982), "A New Distribution-Free 24554 Quantile Estimator", Biometrika, 69(3), 635-640. 24555 24556 Hyndman and Fan (November 1996), "Sample Quantiles in Statistical 24557 Packages", The American Statistician, Vol. 50, No. 4, pp. 361-365. 24558 24559Applications: 24560 Data Analysis 24561 24562Implementation Date: 24563 2002/7 24564 24565Program: 24566 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 24567 LET XQ = 0.05 24568 LET P05 = XQ QUANTILE Y1 24569 LET P05SE = XQ QUANTILE STANDARD ERROR Y1 24570 24571-----QUARTILE COEFFICIENT OF DISPERSION (LET)--------------------------- 24572 24573QUARTILE COEFFICIENT OF DISPERSION 24574 24575Name: 24576 QUARTILE COEFFICIENT OF DISPERSION (LET) 24577 24578Type: 24579 Let Subcommand 24580 24581Purpose: 24582 Compute the quartile coefficient of dispersion of a variable. 24583 24584Description: 24585 The sample quartile coefficient of dispersion is defined as 24586 24587 QCD = (Q3 - Q1)/(Q1 + Q3) 24588 24589 where Q1 is the lower quartile (25-th percentile) and Q3 is the 24590 upper quartile (75-th percentile). 24591 24592 This statistic has been suggested as a robust alternative to the 24593 coefficient of variation. 24594 24595Syntax 1: 24596 LET <par> = QUARTILE COEFFICIENT OF DISPERSION <y> 24597 <SUBSET/EXCEPT/FOR qualification> 24598 where <y> is a response variable; 24599 <par> is a parameter where the quartile coefficient of 24600 dispersion value is saved; 24601 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 24602 24603Syntax 2: 24604 LET <par> = DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION 24605 <y1> <y2> <SUBSET/EXCEPT/FOR qualification> 24606 where <y1> is the first response variable; 24607 <y2> is the second response variable; 24608 <par> is a parameter where the difference of the quartile 24609 coefficient of dispersion values are saved; 24610 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 24611 24612Examples: 24613 LET QCD = QUARTILE COEFFICIENT OF DISPERSION Y1 24614 LET QCD = QUARTILE COEFFICIENT OF DISPERSION Y1 SUBSET TAG > 2 24615 24616 LET QCD = DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION Y1 Y2 24617 24618Note: 24619 Dataplot statistics can be used in a number of commands. For 24620 details, enter 24621 24622 HELP STATISTICS 24623 24624Default: 24625 None 24626 24627Synonyms: 24628 QCD 24629 24630Related Commands: 24631 COEFFICIENT OF VARIATION = Compute the coefficient of variation of 24632 a variable. 24633 COEFFICIENT OF DISPERSION = Compute the coefficient of dispersion of 24634 a variable. 24635 SIGNAL TO NOISE RATIO = Compute the signal to noise ratio of a 24636 variable. 24637 RELATIVE STANDARD DEVI = Compute the standard deviation of a 24638 variable. 24639 MEAN = Compute the mean of a variable. 24640 STANDARD DEVIATION = Compute the standard deviation of a 24641 variable. 24642 24643Reference: 24644 Bonett, D. G. (2006). "Confidence interval for a coefficient of 24645 quartile variation", Computational Statistics & Data Analysis, 24646 50 (11): 2953–2957. 24647 24648Applications: 24649 Data Analysis 24650 24651Implementation Date: 24652 2017/01 24653 2017/06: Added QUARTILE COEFFICIENT OF DISPERSION 24654 24655Program 1: 24656 SKIP 25 24657 READ ZARR13.DAT Y 24658 LET QCD = QUARTILE COEFFICIENT OF DISPERSION Y 24659 24660Program 2: 24661 . Step 1: Create the data 24662 . 24663 skip 25 24664 read gear.dat y x 24665 skip 0 24666 set write decimals 6 24667 . 24668 . Step 2: Define plot control 24669 . 24670 title case asis 24671 title offset 2 24672 label case asis 24673 . 24674 y1label Quartile Coefficient of Dispersion 24675 x1label Group 24676 title Quartile Coefficient of Dispersion for GEAR.DAT 24677 let ngroup = unique x 24678 xlimits 1 ngroup 24679 major x1tic mark number ngroup 24680 minor x1tic mark number 0 24681 tic mark offset units data 24682 x1tic mark offset 0.5 0.5 24683 . 24684 character X 24685 line blank 24686 . 24687 set statistic plot reference line average 24688 quartile coefficient of dispersion plot y x 24689 . 24690 set write decimals 5 24691 tabulate quartile coefficient of dispersion y x 24692 24693Program 3: 24694 SKIP 25 24695 READ IRIS.DAT Y1 TO Y4 X 24696 . 24697 LET A = DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION Y1 Y2 24698 SET WRITE DECIMALS 4 24699 TABULATE DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION Y1 Y2 X 24700 . 24701 XTIC OFFSET 0.2 0.2 24702 X1LABEL GROUP ID 24703 Y1LABEL DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION 24704 CHAR X 24705 LINE BLANK 24706 DIFFERENCE OF COEFFICIENT OF DISPERSION PLOT Y1 Y2 X 24707 CHAR X ALL 24708 LINE BLANK ALL 24709 BOOTSTRAP DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION PLOT ... 24710 Y1 Y2 X 24711 24712-----QUARTILE PLOT--------------------------------------------------- 24713 24714QUARTILE PLOT 24715 24716Name: 24717 QUARTILE PLOT 24718 24719Type: 24720 Graphics Command 24721 24722Purpose: 24723 Generates a quartile plot. 24724 24725Description: 24726 A quartile plot is a plot consisting of subsample quartiles versus 24727 subsample index. The subsample quartile is the quartile of the 24728 data in the subsample. The quartile plot is used to answer the 24729 question-- "Does the subsample spread change over different 24730 subsamples?". It consist of: 24731 Vertical axis = subsample quartile; 24732 Horizontal axis = subsample index. 24733 The quartile plot yields 2 traces: 24734 1. a subsample quartile trace; and 24735 2. a full-sample quartile reference line. 24736 Like usual, the appearance of these 2 traces is controlled by 24737 the first 2 settings of the LINES, CHARACTERS, SPIKES, BARS, 24738 and similar attributes. 24739 24740Syntax: 24741 <UPPER/LOWER> QUARTILE PLOT <y> <x> 24742 <SUBSET/EXCEPT/FOR qualification> 24743 where <y> is the response (= dependent) variable; 24744 <x> is the subsample identifier variable (this variable 24745 appears on the horizontal axis); 24746 LOWER specifies a lower quartile plot and UPPER specifies an 24747 upper quartile plot; 24748 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 24749 24750Examples: 24751 UPPER QUARTILE PLOT Y X 24752 LOWER QUARTILE PLOT Y X1 SUBSET X1 < 12 24753 24754Default: 24755 None 24756 24757Synonyms: 24758 None 24759 24760Related Commands: 24761 CHARACTERS = Sets the type for plot characters. 24762 LINES = Sets the type for plot lines. 24763 MEAN PLOT = Generates a mean plot. 24764 SD PLOT = Generates a standard deviation plot. 24765 BOX PLOT = Generates a box plot. 24766 XBAR CHART = Generates a xbar control chart. 24767 PLOT = Generates a data or function plot. 24768 24769Applications: 24770 Exploratory Data Analysis 24771 24772Implementation Date: 24773 88/2 24774 24775Program: 24776 . PURPOSE--GENERATE A QUARTILE PLOT OF POINT BARROW FREON-11 DATA 24777 SKIP 50 24778 SET READ FORMAT 3F4.0,F5.0,F6.0,F3.0,2F9.0 24779 READ PBF11.DAT YEAR DAY BOT SD F11 FLAG WV CO2 24780 . 24781 RETAIN YEAR DAY BOT SD F11 WV CO2 FLAG SUBSET FLAG 0 24782 LET MONTH=INT(DAY/30.25)+1 24783 . 24784 TITLE QUARTILE PLOT 24785 XLIMITS 0 15 24786 YLIMITS 1 1.01 24787 CHARACTER U U 24788 LINE BLANK SOLID 24789 UPPER QUARTILE PLOT WV MONTH 24790 PRE-ERASE OFF 24791 CHARACTER L L 24792 LOWER QUARTILE PLOT WV MONTH 24793 24794-----QUERY------------------------------------------------------- 24795 24796QUERY 24797 24798Name: 24799 QUERY 24800 24801Type: 24802 Support Command 24803 24804Purpose: 24805 Sends a message to the DATAPLOT service group. This message is 24806 placed in a file which can be scanned periodically by members of 24807 the DATAPLOT service group. 24808 24809Syntax: 24810 QUERY <message> 24811 24812Examples: 24813 QUERY HAVE MODELING QUESTION 24814 QUERY PLEASE CALL J. SMITH (EXT. 3862) 24815 24816Note: 24817 This command is essentially obsolete since most operating systems 24818 have sophisticated electronic mail capabilities. 24819 24820Default: 24821 None 24822 24823Synonyms: 24824 MESSAGE 24825 24826Related Commands: 24827 MAIL = Lists the mail file. 24828 HELP = Lists portions of the help file. 24829 NEWS = Lists the news file. 24830 BUGS = Lists the bugs file. 24831 24832Applications: 24833 XX 24834 24835Implementation Date: 24836 XX 24837 24838Program: 24839 XX 24840 24841-----QUIC------------------------------------------------------- 24842 24843QUIC 24844 24845Name: 24846 QUIC 24847 24848Type: 24849 Output Device Command 24850 24851Purpose: 24852 Direct graphical output to a QMS laser printer using the QUIC 24853 protocol. 24854 24855Syntax 1: 24856 QUIC 24857 24858 This form directs the QUIC output to the terminal screen. 24859 24860Syntax 2: 24861 DEVICE <1/2/3> QUIC 24862 24863 This form designates one of DATAPLOT's 3 devices (it will 24864 typically be device 2) to be a QUIC device. 24865 24866Examples: 24867 QUIC 24868 DEVICE 2 QUIC 24869 DEVICE 3 QUIC 24870 24871Note: 24872 QUIC fonts (for hardware generated characters) can be specified 24873 with the following command: 24874 SET QUIC FONT <font id> 24875 where <font id> is one of the following: 24876 10 - EDP font 24877 104 - Standard Roman Medium 24878 124 - Standard Roman Bold 24879 144 - Standard Roman Italic 24880 16 - Simplex Roman 24881 204 - Apollo Medium 24882 328 - Complex Roman Bold 24883 404 - Q-Typewriter 24884 444 - Q-Typewriter Italic 24885 532 - Union 24886 521 - Tektronix small 24887 522 - Tektronix medium 24888 523 - Tektronix large 24889 524 - Tektronix largest 24890 904 - Q-Gothic 24891 924 - Q-Gothic Italic 24892 536 - Q-Greek 24893 517 - Q-Greek 24894 664 - Special Math 24895 Fonts 10, 104, 124, 144, 16, 204, 328, 404, and 444 are supported 24896 on all QMS printers using QUIC. The others are downloadable fonts 24897 that may or may not be available on a given QMS. Additional 24898 information on QMS fonts can be found in the QMS Programmer's 24899 Manual for Quic. In addition the following SET commands can be 24900 used to specify the margins and resolution of the particular QMS 24901 printer (these should normally not be required): 24902 SET QMS PPI <number> sets the resolution (in points per inch). 24903 The default is 300. 24904 SET QMS [LANDSCAPE/PORTRAIT] LEFT MARGIN sets the left 24905 margin (in dots). 24906 SET QMS [LANDSCAPE/PORTRAIT] RIGHT MARGIN sets the right 24907 margin (in dots). 24908 SET QMS [LANDSCAPE/PORTRAIT] BOTTOM MARGIN sets the bottom 24909 margin (in dots). 24910 SET QMS [LANDSCAPE/PORTRAIT] TOP MARGIN sets the top 24911 margin (in dots). 24912 24913Default: 24914 Off 24915 24916Synonyms: 24917 QMS 24918DEVICE NOTES 24919 1) HARDWARE TEXT - QMS provides numerous hardware fonts. QMS fonts 24920 are fixed size and orientation fonts. Several are typeset 24921 quality fonts. 24922 2) COLOR - This device does not support color or gray scale. 24923 3) HARDWARE FILL - All area fills in software (although QMS 24924 provides a hardware fill, it is not reliable). 24925 4) DASH PATTERNS - Each dash specification generates a different 24926 type of dash pattern. 24927 5) LINE WIDTH - The QMS performs line width in hardware. 24928 6) GRAPHICS INPUT - The CROSS-HAIR command is ignored for this 24929 device. 24930 24931Related Commands: 24932 POSTSCRIPT = Direct graphical output to a Postscript 24933 device. 24934 CALCOMP = Direct graphical output to a Calcomp device. 24935 HPGL = Direct graphical output to an HPGL device. 24936 TEKTRONIX = Direct graphical output to a Tektronix device. 24937 X11 = Direct graphical output to an X11 device. 24938 DEVICE = Specify certain actions for the graphics 24939 output. 24940 SET QMS FONT = Specify the font to use on the QMS device. 24941 SET QMS PPI = Set the resolution of the QMS device. 24942 SET QMS ... MARGIN = Set the margin for the QMS device. 24943 24944Applications: 24945 XX 24946 24947Implementation Date: 24948 89/2 24949 24950Program: 24951 XX 24952 24953-----QUIT------------------------------------------------------- 24954 24955QUIT 24956 24957Name: 24958 QUIT 24959 24960Type: 24961 Support Command 24962 24963Purpose: 24964 Terminates a DATAPLOT run. 24965 24966Syntax: 24967 QUIT 24968 24969Examples: 24970 QUIT 24971 24972Default: 24973 None 24974 24975Related Commands: 24976 XX 24977 24978Synonyms: 24979 EXIT, END, HALT, STOP, BYE 24980 24981Applications: 24982 XX 24983 24984Implementation Date: 24985 Pre-1987 24986 24987Program: 24988 XX 24989 24990-----QWIN------------------------------------------------------- 24991 24992QWIN 24993 24994Name: 24995 QWIN 24996 24997Type: 24998 Output Device Command 24999 25000Purpose: 25001 Direct graphical output to a the screen when using the version of 25002 Dataplot on the IBM-PC under the Windows operating system built 25003 using the Intel Fortran compiler. 25004 25005Description: 25006 The production version of Dataplot is currently built under the 25007 Windows operating system (as of 2016/04 Windows XP, Windows 7, 25008 and Windows 8 are supported) using the Intel Visual Fortran 25009 Composer XE (2013, SP1 version) compiler. 25010 25011 Dataplot is built as a QuickWin application. QuickWin provides 25012 access to some, but not all, parts of the Windows API. QuickWin is 25013 intermediate between a console application and a full blown 25014 Windows application and provides the QuickWin graphics library to 25015 generate graphics on the screen. The command 25016 25017 DEVICE 1 QWIN 25018 25019 is used to activate the Dataplot QuickWin device driver. The 25020 default DPLOGF.TEX provided in the standard Dataplot installation 25021 for Windows will have this command, so typically you do not need to 25022 enter it. 25023 25024Syntax 1: 25025 DEVICE 1 QWIN 25026 25027 This form directs the graphics output to the terminal screen. 25028 25029Syntax 2: 25030 DEVICE 1 QWIN <width> <height> 25031 25032 This form of the command allows you to specify the width and 25033 height of the graphics window in pixel units. 25034 25035Examples: 25036 DEVICE 1 QWIN 25037 DEVICE 1 QWIN 500 350 25038 25039Note: 25040 The Dataplot executable built as a QuickWin application is run 25041 as a stand alone program (we refer to this as the command line 25042 version). For the Tcl/Tk based graphical user interface (GUI) 25043 for Dataplot, a console executable is built that does not support 25044 the QWIN device driver. The QuickWin executable is not 25045 compatible with the Tcl/Tk scripts. 25046 25047Note: 25048 A few notes on the QWIN screen driver. 25049 25050 1) There are 3 distinct windows when running the QuickWin version 25051 of Dataplot under Windows. The largest window is called the 25052 frame window. Upon starting Dataplot, a child window is 25053 automatically started for generating the alphanumeric input 25054 and output (this is called the text window). These two windows 25055 can be resized by the user with standard Windows mouse 25056 operations. When you enter the 25057 25058 DEVICE 1 QWIN 25059 25060 command, a graphics window is opened. 25061 25062 There are some menu items available on each of these windows. 25063 These are standard Windows menu items, not Dataplot specified 25064 menu options (the Help menu has been customized, but otherwise 25065 these are the default QuickWin menus). 25066 25067 In Windows, either the text or graphics window has the 25068 "focus". The window with focus will be the window on top 25069 and this is the window that recieves I/O. The default 25070 Dataplot behaviour is that when a graph is generated, 25071 focus switches to the graphics window and remains there 25072 after the plot is completed. This leaves the graphics 25073 window over the text window. To type a new command, click 25074 the mouse in the text window. Clicking the mouse on a 25075 window switches the focus to that window. Ideally, we 25076 would like to leave the graphics window on top and have the 25077 I/O switch to the text window. However, this doesn't 25078 seem possible at the moment. 25079 25080 The 11/18/96 version added the command: 25081 25082 SET QWIN FOCUS <TEXT/GRAPHICS> 25083 25084 to allow the user to specify which window gets the focus 25085 after the completion of a plot. Specifying TEXT returns 25086 the focus to the text window while specifying GRAPHICS 25087 leaves the focus on the graphics window. The default value 25088 is TEXT. 25089 25090 If the text and graphics windows are tiled, there is less need 25091 to set the focus to the graphics window. 25092 25093 One other quirk is that sometimes the text window does not 25094 scroll properly when Dataplot is first initiated. You can 25095 scroll the window manually via the mouse and scroll bar. Also, 25096 the buffer for scrolling backward in the text window is rather 25097 limited (a few screens worth, but not much further). 25098 25099 Note: The number of scroll lines in the buffer has been 25100 increased to 500 lines. Also, the scrolling 25101 when Dataplot is first initiated now works better. 25102 25103 2) This device driver supports color. Enter the command 25104 SHOW COLORS VGA for a list of available colors. Also, 25105 output sent to a black and white Postscript printer is 25106 NOT affected by the choice of colors for the screen. This 25107 means you can chose foregrand and background colors that 25108 work well on the screen without harming your Postscript 25109 output. 25110 25111 The initial version of the QWIN driver only supports the 25112 15 VGA colors. A probable future enhancement is to 25113 extend the full range of Dataplot colors to super VGA 25114 and direct color monitors. 25115 25116 Note: The QWIN device now supports the full range of 25117 colors supported in Dataplot. 25118 25119 3) Hardware characters are supported. Dataplot requests a 25120 fixed size font at the user specified size. The QuickWin 25121 library returns the closest match to the requested font. 25122 25123 The screen characters may seem smaller than characters 25124 generated with a software font. This is due to the fact 25125 that the QWIN library will match to a smaller size rather 25126 than a larger size. You can specify a software font to the 25127 screen while leaving the hardware font for the file 25128 devices by entering the command: 25129 25130 DEVICE 1 FONT SIMPLEX 25131 25132 We will probably add more complete support for the fonts 25133 provided by the QuickWin library in later releases. 25134 Specifically, this means allowing the user to specify the 25135 desired type face (e.g., Helvetica, Times Roman) and 25136 providing support for proportional spaced fonts. 25137 25138 4) Dashed lines and software line thickness is supported for 25139 the QuickWin device. The CROSS-HAIR command (for graphical 25140 input) is also supported. 25141 25142 5) The Intel Fortran Compiler has trouble if the monitor 25143 is set to "True Color" mode. The sympton is that the 25144 text window does not appear to show any characters 25145 (i.e., it is simply a blank screen). True color is 25146 set from the Windows 95/98/NT control panel. 25147 25148 If your monitor is set to true color mode, enter the 25149 following commands in the "C:\Dataplot\DPLOGF.TEX" 25150 start-up file (the drive name may differ on your system): 25151 25152 SET QWIN COLOR DIRECT 25153 DEVICE 1 QWIN 25154 25155 Note that in this case, the order of the commands is 25156 critical. That is, the color mode must be set when 25157 the QWIN device is initialized, not after. The 25158 command SET QWIN COLOR COLOR VGA resets the default. 25159 25160 For true color, the QWIN device driver supports the 25161 full range of color supported by Dataplot (enter 25162 HELP COLORS for a description of the Dataplot color 25163 model). The default VGA mode only supports 16 colors. 25164 25165 The foreground and background colors for the text 25166 window can be set for both standard VGA and the true 25167 color mode by entering the following commands after 25168 the SET QWIN COLOR <DIRECT/VGA> command but before the 25169 DEVICE 1 QWIN command: 25170 25171 SET QWIN TEXT BACKGROUND COLOR <index> 25172 SET QWIN TEXT FOREGROUND COLOR <index> 25173 25174 where <index> is an integer identifying the desired 25175 color (HELP COLOR gives the index to color mapping). 25176 For the default VGA mode, <index> is limtited to 25177 0 to 15. For direct mode, <index> is between 0 and 88. 25178 The default is a white foreground on a black background. 25179 25180 The colors for the graphics window are set with the 25181 normal Dataplot COLOR commands (e.g., LINE COLOR YELLOW). 25182 25183 Note: The above section was relevant for older versions 25184 of the Intel compiler and older versions of the 25185 Windows operating systems. You should no longer need 25186 to enter any of these commands. 25187 25188Note: 25189 The following command line options are now supported: 25190 25191 a) The size of the initial frame window (in pixels) can be set by 25192 selecting one of the following options: 25193 25194 -svga -large -extrawide 25195 25196 where "-svga" sets a size of 950 by 700, -large sets a size of 25197 1150 by 1000, and -extrawide sets a size of 1600 by 1000. These 25198 values are the number of pixels. If none of these is entered, 25199 the -svga settings will be used. 25200 25201 Alternatively, you can enter explicit values for the height and 25202 width of the frame window with the -w and -h options. For example, 25203 to set the width and height to 1150 and 1000, respectively, enter 25204 25205 -w1150 -h1000 25206 25207 The recommended choice is basically a matter of taste and the 25208 resolution you have set for your monitor. 25209 25210 b) You can use the following option to set "true color" mode: 25211 25212 -true 25213 25214 This is not preferred over the SET QWIN COLOR DIRECT as it 25215 will show the initial sign-on message. 25216 25217 Note: This option is no longer needed and should not be used. 25218 25219 c) By default, Dataplot overlaps the text and graphics windows. 25220 You can specify tiled mode with the following option: 25221 25222 -tile 25223 25224 You can also enter 25225 25226 -notile 25227 25228 to specify the non-tiled mode. 25229 25230 Tile mode has the advantage that the text and graphics windows 25231 do not overlap. The advantage of non-tiled mode is that the 25232 graphics window has a landscape orientation which is more similar 25233 to what the printed graphics will have. 25234 25235 The order for these options does not matter. 25236 25237Note: 25238 The menus accessible on the frame window are the default menus 25239 generated by the Intel compiler. 25240 25241 As of the 11/2002 version, the menu items under the Help menu 25242 now access Dataplot help rather than help for the compiler. 25243 25244Note: 25245 The handling of text with hardware fonts was upgraded for the 25246 2016/04 version. 25247 25248 The following two commands were added: 25249 25250 SET QWIN FONT WEIGHT <BOLD/NORMAL> 25251 SET QWIN FONT STYLE <ITALIC/NORMAL> 25252 25253 These commands allow you to request bold and italic appearance 25254 for fonts. 25255 25256 The SET QWIN FONT command was updated to support the following 25257 specific fonts 25258 25259 SET QWIN FONT ARIAL 25260 SET QWIN FONT TIMES NEW ROMAN 25261 SET QWIN FONT SYMBOL 25262 SET QWIN FONT ROMAN 25263 SET QWIN FONT MODERN 25264 SET QWIN FONT SCRIPT 25265 SET QWIN FONT COURIER 25266 SET QWIN FONT HELVETICA 25267 SET QWIN FONT PALATINO 25268 SET QWIN FONT TERMINAL 25269 SET QWIN FONT SYSTEM 25270 SET QWIN FONT VERDANA 25271 SET QWIN FONT GEORGIA 25272 25273 The fonts installed on a given system may vary on specific 25274 platforms. The above fonts were chosen because they are 25275 relatively common and should be available on most systems. 25276 However, it is possible that you may not have one or more of 25277 these fonts on your system. 25278 25279 Note that when Dataplot requests a font (the font family, the 25280 height and width, the use of bold or italic), the QuickWin 25281 library will try to match to the closest available font (the 25282 priority order is height, font family, width, and fixed or 25283 proportional font). 25284 25285 The SYMBOL font can be used to print Greek characters using 25286 hardware text. 25287 25288Note: 25289 The QuickWin library was originally part of the MicroSoft Fortran 25290 compiler. The Microsoft Fortran compiler became the Compaq Fortran 25291 compiler and then the Digital Visual Fortrtan compiler before being 25292 merged into the Intel Fortran compiler. 25293 25294Default: 25295 None 25296 25297Synonyms: 25298 None 25299 25300DEVICE NOTES 25301 1) HARDWARE TEXT - limited support. Dataplot requests a fixed 25302 space font at the user requested size. The QuickWin library 25303 returns the closest matching font. 25304 2) COLOR - the QWIN driver supports the full range of colors 25305 supported by Dataplot. 25306 3) HARDWARE FILL - Solid fills are generated in software. 25307 4) DASH PATTERNS - Dash patterns are supported. 25308 5) LINE WIDTH - Thick lines are generated in software as multiple 25309 lines. 25310 6) GRAPHICS INPUT - The CROSS-HAIR command is supported for this 25311 device. 25312 25313Related Commands: 25314 HPGL = Direct graphical output to an HPGL device. 25315 DEVICE = Specify certain actions for the graphics 25316 output. 25317 POSTSCRIPT = Direct graphical output to a Postscript 25318 device. 25319 25320Applications: 25321 Screen Graphics 25322 25323Implementation Date: 25324 11/1996 25325 2002/11: Added the "-tile" option 25326 2002/11: The "Help" menus modified to access Dataplot (rather than 25327 the compiler) help 25328 2014/12: Increase the size of the buffer in the text window and 25329 fix the initial scrolling 25330 2015/10: Check if graphics window is already open when a 25331 DEVICE 1 QWIN command is entered 25332 2016/04: Updated handling of text with hardware fonts 25333 2016/04: Added SET QWIN FONT WEIGHT 25334 2016/04: Added SET QWIN FONT STYLE 25335 25336Program: 25337 DEVICE 1 QWIN 25338 PLOT SIN(X) FOR X = -6 0.1 6 25339 25340-----QWIN SYSTEM (SET)--------------------------------------- 25341 25342QWIN SYSTEM 25343 25344Name: 25345 QWIN SYSTEM (SET) 25346 25347Type: 25348 Set Subcommand 25349 25350Purpose: 25351 For the version of Dataplot built with the Visual Fortran compiler, 25352 it specifies whether operating system commands are invoked with 25353 the SYSTEMQQ library function or the WinExec library function. 25354 25355Description: 25356 The Dataplot command SYSTEM is used to invoke an operating system 25357 command or an external program (e.g., a web browser). In addition, 25358 several other Dataplot commands (e.g., WEB HELP) invoke external 25359 programs. Note that invoking operating system commands and 25360 external programs is not part of the Fortran standard, so this 25361 capability in Dataplot is operating system and compiler dependent. 25362 25363 The command line version of Dataplot is built using the Visual 25364 Fortran (previously the Microsoft) compiler as a QuickWin (QWIN) 25365 application. By default, the SYSTEMQQ library routine is used to 25366 invoke operating system commands and external programs. The 25367 primary drawback of this option is that control does not return to 25368 Dataplot until the operating system command completes execution. 25369 25370 Alternatively, the WinExec function can be used. The advantage of 25371 this method is that control passes back to Dataplot after the 25372 command is issued (i.e., it doesn't wait for the command to 25373 complete). However, the drawback is that DOS type commands do not 25374 work. 25375 25376 The basic recommendation is that if you want to execute a Windows 25377 application (e.g., the browser, notepad, Word, etc.), then set this 25378 option to WINEXEC. However, to issue a DOS type command via the 25379 Dataplot SYSTEM command, you should set this option to SYSTEMQQ (the 25380 default). 25381 25382 In particular, I recommend setting this option to WINEXEC before 25383 using the WEB HELP (or any other command starting with WEB) command. 25384 This allows you to enter additional Dataplot commands without 25385 exiting the browser. 25386 25387Syntax: 25388 SET QWIN SYSTEM <SYSTEMQQ/WINEXEC> 25389 where SYSTEMQQ specifies that calls to the operating system are 25390 invoked with SYSTEMQQ and WINEXEC specificies that calls to 25391 to the operating system are invoked with WinExec. 25392 25393Examples: 25394 SET QWIN SYSTEM WINEXEC 25395 SET QWIN SYSTEM SYSTEMQQ 25396 25397Note: 25398 This command only applies tom the command line version of Dataplot 25399 under Microsoft Windows (i.e., the executable built with the 25400 Visual Fortran (previously the Microsoft) compiler. It is 25401 ignored on all other systems. 25402 25403Default: 25404 The default is SYSTEMQQ. 25405 25406Synonyms: 25407 None 25408 25409Related Commands: 25410 WEB HELP = View the Dataplot online Reference Manual. 25411 SYSTEM = Enter an operating system command. 25412 25413Applications: 25414 Interacting with Microsoft Windows 25415 25416Implementation Date: 25417 2002/11 25418 25419Program: 25420 SET QWIN SYSTEM WINEXEC 25421 WEB HELP PLOT 25422 SET QWIN SYSTEM SYSTEMQQ 25423 SYSTEM DIR C:\DATAPLOT\DATA | MORE 25424 25425--------------------------------------------------------- 25426 25427 25428 25429 25430 25431 25432 25433 25434 25435 25436 25437 25438 25439 25440 25441 25442 25443 25444 25445 25446 25447 25448 25449 25450 25451 25452 25453 25454 25455 25456 25457 25458 25459 25460 25461 25462 25463 25464 25465 25466 25467 25468 25469 25470 25471 25472 25473 25474 25475 25476 25477 25478 25479 25480 25481 25482 25483 25484 25485 25486 25487 25488 25489 25490 25491 25492 25493 25494 25495 25496 25497 25498 25499 25500------------------------- *R* ZZZZZ-------------------- 25501 25502-----R CHART------------------------------------------------------- 25503 25504R CHART 25505 25506Name: 25507 R CHART 25508 25509Type: 25510 Graphics Command 25511 25512Purpose: 25513 Generates a range control chart. 25514 25515Description: 25516 A range control chart is a data analysis analysis technique for 25517 determining if a measurement process has gone out of statistical 25518 control. The R chart is sensitive to changes in variation in the 25519 measurement process. It consist of: 25520 Vertical axis = the range for each sub-group; 25521 Horizontal axis = sub-group designation. 25522 In addition, horizontal lines are drawn at the mean range value 25523 and at the upper and lower control limits. 25524 25525Syntax: 25526 R CHART <y> <x> <SUBSET/EXCEPT/FOR qualification> 25527 where <y> is the response (= dependent) variable (containing the 25528 raw data values); 25529 <x> is an independent variable (containing the sub-group 25530 identifications); 25531 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 25532 25533Examples: 25534 R CHART Y X 25535 25536Note: 25537 The distribution of the response variable is assumed to be normal. 25538 This assumption is the basis for calculating the upper and lower 25539 control limits. 25540 25541Note: 25542 The attributes of the 4 traces can be controlled by the standard 25543 LINES, CHARACTERS, BARS, and SPIKES commands. Trace 1 is the 25544 response variable, trace2 is the mean line, and traces 3 and 4 are 25545 the control limits. Some analysts prefer to draw the response 25546 variable as a spike or character rather than a connected line. 25547 25548Default: 25549 None 25550 25551Synonyms: 25552 RANGE CHART for R CHART 25553 R CONTROL CHART for R CHART 25554 RANGE CONTROL CHART for R CHART 25555 25556Related Commands: 25557 X CHART = Generates a mean control chart. 25558 S CHART = Generates a standard deviation control chart. 25559 P CHART = Generates a p control chart. 25560 NP CHART = Generates a Np control chart. 25561 U CHART = Generates a U control chart. 25562 C CHART = Generates a C control chart. 25563 CHARACTERS = Sets the types for plot characters. 25564 LINES = Sets the types for plot lines. 25565 SPIKES = Sets the on/off switches for plot spikes. 25566 BARS = Sets the on/off switches for plot bars. 25567 PLOT = Generates a data or function plot. 25568 LAG PLOT = Generates a lag plot. 25569 4-PLOT = Generates 4-plot univariate analysis. 25570 RANGE PLOT = Generates a range (vs subset) plot. 25571 25572Applications: 25573 Quality Control 25574 25575Implementation Date: 25576 88/2 25577 25578Program: 25579 SKIP 25 25580 READ GEAR.DAT DIAMETER BATCH 25581 . 25582 LINE SOLID SOLID DOT DOT 25583 TITLE AUTOMATIC 25584 X1LABEL GROUP-ID 25585 Y1LABEL RANGE 25586 RANGE CONTROL CHART DIAMETER BATCH 25587 25588-----RADIANS------------------------------------------------------- 25589 25590RADIANS 25591 25592Name: 25593 RADIANS 25594 25595Type: 25596 Support Command 25597 25598Purpose: 25599 Specifies that all subsequent trigonometric calculations (e.g., 25600 LET Y = SIN(X) and ANGLE 1.570746) be carried out in radians (as 25601 opposed to degrees or grads). 25602 25603Syntax: 25604 RADIANS <ON or OFF> 25605 where ON specifies that radian units will be used while OFF 25606 reverts the units to degrees. 25607 25608Examples: 25609 RADIANS 25610 RADIANS ON 25611 RADIANS OFF 25612 25613Note: 25614 Entering the RADIANS command without any arguments is equivalent 25615 to entering RADIANS ON. 25616 25617Default: 25618 Radians 25619 25620Synonyms: 25621 None 25622 25623Related Commands: 25624 TEXT = Writes a text string. 25625 DEGREES = Sets the angle units to degrees. 25626 GRADS = Sets the angle units to grads. 25627 ANGLE UNITS = Sets the angle units (to degrees/radians/grads). 25628 ANGLE = Sets the angle for TEXT string. 25629 FONT = Sets the font for TEXT characters. 25630 25631Applications: 25632 Trigonometry 25633 25634Implementation Date: 25635 Pre-1987 25636 25637Program: 25638 RADIANS 25639 PLOT SIN(X) FOR X = -6 0.1 6 25640 25641-----RANDOM COMPOSITION (LET)----------------------------------------- 25642 25643RANDOM COMPOSITION 25644 25645Name: 25646 RANDOM COMPOSITION (LET) 25647 25648Type: 25649 Let Subcommand 25650 25651Purpose: 25652 Generate a random composition. 25653 25654Description: 25655 Given positive integers n and k, a composition of n into k parts 25656 is defined as 25657 25658 n = r1 + r2 + ... + rk (r(i) >= 0, i = 1,k) 25659 25660 The number of compositions is given by 25661 25662 (n+k-1 n) = (n+k-1)!/[(n!*(k-1)!] 25663 25664 This command generates a single random composition. 25665 25666 The output is an array of size k. 25667 25668Syntax: 25669 LET <y> = RANDOM COMPOSITION FOR I = 1 1 <k> 25670 where <k> is a number or parameter that specifies the size of 25671 the composition; 25672 and <y> is a variable where the random composition is saved. 25673 25674 This command must be preceeded with the command 25675 25676 LET N = <value> 25677 25678Examples: 25679 LET N = 5 25680 LET K = 3 25681 LET Y = RANDOM COMPOSITION FOR I = 1 1 K 25682 25683Note: 25684 Dataplot implements this command using the RANCOM algorithm 25685 described in Nijenhuis and Wilf (see Reference section 25686 below). 25687 25688Note: 25689 Dataplot supports a number of different random number 25690 generators. Enter HELP RANDOM NUMBER GENERATOR for details. 25691 25692 The SEED command can be used to specify a seed for the random 25693 number generator. 25694 25695Default: 25696 None 25697 25698Synonyms: 25699 None 25700 25701Related Commands: 25702 LET = Generate data transformations. 25703 RANDOM PERMUTATION = Generate a random permutation. 25704 RANDOM SUBSET = Generate a random subset. 25705 RANDOM K-SET OF N-SET = Generate a random k-set of n-set. 25706 RANDOM PARTITION = Generate a random partition. 25707 RANDOM EQUIVALENCE RELATION = Generate a random equivalence relation. 25708 NEXT SUBSET = Generate the next subset of a set. 25709 NEXT PERMUTATION = Generate the next permutation. 25710 NEXT K-SET OF N-SET = Generate the next k-set of n-set. 25711 NEXT COMPOSITION = Generate the next composition. 25712 NEXT PARTITION = Generate the next partition. 25713 NEXT EQUIVALENCE RELATION = Generate the next composition. 25714 25715References: 25716 Nijenhuis and Wilf (1978), "Combinatorial Algorithms", 25717 Second Edition, Academic Press, Chapter 6. 25718 25719Applications: 25720 Combinatorial Analysis 25721 25722Implementation Date: 25723 2008/4 25724 25725Program: 25726 LET N = 8 25727 LET K = 3 25728 LET Y = RANDOM COMPOSITION FOR I = 1 1 K 25729 PRINT Y 25730 25731-----RANDOM EQUIVALENCE RELATION (LET)------------------------------- 25732 25733RANDOM EQUIVALENCE RELATION 25734 25735Name: 25736 RANDOM EQUIVALENCE RELATION (LET) 25737 25738Type: 25739 Let Subcommand 25740 25741Purpose: 25742 Generate a random equivalence relation of an n-element set. 25743 25744Description: 25745 Given a set S = {1, 2, ..., n}, a random partition of S 25746 is defined as a collection of sets T1, T2, ... , Tk 25747 satisfying 25748 25749 1) The intersection of T(i) and T(j) is the empty 25750 set for i not equal j. 25751 25752 2) The union of all k sets contains all the elements 25753 of S. 25754 25755 For example, if n = 3, then there are 5 possible partitions: 25756 25757 {1, 2, 3} 25758 {1,2} {3} 25759 {1, 3} {2} 25760 {2, 3} {1} 25761 {1} {2} {3} 25762 25763 The output of this command is an array of size n where 25764 the ith element identifies the class which i belongs to. 25765 For example, the following array (for n = 5) 25766 25767 3 3 1 2 2 25768 25769 identifies the partition 25770 25771 {3} {4, 5} {1, 2} 25772 25773Syntax: 25774 LET <y> = RANDOM EQUIVALENCE RELATION 25775 where <y> is a variable where the random equivalence relation 25776 is saved. 25777 25778 This command must be preceeded with the command 25779 25780 LET N = <value> 25781 25782Examples: 25783 LET N = 5 25784 LET Y = RANDOM EQUIVALENCE RELATION 25785 25786Note: 25787 Dataplot implements this command using the RANEQU algorithm 25788 described in Nijenhuis and Wilf (see Reference section 25789 below). 25790 25791Note: 25792 Dataplot supports a number of different random number 25793 generators. Enter HELP RANDOM NUMBER GENERATOR for details. 25794 25795 The SEED command can be used to specify a seed for the random 25796 number generator. 25797 25798Default: 25799 None 25800 25801Synonyms: 25802 None 25803 25804Related Commands: 25805 LET = Generate data transformations. 25806 RANDOM PERMUTATION = Generate a random permutation. 25807 RANDOM SUBSET = Generate a random subset. 25808 RANDOM K-SET OF N-SET = Generate a random k-set of n-set. 25809 RANDOM COMPOSITION = Generate a random composition. 25810 RANDOM PARTITION = Generate a random partition. 25811 NEXT SUBSET = Generate the next subset of a set. 25812 NEXT PERMUTATION = Generate the next permutation. 25813 NEXT K-SET OF N-SET = Generate the next k-set of n-set. 25814 NEXT COMPOSITION = Generate the next composition. 25815 NEXT PARTITION = Generate the next partition. 25816 NEXT EQUIVALENCE RELATION = Generate the next composition. 25817 25818References: 25819 Nijenhuis and Wilf (1978), "Combinatorial Algorithms", 25820 Second Edition, Academic Press, Chapter 12. 25821 25822Applications: 25823 Combinatorial Analysis 25824 25825Implementation Date: 25826 2008/6 25827 25828Program: 25829 LET N = 8 25830 LET Y = RANDOM EQUIVALENCE RELATION 25831 PRINT Y 25832 25833-----RANDOM ERROR QUANTITY (LET)----------------------------------------- 25834 25835RANDOM ERROR QUANTITY 25836 25837Name: 25838 RANDOM ERROR QUANTITY (LET) 25839 25840Type: 25841 Let Subcommand 25842 25843Purpose: 25844 Compute the random error quantity. 25845 25846Description: 25847 In a two sample proficiency study, a laboratory measures two 25848 samples. We refer to these as sample X and sample Y. The 25849 random error quantity is then defined as 25850 25851 REQ = [(X(i) - Y(i)) - (Xmed - Ymed)] 25852 25853 with Xmed and Ymed denoting the medians of samples X and Y, 25854 respectively. 25855 25856 The ASTM E 2489 - 06 standard gives the following rationale for the 25857 random error quantity. 25858 25859 1. The medians for each sample define consensus values 25860 for each sample. 25861 25862 2. For a given laboratory, X(i) contains variation from the 25863 consensus value (the median value) due to random error 25864 (within-laboratory error) and systematic error (bias). 25865 Likewise for Y(i). 25866 25867 3. It is assumed that the systematic error is the same for sample X 25868 and sample Y for a given laboratory. Based on this, X(i) - Y(i) 25869 will subtract out the systematic error leaving only random 25870 error. 25871 25872 4. Subtracting Xmed - Ymed removes any difference that appears 25873 for the medians of sample X and sample Y. 25874 25875 5. The random error quantity should then contain only the 25876 laboratories random error. These values can be used to 25877 compare the within-laboratory performance of the various 25878 laboratories. 25879 25880Syntax: 25881 LET <yout> = RANDOM ERROR QUANTITY <x> <y> 25882 <SUBSET/EXCEPT/FOR qualification> 25883 where <x> is the variable containing the measurements for sample X; 25884 <y> is the variable containing the measurements for sample Y; 25885 <yout> is a variable where the computed random error quantities 25886 are saved; 25887 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 25888 25889 Note that <x> and <y> are paired so they must be of the same length. 25890 25891Examples: 25892 LET RANERR = RANDOM ERROR QUANTITY X Y 25893 25894Default: 25895 None 25896 25897Synonyms: 25898 None 25899 25900Related Commands: 25901 TWO SAMPLE PROFICIENCY TEST = Perform a two sample proficiency test 25902 based on ASTM E 2489. 25903 MEDIAN = Compute the median of a variable. 25904 25905Reference: 25906 "Standard Practice for Statistical Analysis of One-Sample 25907 and Two-Sample Proficiency Testing Programs", ASTM 25908 International, 100 Barr Harbor Drive, PO BOX C700, 25909 West Conshohoceken, PA 19428-2959, USA. 25910 25911Applications: 25912 Proficiency Testing 25913 25914Implementation Date: 25915 2014/12 25916 25917Program: 25918 skip 25 25919 read e2489b.dat lab y1 y2 25920 . 25921 let ranerr = random error quantity y1 y2 25922 set write decimals 2 25923 print lab ranerr 25924 25925-----RANDOM K-SET OF N-SET (LET)----------------------------------------- 25926 25927RANDOM K-SET OF N-SET 25928 25929Name: 25930 RANDOM K-SET OF N-SET (LET) 25931 25932Type: 25933 Let Subcommand 25934 25935Purpose: 25936 Generate a random k-set of a an n-set. 25937 25938Description: 25939 Given a set of n elements {1, 2, ..., n}, a basic 25940 combinatorial problem is the combination of n things 25941 taken k at a time. For a given n and k, there are 25942 25943 (n k) = n!/[k!*(n-k)!] 25944 25945 k-sets of the original n-set. 25946 25947 This command generates a single random k-set. 25948 25949 The output is an array of size k that identifies the 25950 elements included in the k-set. 25951 25952Syntax: 25953 LET <y> = RANDOM K-SET OF N-SET FOR I = 1 1 <k> 25954 where <k> is a number or parameter that specifies the size of 25955 the k-set; 25956 and where <y> is a variable where the random k-set is saved. 25957 25958 This command must be preceeded with the command 25959 25960 LET N = <value> 25961 25962Examples: 25963 LET N = 5 25964 LET K = 3 25965 LET Y = RANDOM K-SET OF N-SET FOR I = 1 1 K 25966 25967Note: 25968 Dataplot implements this command using the algorithm 25969 RANKSB described in Nijenhuis and Wilf (see Reference section 25970 below). 25971 25972Note: 25973 Dataplot supports a number of different random number 25974 generators. Enter HELP RANDOM NUMBER GENERATOR for details. 25975 25976 The SEED command can be used to specify a seed for the random 25977 number generator. 25978 25979Default: 25980 None 25981 25982Synonyms: 25983 None 25984 25985Related Commands: 25986 LET = Generate data transformations. 25987 RANDOM PERMUTATION = Generate a random permutation. 25988 RANDOM SUBSET = Generate a random subset. 25989 RANDOM COMPOSITION = Generate a random composition. 25990 RANDOM PARTITION = Generate a random partition. 25991 RANDOM EQUIVALENCE RELATION = Generate a random equivalence relation. 25992 NEXT SUBSET = Generate the next subset of a set. 25993 NEXT PERMUTATION = Generate the next permutation. 25994 NEXT K-SET OF N-SET = Generate the next k-set of n-set. 25995 NEXT COMPOSITION = Generate the next composition. 25996 NEXT PARTITION = Generate the next partition. 25997 NEXT EQUIVALENCE RELATION = Generate the next composition. 25998 25999References: 26000 Nijenhuis and Wilf (1978), "Combinatorial Algorithms", 26001 Second Edition, Academic Press, Chapter 4. 26002 26003Applications: 26004 Combinatorial Analysis 26005 26006Implementation Date: 26007 2008/4 26008 26009Program: 26010 LET N = 8 26011 LET K = 3 26012 LET Y = RANDOM K-SET OF N-SET FOR I = 1 1 K 26013 PRINT Y 26014 26015-----RANDOM PARTITION (LET)----------------------------------------- 26016 26017RANDOM PARTITION 26018 26019Name: 26020 RANDOM PARTITION (LET) 26021 26022Type: 26023 Let Subcommand 26024 26025Purpose: 26026 Generate a random partition of a positive integer. 26027 26028Description: 26029 Given a positive integer n, a partition of n is defined as 26030 26031 n = r1 + r2 + ... + rk (r1 >= r2 >= ... >= rk) 26032 26033 where r1, r2, ...., rk are positive integers. 26034 26035 For example, if n = 6, then there are 3 partitions: 26036 26037 6 = 4 + 1 + 1 26038 = 3 + 2 + 1 26039 = 2 + 2 + 2 26040 26041Syntax: 26042 LET <y> = RANDOM PARTITION 26043 where <y> is a variable where the random partition is saved. 26044 26045 This command must be preceeded with the command 26046 26047 LET N = <value> 26048 26049Examples: 26050 LET N = 5 26051 LET Y = RANDOM PARTITION 26052 26053Note: 26054 Dataplot implements this command using the RANPAR algorithm 26055 described in Nijenhuis and Wilf (see Reference section 26056 below). 26057 26058Note: 26059 Dataplot supports a number of different random number 26060 generators. Enter HELP RANDOM NUMBER GENERATOR for details. 26061 26062 The SEED command can be used to specify a seed for the random 26063 number generator. 26064 26065Default: 26066 None 26067 26068Synonyms: 26069 None 26070 26071Related Commands: 26072 LET = Generate data transformations. 26073 RANDOM PERMUTATION = Generate a random permutation. 26074 RANDOM SUBSET = Generate a random subset. 26075 RANDOM K-SET OF N-SET = Generate a random k-set of n-set. 26076 RANDOM COMPOSITION = Generate a random composition. 26077 RANDOM EQUIVALENCE RELATION = Generate a random equivalence relation. 26078 NEXT SUBSET = Generate the next subset of a set. 26079 NEXT PERMUTATION = Generate the next permutation. 26080 NEXT K-SET OF N-SET = Generate the next k-set of n-set. 26081 NEXT COMPOSITION = Generate the next composition. 26082 NEXT PARTITION = Generate the next partition. 26083 NEXT EQUIVALENCE RELATION = Generate the next composition. 26084 26085References: 26086 Nijenhuis and Wilf (1978), "Combinatorial Algorithms", 26087 Second Edition, Academic Press, Chapter 10. 26088 26089Applications: 26090 Combinatorial Analysis 26091 26092Implementation Date: 26093 2008/4 26094 26095Program: 26096 LET N = 8 26097 LET Y = RANDOM PARTITION 26098 PRINT Y 26099 26100-----RANDOM PERMUTATION (LET)----------------------------------------- 26101 26102RANDOM PERMUTATION 26103 26104Name: 26105 RANDOM PERMUTATION (LET) 26106 26107Type: 26108 Let Subcommand 26109 26110Purpose: 26111 Generate a set of random permutations. 26112 26113Description: 26114 For a given size N, the integers from 1 to N are randomly sampled 26115 (without replacement) until all elements have been selected. 26116 26117 This command is useful for randomly assigning a list of items (to 26118 groups, treatments, etc.). 26119 26120Syntax: 26121 LET <resp> = RANDOM PERMUTATION FOR I = <start> <inc> <stop> 26122 where <start> is a number or parameter that identifies the first 26123 row of <resp> in which the permutated values are saved 26124 (typically it has a value of 1); 26125 <inc> is a number or parameter that identifies the row 26126 increment of <resp> in which the permutated values are 26127 saved (typically it has a value of 1); 26128 <stop> is a number or parameter that identifies the last row 26129 of <resp> in which the permutated values are saved; 26130 <resp> is a variable where the permutated values are saved. 26131 26132Examples: 26133 LET RP = RANDOM PERMUTATION FOR I = 1 1 100 26134 26135Note: 26136 The following are similar: 26137 LET Y1 = RANDOM PERMUTATION FOR I = 1 1 N 26138 and 26139 LET N = 100 26140 LET Y2 = DISCRETE UNIFORM RANDOM NUMBERS FOR I = 1 1 N 26141 The distinction is that the first command (RANDOM PERMUTATIONS) 26142 does the sampling without replacement while the second command does 26143 the sampling with replacement (so you can have repeat values). 26144 26145Note: 26146 The SEED command can be used to specify a seed for the random 26147 number generation. 26148 26149Default: 26150 None 26151 26152Synonyms: 26153 None 26154 26155Related Commands: 26156 LET = Generate data transformations. 26157 BOOTSTRAP SAMPLE = Generate a bootstrap sample. 26158 BOOTSTRAP INDEX = Generate a bootstrap index. 26159 JACKNIFE INDEX = Generate a jacknife index. 26160 BOOTSTRAP PLOT = Generate a bootstrap plot. 26161 JACKNIFE PLOT = Generate a jacknife plot. 26162 26163Applications: 26164 Experimental Design 26165 26166Implementation Date: 26167 Pre-1987 26168 26169Program: 26170 LET N = 35 26171 LET Y = RANDOM PERMUTATION FOR I = 1 1 N 26172 PRINT Y 26173 26174-----RANDOM NUMBER GENERATOR (SET)------------------------------------ 26175 26176RANDOM NUMBER GENERATOR 26177 26178Name: 26179 RANDOM NUMBER GENERATOR (SET) 26180 26181Type: 26182 Set Subcommand 26183 26184Purpose: 26185 Specify which uniform random number generator to use. 26186 26187Description: 26188 Random numbers for all supported probability distributions 26189 are ultimately based on an underlying uniform (0,1) distribution. 26190 26191 Much research has been devoted to developing good uniform 26192 random number generators. Dataplot now supports a number of 26193 alternative uniform random number generators. 26194 26195 Note that the default generator (i.e., the one that has been in 26196 Dataplot for many years) is based on Fibonacci sequence as 26197 defined by Marsagalia. Note that this is equivalent to the 26198 generator UNI of Jim Blue, David Kahaner, and George Marsagalia 26199 that is in the NIST CMLIB library. 26200 26201 Support is now provided for a linear congruential generator 26202 written by Fullerton (NIST CMLIB routine RUNIF) and a multiplicative 26203 congruential generator (ACM algorithm 599). In addition, 26204 two generators based on the generalized feedback shift 26205 register (GFSR) methods are supported. The first is based on the 26206 original algorithm of Lewis and Payne (Journal of the ACM, 26207 Volume 20, pp. 456-468). The second is an alternative 26208 implementation given by Fushimi and Tezuka (Journal of the 26209 ACM, Volume 26, pp. 516-523). Both are based on codes 26210 given by Monohan (2000) in "Numerical Methods of Statistics". 26211 Support is also provided for the Applied Statistics algorithm 26212 183. AS183 is based on the fractional part of the sum of 3 26213 multiplicative congruential generators. It requires 3 integers 26214 be specified initially. Dataplot uses the multiplicative 26215 congruenetial generator (which depends on the SEED command) 26216 to randomly generate these 3 integers. 26217 26218 These 6 generators are used to generate uniform random numbers. 26219 Random numbers for other distributions are then derived from 26220 these uniform random numbers. 26221 26222 Note that you can use the SEED command to change the random numbers 26223 generated as well. The SEED does not apply to the 2 GFSR 26224 generators (these each have their own initialization routines). 26225 26226Syntax: 26227 SET RANDOM NUMBER GENERATOR <generator> 26228 where <generator> is one of the following: 26229 26230 FIBONACCI 26231 LINEAR CONGRUENTIAL 26232 MULTIPLICATIVE CONGRUENTIAL 26233 GFSR 26234 FUSHIMI 26235 AS183 26236 GENZ 26237 LUXURY 26238 FIBONACCI CONGRUENTIAL 26239 MERSENNE TWISTER 26240 26241Examples: 26242 SET RANDOM NUMBER GENERATOR FIBONACCI 26243 SET RANDOM NUMBER GENERATOR LINEAR CONGRUENTIAL 26244 SET RANDOM NUMBER GENERATOR MULTIPLICATIVE CONGRUENTIAL 26245 SET RANDOM NUMBER GENERATOR GFSR 26246 SET RANDOM NUMBER GENERATOR FUSHIMI 26247 SET RANDOM NUMBER GENERATOR AS183 26248 SET RANDOM NUMBER GENERATOR GENZ 26249 SET RANDOM NUMBER GENERATOR LUXURY 26250 SET RANDOM NUMBER GENERATOR FIBONACCI CONGRUENTIAL 26251 SET RANDOM NUMBER GENERATOR MERSENNE TWISTER 26252 26253Note: 26254 The following additional random number generators have been 26255 added: 26256 26257 1) GENZ - Alan Genz implementation of Pierre L'Ecuyer 26258 generator described in "Combined Multiple Recursive 26259 Random Number Generators" (see Reference section below). 26260 26261 2) LUXURY - based on the Marsagalia and Zaman 26262 borrow-and-carry generator. Uses a code written 26263 by F. James and incorporating improvements by 26264 M. Luscher. 26265 26266 3) FIBONNACI CONGRUENTIAL - combines the Fibonnaci generator 26267 with a congruential generator. Method from Kahander and 26268 Marsagalia in "Numerical Methods and Software". 26269 26270 4) MERSENNE TWISTER - original C algorithm coded by 26271 Takuji Nishimura. Dataplot uses the Fortran 90 26272 translation provided by Hiroshi Takano. This generator 26273 may not work as intended on versions of Dataplot compiled 26274 with Fortran 77 compilers. It uses some intrinsic 26275 functions that are part of the Fortran 90 standard, 26276 but not the Fortran 77 standard. Some Fortran 77 26277 compilers may support these functions, but this support 26278 is optional. 26279 26280Default: 26281 FIBONACCI 26282 26283Synonyms: 26284 None 26285 26286Related Commands: 26287 RANDOM NUMBERS = Generate random numbers for 60+ distributions. 26288 PROBABILITY PLOT = Generate a probability plot. 26289 HISTOGRAM = Generate a histogram. 26290 RUNS TEST = Generate a runs test. 26291 26292Reference: 26293 "Applied Statistics Algorithms", P. Griffiths and I. D. Hill, 26294 Ellis Horwood Limited, 1985. 26295 26296 "Numerical Analysis for Statistics", John Monohan, 26297 Oxford University Press, 2000. 26298 26299 "Combined Multiple Recursive Random Number Generators", 26300 Pierre L'Ecuyer, Operations Research 44, 1996, pp. 816-822. 26301 26302 M. Luscher, Computer Physics Communications, 79 (1994) 100. 26303 26304 F. James, Computer Physics Communications, 79 (1994) 111. 26305 26306 "Numerical Methods and Software", David Kahaner, Cleve Moler, 26307 and Stephen Nash, Prentice-Hall, 1989. 26308 26309Applications: 26310 Random number generation 26311 26312Implementation Date: 26313 2002/5 26314 2003/5: Added support for the Alan Genz and Luxury random number 26315 generators 26316 2003/10: Added support for the Fibonnaci-Congruential and 26317 Mersenne twister random number generators 26318 26319Program: 26320 title case asis 26321 case asis 26322 . 26323 multiplot corner coordinates 0 0 100 100 26324 multiplot scale factor 2 26325 multiplot 2 2 26326 . 26327 let y = uniform random numbers for i = 1 1 1000 26328 title Dataplot (Fibonacci) Random Numbers 26329 uniform prob plot y 26330 move 50 8 26331 just center 26332 text PPCC = ^ppcc 26333 . 26334 set random number generator linear congruential 26335 let y2 = uniform random numbers for i = 1 1 1000 26336 title Linear Congruential Random Numbers 26337 uniform prob plot y2 26338 move 50 8 26339 just center 26340 text PPCC = ^ppcc 26341 . 26342 set random number generator multiplicative congruential 26343 let y3 = uniform random numbers for i = 1 1 1000 26344 title Multiplicative Congruential Random Numbers 26345 uniform prob plot y3 26346 move 50 8 26347 just center 26348 text PPCC = ^ppcc 26349 . 26350 end of multiplot 26351 26352-----RANDOM SUBSET (LET)----------------------------------------- 26353 26354RANDOM SUBSET 26355 26356Name: 26357 RANDOM SUBSET (LET) 26358 26359Type: 26360 Let Subcommand 26361 26362Purpose: 26363 Generate a random subset. 26364 26365Description: 26366 A basic combinatorial problem is to generate the 2**n subsets 26367 of the set {1, 2, ..., n}. 26368 26369 This command generates a single random subset among the 26370 2**n possible subsets. 26371 26372 The output is an array of zero and one values where zero 26373 for the ith element of the set indicates the element is not 26374 present and a value of one indicates the ith element is 26375 present. For example, if n = 5 an output array of 26376 26377 1 0 0 1 1 26378 26379 specifies that elements 1, 4, and 5 are present while 26380 elements 2 and 3 are not. 26381 26382Syntax: 26383 LET <y> = RANDOM SUBSET FOR I = 1 1 <n> 26384 where <n> is a number or parameter that specifies the size of 26385 the set; 26386 and <y> is a variable where the random subset is saved. 26387 26388Examples: 26389 LET N = 5 26390 LET Y1 = RANDOM SUBSET FOR I = 1 1 N 26391 26392Note: 26393 Dataplot implements this command using the algorithm 26394 described in Nijenhuis and Wilf (see Reference section 26395 below). 26396 26397Note: 26398 Dataplot supports a number of different random number 26399 generators. Enter HELP RANDOM NUMBER GENERATOR for details. 26400 26401 The SEED command can be used to specify a seed for the random 26402 number generator. 26403 26404Default: 26405 None 26406 26407Synonyms: 26408 None 26409 26410Related Commands: 26411 LET = Generate data transformations. 26412 RANDOM PERMUTATION = Generate a random permutation. 26413 RANDOM K-SET OF N-SET = Generate a random k-set of n-set. 26414 RANDOM COMPOSITION = Generate a random composition. 26415 RANDOM PARTITION = Generate a random partition. 26416 RANDOM EQUIVALENCE RELATION = Generate a random equivalence relation. 26417 NEXT SUBSET = Generate the next subset of a set. 26418 NEXT PERMUTATION = Generate the next permutation. 26419 NEXT K-SET OF N-SET = Generate the next k-set of n-set. 26420 NEXT COMPOSITION = Generate the next composition. 26421 NEXT PARTITION = Generate the next partition. 26422 NEXT EQUIVALENCE RELATION = Generate the next composition. 26423 26424References: 26425 Nijenhuis and Wilf (1978), "Combinatorial Algorithms", 26426 Second Edition, Academic Press, Chapter 2. 26427 26428Applications: 26429 Combinatorial Analysis 26430 26431Implementation Date: 26432 2008/4 26433 26434Program: 26435 LET N = 10 26436 LET Y = RANDOM SUBSET FOR I = 1 1 N 26437 PRINT Y 26438 26439-----RANGE (LET)--------------------------------------------------- 26440 26441RANGE 26442 26443Name: 26444 RANGE (LET) 26445 26446Type: 26447 Let Subcommand 26448 26449Purpose: 26450 Compute the range of a variable. 26451 26452Description: 26453 The range is the difference between the largest and smallest value. 26454 26455Syntax: 26456 LET <par> = RANGE <y1> <SUBSET/EXCEPT/FOR qualification> 26457 where <y1> is the variable for which the range is to be computed; 26458 <par> is a parameter where the computed range is saved; 26459 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 26460 26461Examples: 26462 LET A = RANGE Y1 26463 LET A = RANGE Y1 SUBSET TAG > 2 26464 26465Default: 26466 None 26467 26468Synonyms: 26469 None 26470 26471Related Commands: 26472 MEAN (LET) = Compute the mean of a variable. 26473 STANDARD DEVIATION (LET) = Compute the standard deviation of 26474 a variable. 26475 26476Applications: 26477 Exploratory Data Analysis 26478 26479Implementation Date: 26480 XX 26481 26482Program: 26483 LET X1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 26484 LET A = RANGE Y1 26485 26486-----RANGE PLOT-------------------------------------------------- 26487 26488RANGE PLOT 26489 26490Name: 26491 RANGE PLOT 26492 26493Type: 26494 Graphics Command 26495 26496Purpose: 26497 Generates a range plot. 26498 26499Description: 26500 A range plot is a plot consisting of subsample ranges versus 26501 subsample index. The subsample range is the difference between the 26502 maximum and minimum of the data in the subsample. The range plot 26503 is used to answer the question-- "Does the subsample variation 26504 change over different subsamples?". It consists of: 26505 Vertical axis = subsample range; 26506 Horizontal axis = subsample index. 26507 The range plot yields 2 traces: 26508 1. a subsample range trace; and 26509 2. a full-sample range reference line. 26510 Like usual, the appearance of these 2 traces is 26511 controlled by the first 2 settings of the LINES, 26512 CHARACTERS, SPIKES, BARS, and similar attributes. 26513 26514Syntax: 26515 RANGE PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 26516 where <y> is the response (= dependent) variable; 26517 <x> is the subsample identifier variable (this variable 26518 appears on the horizontal axis); 26519 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 26520 26521Examples: 26522 RANGE PLOT Y X 26523 RANGE PLOT Y X1 26524 26525Default: 26526 None 26527 26528Synonyms: 26529 R PLOT 26530 26531Related Commands: 26532 CHARACTERS = Sets the type for plot characters. 26533 LINES = Sets the type for plot lines. 26534 STANDARD DEVIATION PLOT = Generates a standard deviation plot. 26535 VARIANCE PLOT = Generates a variance plot. 26536 MEAN PLOT = Generates a mean plot. 26537 MEDIAN PLOT = Generates a median plot. 26538 BOX PLOT = Generates a box plot. 26539 RANGE CHART = Generates a range control chart. 26540 S CHART = Generates a standard deviation control 26541 chart. 26542 PLOT = Generates a data or function plot. 26543 26544Applications: 26545 Quality Control 26546 26547Implementation Date: 26548 88/2 26549 26550Program: 26551 SKIP 25 26552 READ GEAR.DAT Y X 26553 LINE BLANK DASH 26554 CHARACTER X BLANK 26555 XTIC OFFSET 0.2 0.2 26556 Y1LABEL RANGE 26557 X1LABEL SAMPLE ID 26558 TITLE AUTOMATIC 26559 RANGE PLOT Y X 26560 26561-----RANK2 (LET)--------------------------------------------------- 26562 26563RANK2 26564 26565Name: 26566 RANK2 (LET) 26567 26568Type: 26569 Let Subcommand 26570 26571Purpose: 26572 Rank the elements of a response variable when there are one, 26573 two, or three group-id variables. 26574 26575Description: 26576 The RANK command is used to rank a response variable. However, 26577 there may be cases where you want to rank the data withing 26578 groups. The RANK2, RANK3, and RANK4 commands let you perform 26579 the ranking for the cases with one, two, or three group-id 26580 variables, respectively. 26581 26582 Nonparameteric analysis is often based on ranked data rather 26583 than the original data. This command may be helpful in implementing 26584 nonparameteric methods that are not directly supported by Dataplot. 26585 26586Syntax 1: 26587 LET <y2> = RANK2 <y1> <x1> 26588 <SUBSET/EXCEPT/FOR qualification> 26589 where <y1> is a response variable to be ranked; 26590 <x1> is a group-id variable; 26591 <y2> is a variable where the ranked <y1> values are saved; 26592 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 26593 26594 This syntax is used for the case where we are ranking based 26595 on one group-id variable. 26596 26597Syntax 2: 26598 LET <y2> = RANK3 <y1> <x1> <x2> 26599 <SUBSET/EXCEPT/FOR qualification> 26600 where <y1> is a response variable to be ranked; 26601 <x1> is the first group-id variable; 26602 <x2> is the second group-id variable; 26603 <y2> is a variable where the ranked <y1> values are saved; 26604 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 26605 26606 This syntax is used for the case where we are ranking based 26607 on two group-id variables. 26608 26609Examples: 26610 LET Y2 = RANK2 Y X1 26611 LET Y2 = RANK2 Y X1 X2 26612 LET Y2 = RANK2 Y X1 SUBSET X1 > 2 26613 26614Note: 26615 The response values are ranked in ascending order. 26616 26617Note: 26618 The groups in the data do not need to be pre-sorted or 26619 contiguous. The ranked response variable will be in the 26620 same order as the original response variable (i.e., the 26621 groups are not sorted on output). 26622 26623 If you want to extract the rankings for a specific group, 26624 you can do something like the following 26625 26626 LET Y2 = RANK3 Y X1 X2 26627 LET ZY2 = Y2 26628 LET ZY = Y 26629 RETAIN ZY2 ZY SUBSET X1 =2 SUBSET X2 = 3 26630 26631Default: 26632 None 26633 26634Synonyms: 26635 None 26636 26637Related Commands: 26638 RANK = Rank the elements of a variable. 26639 SORT = Sort the elements of a variable. 26640 SORTC = Sort the elements of a variable and carry one or 26641 more variables along. 26642 COCODE = Generate a cocoded variable. 26643 CODE = Generate a coded variable. 26644 SEQUENCE = Generate a sequence of numbers. 26645 PATTERN = Generate numbers with a specific pattern. 26646 26647Applications: 26648 Data Management 26649 26650Implementation Date: 26651 2008/12 26652 26653Program 1: 26654 skip 25 26655 read gear.dat y x 26656 . 26657 let y2 = rank2 y x 26658 . 26659 set write decimals 3 26660 print x y y2 26661 26662Program 2: 26663 skip 25 26664 read ripken.dat y x1 x2 x3 x4 26665 . 26666 let y2 = rank3 y x1 x2 26667 . 26668 set write decimals 3 26669 print x1 x2 y y2 26670 26671-----RANK INDEX (LET)--------------------------------------------- 26672 26673RANK INDEX 26674 26675Name: 26676 RANK INDEX (LET) 26677 26678Type: 26679 Let Subcommand 26680 26681Purpose: 26682 Compute the ranks of a variable where each rank will be a unique 26683 integer value. 26684 26685Description: 26686 When the RANK command encouters ties in the response variable, 26687 all tied values are given the same average rank. For example, 26688 if ranks 5 and 6 denote the same value, then each would be 26689 assinged a rank of 5.5. 26690 26691 The RANK INDEX command performs ranking. However, it handles 26692 ties differently. For example, if ranks 5 and 6 denote the same 26693 value, this command will return 5 and 6 as the ranks rather than 26694 5.5 for both. 26695 26696 This command is useful when you want to use the rank as an index 26697 to another variable. An example is given in the program example 26698 below. 26699 26700Syntax: 26701 LET <y> = RANK INDEX <x> <SUBSET/EXCEPT/FOR qualification> 26702 where <x> is the variable for which the ranks are to be computed; 26703 <y> is a variable where the computed ranks are saved; 26704 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 26705 26706Examples: 26707 LET Y = RANK INDEX X 26708 26709Default: 26710 None 26711 26712Synonyms: 26713 None 26714 26715Related Commands: 26716 RANK (LET) = Rank the elements in a variable. 26717 RANK2 (LET) = Rank the elements in a variable where there is 26718 grouping in the data. 26719 SORT (LET) = Sort the elements in a variable. 26720 SORTC (LET) = Sort the elements in a variable and carry one or 26721 more variables along. 26722 26723Applications: 26724 Nonparametric statistics 26725 26726Implementation Date: 26727 2010/6 26728 26729Program: 26730 skip 25 26731 read splett2.dat y x 26732 let string s1 = Tinius1 26733 let string s2 = Tinius2 26734 let string s3 = Satec 26735 let string s4 = Tokyo 26736 . 26737 let xsort iindx = sort by median y x 26738 set let cross tabulate collapse 26739 let y2 = cross tabulate median y x 26740 let x2 = rank index y2 26741 loop for k = 1 1 4 26742 let ival = x2(k) 26743 let string t^ival = ^s^k 26744 end of loop 26745 x1tic mark label case asis 26746 x1tic mark label format alpha 26747 x1tic mark label content ^t1 ^t2 ^t3 ^t4 26748 . 26749 char box plot 26750 line box plot 26751 fences on 26752 . 26753 xlimits 1 4 26754 major xtic mark number 4 26755 minor xtic mark number 0 26756 xtic offset 0.5 0.5 26757 . 26758 title case asis 26759 title offset 2 26760 title Charpy V-NIST Notch Testing 26761 label case asis 26762 x1label Machine Manufacturer 26763 y1label Absorbed Energy 26764 . 26765 box plot y xsort 26766 26767-----RANK (LET)--------------------------------------------------- 26768 26769RANK 26770 26771Name: 26772 RANK (LET) 26773 26774Type: 26775 Let Subcommand 26776 26777Purpose: 26778 Compute the ranks of a variable. 26779 26780Syntax: 26781 LET <resp> = RANK <y1> <SUBSET/EXCEPT/FOR qualification> 26782 where <y1> is the variable for which the ranks are to be computed; 26783 <resp> is a variable where the computed ranks are saved; 26784 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 26785 26786Examples: 26787 LET A = RANK Y1 26788 26789Note: 26790 Ties are assigned an average rank. For example, if the 2nd and 3rd 26791 highest values are equal, each is assigned a rank of 2.5. 26792 26793Note: 26794 Many nonparametric statistical methods are based on ranks. The 26795 program sample shows the use of ranks in computing the 26796 Kruskal-Wallis test for one-way ANOVA. 26797 26798Default: 26799 None 26800 26801Synonyms: 26802 None 26803 26804Related Commands: 26805 SORT (LET) = Sort the elements in a variable. 26806 SORTC (LET) = Sort the elements in a variable and carry one or 26807 more variables along. 26808 26809Applications: 26810 Nonparametric statistics 26811 26812Implementation Date: 26813 XX 26814 26815Program: 26816 . Perform a Kruskal-Wallis non-parametric 1-way ANOVA 26817 . Data from "Probability and Statistics for Engineers and 26818 . Scientists" by Walpole and Myers. 26819 LET P = 3 26820 LET X1 = DATA 24.0 16.7 22.8 19.8 18.9 26821 LET X2 = DATA 23.2 19.8 18.1 17.6 20.2 17.8 26822 LET X3 = DATA 18.4 19.1 17.3 17.3 19.7 18.9 18.8 19.3 26823 . 26824 LOOP FOR K = 1 1 P 26825 LET N^K = SIZE X^K 26826 LET TAG^K = K FOR I = 1 1 N^K 26827 END OF LOOP 26828 LOOP FOR L = 2 1 P 26829 LET TEMP = X^L 26830 EXTEND X1 TEMP 26831 LET TEMP = TAG^L 26832 EXTEND TAG1 TEMP 26833 DELETE TEMP 26834 END OF LOOP 26835 . 26836 LET N = SIZE X1 26837 LET R = RANK X1 26838 LET SUM1 = 0 26839 LOOP FOR K = 1 1 P 26840 LET R^K = SUM R SUBSET TAG1 = K 26841 LET SUM1 = SUM1 + (R^K)**2/N^K 26842 END OF LOOP 26843 . 26844 LET H = SUM1*(12/(N*(N+1))) - 3*(N+1) 26845 LET ALPHA = 0.95 26846 LET DF = P - 1 26847 LET CRITICAL = CHSPPF(ALPHA,DF) 26848 . 26849 CAPTURE KRUSKAL_WALLIS_OUT.DAT 26850 PRINT " " 26851 PRINT "H0: ^P INDEPENDENT SAMPLES ARE FROM IDENTICAL POPULATIONS" 26852 PRINT "HA: ^P INDEPENDENT SAMPLES ARE FROM DIFFERENT POPULATIONS" 26853 PRINT "KRUSKAL-WALLIS H STATISTIC = ^H" 26854 PRINT "CHI-SQUARE CRITICAL VALUE = ^CRITICAL" 26855 IF H <= CRITICAL 26856 PRINT "ACCEPT NULL HYPOTHESIS" 26857 END OF IF 26858 IF H > CRITICAL 26859 PRINT "REJECT NULL HYPOTHESIS" 26860 END OF IF 26861 END OF CAPTURE 26862 26863-----RANK COMOVEMENT (LET)-------------------------------- 26864 26865RANK COMOVEMENT 26866 26867Name: 26868 RANK COMOVEMENT (LET) 26869 26870Type: 26871 Let Subcommand 26872 26873Purpose: 26874 Compute the rank Leigh-Perlman comovement coefficient for a 26875 variable. 26876 26877Description: 26878 The comovement coefficient is the sum of cross products divided by 26879 N-1. It is computed as: 26880 COMOVE = SUMXY/(SQRT(SUMX)*SQRT(SUMY)) 26881 where 26882 SUMXY = SUM ((X(i)-X(i-1))*(Y(i)-Y(I-1))) 26883 SUMX = SUM(X(i)-X(i-1)) 26884 SUMY = SUM(Y(i)-Y(i-1)) 26885 and the summations are done from 2 to N. The computed coefficient 26886 has a value between -1 and +1. 26887 26888 The rank comovement coefficient is computed from the ranks of the 26889 data rather than the original data. However, it uses the same 26890 computational formula given above. 26891 26892Syntax: 26893 LET <par> = RANK COMOVEMENT <y1> <y2> 26894 <SUBSET/EXCEPT/FOR qualification> 26895 where <y1> is the first response variable; 26896 <y2> is the second response variable; 26897 <par> is a parameter where the computed rank comovement is 26898 stored; 26899 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 26900 26901Examples: 26902 LET A = RANK COMOVEMENT Y1 Y2 26903 LET A = RANK COMOVEMENT Y1 Y2 SUBSET TAG > 2 26904 26905Note: 26906 The two variables must have the same number of elements. 26907 26908Default: 26909 None 26910 26911Synonyms: 26912 None 26913 26914Related Commands: 26915 COMOVEMENT = Compute the comovement of two variables. 26916 CORRELATION = Compute the correlation of a variable. 26917 RANK CORRELATION = Compute the rank correlation of a variable. 26918 COVARIANCE = Compute the covariance between two variables. 26919 VARIANCE = Compute the variance of a variable. 26920 26921Reference: 26922 "An Index for Comovement of Time Sequences with Geophysical 26923 Applications: A Working Paper", Penn State Interface Conference on 26924 Astronomy, August, 1991. 26925 26926Applications: 26927 XX 26928 26929Implementation Date: 26930 91/8 26931 26932Program: 26933 LET Y1 = EXPONENTIAL RANDOM NUMBERS FOR I = 1 1 100 26934 LET Y2 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 26935 LET A1 = RANK COMOVEMENT Y1 Y2 26936 26937-----RANK CORRELATION (LET)-------------------------------- 26938 26939RANK CORRELATION 26940 26941Name: 26942 RANK CORRELATION (LET) 26943 26944Type: 26945 Let Subcommand 26946 26947Purpose: 26948 Compute the Spearman rank correlation between two variables. 26949 26950Description: 26951 If the measurements in the two samples are replaced with their ranks 26952 (and average ranks in the case of ties) and the Pearson correlation 26953 coefficient (HELP CORRELATION for details) is computed, the result is 26954 the Spearman rho correlation coefficient. 26955 26956 The rank correlation is recommended in the following cases: 26957 1) When the underlying data does not have a meaningful numerical 26958 measure, but it can be ranked; 26959 2) When the relationship between the two variables is not 26960 linear; 26961 3) When the normality assumption for two variables is not 26962 valid. 26963 26964Syntax: 26965 LET <par> = RANK CORRELATION <y1> <y2> 26966 <SUBSET/EXCEPT/FOR qualification> 26967 where <y1> is the first response variable; 26968 <y2> is the second response variable; 26969 <par> is a parameter where the computed rank correlation is 26970 stored; 26971 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 26972 26973Examples: 26974 LET A = RANK CORRELATION Y1 Y2 26975 LET A = RANK CORRELATION Y1 Y2 SUBSET TAG > 2 26976 26977Note: 26978 The two variables must have the same number of elements. 26979 26980Default: 26981 None 26982 26983Synonyms: 26984 None 26985 26986Related Commands: 26987 CORRELATION (LET) = Compute the Pearson correlation 26988 coefficient between two variables. 26989 AUTOCORRELATION (LET) = Compute the autocorrelation of a variable. 26990 RANK COVARIANCE (LET) = Compute the rank covariance between two 26991 variables. 26992 26993Applications: 26994 Exploratory Data Analysis 26995 26996Implementation Date: 26997 Pre-1987 26998 26999Program: 27000 LET Y1 = DATA 14 17 28 17 16 13 24 25 18 31 27001 LET Y2 = DATA 0.9 1.1 1.6 1.3 1.0 0.8 1.5 1.4 1.2 2.0 27002 LET A1 = RANK CORRELATION Y1 Y2 27003 27004-----RANK CORRELATION INDEPENDENCE TEST-------------------------------------- 27005 27006RANK CORRELATION INDEPENDENCE TEST 27007 27008Name: 27009 RANK CORRELATION INDEPENDENCE TEST 27010 27011Type: 27012 Analysis Command 27013 27014Purpose: 27015 Perform a Spearman rho rank correlation test for whether two samples 27016 are independent (i.e., not correlated). 27017 27018Description: 27019 If the measurements in the two samples are replaced with their ranks 27020 (and average ranks in the case of ties) and the Pearson correlation 27021 coefficient (HELP CORRELATION for details) is computed, the result is 27022 the Spearman rho correlation coefficient. 27023 27024 A value of +1 indicates perfect positive correlation, a value 27025 of -1 indicates perfect negative correlation, and a value of 0 27026 indicates no relation (i.e., independence). 27027 27028 The rank correlation independence test is a test whether the 27029 rank correlation coefficient is equal to zero. 27030 27031 For larger n (e.g., n > 30) or the case where there are many ties, 27032 the p-th upper quantile of the rank correlation statistic can be 27033 approximated by 27034 27035 w(p) = z(p)/SQRT(n-1) 27036 27037 with z(p) and n denoting the p-th quantile of the standard 27038 normal distribution and the sample size, respectively. The 27039 lower quantile is the negative of the upper quantile. 27040 27041 For a two-sided test, the p-value is computed as twice the 27042 minimum of the lower tailed and upper tailed quantiles. 27043 27044 For n <= 30, tabulated quantiles (from Table A10 on p. 542 of 27045 Conover) are used. These quantiles are exact when there are 27046 no ties in the data. 27047 27048Syntax 1: 27049 <LOWER TAILED/UPPER TAILED> RANK CORRELATION INDEPENDENCE TEST 27050 <y1> <y2> 27051 <SUBSET/EXCEPT/FOR qualification> 27052 where <LOWER TAILED/UPPER TAILED> is an optional keyword that 27053 specifies either a lower tailed or an upper tailed 27054 test; 27055 <y1> is the first response variable; 27056 <y2> is the second response variable; 27057 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 27058 27059 If neither LOWER TAILED or UPPER TAILED is specified, a two-tailed 27060 test is performed. 27061 27062 Lower tailed tests are used to test for negative correlation and 27063 upper tailed tests are used to test for positive correlation). 27064 27065Syntax 2: 27066 <LOWER TAILED/UPPER TAILED> RANK CORRELATION INDEPENDENCE TEST 27067 <y1> ... <yk> 27068 <SUBSET/EXCEPT/FOR qualification> 27069 where <LOWER TAILED/UPPER TAILED> is an optional keyword that 27070 specifies either a lower tailed or an upper tailed 27071 test; 27072 <y1> ... <yk> is a list of 1 to 30 response variables; 27073 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 27074 27075 This syntax will perform all the pair-wise tests for the <y1> ... 27076 <yk> response variables. For example, 27077 27078 RANK CORRELATION INDEPENDENCE TEST Y1 TO Y4 27079 27080 is equivalent to 27081 27082 RANK CORRELATION INDEPENDENCE TEST Y1 Y2 27083 RANK CORRELATION INDEPENDENCE TEST Y1 Y3 27084 RANK CORRELATION INDEPENDENCE TEST Y1 Y4 27085 RANK CORRELATION INDEPENDENCE TEST Y2 Y3 27086 RANK CORRELATION INDEPENDENCE TEST Y2 Y4 27087 RANK CORRELATION INDEPENDENCE TEST Y3 Y4 27088 27089Examples: 27090 RANK CORRELATION INDEPENDENCE TEST Y1 Y2 27091 RANK CORRELATION INDEPENDENCE TEST Y1 TO Y5 27092 LOWER TAILED RANK CORRELATION INDEPENDENCE TEST Y1 Y2 27093 UPPER TAILED RANK CORRELATION INDEPENDENCE TEST Y1 Y2 27094 27095Note: 27096 This command can be used to test for trend in a univariate 27097 variable. For example 27098 27099 LET N = SIZE Y 27100 LET X = SEQUENCE 1 1 N 27101 RANK CORRELATION INDEPENDENCE TEST Y X 27102 27103 According to Conover, this test is more powerful than the 27104 Cox and Stuart test. However, it is not as widely applicable 27105 as the Cox and Stuart test. 27106 27107 This test for trend is referred to as the Daniels test for trend. 27108 27109Note: 27110 The KENDALL TAU INDEPENDENCE TEST can be used to perform 27111 a test for independence based on the Kendall tau statistic. 27112 27113 The CORRELATION CONFIDENCE LIMITS command can be used to generate 27114 a confidence interval for the Pearson correlation coefficient. 27115 This can be used for a parametric test for independence (i.e., 27116 does the confidence interval contain zero?). 27117 27118Note: 27119 By default, critical values are based on tabulated values for 27120 n <= 30. The command 27121 27122 SET RANK CORRELATION CRITICAL VALUES NORMAL APPROXIMATION 27123 27124 can be used to specify that they should be based on the normal 27125 approximation given above. This may be preferred if there are 27126 ties in the data. To reset the default, enter the command 27127 27128 SET RANK CORRELATION CRITICAL VALUES TABLE 27129 27130Note: 27131 The RANK CORRELATION INDEPENDENCE TEST will accept matrix arguments. 27132 If a matrix is given, the data elements in the matrix will be collected 27133 in column order to form a vector before performing the test. 27134 27135Note: 27136 Dataplot saves the following internal parameters after a 27137 rank correlation independence test: 27138 27139 STATVAL = the value of the test statistic 27140 STATCDF = the CDF of the test statistic 27141 PVALUE = the p-value for the two-sided test 27142 PVALUELT = the p-value for the lower tailed test 27143 PVALUEUT = the p-value for the upper tailed test 27144 CUTLOW90 = the 90% lower tailed critical value 27145 CUTUPP90 = the 90% upper tailed critical value 27146 CUTLOW95 = the 95% lower tailed critical value 27147 CUTUPP95 = the 95% upper tailed critical value 27148 CTLOW975 = the 97.5% lower tailed critical value 27149 CTUPP975 = the 97.5% upper tailed critical value 27150 CUTLOW99 = the 99% lower tailed critical value 27151 CUTUPP99 = the 99% upper tailed critical value 27152 CTLOW995 = the 99.5% lower tailed critical value 27153 CTUPP995 = the 99.5% upper tailed critical value 27154 CTLOW999 = the 99.9% lower tailed critical value 27155 CTUPP999 = the 99.9% upper tailed critical value 27156 27157Note: 27158 The following statistics can also be computed 27159 27160 LET A = RANK CORRELATION Y1 Y2 27161 LET A = RANK CORRELATION CDF Y1 Y2 27162 LET A = RANK CORRELATION PVALUE Y1 Y2 27163 LET A = RANK CORRELATION LOWER TAILED PVALUE Y1 Y2 27164 LET A = RANK CORRELATION UPPER TAILED PVALUE Y1 Y2 27165 27166 The cdf and p-values are based on the normal approximation 27167 given above. 27168 27169 To see a list of commands in which these statistics can be 27170 used, enter 27171 27172 HELP STATISTICS 27173 27174Note: 27175 The run sequence plot can be used to graphically assess 27176 whether or not there is trend in the data. The 4-plot can 27177 be used to assess the more general assumption of 27178 "independent, identically distributed" data. 27179 27180 The paired data can also be analyzed using other techniques for 27181 comparing two response variables (e.g., t-test, bihistogram, 27182 quantile-quantile plot). 27183 27184Default: 27185 None 27186 27187Synonyms: 27188 None 27189 27190Related Commands: 27191 KENDALL TAU INDEPENDENCE TEST = Compute an independence test 27192 based on the Kendall tau statistic. 27193 CORRELATION CONFIDENCE LIMITS = Generate confidence limits for the 27194 Pearson correlation coefficient. 27195 COX AND STUART TEST = Compute a Cox and Stuart trend test. 27196 T-TEST = Compute a t-test. 27197 4-PLOT = Generate a 4-plot. 27198 RUN SEQUENCE PLOT = Generate a run sequence plot. 27199 BIHISTOGRAM = Generates a bihistogram. 27200 QUANTILE-QUANTILE PLOT = Generate a quantile-quantile plot. 27201 27202Reference: 27203 Conover (1999), "Practical Nonparametric Statistics", 27204 Third Edition, Wiley, pp. 319-327. 27205 27206Applications: 27207 Confirmatory Data Analysis 27208 27209Implementation Date: 27210 2013/3 27211 27212Program: 27213 skip 25 27214 read kendall.dat y1 y2 27215 set write decimals 5 27216 . 27217 let statval = rank correlation y1 y2 27218 let statcdf = rank correlation cdf y1 y2 27219 let pvalue = rank correlation pvalue y1 y2 27220 let pvallt = rank correlation lower tailed pvalue y1 y2 27221 let pvalut = rank correlation upper tailed pvalue y1 y2 27222 print statval statcdf pvalue pvallt pvalut 27223 . 27224 rank correlation independence test y1 y2 27225 . 27226 upper tailed rank correlation independence test y1 y2 27227 . 27228 set rank correlation critical values normal approximation 27229 upper tailed rank correlation independence test y1 y2 27230 27231-----RANK COVARIANCE (LET)-------------------------------- 27232 27233RANK COVARIANCE 27234 27235Name: 27236 RANK COVARIANCE (LET) 27237 27238Type: 27239 Let Subcommand 27240 27241Purpose: 27242 Compute the rank covariance between two variables. 27243 27244Description: 27245 The covariance is computed as: 27246 cov(x,y) = sum(x-xmean)*sum(y-ymean)/(N-1) 27247 The rank covariance uses the above formula on the ranks of the 27248 data rather than the original data. 27249 27250 The rank covariance is recommended in the following cases: 27251 1) When the underlying data does not have a meaningful numerical 27252 measure, but it can be ranked; 27253 2) When the relationship between the two variables is not linear; 27254 3) When the normality assumption for two variables is not valid. 27255 27256Syntax: 27257 LET <par> = RANK COVARIANCE <y1> <y2> 27258 <SUBSET/EXCEPT/FOR qualification> 27259 where <y1> is the first response variable; 27260 <y2> is the second response variable; 27261 <par> is a parameter where the computed rank covariance is 27262 stored; 27263 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 27264 27265Examples: 27266 LET A = RANK COVARIANCE Y1 Y2 27267 LET A = RANK COVARIANCE Y1 Y2 SUBSET TAG > 2 27268 27269Default: 27270 None 27271 27272Synonyms: 27273 None 27274 27275Related Commands: 27276 CORRELATION (LET) = Compute the Pearson correlation 27277 coefficient between two variables. 27278 AUTOCORRELATION (LET) = Compute the autocorrelation of a variable. 27279 RANK CORRELATION (LET) = Compute the rank correlation between two 27280 variables. 27281 27282Applications: 27283 Exploratory Data Analysis 27284 27285Implementation Date: 27286 XX 27287 27288Program: 27289 LET Y1 = DATA 14 17 28 17 16 13 24 25 18 31 27290 LET Y2 = DATA 0.9 1.1 1.6 1.3 1.0 0.8 1.5 1.4 1.2 2.0 27291 LET A1 = RANK COVARIANCE Y1 Y2 27292 27293-----RANK SUM TEST-------------------------------------- 27294 27295RANK SUM TEST 27296 27297Name: 27298 RANK SUM TEST 27299 27300Type: 27301 Analysis Command 27302 27303Purpose: 27304 Perform a two sample rank sum test. 27305 27306Description: 27307 The t-test is the standard test for testing that the 27308 difference between population means for two non-paired 27309 samples are equal. If the populations are non-normal, 27310 particularly for small samples, then the t-test may not 27311 be valid. The rank sum test is an alternative that can 27312 be applied when distributional assumptions are suspect. 27313 However, it is not as powerful as the t-test when the 27314 distributional assumptions are in fact valid. 27315 27316 The rank sum test is also commonly called the Mann-Whitney 27317 rank sum test or simply the Mann-Whitney test. Note that 27318 even though this test is commonly called the Mann-Whitney 27319 test, it was in fact developed by Wilcoxon. 27320 27321 To form the rank sum test, rank the combined samples. 27322 Then compute the sum of the ranks for sample one, T1, and 27323 the sum of the ranks for sample two, T2. If the sample 27324 sizes are equal, the rank sum test statistic is the minimum 27325 of T1 and T2. If the sample sizes are unequal, then 27326 find T1 equal the sum of the ranks for the smaller sample. 27327 Then compute T2 = N1(N1 + N2 + 1) - T1. T is the minimum 27328 of T1 and T2. Sufficiently small values of T cause 27329 rejection of the null hypothesis that the sample means 27330 are equal. 27331 27332 Significance levels have been tabulated for small values of 27333 N1 and N2. For sufficiently large N1 and N2, the following 27334 normal approximation is used: 27335 27336 Z = (ABS(u - T) - 0.5)/sigma 27337 27338 where 27339 27340 u = N1*(N1 + N2 + 1)/2 27341 sigma = SQRT(N2*u/6) 27342 27343Syntax: 27344 RANK SUM TEST <y1> <y2> <SUBSET/EXCEPT/FOR qualification> 27345 where <y1> is the first response variable; 27346 <y2> is the second response variable; 27347 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 27348 27349Examples: 27350 RANK SUM TEST Y1 Y2 27351 RANK SUM TEST Y1 Y2 SUBSET TAG > 2 27352 27353Note: 27354 Dataplot saves the following internal parameters after a 27355 sign test: 27356 27357 STATVAL = The rank sum test statistic 27358 STATCD2 = the normal cdf value of T (only applies for 27359 sufficiently large N1 and N2) 27360 CUTLOW90 = 0.05 critical value 27361 CUTUPP90 = 0.95 critical value 27362 CUTLOW95 = 0.025 critical value 27363 CUTUPP95 = 0.975 critical value 27364 CUTLOW99 = 0.005 critical value 27365 CUTUPP99 = 0.995 critical value 27366 27367 Note that the above critical values are the lower and upper 27368 tails for two sided tests (i.e., each tail is alpha/2. For 27369 example, CUTLOW90 is the lower 5% of the normal percent point 27370 function (adjusted for the mean and standard deviation). This 27371 is the critical regions for alpha = 0.10, so there is 0.05 in 27372 each tail. 27373 27374Note: 27375 The following statistics are also supported: 27376 27377 LET A = MANN WHITNEY RANK SUM TEST Y1 Y2 27378 LET A = MANN WHITNEY RANK SUM TEST CDF Y1 Y2 27379 LET A = MANN WHITNEY RANK SUM TEST PVALUE Y1 Y2 27380 LET A = MANN WHITNEY RANK SUM LOWER TAILED PVALUE Y1 Y2 27381 LET A = MANN WHITNEY RANK SUM UPPER TAILED PVALUE Y1 Y2 27382 27383 In addition to the above LET command, built-in statistics are 27384 supported for about 20+ different commands (enter HELP STATISTICS 27385 for details). 27386 27387Default: 27388 None 27389 27390Synonyms: 27391 The following are synonyms for RANK SUM TEST: 27392 27393 MANN WHITNEY RANK SUM TEST 27394 MANN WHITNEY RANK SUM 27395 MANN WHITNEY TEST 27396 MANN WHITNEY 27397 RANK SUM 27398 27399Related Commands: 27400 T-TEST = Compute a t-test. 27401 SIGN TEST = Compute a sign test. 27402 SIGNED RANK TEST = Compute a signed rank test. 27403 CHI-SQUARED 2 SAMPLE TEST = Compute a two sample chi-square 27404 test. 27405 BIHISTOGRAM = Generates a bihistogram. 27406 QUANTILE-QUANTILE PLOT = Generate a quantile-quantile plot. 27407 BOX PLOT = Generates a box plot. 27408 27409Reference: 27410 "Statistical Methods", Eigth Edition, Snedecor and Cochran, 27411 1989, Iowa State University Press, pp. 142-144. 27412 27413Applications: 27414 Confirmatory Data Analysis 27415 27416Implementation Date: 27417 1999/5 27418 27419Program: 27420 SKIP 25 27421 READ NATR323.DAT Y1 Y2 27422 RETAIN Y2 SUBSET Y2 > -90 27423 RANK SUM TEST Y1 Y2 27424 27425 The following output is generated. 27426 27427 27428 MANN WHITNEY RANK SUM TEST 27429 (2-SAMPLE) 27430 HYPOTHESIS BEING TESTING--POPULATION MEANS MU1 = MU2 27431 SAMPLE SIZE FOR VARIABLE 1 = 13 27432 SAMPLE SIZE FOR VARIABLE 2 = 8 27433 RANK SUM FOR VARIABLE 1 = 180.0000 27434 RANK SUM FOR VARIABLE 2 = 51.00000 27435 RANK SUM TEST STATITIC (U) = 51.00000 27436 27437 HYPOTHESIS ACCEPTANCE INTERVAL CONCLUSION 27438 MU1 = MU2 U > 60.00000 REJECT 27439 27440-----RATIO (LET)------------------------------------------- 27441 27442RATIO 27443 27444Name: 27445 RATIO (LET) 27446 27447Type: 27448 Let Subcommand 27449 27450Purpose: 27451 Compute the ratio of the sum of two variables. 27452 27453Description: 27454 This statistic computes 27455 27456 SUM[i=1 to n][Y1(i)]/SUM[i=1 to n][Y2(i)] 27457 27458 In the current implementation, Y1 and Y2 are assumed to 27459 have the same number of elements. 27460 27461 In the typical use of this command, Y2 denotes the 27462 number of cases or number of trials while Y1 denotes 27463 the corresponding number of successes or failures (e.g., 27464 the number of successes might be the number of false 27465 negatives or false positives). This statistic then computes 27466 the success rate over all groups. 27467 27468Syntax: 27469 LET <par> = RATIO <y1> <y2> <SUBSET/EXCEPT/FOR qualification> 27470 where <y1> is the first response variable; 27471 <y2> is the second response variable; 27472 <par> is a parameter where the computed ratio is 27473 stored; 27474 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 27475 27476Examples: 27477 LET A = RATIO Y1 Y2 27478 LET A = RATIO Y1 Y2 SUBSET TAG > 2 27479 27480Note: 27481 The following additional commands are supported 27482 27483 TABULATE RATIO Y1 Y2 X 27484 CROSS TABULATE RATIO Y1 Y2 X1 X2 27485 27486 RATIO PLOT Y1 Y2 X 27487 RATIO CROSS TABULATE PLOT Y1 Y2 X1 X2 27488 27489 BOOTSTRAP RATIO PLOT Y1 Y2 27490 JACKNIFE RATIO PLOT Y1 Y2 27491 27492Default: 27493 None 27494 27495Synonyms: 27496 None 27497 27498Related Commands: 27499 TABULATE = Compute a statistic for data with a 27500 single grouping variable. 27501 CROSS TABULATE = Compute a statistic for data with 27502 two grouping variables. 27503 STATISTIC PLOT = Generate a plot of a statistic for data 27504 with a single grouping variable. 27505 CROSS TABULATE PLOT = Generate a plot of a statistic for data 27506 with two grouping variables. 27507 BOOTSTRAP PLOT = Generate a bootstrap plot for a given 27508 statistic. 27509 27510Applications: 27511 Linear Regression 27512 27513Implementation Date: 27514 12/2005 27515 27516Program: 27517 LET Y1 = DATA 2 4 0 1 8 5 5 5 2 2 27518 LET Y2 = 10 FOR I = 1 1 10 27519 LET A = RATIO Y1 Y2 27520 27521-----RATIO OF MEANS CONFIDENCE INTERVAL-------------------------- 27522 27523RATIO OF MEANS CONFIDENCE INTERVAL 27524 27525Name: 27526 RATIO OF MEANS CONFIDENCE INTERVAL 27527 27528Type: 27529 Analysis Command 27530 27531Purpose: 27532 Generates a confidence interval for the ratio of two means 27533 for paired samples. 27534 27535Description: 27536 There are cases where a measurement is actually the ratio of 27537 two different measurements. That is, 27538 27539 R(i) = Y(i)/X(i) 27540 27541 It is often desired to generate the confidence interval for 27542 this ratio. Note that computing a standard confidence interval 27543 for R does not generate satisfactory results. This is due to 27544 the fact that, assuming Y and X are independent, 27545 27546 E[Rhat] = E[Yhat/Xhat] 27547 = E[Yhat]*E[1/Xhat] 27548 27549 However, E[1/Xhat] is not equal to 1/E[Xhat]. 27550 27551 There have been a number of approaches to this problem. This 27552 command supports three different methods. 27553 27554 Fieller derived confidence intervals for the case where Y and X are 27555 distributed as bivariate normal. Define the quantities 27556 27557 Xbar = mean of X 27558 Ybar = mean of Y 27559 sigmahat**2(Xbar) = variance of Xbar 27560 = 1/(N*(N-1))*SUM[i=1 to N][(X(i)-Xbar)**2] 27561 sigmahat**2(Ybar) = variance of Ybar 27562 = 1/(N*(N-1))*SUM[i=1 to N][(Y(i)-Ybar)**2] 27563 sigmahat(Ybar,Xbar) = 1/(N*(N-1))* 27564 SUM[i=1 to N][X(i) - Xbar)*(Y(i)-Ybar)] 27565 t(q) = t percent point value with N - 1 degrees of 27566 freedom 27567 27568 The test statistic is 27569 27570 Rhat = Ybar/Xbar 27571 27572 For Fieller's confidence limits, we first compute 27573 27574 Xbar**2/sigmahat(Xbar)**2 27575 27576 If this quantity is less than or equal to t**2(q), then an unbounded 27577 interval results and Dataplot will not generate the confidence 27578 interval. Basically, this results if the confidence interval for X 27579 contains zero. 27580 27581 If this quantity is less than or equal to t**2(q), then the following 27582 confidence interval is obtained 27583 27584 Lower Limit = {(Xbar*Ybar - t**2(q)*sigmahat(Xbar,Ybar)) - 27585 SQRT[(Xbar*Ybar - t**2(q)*sigmahat(Xbar,Ybar))**2 - 27586 (Xbar**2 - t**2(q)*sigmahat**2(Xbar)* 27587 (Ybar**2 - t**2(q)*sigmahat**2(Ybar)]}/ 27588 (Xbar**2 - t**2(q)*sigmahat(Xbar)) 27589 27590 Upper Limit = {(Xbar*Ybar - t**2(q)*sigmahat(Xbar,Ybar)) + 27591 SQRT[(Xbar*Ybar - t**2(q)*sigmahat(Xbar,Ybar))**2 - 27592 (Xbar**2 - t**2(q)*sigmahat**2(Xbar)* 27593 (Ybar**2 - t**2(q)*sigmahat**2(Ybar)]}/ 27594 (Xbar**2 - t**2(q)*sigmahat(Xbar)) 27595 27596 The large sample approximation method (this is called the Taylor or 27597 delta-method in the Franz paper) generates the following confidence 27598 interval 27599 27600 Lower Limit = Rhat - t(alpha/2,n-1)*Rhat* 27601 SQRT{C(Ybar,Ybar) + C(Xbar,Xbar) - 2*C(Ybar,Xbar)} 27602 27603 Upper Limit = Rhat + t(alpha/2,n-1)*Rhat* 27604 SQRT{C(Ybar,Ybar) + C(Xbar,Xbar) - 2*C(Ybar,Xbar)} 27605 27606 where 27607 27608 C(Ybar,Ybar) = (1/N)*s**2(Y)/Ybar**2 27609 C(Xbar,Xbar) = (1/N)*s**2(X)/Xbar**2 27610 C(Ybar,Xbar) = (1/N)*s(Y,X))/(Xbar*Ybar) 27611 27612 with s(Y), s(X), and s(Y,X) denoting the standard deviation of X, 27613 the standard deviation of Y and the covariance between Y and X, 27614 respectively. 27615 27616 The log ratio method generates the following confidence interval 27617 27618 Lower Limit = Rhat*EXP{-t(alpha/2,n-1)* 27619 SQRT{C(YBAR,YBAR) + C(XBAR,XBAR) - 2*C(YBAR,XBAR)} 27620 Upper Limit = Rhat*EXP{t(alpha/2,n-1)* 27621 SQRT{C(YBAR,YBAR) + C(XBAR,XBAR) - 2*C(YBAR,XBAR)} 27622 27623 The large sample approximation and the log ratio method do not 27624 generate unbounded intervals. Also, the log ratio method can 27625 generate asymmetric intervals. 27626 27627 Note that there is some disagreement in the literature about the 27628 appropriateness of these methods. For example, Franz argues that 27629 the unbounded intervals are a result of the denominator being close 27630 to zero with the consequence that the ratio can assume arbitrarily 27631 large values. Therefore any method that does not allow for unbounded 27632 intervals is not valid. On the other hand, Sherman argues that the 27633 unbounded Fieler intervals are simply nonsensical and advocates the 27634 use of the large sample approximation and log ratio methods. 27635 27636 To specify the method to use, enter the command 27637 27638 SET RATIO OF MEANS METHOD <FIELER/LOG RATIO/LARGE SAMPLE> 27639 27640Syntax: 27641 RATIO OF MEANS CONFIDENCE INTERVAL <y1> <y2> 27642 <SUBSET/EXCEPT/FOR qualification> 27643 where <y1> is the first (numerator) response variable; 27644 <y2> is the second (denominator) response variable; 27645 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 27646 27647 The variables <y1> and <y2> must be of the same length and are assumed 27648 to be paired. 27649 27650Examples: 27651 RATIO OF MEANS CONFIDENCE INTERVAL Y X 27652 RATIO OF MEANS CONFIDENCE INTERVAL Y X SUBSET TAG > 2 27653 RATIO OF MEANS CONFIDENCE INTERVAL Y1 Y2 SUBSET Y1 > 0 27654 27655Note: 27656 A table of confidence intervals is printed for alpha levels of 27657 50.0, 75.0, 90.0, 95.0, 99.0, 99.9, 99.99, and 99.999. The sample 27658 sizes, sample means, sample standard deviations, and the standard 27659 error are also printed. The t-value and t-value X standard 27660 error are printed in the table. 27661 27662Note: 27663 The RATIO OF MEANS CONFIDENCE LIMIT command automatically saves the 27664 following parameters: 27665 27666 CUTLOW90 = the lower 90% confidence limit 27667 CUTUPP90 = the upper 90% confidence limit 27668 CUTLOW95 = the lower 95% confidence limit 27669 CUTUPP95 = the upper 95% confidence limit 27670 CUTLOW99 = the lower 99% confidence limit 27671 CUTUPP99 = the upper 99% confidence limit 27672 CTLOW999 = the lower 99.9% confidence limit 27673 CTUPP999 = the upper 99.9% confidence limit 27674 27675Note: 27676 In addition to the RATIO OF MEANS CONFIDENCE LIMIT command, the 27677 following commands can also be used: 27678 27679 LET A = RATIO OF MEANS Y X 27680 27681 LET ALPHA = <value> 27682 LET A = RATIO OF MEANS LOWER CONFIDENCE LIMIT Y X 27683 LET A = RATIO OF MEANS UPPER CONFIDENCE LIMIT Y X 27684 27685 These statistics can be used in a number of commands. For 27686 details, enter 27687 27688 HELP STATISTICS 27689 27690Default: 27691 None 27692 27693Synonyms: 27694 None 27695 27696Related Commands: 27697 CONFIDENCE LIMITS = Generate a confidence interval 27698 for the mean. 27699 DIFFERENCE OF MEANS CONF LIMIT = Generate a confidence interval 27700 for the difference of two means. 27701 T-TEST = Perform a two sample t-test. 27702 BIHISTOGRAM = Generate a bihistogram. 27703 QUANTILE-QUANTILE PLOT = Generate a quantile-quantile 27704 plot. 27705 KOLMOGOROV-SMIRNOV TWO SAMPLE TEST = Generate a Kolmogorov- 27706 Smirnov two sample test. 27707 27708Reference: 27709 V. H. Franz ((2007), "Ratios: A Short Guide to Confidence Limits and 27710 Proper Use," arXiv:0710.2024 [stat.AP]. 27711 27712 E. C. Fieler (1940), "The Biological Standardization of Insulin," 27713 Supplement to the Journal of the Royal Statistical Society, Vol. 7, 27714 No. 1, pp. 1-64. 27715 27716 E. C. Fieler (1940), "A Fundamental Formula in the Statistics of 27717 Biological Assays and Some Applications", Quarterly Journal of 27718 Pharmacy and Pharmacology, Vol. 17, pp. 117-123. 27719 27720 E. C. Fieler (1940), "Some Problems in Interval Estimation," Journal 27721 of the Royal Statistical Society (B), Vol. 16, No. 2, pp. 175-185. 27722 27723 Sherman, Maity, and Wang (2011), "Inferences for the Ratio: Fieller's 27724 Interval, Log Ratio, and Large Sample Based Confidence Intervals", 27725 AStA Adv Stat Anal 95:313–323. 27726 27727 Cochran (1977), "Sampling Techniques," Wiley, New York. 27728 27729 Lohr (2009), "Sampling: Design and Analysis," Second Edition, 27730 Brooks/Cole, Pacific Grove. 27731 27732Applications: 27733 Confirmatory Data Analysis 27734 27735Implementation Date: 27736 2019/09 27737 27738Program 1: 27739 . Step 1: Define data (taken from Sherman article, original source 27740 . 27741 . Lehtonen and Pahkinen (2004), "Practical Methods for 27742 . Design and Analysis of Complex Surveys," 2nd Edition, 27743 . New York: Wiley. 27744 . 27745 read y x 27746 4123 26881 27747 760 4896 27748 721 3730 27749 142 556 27750 187 1463 27751 331 1946 27752 127 834 27753 219 932 27754 end of data 27755 . 27756 . Step 2: Large sample interval 27757 . 27758 let alpha = 0.95 27759 set write decimals 4 27760 set ratio of means method large sample 27761 let r1 = ratio of means y x 27762 let r1ll = ratio of means lower confidence limit y x 27763 let r1ul = ratio of means upper confidence limit y x 27764 . 27765 ratio of means confidence limit y x 27766 pause 27767 . 27768 set ratio of means method log ratio 27769 let r2 = ratio of means y x 27770 let r2ll = ratio of means lower confidence limit y x 27771 let r2ul = ratio of means upper confidence limit y x 27772 . 27773 ratio of means confidence limit y x 27774 pause 27775 . 27776 set ratio of means method fieler 27777 let r3 = ratio of means y x 27778 let r3ll = ratio of means lower confidence limit y x 27779 let r3ul = ratio of means upper confidence limit y x 27780 . 27781 ratio of means confidence limit y x 27782 27783Program 2: 27784 . Step 1: Define data 27785 . 27786 read y x 27787 0.1268825E+10 0.1246669E+10 27788 0.1295448E+10 0.1246669E+10 27789 0.1295448E+10 0.1268825E+10 27790 0.1168487E+08 0.1014325E+08 27791 0.1141398E+08 0.1014325E+08 27792 0.1168487E+08 0.1141398E+08 27793 0.3298360E+06 0.2902920E+06 27794 0.3298360E+06 0.1718490E+06 27795 0.2902920E+06 0.1718490E+06 27796 0.2415666E+07 0.1637297E+07 27797 0.2415666E+07 0.1347629E+07 27798 0.1637297E+07 0.1347629E+07 27799 0.9904356E+08 0.9530938E+08 27800 0.1049126E+09 0.9530938E+08 27801 0.1049126E+09 0.9904356E+08 27802 0.4930919E+08 0.4662120E+08 27803 0.4934958E+08 0.4662120E+08 27804 0.4934958E+08 0.4930919E+08 27805 0.1278483E+08 0.1232513E+08 27806 0.1286868E+08 0.1232513E+08 27807 0.1286868E+08 0.1278483E+08 27808 0.7029193E+07 0.4878485E+07 27809 0.7029193E+07 0.3244763E+07 27810 0.4878485E+07 0.3244763E+07 27811 0.1490000E+07 0.1040000E+07 27812 0.1860000E+07 0.1040000E+07 27813 0.1860000E+07 0.1490000E+07 27814 0.2680523E+07 0.2601516E+07 27815 0.2724237E+07 0.2601516E+07 27816 0.2724237E+07 0.2680523E+07 27817 0.8905137E+07 0.8303097E+07 27818 0.8905137E+07 0.8271071E+07 27819 0.8303097E+07 0.8271071E+07 27820 0.6956520E+06 0.6798450E+06 27821 0.6921780E+06 0.6798450E+06 27822 0.6956520E+06 0.6921780E+06 27823 0.3290000E+09 0.2890000E+09 27824 0.3300000E+09 0.2890000E+09 27825 0.3300000E+09 0.3290000E+09 27826 0.7091179E+05 0.6553055E+05 27827 0.7443393E+05 0.6553055E+05 27828 0.7443393E+05 0.7091179E+05 27829 0.8031739E+08 0.5416613E+08 27830 0.8031739E+08 0.4975062E+08 27831 0.5416613E+08 0.4975062E+08 27832 0.6830980E+07 0.6738330E+07 27833 0.6973430E+07 0.6738330E+07 27834 0.6973430E+07 0.6830980E+07 27835 0.2010000E+07 0.1980000E+07 27836 0.2600000E+07 0.2010000E+07 27837 0.2600000E+07 0.1980000E+07 27838 0.3193846E+08 0.3059341E+08 27839 0.3222820E+08 0.3059341E+08 27840 0.3222820E+08 0.3193846E+08 27841 0.1784258E+08 0.1460987E+08 27842 0.1784258E+08 0.1099276E+08 27843 0.1460987E+08 0.1099276E+08 27844 0.3150562E+09 0.3052555E+09 27845 0.3150562E+09 0.2994084E+09 27846 0.3052555E+09 0.2994084E+09 27847 0.7998000E+08 0.7574000E+08 27848 0.8017000E+08 0.7574000E+08 27849 0.8017000E+08 0.7998000E+08 27850 0.3983000E+08 0.3886000E+08 27851 0.4086000E+08 0.3886000E+08 27852 0.4086000E+08 0.3983000E+08 27853 0.2334030E+07 0.1387010E+07 27854 0.2544590E+07 0.2334030E+07 27855 0.2544590E+07 0.1387010E+07 27856 0.3126721E+09 0.2310785E+09 27857 0.2490103E+09 0.2310785E+09 27858 0.3126721E+09 0.2490103E+09 27859 0.1000900E+03 0.9977000E+02 27860 0.1255000E+03 0.9977000E+02 27861 0.1255000E+03 0.1000900E+03 27862 0.9860323E+04 0.9400626E+04 27863 0.9882525E+04 0.9400626E+04 27864 0.9882525E+04 0.9860323E+04 27865 0.2548997E+04 0.2482806E+04 27866 0.2640000E+08 0.2510000E+08 27867 0.2680000E+08 0.2510000E+08 27868 0.2680000E+08 0.2640000E+08 27869 end of data 27870 . 27871 set write decimals 4 27872 . 27873 . Step 2: Large sample interval 27874 . 27875 set ratio of means method large sample 27876 ratio of means confidence limit y x 27877 . 27878 . Step 3: Log Ratio interval 27879 . 27880 set ratio of means method log ratio 27881 ratio of means confidence limit y x 27882 . 27883 . Step 4: Fieler interval 27884 . 27885 set ratio of means method fieler 27886 ratio of means confidence limit y x 27887 27888-----RAYCDF (LET)-------------------------------- 27889 27890RAYCDF 27891 27892Name: 27893 RAYCDF (LET) 27894 27895Type: 27896 Library Function 27897 27898Purpose: 27899 Compute the Rayleigh cumulative distribution function. 27900 27901Description: 27902 The Rayleigh distribution is a special case of the 27903 chi distribution with degrees of freedom parameter = 2 and 27904 scale parameter sigma. It is also a special case of the 27905 Weibull distribution with shape parameter = 2 and scale 27906 parameter = SQRT(2). Note that some sources may define the 27907 Rayleigh distribution as a Weibull with shape parameter = 2 27908 and scale parameter = 1. 27909 27910 The Rayleigh distribution has the following cumulative 27911 disribution function: 27912 27913 F(x,mu,sigma)=1 - EXP(-(1/2)**(x-mu)/sigma)**2) 27914 x > mu, sigma > 0 27915 27916 with mu and sigma denoting the location and scale parameters, 27917 respectively. 27918 27919 The standard Rayleigh distribution is the case with 27920 mu = 0 and sigma = 1. 27921 27922Syntax: 27923 LET <y> = RAYCDF(<x>,<loc>,<scale>) 27924 <SUBSET/EXCEPT/FOR qualification> 27925 where <x> is a variable or a parameter; 27926 <loc> is an optional number or parameter that specifies the 27927 value of the location parameter; 27928 <scale> is an optional positive number or parameter that 27929 specifies the value of the scale parameter; 27930 <y> is a variable or a parameter (depending on what <x> is) 27931 where the computed Rayleigh cdf value 27932 is stored; 27933 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 27934 27935Examples: 27936 LET Y = RAYCDF(3) 27937 LET Y = RAYCDF(X1,0,SIGMA) 27938 PLOT RAYCDF(X,0,SIGMA) FOR X = 0.01 0.01 5 27939 27940Note: 27941 Library functions are distinguished from let subcommands 27942 in the following ways. 27943 1) Functions enclose the input value in parenthesis. Let 27944 subcommands use spaces. 27945 2) Functions can accept (and return) either parameters 27946 (i.e., single values) or variables (i.e., an array of 27947 values) while let subcommands are specific in which they 27948 accept as input and what they return as output. 27949 3) Functions can accept expressions while let subcommands 27950 do not. For example, the following is legal: 27951 LET Y2 = ABS(Y1-INT(Y1)) 27952 For let subcommands, you typically have to do something 27953 like the following: 27954 LET YTEMP = Y**2 + 8 27955 LET A = SUM YTEMP 27956 27957Default: 27958 None 27959 27960Synonyms: 27961 None 27962 27963Related Commands: 27964 RAYPDF = Compute the Rayleigh probability density function. 27965 RAYPPF = Compute the Rayleigh percent point function. 27966 MAXPDF = Compute the Maxwell probability density function. 27967 CHPDF = Compute the chi probability density function. 27968 WEIPDF = Compute the Weibull probability density function. 27969 NORPDF = Compute the normal probability density function. 27970 LGNPDF = Compute the lognormal probability density function. 27971 27972Reference: 27973 "Continuous Univariate Distributions: Volume I", Second Edition, 27974 Johnson, Kotz, and Balakrishnan, Wiley, 1994, pp. 453, 686. 27975 27976Applications: 27977 Distributional Modeling, Statistical Physics 27978 27979Implementation Date: 27980 6/2004 27981 27982Program: 27983 Y1LABEL Probability 27984 X1LABEL X 27985 LABEL CASE ASIS 27986 TITLE CASE ASIS 27987 TITLE Rayleigh Cumulative Disribution 27988 PLOT RAYCDF(X) FOR X = 0 0.01 5 27989 27990-----RAYPDF (LET)-------------------------------- 27991 27992RAYPDF 27993 27994Name: 27995 RAYPDF (LET) 27996 27997Type: 27998 Library Function 27999 28000Purpose: 28001 Compute the Rayleigh probability density function. 28002 28003Description: 28004 The Rayleigh distribution is a special case of the 28005 chi distribution with degrees of freedom parameter = 2 and 28006 scale parameter sigma. It is also a special case of the 28007 Weibull distribution with shape parameter = 2 and scale 28008 parameter = SQRT(2). Note that some sources may define the 28009 Rayleigh distribution as a Weibull with shape parameter = 2 28010 and scale parameter = 1. 28011 28012 The Rayleigh distribution has the following probability 28013 density function: 28014 28015 f(x,mu,sigma)=((x-mu)/sigma**2)*EXP(-(1/2)*(x-mu)**2/(sigma**2)) 28016 x > mu, sigma > 0 28017 28018 with mu and sigma denoting the location and scale parameters, 28019 respectively. 28020 28021 The standard Rayleigh distribution is the case with 28022 mu = 0 and sigma = 1. 28023 28024Syntax: 28025 LET <y> = RAYPDF(<x>,<loc>,<scale>) 28026 <SUBSET/EXCEPT/FOR qualification> 28027 where <x> is a variable or a parameter; 28028 <loc> is an optional number or parameter that specifies the 28029 value of the location parameter; 28030 <scale> is an optional positive number or parameter that 28031 specifies the value of the scale parameter; 28032 <y> is a variable or a parameter (depending on what <x> is) 28033 where the computed Rayleigh pdf value 28034 is stored; 28035 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 28036 28037Examples: 28038 LET Y = RAYPDF(3) 28039 LET Y = RAYPDF(X1,0,SIGMA) 28040 PLOT RAYPDF(X,0,SIGMA) FOR X = 0.01 0.01 5 28041 28042Note: 28043 To generate Rayleigh random numbers, enter the command 28044 28045 LET Y = RAYLEIGH RANDOM NUMBERS FOR I = 1 1 N 28046 28047 To generate a Rayleigh probability plot or a Rayleigh 28048 Kolmogorov-Smirnov or chi-square goodness of fit test, 28049 enter the following commands 28050 28051 RAYLEIGH PROBABILITY PLOT Y 28052 RAYLEIGH KOLMOGOROV SMIRNOV GOODNESS OF FIT Y 28053 RAYLEIGH CHI-SQUARE GOODNESS OF FIT Y 28054 28055 The location and scale parameters for the Rayleigh distribution 28056 can be estimated by generating the Rayleigh probability 28057 plot (the intercept and slope of the line fit to the probability 28058 plot, PPA0 and PPA1, are estimates of location and scale). 28059 28060 Alternatively, you can estimate the location and scale 28061 parameters using maximum likelihood: 28062 28063 RAYLEIGH MAXIMUM LIKELIHOOD Y 28064 28065 The maximum likelihood estimate of the scale parameter is: 28066 28067 sigmahat = SQRT(SUM[i=1 to n][X(i)**2]/(2*n)) 28068 28069 with X containing the data and n denoting the sample size. 28070 By default, Dataplot will use the sample minimum as the 28071 estimate of location (and subtract this value from X before 28072 computing the maximum likelihood estimate of sigma). If you 28073 want to specify a different estimate of location, enter the 28074 command 28075 28076 LET RAYLOC = <value> 28077 28078Note: 28079 Library functions are distinguished from let subcommands 28080 in the following ways. 28081 1) Functions enclose the input value in parenthesis. Let 28082 subcommands use spaces. 28083 2) Functions can accept (and return) either parameters 28084 (i.e., single values) or variables (i.e., an array of 28085 values) while let subcommands are specific in which they 28086 accept as input and what they return as output. 28087 3) Functions can accept expressions while let subcommands 28088 do not. For example, the following is legal: 28089 LET Y2 = ABS(Y1-INT(Y1)) 28090 For let subcommands, you typically have to do something 28091 like the following: 28092 LET YTEMP = Y**2 + 8 28093 LET A = SUM YTEMP 28094 28095Default: 28096 None 28097 28098Synonyms: 28099 None 28100 28101Related Commands: 28102 RAYCDF = Compute the Rayleigh cumulative distribution function. 28103 RAYPPF = Compute the Rayleigh percent point function. 28104 MAXPDF = Compute the Maxwell cumulative distribution function. 28105 CHPDF = Compute the chi probability density function. 28106 WEIPDF = Compute the Weibull probability density function. 28107 NORPDF = Compute the normal probability density function. 28108 LGNPDF = Compute the lognormal probability density function. 28109 28110Reference: 28111 "Continuous Univariate Distributions: Volume I", Second Edition, 28112 Johnson, Kotz, and Balakrishnan, Wiley, 1994, pp. 453, 686. 28113 28114Applications: 28115 Distributional Modeling, Statistical Physics 28116 28117Implementation Date: 28118 6/2004 28119 28120Program: 28121 Y1LABEL Probability 28122 X1LABEL X 28123 TITLE Rayleigh Probability Density 28124 LABEL CASE ASIS 28125 TITLE CASE ASIS 28126 PLOT RAYPDF(X) FOR X = 0 0.01 5 28127 28128-----RAYPPF (LET)-------------------------------- 28129 28130RAYPPF 28131 28132Name: 28133 RAYPPF (LET) 28134 28135Type: 28136 Library Function 28137 28138Purpose: 28139 Compute the Rayleigh percent point function. 28140 28141Description: 28142 The Rayleigh distribution is a special case of the 28143 chi distribution with degrees of freedom parameter = 2 and 28144 scale parameter sigma. It is also a special case of the 28145 Weibull distribution with shape parameter = 2 and scale 28146 parameter = SQRT(2). Note that some sources may define the 28147 Rayleigh distribution as a Weibull with shape parameter = 2 28148 and scale parameter = 1. 28149 28150 The Rayleigh distribution has the following percent point 28151 function: 28152 28153 G(x,mu,sigma) = mu + sigma*SQRT(2*LOG(1/(1-P))) 28154 0 <= p < 1; sigma > 0 28155 28156 with mu and sigma denoting the location and scale parameters, 28157 respectively. 28158 28159 The standard Rayleigh distribution is the case with 28160 mu = 0 and sigma = 1. 28161 28162Syntax: 28163 LET <y> = RAYPPF(<p>,<loc>,<scale>) 28164 <SUBSET/EXCEPT/FOR qualification> 28165 where <p> is a variable,number, or a parameter in the interval 28166 [0,1); 28167 <loc> is an optional number or parameter that specifies the 28168 value of the location parameter; 28169 <scale> is an optional positive number or parameter that 28170 specifies the value of the scale parameter; 28171 <y> is a variable or a parameter (depending on what <x> is) 28172 where the computed Rayleigh ppf value 28173 is stored; 28174 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 28175 28176Examples: 28177 LET Y = RAYPPF(0.95) 28178 LET Y = RAYPPF(P1,0,SIGMA) 28179 PLOT RAYPPF(P,0,SIGMA) FOR P = 0 0.01 0.99 28180 28181Note: 28182 Library functions are distinguished from let subcommands 28183 in the following ways. 28184 1) Functions enclose the input value in parenthesis. Let 28185 subcommands use spaces. 28186 2) Functions can accept (and return) either parameters 28187 (i.e., single values) or variables (i.e., an array of 28188 values) while let subcommands are specific in which they 28189 accept as input and what they return as output. 28190 3) Functions can accept expressions while let subcommands 28191 do not. For example, the following is legal: 28192 LET Y2 = ABS(Y1-INT(Y1)) 28193 For let subcommands, you typically have to do something 28194 like the following: 28195 LET YTEMP = Y**2 + 8 28196 LET A = SUM YTEMP 28197 28198Default: 28199 None 28200 28201Synonyms: 28202 None 28203 28204Related Commands: 28205 RAYCDF = Compute the Rayleigh cumulative distribution function. 28206 RAYPDF = Compute the Rayleigh probability density function. 28207 MAXPDF = Compute the Maxwell cumulative distribution function. 28208 CHPDF = Compute the chi probability density function. 28209 WEIPDF = Compute the Weibull probability density function. 28210 NORPDF = Compute the normal probability density function. 28211 LGNPDF = Compute the lognormal probability density function. 28212 28213Reference: 28214 "Continuous Univariate Distributions: Volume I", Second Edition, 28215 Johnson, Kotz, and Balakrishnan, Wiley, 1994, pp. 453, 686. 28216 28217Applications: 28218 Distributional Modeling 28219 28220Implementation Date: 28221 6/2004 28222 28223Program: 28224 X1LABEL Probability 28225 Y1LABEL X 28226 TITLE Rayleigh Percent Point 28227 LABEL CASE ASIS 28228 TITLE CASE ASIS 28229 PLOT RAYPPF(P) FOR P = 0 0.01 0.99 28230 28231-----RC (LET)---------------------------------------------- 28232 28233RC 28234 28235Name: 28236 RC (LET) 28237 28238Type: 28239 Library Function 28240 28241Purpose: 28242 Compute Carlson's degenrate elliptic integral. 28243 28244Description: 28245 Carlson's degenerate elliptic integral is defined as: 28246 RC(x,y)=0.5*INTEGRAL[1/SQRT((t+x)*(t+y)**2)]dt 28247 where INTEGRAL is the integral from 0 to infinity. The parameters 28248 x and y must all be non-negative. 28249 28250Syntax: 28251 LET <a> = RC(<x>,<y>,<z>) <SUBSET/EXCEPT/FOR qualification> 28252 where <x> is a non-negative number, parameter, or variable; 28253 <y> is a non-negative number, parameter, or variable; 28254 <a> is a variable or a parameter (depending on what <x>, 28255 <y>, and <z> are) where the computed values are stored; 28256 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 28257 28258Examples: 28259 LET A = RC(2,1) 28260 LET A = RC(X,4) 28261 LET X2 = RC(1,Y) 28262 28263Note: 28264 The Carlson elliptic integrals are computed using the RC, RD, RF, 28265 and RJ routines from the SLATEC Common Mathematical Library. 28266 SLATEC is a large set of high quality, portable, public domain 28267 Fortran routines for various mathematical capabilities maintained 28268 by seven federal laboratories. 28269 28270Note: 28271 DATAPLOT computes Legendre elliptic integrals by computing the 28272 equivalent Carlson elliptic integrals. See the documentation for 28273 the ELLIP1, ELLIP2, ELLIP3, ELLIPC1, and ELLIPC2 functions for 28274 details on computing Legendre elliptic functions in DATAPLOT. 28275 28276Note: 28277 Library functions are distinguished from let subcommands 28278 in the following ways. 28279 1) Functions enclose the input value in parenthesis. Let 28280 subcommands use spaces. 28281 2) Functions can accept (and return) either parameters 28282 (i.e., single values) or variables (i.e., an array of 28283 values) while let subcommands are specific in which they 28284 accept as input and what they return as output. 28285 3) Functions can accept expressions while let subcommands 28286 do not. For example, the following is legal: 28287 LET Y2 = ABS(Y1-INT(Y1)) 28288 For let subcommands, you typically have to do something 28289 like the following: 28290 LET YTEMP = Y**2 + 8 28291 LET A = SUM YTEMP 28292 28293Default: 28294 None 28295 28296Synonyms: 28297 None 28298 28299Related Commands: 28300 RF = Compute the Carlson elliptic integral of the first kind. 28301 RD = Compute the Carlson elliptic integral of the second kind. 28302 RJ = Compute the Carlson elliptic integral of the third kind. 28303 ELLIPC1 = Compute the Legendre complete elliptic integral of the 28304 first kind. 28305 ELLIPC2 = Compute the Legendre complete elliptic integral of the 28306 second kind. 28307 ELLIP1 = Compute the Legendre elliptic integral of the first 28308 kind. 28309 ELLIP2 = Compute the Legendre elliptic integral of the second 28310 kind. 28311 ELLIP3 = Compute the Legendre's elliptic integral of the third 28312 kind. 28313 28314Reference: 28315 "Algorithms for Incomplete Elliptic Integrals by Duplication", 28316 Carlson, ACM Transactions on Mathematical Software, 7, 28317 pp. 398-403. 28318 28319 "Handbook of Mathematical Functions, Applied Mathematics Series, 28320 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 28321 1964 (chapter 17). 28322 28323Applications: 28324 Special Functions 28325 28326Implementation Date: 28327 94/9 28328 28329Program: 28330 TITLE CARLSON ELLIPTIC FUNCTIONS 28331 PLOT RC(X,1) FOR X = 0.1 0.1 10 AND 28332 PLOT RC(1,X) FOR X = 0.1 0.1 10 28333 28334-----RD (LET)---------------------------------------------- 28335 28336RD 28337 28338Name: 28339 RD (LET) 28340 28341Type: 28342 Library Function 28343 28344Purpose: 28345 Compute Carlson's elliptic integral of the second kind. 28346 28347Description: 28348 Carlson's elliptic integral of the second kind is defined as: 28349 RD(x,y,z,p)=1.5*INTEGRAL[1/SQRT((t+x)*(t+y)*(t+z)**3)]dt 28350 where INTEGRAL is the integral from 0 to infinity. The parameters 28351 x, y, and z must all be non-negative with at most one of them 28352 being zero. The p parameter must be non-zero. 28353 28354Syntax: 28355 LET <a> = RD(<x>,<y>,<z>) <SUBSET/EXCEPT/FOR qualification> 28356 where <x> is a non-negative number, parameter, or variable; 28357 <y> is a non-negative number, parameter, or variable; 28358 <z> is a non-negative number, parameter, or variable; 28359 <a> is a variable or a parameter (depending on what, <p>, 28360 <x>, <y>, and <z> are) where the computed values are 28361 stored; 28362 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 28363 28364Examples: 28365 LET A = RD(2,1,3) 28366 LET A = RD(X,0,4) 28367 LET X2 = RD(1,1,Y) 28368 28369Note: 28370 The Carlson elliptic integrals are computed using the RC, RD, RF, 28371 and RJ routines from the SLATEC Common Mathematical Library. 28372 SLATEC is a large set of high quality, portable, public domain 28373 Fortran routines for various mathematical capabilities maintained 28374 by seven federal laboratories. 28375 28376Note: 28377 DATAPLOT computes Legendre elliptic integrals by computing the 28378 equivalent Carlson elliptic integrals. See the documentation for 28379 the ELLIP1, ELLIP2, ELLIP3, ELLIPC1, and ELLIPC2 functions for 28380 details on computing Legendre elliptic functions in DATAPLOT. 28381 28382Note: 28383 Library functions are distinguished from let subcommands 28384 in the following ways. 28385 1) Functions enclose the input value in parenthesis. Let 28386 subcommands use spaces. 28387 2) Functions can accept (and return) either parameters 28388 (i.e., single values) or variables (i.e., an array of 28389 values) while let subcommands are specific in which they 28390 accept as input and what they return as output. 28391 3) Functions can accept expressions while let subcommands 28392 do not. For example, the following is legal: 28393 LET Y2 = ABS(Y1-INT(Y1)) 28394 For let subcommands, you typically have to do something 28395 like the following: 28396 LET YTEMP = Y**2 + 8 28397 LET A = SUM YTEMP 28398 28399Default: 28400 None 28401 28402Synonyms: 28403 None 28404 28405Related Commands: 28406 RF = Compute the Carlson elliptic integral of the first kind. 28407 RJ = Compute the Carlson elliptic integral of the third kind. 28408 RC = Compute the degenerate Carlson elliptic integral. 28409 ELLIPC1 = Compute the Legendre complete elliptic integral of the 28410 first kind. 28411 ELLIPC2 = Compute the Legendre complete elliptic integral of the 28412 second kind. 28413 ELLIP1 = Compute the Legendre elliptic integral of the first 28414 kind. 28415 ELLIP2 = Compute the Legendre elliptic integral of the second 28416 kind. 28417 ELLIP3 = Compute the Legendre's elliptic integral of the third 28418 kind. 28419 28420Reference: 28421 "Algorithms for Incomplete Elliptic Integrals by Duplication", 28422 Carlson, ACM Transactions on Mathematical Software, 7, 28423 pp. 398-403. 28424 28425 "Handbook of Mathematical Functions, Applied Mathematics Series, 28426 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 28427 1964 (chapter 17). 28428 28429Applications: 28430 Special Functions 28431 28432Implementation Date: 28433 94/9 28434 28435Program: 28436 TITLE CARLSON ELLIPTIC FUNCTIONS 28437 PLOT RD(X,1,2) FOR X = 0.1 0.1 10 AND 28438 PLOT RD(1,X,2) FOR X = 0.1 0.1 10 AND 28439 PLOT RD(1,2,X) FOR X = 0.1 0.1 10 28440 28441-----READ------------------------------------------------------- 28442 28443READ 28444 28445Name: 28446 READ 28447 28448Type: 28449 Support Command 28450 28451Purpose: 28452 Reads data into variables 28453 1) from an ASCII mass storage file; 28454 2) from within a CALLed DATAPLOT sub-program; 28455 3) from the terminal. 28456 28457Description: 28458 The READ command is primarily intended for reading from the terminal 28459 or from ASCII files. Dataplot has limited support for binary data 28460 files (see the Note sections below with regards to reading Fortran 28461 unformatted files and image data). 28462 28463 Also, Dataplot does not currently support directly reading files 28464 from other statistical/spreadsheet programs or database files. 28465 Some support may be provided in future releases, but for now 28466 you need to save the data from these programs in an ASCII file 28467 in order to read them into Dataplot. XML based data files are 28468 becoming increasingly popular as well. At this time, Dataplot does 28469 not support XML based data files. 28470 28471 IDEAL CASE 28472 28473 By default, Dataplot assumes rectangular data files containing 28474 numeric data where the data columns are separated by one or 28475 more spaces. Commas or tabs may be used as delimiters as well. 28476 28477 In this case, you can read the file with a command like the 28478 following: 28479 28480 READ FILE.DAT Y X1 X2 28481 28482 The first argument after the READ is the name of the ASCII file. 28483 The remaining arguments identify the variable names. Variable 28484 names can be up to eight characters long and should be limited 28485 to alphabetic (A-Z) and numeric (0-9) characters. Although 28486 other characters can in fact be used, this is discouraged 28487 since their use can cause problems in some contexts. Variable 28488 names are not case sensitive (Dataplot converts all alphabetic 28489 characters to upper case). 28490 28491 Dataplot recognizes the first argument as a file name if it 28492 finds a "." in the name. If no "." is found, Dataplot assumes 28493 the first argument is a variable name and it tries to read 28494 from the keyboard rather than the file. 28495 28496 For this ideal case, the following are the basic rules. 28497 28498 1) If there are k variables listed on the READ statement, then 28499 each line image must have at least k data values. Only the 28500 first k data values are read (this is how the READ command 28501 differs from the SERIAL READ command), and these are read 28502 into successive elements of the individual variables. Thus 28503 28504 READ X Y 28505 1 1 1 28506 2 4 8 28507 3 9 27 28508 END OF DATA 28509 28510 results in X containing the 3 elements 1, 2, and 3; Y 28511 containing the 3 elements 1, 4, and 9; and the values 1, 8, 28512 and 27 not being read at all. 28513 28514 2) In scanning for the k variables, the full line image is 28515 scanned. By default, the full line image is 255 characters. 28516 28517 The COLUMN LIMITS can be used to restrict the read to certain 28518 columns. The case where the data line is longer than 255 28519 characters is discussed below. 28520 28521 3) Data values on a line image must be separated by at least one 28522 blank or comma. Non-printing characters, such as tabs, are 28523 treated as spaces. 28524 28525 4) Data values may be free-format. That is, they need not be 28526 aligned in specific columns. If your data file is aligned 28527 in specific columns, you may be able to significantly speed 28528 up the read by specifying a format for the data. This is 28529 discussed below. 28530 28531 5) The format of individual data values is general. It can be 28532 integer, floating point, or exponential. It is stored 28533 internally as a single precision real number. 28534 28535 Support for character data is discussed below. 28536 28537 6) All reads start from the beginning of the file. The SKIP and 28538 ROW LIMITS can be used to skip header lines are to restrict 28539 which row of the file are read. 28540 28541 7) The analyst need not be concerned about the number of 28542 observations for each variable; DATAPLOT automatically 28543 determines and reports this value at the end of the read. 28544 28545 8) The read terminates when a line image is encountered which 28546 consists of 28547 28548 END OF DATA 28549 or 28550 28551 END DATA 28552 28553 or when the end of the file is reached. 28554 28555 Many ASCII files will not be in the "ideal" format. The remainder of 28556 this section discusses various issues that may cause problems when 28557 reading ASCII files and provides suggestions on how to deal with these 28558 issues. The following topics are discussed: 28559 28560 1) Viewing ASCII files within Dataplot 28561 2) Header lines/restricted rows or columns 28562 3) Long data records 28563 4) Automatic variable names 28564 5) Reading fixed columns 28565 6) Reading variables with unequal lengths 28566 7) Reading character data 28567 8) Reading row oriented data 28568 9) Comment lines in data files 28569 10) Reading Excel (or other spreadsheet) files 28570 11) Cut and Paste 28571 12) Comma as decimal point 28572 13) Missing values and undefined numbers 28573 14) Reading date and time fields 28574 15) Reading IP addresses 28575 16) Reading monetary data (e.g., $23,461.58) 28576 17) Reading numeric values with trailing "+" or "-" or "*" or "%" 28577 18) Commas within character fields 28578 19) Reading binary data 28579 20) Reading image data 28580 21) What if all of the data will not fit into memory? 28581 28582 If you create the ASCII file yourself, it is recommended that 28583 you create it with variables of equal length (pick some numeric 28584 value to signify missing data) and with data items separated by one 28585 or more spaces. Inclusion of a header giving a description of 28586 the data file is optional, but we find it helpful (Dataplot 28587 can skip over the header lines). When the ASCII files are created 28588 by another program (e.g., Excel), then you may have less control 28589 over the format of the file. Hopefully, most ASCII files you 28590 encounter can be handled using the commands discussed below. 28591 28592 28593 VIEWING THE ASCII FILE WITHIN DATAPLOT 28594 28595 In order to identify some of the issues discussed below, it is 28596 often helpful to view the ASCII file before trying to read it into 28597 Dataplot. You can do this with the command 28598 28599 LIST FILE.DAT 28600 28601 This will list the file 20 lines (you can change the number 28602 of lines with the SET LIST LINES command) at a time. You 28603 can then enter a carriage return to view the next 20 lines or 28604 a "no" to stop viewing the file. 28605 28606 For some of the commands given below, you need to either know 28607 approriate line numbers or column numbers. 28608 28609 To view the file with line numbers, enter the command 28610 28611 NLIST FILE.DAT 28612 28613 To identify appropriate columns, enter the command 28614 28615 RULER 28616 28617 This will identify the first 80 columns. 28618 28619 28620 HEADER LINES/RESTRICTED ROWS OR COLUMNS 28621 28622 Many data files contain header lines at the beginning of the 28623 file that provide a description of the file. In order to 28624 skip over these lines, enter the command 28625 28626 SKIP N 28627 28628 where N identifies how many lines to skip. 28629 28630 Most of the sample data files that are distributed with Dataplot 28631 contain a line starting with hyphens ("---"). You can use the 28632 command 28633 28634 SKIP AUTOMATIC 28635 28636 for these files. Dataplot will skip all lines until a line 28637 starting with three or more hypens is encoutered. 28638 28639 In a related issue, if you want to restrict the read to certain 28640 rows in the file, you can enter the command 28641 28642 ROW LIMITS N1 N2 28643 28644 with N1 and N2 denoting the first and last rows to read, 28645 respectively. 28646 28647 You can also restrict the read to certain columns of the file 28648 using the command 28649 28650 COLUMN LIMITS C1 C2 28651 28652 with C1 denoting the first column to read and C2 the last column 28653 to read. 28654 28655 28656 LONG DATA RECORDS 28657 28658 When reading from the keyboard, Dataplot restricts a single record 28659 to a maximum of 255 columns. 28660 28661 When reading from a file, Dataplot previously restricted a single 28662 record to a maximum of 132 columns. The March, 2003 version raised 28663 the default limit to 255 characters. In addition, the following 28664 command was added: 28665 28666 MAXIMUM RECORD LENGTH N 28667 28668 with N denoting the size of the largest record to be read. 28669 28670 Dataplot accepts values of N up to 9999. However, be aware 28671 that some Fortran compilers may impose their own limit. These 28672 limits tend not to be well documented, but with modern compilers 28673 they tend to be sufficiently large that this should not be a 28674 problem in practice. 28675 28676 Note that if you specify a MAXIMUM RECORD LENGTH command, you 28677 should also specify the COLUMN LIMITS command. For example, 28678 28679 MAXIMUM RECORD LENGTH 512 28680 COLUMN LIMITS 1 512 28681 28682 If you specify a SET READ FORMAT command (discussed below), you 28683 do not need to specify the maximum record length. 28684 28685 28686 AUTOMATIC VARIABLE NAMES 28687 28688 Dataplot normally reads variable names on the READ command. 28689 However, many ASCII files will have the name of the variables 28690 given directly in the file or Dataplot can assign the variable 28691 names automatically. 28692 28693 Specific methods include the following. 28694 28695 1. Many of the sample files provided in the Dataplot 28696 installation use a syntax like 28697 28698 Y X1 X2 28699 ---------------- 28700 <data values> 28701 28702 For these files, you can enter the commands 28703 28704 SKIP AUTOMATIC 28705 SET VARIABLE NAMES FILE 28706 READ FILE.DAT 28707 28708 In this case, Dataplot will skip all lines until a line 28709 starting with three or more hypens is encountered. It 28710 will then backspace to the previous line and read the 28711 variable names from that line. 28712 28713 Alternatively, you can specify the number of lines to skip with 28714 the command 28715 28716 SKIP N 28717 28718 where N specifies the number of lines in the header. If the 28719 SET VARIABLE NAME FILE command has been given, Dataplot will look 28720 at the last line of the header (i.e., line N). If it starts with 28721 three or more hyphens, then Dataplot assumes that the variable 28722 names are on line N-1. If line N does not start with hyphens, 28723 then Dataplot assumes that the variable names are on line N. 28724 28725 2. Many non-Dataplot ASCII data files will have the variable names on 28726 the first line of the file. For these files, you can enter the 28727 commands 28728 28729 SET VARIABLE LABELS ON 28730 READ FILE.DAT 28731 28732 Dataplot then assumes line one of the file contains the variable 28733 names and the data start with line two. 28734 28735 This is equivalent to using 28736 28737 SKIP 1 28738 SET VARIABLE NAMES FILE 28739 READ FILE.DAT 28740 28741 3. If you would like Dataplot to simply assign the variable 28742 names, enter the commands 28743 28744 SET VARIABLE NAMES AUTOMATIC 28745 READ FILE.DAT 28746 28747 Dataplot will read the first line of the file to determine 28748 the number of variables. It will then assign the names 28749 COL1, COL2, and so on to the variable names. Prior to 28750 2014/10, Dataplot used default names of X1, X2, and so on. 28751 You can specify what to use for the base of the variable 28752 names by entering the command 28753 28754 SET AUTOMATIC VARIABLE BASE NAME <value> 28755 28756 The use of SET VARIABLE NAMES AUTOMATIC applies to either the 28757 SKIP AUTOMATIC or the SKIP N cases. 28758 28759 Note that Dataplot's usual rules for variable names still apply. 28760 That is, a maximum of eight characters will be used and spaces (commas 28761 can also be used as the delimiter and non-printing characters such as 28762 tabs will be treated as spaces) will delimit variable names. The use 28763 of special (i.e., not a number and not an alphabetic character) 28764 characters is discouraged. You may need to edit the file if the 28765 variable names do not follow these rules (more than eight characters will 28766 simply be ignored, so the issue is more one of duplicate variable names 28767 in the first eight characters). 28768 28769 The SET VARIABLE NAMES <AUTOMATIC/FILE> command was implemented 2014/10. 28770 Prior to that, the SKIP AUTOMATIC worked equivalently to the 28771 SET VARIABLE NAMES FILE and the SKIP N worked equivalently to the 28772 SET VARIABLE NAMES AUTOMATIC. The default is AUTOMATIC. 28773 28774 28775 READING FIXED COLUMNS 28776 28777 By default, Dataplot performs free format reads. That is, 28778 you do not need to line up the columns neatly. You do need 28779 to provide one or more spaces (tabs, commas, colons, semi-colons, 28780 parenthesis, or brackets can be used as well) between data fields. 28781 28782 Many data files will contain fixed fields. There are several reasons 28783 you may want or need to take advantage of these fixed fields rather 28784 than using a free format read. 28785 28786 1. If your data fields do not contain spaces (or some other 28787 delimiter) between data columns, you need to tell 28788 Dataplot how to interpret the columns. 28789 28790 2. In some cases, you may only want to read selected 28791 variables in the data file. 28792 28793 3. Using a formatted read can significantly speed up the reading 28794 of the data. If you have small or moderate size data files (say 28795 500 rows or fewer), this is really not an issue. However, if you 28796 are reading 50,000 rows, you can significantly speed up the read 28797 by specifying the format. 28798 28799 4. If the data fields have unequal lengths, Dataplot will not 28800 interpret the data file correctly with a free format read. 28801 It assigns the data items in the order they are encountered 28802 to the variable names in the order they are given. Dataplot 28803 does not try to guess if a data item is missing based on the 28804 columns. 28805 28806 The issue of unequal lengths is discussed in detail in the 28807 next section. 28808 28809 There are two basic cases for fixed fields. 28810 28811 1. The data fields are justified by the decimal point. 28812 28813 In this case, you can use the 28814 28815 SET READ FORMAT <format> 28816 28817 command to specify a Fortran-like format to read the file. 28818 Enter HELP READ FORMAT for details. 28819 28820 Using a formatted read is significantly faster than a 28821 free format read. 28822 28823 2. Many programs will write ASCII files with fixed columns, 28824 but the data fields will be either left or right justified 28825 rather than lined up by the decimal point. 28826 28827 In this case, you can use a special form of the 28828 COLUMN LIMITS command that was introduced with the 28829 January, 2004 version. Normally, the first and last columns 28830 to read are specified. However, you can now enter variables for 28831 the lower and upper limits as in the following example: 28832 28833 LET LOWER = DATA 1 21 41 28834 LET UPPER = DATA 10 30 50 28835 COLUMN LIMITS LOWER UPPER 28836 28837 That is, if variables rather than parameters are specified, 28838 separate column limits are specified for each data field. 28839 In this case, the first data field is between columns 28840 1 and 10, the second field is between columns 21 and 30, and 28841 the third field is between 41 and 50. 28842 28843 When this syntax is used, only one variable is read for 28844 each specified field. If the field is blank, then this is 28845 interpreted as a missing value. 28846 28847 28848 READING VARIABLES OF UNEQUAL LENGTH 28849 28850 Dataplot normally expects all variables to be of equal length. 28851 If some variables have missing rows, this can have undesired 28852 results. Dataplot will assign the first value read to the 28853 first variable name, the second value to second variable and 28854 so on. If fewer values than variables are specified, then variables 28855 that have no data values are not read at all (even if they have 28856 values for other rows). 28857 28858 If you have a data file where the columns have unequal lengths, 28859 you can do one of the following things. 28860 28861 1. Pick some value to represent a missing value and fill 28862 in missing data points with that value. After reading 28863 the data, you can use a RETAIN command to remove them. 28864 For example, if you use -99 to signify a missing value, 28865 you can enter 28866 28867 RETAIN Y SUBSET Y > -99 28868 28869 Alternatively, you can use a SUBSET clause on subsequent 28870 plot and analysis commands. 28871 28872 2. Use the variable form of the COLUMN LIMITS command as 28873 described above. By default, when a blank field is 28874 encountered, it is set to zero. You can specify the 28875 value to use by entering the command 28876 28877 SET READ MISSING VALUE <value> 28878 28879 This option depends on having consistent columns for 28880 each of the data fields. 28881 28882 3. If your data has both columns of unequal length and 28883 inconsistent columns for given data fields, an alternative 28884 is to use a comma delimited data file. That is, separate 28885 data values with a comma. If there is no data data between 28886 successive commas, this is treated as a missing value. The 28887 default is to assign a value of zero. Alternatively, you 28888 can use the SET READ MISSING VALUE command described above. 28889 28890 You can specify a delimiter other than a comma with the 28891 command 28892 28893 SET READ DELIMITER <character> 28894 28895 The variable form of the COLUMN LIMITS, the 28896 SET READ MISSING VALUE, and the SET READ DELIMITER commands 28897 were introduced in the January, 2004 version. The 28898 interpretation of successive commas as a missing value was 28899 also introduced in the January, 2004 version. 28900 28901 28902 READING DATA WITH CHARACTER FIELDS 28903 28904 Dataplot has not previously supported character data. The one 28905 execption is that you could read row labels with the READ ROW LABEL 28906 command (enter HELP READ ROW LABEL for details). If encountered, 28907 Dataplot would generate an error message and not read the data file 28908 correctly. 28909 28910 With the January 2004 version, we have introduced some limited 28911 support for character data. Specifically, we have added the command 28912 28913 SET CONVERT CHARACTER <ON/CATEGORICAL/IGNORE/ERROR> 28914 28915 Setting this to ERROR will continue the current Dataplot action of 28916 reporting character data as an error. This is recommended for the 28917 case when a file is suppossed to contain only numeric data and the 28918 presence of character data is in fact indicative of an error in the 28919 data file. 28920 28921 Setting this to IGNORE will instruct Dataplot to simply ignore any 28922 fields containing character data. This can be useful if you simply 28923 want to extract the numeric data fields in the file without 28924 entering COLUMN LIMITS or SET READ FORMAT commands. 28925 28926 Setting this to ON will read character fields and write them to the 28927 file "dpzchf.dat". Note that Dataplot saves numeric data 28928 "in memory" for fast access. Since character data has limited 28929 use in Dataplot, we have decided to save character data 28930 externally to minimize memory requirements. Dataplot keeps a 28931 separate name table for the character data fields (the names for 28932 character variables are stored in the file "dpzchf.dat"). 28933 28934 Setting this to CATEGORICAL is similar to ON. However, CATEGORICAL 28935 will additionally create a coded numeric variable in addtion to 28936 the character variable. The numeric variable is useful for computing 28937 purposes while the character variable is used for labeling purposes. 28938 28939 There are some restrictions on when Dataplot will try to 28940 read character data: 28941 28942 1) This only applies to the variable read case. That 28943 is, READ PARAMETER and READ MATRIX will ignore 28944 character fields or treat them as an error. 28945 28946 2) Dataplot will only try to read character data from 28947 a file. When reading from the keyboard (i.e., when 28948 READ is specified with no file name), character data 28949 will be ignored when a SET CONVERT CHARACTER ON is 28950 specified. 28951 28952 Note: The 2020/01 version of Dataplot has removed this 28953 restriction. You can now read character data from 28954 the terminal. 28955 28956 3) This capability is not supported for the SERIAL READ 28957 case. 28958 28959 4) The SET READ FORMAT command does not accept the 28960 "A" format specification for reading character 28961 fields. 28962 28963 5) A maximum of 20 character variables will be saved. 28964 28965 6) A maximum of 24 characters for each character variable 28966 will be saved. 28967 28968 7) The character variables from at most one data file 28969 will be saved in a given session. 28970 28971 Some of these restrictions may be addressed in subsequent 28972 releases of Dataplot. 28973 28974 Currently, Dataplot has limited support for character variables. 28975 Specifically, 28976 28977 1) The row label can be used for the plot character by 28978 entering the command 28979 28980 CHARACTER ROWLABEL 28981 28982 2) You can convert a character variable to a coded numeric 28983 variable with the command 28984 28985 LET Y = CHARACTER CODE IX 28986 LET Y = ALPHABETIC CHARACTER CODE IX 28987 28988 with IX denoting the name of the character variable. These 28989 command assigns a numeric value for each unique name in 28990 the character variable. 28991 28992 For the CHARACTER CODE case, the coding is from 1 to K where 28993 K is the number of unique values. The order is based on 28994 the order these values are found in the file. 28995 28996 For the ALPHABETIC CHARACTER CODE case, the coding is from 28997 1 to K where K is the number of unique values. The order is 28998 performed in alpabetical order. 28999 29000 We anticipate additional use of character variables in subsequent 29001 releases of Dataplot. 29002 29003 If your character fields contain non-numeric/non-alphabetic characters, 29004 then it is recommended that the character fields be enclosed in 29005 quotes. When Dataplot encounters a quote (either a single or double 29006 quote), it interprets everything until a matching quote is found 29007 as part of that character field. If the quotes are not used, 29008 then spaces, tabs, parenthesis, brackets, colons, and semi-colons 29009 are interpreted as delimiters that signify the end of that data item. 29010 29011 29012 READING ROW ORIENTED DATA 29013 29014 Dataplot assumes a column oriented format. That is, a row of 29015 data represents a single record (or case) and a column of data 29016 represents a variable. If a data file has a row orientation, then 29017 this is reversed. A row of data represents a variable and a column 29018 of data represents a record (or case). 29019 29020 The following example shows one way of correctly reading the data 29021 into Dataplot. Suppose that your data file contains five rows with 29022 each row corresponding to a single variable. You can do the following: 29023 29024 LOOP FOR K = 1 1 5 29025 ROW LIMITS K K 29026 SERIAL READ FILE.DAT X^K 29027 END OF LOOP 29028 29029 Note: The 2018/10 version of Dataplot added a "READ ROW" command that 29030 will read each row into a separate Dataplot variable. 29031 29032 29033 COMMENT LINES IN DATA FILES 29034 29035 It is sometimes convenient to include comments in data files. 29036 If these comments are contained at the beginning of the file, then 29037 the SKIP command can be used. To have Dataplot check for comment 29038 lines in the data file, enter the command 29039 29040 COMMENT CHECK ON 29041 29042 The default comment character is a ".". That is, any line starting 29043 with a ". " is treted as a comment line and ignored. To specify 29044 a different comment character, enter the command 29045 29046 COMMENT CHARACTER <char> 29047 29048 with <char> denoting the desired comment character. 29049 29050 29051 EXCEL FILES 29052 29053 At the current time (1/2004), Dataplot does not support the 29054 direct reading of Excel data files. We are planning to add 29055 this capability in a future release of Dataplot. Until that 29056 time, you need to save the data in Excel to an ASCII file and 29057 read that ASCII file into Dataplot. 29058 29059 Excel provides the following options for writing ASCII data 29060 files: 29061 29062 1. Formatted text (space delimited) (.PRN extension) 29063 29064 This format will use consistent columns for the data fields. 29065 The variable form of the COLUMN LIMITS command can be used 29066 when the data columns have unequal length. 29067 29068 Character fields will often not have the separating space. The 29069 variable form of the COLUMN LIMITS command can be used in this 29070 case as well. 29071 29072 2. CSV (Comma delimited) (.CSV extension) 29073 29074 This format will separate data fields with a single comma. 29075 Missing data is represented with successive commas. Dataplot 29076 can now (as of the January 2004 version) handle this correctly. 29077 29078 3. Text (Tab delimited) (.TXT extension) 29079 Text (MS-DOS) (.TXT extension) 29080 29081 These files will separate data fields with a tab character. 29082 Note that Dataplot converts all non-printing characters 29083 (including tabs) to a single space character. 29084 29085 This format is not appropriate for data containing variables 29086 with unequal lengths since it will not generate consistent 29087 columns for the data fields. Use either the space delimited 29088 or comma delimited file for that case. 29089 29090 Other spreadsheets will typically have similar options. However, the 29091 details may vary depending on the specific spreadsheet program. 29092 29093 Note that directly exporting the Excel data to an ASCII file tends 29094 to work well when the data sheet is "clean". That, is you basically 29095 have a single rectangular set of data cells. If your spreadsheet 29096 contains graphs or multiple rectangular areas of data, then the 29097 generated ASCII file will tend to be difficult to work with. In 29098 this case, it is recommended that you either copy the relevant data 29099 to a clean sheet or paste it into an ASCII editor and save the file 29100 from there. 29101 29102 The next section discusses cut and paste within Dataplot. In many 29103 cases, this may provide the simplest way to retrieve data from a 29104 spreadsheet. 29105 29106 Note: The 2020/02 version of Dataplot added the READ EXCEL command 29107 to read Excel files using a Python script. Enter 29108 HELP READ EXCEL for details. 29109 29110 CUT AND PASTE 29111 29112 In some contexts, it may be desirable to simply cut and paste relevant 29113 data into Dataplot. For example, this can provide an alternative way 29114 to import data from spreadsheets and other statistical software. 29115 29116 How well cut and paste works is dependent on the operating system and 29117 the compiler used to build Dataplot. If you do this, we recommend 29118 limiting it to the case of numeric data. 29119 29120 Some specific cases are 29121 29122 1. Linux systems with the gfortran compiler 29123 29124 As an example, suppose that the system clipboard contains three 29125 columns of data. You can then do something like 29126 29127 READ Y X1 X2 29128 <paste the contents of the clipboard> 29129 END OF DATA 29130 29131 That is, you do a terminal read, paste your data, and then 29132 enter an END OF DATA command to terminate the READ. 29133 29134 2. Windows systems with the Intel compiler 29135 29136 For earlier versions of the compiler, the operations described 29137 for Linux/gfortran worked for this environment as well. However, 29138 for the version of the compiler currently being used, this is 29139 no longer working. Some testing has shown that it works for one 29140 or two lines, but Dataplot crashes for more than that. We are 29141 investigating this to see if we can get it working again. 29142 29143 Note: The 2014/12 version of Dataplot added numerous commands 29144 for reading from (and writing to) the clipboard. The 29145 initial implementation is for the Windows environments, 29146 although this should be extended to Linux and Mac OS X 29147 platforms in subsequent releases. Enter HELP CLIPBOARD 29148 for details. In many cases, using the READ CLIPBOARD 29149 capability may be the easiest method for reading 29150 spreadsheet data into Dataplot. 29151 29152 3. Tcl/Tk GUI 29153 29154 The spreadsheet in the Dataplot Tcl/Tk GUI does not accept 29155 paste operations in the data spreadsheet. 29156 29157 COMMA AS DECIMAL POINT 29158 29159 Dataplot follows the United States convention where the decimal 29160 point is the period ".". Some locales may use a different 29161 character to denote the decimal point. In particular, some 29162 countries use the comma ",". 29163 29164 To allow Dataplot to read files that use a character other than 29165 the "." for the decimal point, enter the command 29166 29167 SET DECIMAL POINT <value> 29168 29169 where <value> denotes the character that specifies the decimal point. 29170 29171 Note this support is fairly limited. Specifically, it applies 29172 to free-format reads (i.e., no SET READ FORMAT command has been 29173 entered). In addition, 29174 29175 1. This option is not supported for the WRITE command. WRITE 29176 will always use a period for the decimal point. 29177 29178 2. Dataplot alphanumeric output (e.g., the output from the FIT 29179 command) is generated with the period as the decimal point. 29180 29181 3. As mentioned above, if you read your data with a 29182 SET READ FORMAT command, the data must use the period 29183 for the decimal point. 29184 29185 MISSING VALUES AND UNDEFINED NUMBERS 29186 29187 Some software programs will have special characters to denote 29188 missing values or undefined values (e.g., the result of trying 29189 to divide by 0). 29190 29191 In particular, Unix/Linux software often uses "nan" to denote an 29192 undefined number. If Dataplot encounters an "nan" in a numeric 29193 field, it will convert it to the Dataplot "missing value". The "nan" 29194 search is not case sensitive (i.e., it will check for "NAN", "NaN", 29195 etc.). You can specify what Dataplot will use for the missing value 29196 by entering the command 29197 29198 SET READ MISSING VALUE <value> 29199 29200 where <value> is a numeric value. 29201 29202 Missing value flags are specific to individual programs. You can 29203 specify a character string that denotes a missing value with the 29204 command 29205 29206 SET DATA MISSING VALUE <value> 29207 29208 where <value> is a string with 1 to 4 characters. If Dataplot 29209 encounters <value> in a numeric field, it will convert it to the 29210 Dataplot "missing value". The missing value string is not case 29211 sensitive. You can specify what Dataplot will use for the missing 29212 value by entering the command 29213 29214 SET READ MISSING VALUE <value> 29215 29216 where <value> is a numeric value. 29217 29218 The above discussion was for missing numeric data. If you have 29219 missing data for a character field, you can specify the string 29220 that will denoted missing data by entering the command 29221 29222 SET READ CHARACTER MISSING VALUE <string> 29223 29224 The default string is ZZZZNULL. 29225 29226 READING DATE AND TIME FIELDS 29227 29228 Date and time fields will typically have syntax like 29229 29230 2016/06/22 29231 12:43:08 29232 29233 Dataplot treats the "/" and ":" as indicating character fields 29234 (based on the SET CHARACTER CONVERT command, this will either cause 29235 an error, result in this field being ignored, or the field being 29236 read as a character variable). 29237 29238 The following commands were added (2016/06) to help deal with date and 29239 time fields. 29240 29241 SET DATE DELIMITER <character> 29242 SET TIME DELIMITER <character> 29243 29244 Although Dataplot does not have explicit date or time variables, 29245 these commands allow the components of date and time fields to 29246 be read as separate numeric variables. For example, 29247 29248 SET DATE DELIMITER / 29249 SET TIME DELIMITER : 29250 READ YEAR MONTH DAY HOUR MIN SEC 29251 2016/06/22 23:19:03 29252 END OF DATA 29253 29254 READING IP ADDRESSES 29255 29256 IP addresses typically have a syntax like 29257 29258 129.6.37.209 29259 29260 By default, Dataplot will generate an error when trying to read a 29261 field of this type. To address this, you can enter the command 29262 29263 SET READ IP ADDRESSES ON 29264 29265 If this switch is ON, Dataplot will scan the line and if a field is 29266 encountered that conains more than one period ".", Dataplot will 29267 convert these periods to spaces before parsing the line. 29268 29269 The default is OFF since this adds additional processing time to 29270 the READ and most data sets do not contain IP addresses. 29271 29272 READING MONETARY DATA 29273 29274 Monetary data may sometimes be given as 29275 29276 $11,456.12 $1,021,111.10 29277 29278 The "$" and "," in these numeric fields will cause problems. The 29279 "$" will be treated as a non-numeric value (depending on other 29280 SET commands, this will be treated as an error or the numeric field 29281 will be read as a character field). The comma is typically treated 29282 as a field delimiter. If you have this kind of data, enter the 29283 commands 29284 29285 set read dollar sign ignore on 29286 set read comma ignore on 29287 29288 To reset the defaults, enter 29289 29290 set read dollar sign ignore off 29291 set read comma ignore off 29292 29293 Note that if you enter the SET READ COMMA IGNORE ON command, the 29294 comma will no longer be treated as the delimiter. Dataplot cannot 29295 currently handle the case where the comma is used both for monetary 29296 data and also as a field delimiter. 29297 29298 READING NUMERIC VALUES WITH TRAILING "+" OR "-" OR "*" OR "%" 29299 29300 On occassion, numeric fields may have a trailing "+", a trailing 29301 "-", a trailing "*" or a trailing "%". 29302 29303 The "+" is typically used to indicate that the value is greater 29304 than or equal to the entered value. Likewise, the "-" is used to 29305 indicate that the value is less than or equal to the entered value. 29306 This may be used when data is truncated at a high or low value. If 29307 you have data that uses this convention, enter 29308 29309 set read trailing plus minus ignore on 29310 29311 Dataplot does not have any convention for indicating that a number 29312 in fact means "greater than" or "less than", so it will read the 29313 numeric value and simply ignore the "+" or "-". 29314 29315 To reset the defualt, enter 29316 29317 set read trailing plus minus ignore off 29318 29319 Trailing asterisks ("*") are sometimes used to indicate statistical 29320 significance. To ignore these asterisks, enter 29321 29322 set read asterisk ignore on 29323 29324 If this command is not given, the field will be treated as a 29325 character field. To reset the default, enter 29326 29327 set read asterisk ignore off 29328 29329 Percentage data will sometimes include a trailing percent sign 29330 ("%"). To ignore the percent sign, enter 29331 29332 set read percent sign ignore on 29333 29334 If this command is not given, the field will be treated as a 29335 character field. To reset the default, enter 29336 29337 set read percent sign ignore off 29338 29339 COMMAS WITHIN CHARACTER FIELDS 29340 29341 If you are reading data that may contain character fields, you can 29342 specify whether you want commas in the character fields to be 29343 treated as part of the character field or as a delimiter. 29344 29345 To have the comma treated as a delimiter, enter 29346 29347 set character field comma delimiter on 29348 29349 To have the comma not be interpreted as a delimiter (i.e., it 29350 will simply be another character in the character field), enter 29351 29352 set character field comma delimiter off 29353 29354 The default is OFF. 29355 29356 READING BINARY DATA 29357 29358 Currently, the only types of binary data that Dataplot currently 29359 supports are: 29360 29361 1) A few types of image files can be read on some platforms. 29362 This is discussed in the next section. 29363 29364 2) Dataplot may be able to read some files created using Fortran 29365 unformatted data files. Dataplot is most likely to have success 29366 reading unformatted Fortran files that contain only numeric data 29367 and use a consistent record structure. Unformatted Fortran 29368 files that contain a mixture of character and numeric data 29369 will not be read successfully. 29370 29371 Support for other types of binary files may be added in future 29372 releases. However, this support will probably be for specific 29373 types of binary files as oppossed to arbitrary binary files. 29374 29375 The advantage of using unformatted Fortran files is that file sizes 29376 may be significantly smaller and reading the data can be significantly 29377 faster. One potential use of unformatted Fortran files is to save 29378 a large data file that you will read many times in Dataplot. 29379 29380 The disadvantages of using unformatted Fortran files are that they 29381 are not human readable, they cannot be edited or modified using an 29382 ASCII editor, and, most importantly, they are not portable between 29383 operating systems and compilers. That is, unformatted Fortran files 29384 typically need to be read using the same operating system and compiler 29385 that was used to create them. 29386 29387 For details on using unformatted Fortran files, enter 29388 29389 HELP SET READ FORMAT 29390 29391 READING IMAGE DATA 29392 29393 If Dataplot was built with support for the GD library, Dataplot 29394 can read image data in PNG, JPEG, or GIF format. If you have 29395 image data in another format, you may be able to use an image 29396 conversion program (e.g., NetPBM or ImageMagick) to convert it 29397 to one of the supported formats. 29398 29399 For further information, enter 29400 29401 HELP READ IMAGE 29402 29403 WHAT IF ALL THE DATA WILL NOT FIT INTO MEMORY? 29404 29405 Dataplot was designed primarily for interactive usage. For this reason, 29406 it reads all data into memory. The current default is to have a 29407 workspace that accomodates 10 columns with 1,500,000 rows (you can 29408 re-dimension to obtain more columns at the expense of fewer rows, however 29409 you cannot increase the maximum number of rows). 29410 29411 With the advent of "big data", there are more data files that cannot be 29412 read into Dataplot's available memory. For these data files, there are 29413 several things that can potentially be done 29414 29415 1. For some platforms, if you have a large amount of memory you may 29416 be able to build a version of Dataplot that raises the maximum 29417 number of rows. For example, on a Linux system with 64MB of RAM, 29418 we were able to build a version that supports a maximum of 29419 10,000,000 rows. Contact Alan Heckert if you need assistance 29420 with this. 29421 29422 2. The STREAM READ command was added. This command uses one pass 29423 algorithms to do a number of things. 29424 29425 a. You can create a new file that uses SET WRITE FORMAT. This 29426 is typically done once so that you can use SET READ FORMAT on 29427 subsequent reading of the data file (this can substantially 29428 speed up processing of these large files). 29429 29430 b. You can generate various summary statistics either for the full 29431 data set or for groups in the data. 29432 29433 c. You can generate cross tabulation statistics (up to 4 29434 cross tabulation variables may be specified). 29435 29436 d. You can create various types of distance (e.g., Euclidean 29437 distances, correlation distances) matrices either for the full 29438 data set or for cross tabulations of the data. 29439 29440 Distance matrices are often used for various types of 29441 multivariate analysis. 29442 29443 e. You can generate approximate percentiles either for the full 29444 data set or for cross tabulations of the data. Based on this, 29445 you can perform distributional modeling for a single variable 29446 or distributional comparisons between variables (e.g., 29447 quantile quantile plots, bihistograms, two sample KS tests, and 29448 so on). 29449 29450 The STREAM READ command allows you to do a fair bit of exploratory 29451 analyses on these large data sets even though the full data set is 29452 not read into memory. 29453 29454Syntax 1: 29455 READ <x1> <x2> ... <xk> 29456 where <x1>, <x2>, ... <xk> are the desired names for the variables 29457 into which the data are read. 29458 29459 This syntax is used to read from the terminal or from within a 29460 macro file. All lines are read until an END OF DATA is 29461 encountered. 29462 29463Syntax 2: 29464 READ <file> <x1> <x2> <x3> etc. 29465 where <file> is the name of the mass storage file where the data 29466 resides; 29467 and <x1>, <x2>, ... <xk> are the desired names for the variables 29468 into which the data in <file> are read. 29469 29470 This syntax is used to read from a file. All lines are read until 29471 an END OF DATA or the physical end of file is encountered. 29472 29473Examples: 29474 READ CALIB. PRES TEMP TIME 29475 READ ASTM.DAT Y1 Y2 Y3 X DAY LAB 29476 READ Y1 Y2 Y3 X DAY LAB 29477 29478Note: 29479 By default, Dataplot does free format reads. However, it has the 29480 capability for supporting Fortran style formats. Formatted reads 29481 can be about 10 times faster on many systems which can be helpful 29482 for large data files. Enter HELP READ FORMAT for more details. 29483 29484 Note that Fortran formats are based on the decimal point lining up 29485 consistenly between rows. Spreadsheet programs such as Excel tend to 29486 generate either right justified or left justified columns when 29487 generating fixed width ASCII files. These are typically not 29488 consistent with Fortran formatted reads. 29489 29490Note: 29491 Blank lines in data files are ignored. 29492 29493Note: 29494 In order to determine whether the first argument is a file name or 29495 a variable name, it looks for a period in the name. If it finds 29496 one, it assumes a file name. If it does not, it assumes a variable 29497 name. If your file name does not contain a period, attach a 29498 trailing period (no spaces) to the file name on the READ command. 29499 29500Note: 29501 Dataplot does not assume specific extensions for file names. Although 29502 using conventions (e.g., ".DAT" or ".TXT" for data files, ".DP" for 29503 Dataplot macros) can be helpful for distinguishing between types of 29504 files, this is more for the analysts convenience. Dataplot itself 29505 does not enforce any conventions. 29506 29507 File names have the following restrictions: 29508 29509 1. The file name should be a valid file name for the local 29510 operating system. 29511 29512 2. The file name should contain a period "." in the file name 29513 itself or as a trailing character. Dataplot strips off trailing 29514 periods on those systems where it is appropriate to do so. On 29515 systems where trailing periods can be a valid file name (e.g., 29516 Unix), Dataplot tries to open the file with the trailing period. 29517 If this fails, it then tries to open the file with the trailing 29518 period stripped off. 29519 29520 3. If the file name contains spaces or hyphens, then it needs to be 29521 enclosed in quotes. 29522 29523 4. File names are currently limited to 80 characters. This can 29524 in particular be a problem if the file name is contained within 29525 a long path name. The following can be helpful in these cases. 29526 29527 a. You can use the CD command to make the path where the file 29528 is stored the current directory. This is most useful for 29529 data files. For example, 29530 29531 pwd 29532 cd <path where data file resided> 29533 read file.dat ... 29534 cd ^CURDIR 29535 29536 The pwd command is used to save the current directory. The 29537 cd command is then used to set the current directory to the 29538 path where the data resides, the read is performed, and then 29539 the cd command is used to restore the original working 29540 directory (the cd command saves the current path in the 29541 string CURDIR). 29542 29543 b. You can use the SEARCH DIRECTORY command to specify an 29544 additional directory to search for file names. 29545 29546Note: 29547 File names are case sensitive on Unix/Linux/Mac OS X systems. For these 29548 systems, Dataplot attempts to open the file as given. If this fails, it 29549 attempts to open the file as all upper case characters. If this fails, it 29550 attempts to open the file as all lower case characters. 29551 29552 As a further caution for Unix/Linux hosts, certain expansion characters 29553 (specifically ~ to refer to your home directory) are interpreted 29554 by the shell and are not recognized by the Fortran compiler. These 29555 expansion characters are interpreted as literal characters and do 29556 not yield the intended file name. 29557 29558Note: 29559 In general, Dataplot does not read binary data. However, it can 29560 read and write binary data using Fortran unformatted I/O. Note that 29561 although the Fortran standard includes unformatted I/O, the 29562 implementation details are left to the individual compiler. This 29563 means that Fortran unformatted files are not portable across systems 29564 and compilers. 29565 29566 The primary use for this option is if you have a large data file that 29567 you will be accessing frequently. In this case, it can speed up the 29568 I/O to save a binary version of the file (you should keep the original 29569 ASCII version). 29570 29571 For details, enter HELP SET READ FORMAT. 29572 29573Note: 29574 Many data sets are now collected as images. On some implementations, 29575 Dataplot can use the GD library to read image data into numeric arrays. 29576 29577 Although the GD library supports a limited number of image formats, 29578 open source software packages such as Image Magick and Netpbm can be 29579 used to convert a large number of image formats to ones supported by 29580 the GD library. 29581 29582 For details, enter HELP READ IMAGE. 29583 29584Note: 29585 There are variants of this command for reading matrices, parameters, 29586 and strings/functions. See the Related Commands section below. 29587 29588Note: 29589 After a READ command, Dataplot creates the following parameters: 29590 29591 ISKIP - the number of header lines skipped 29592 NUMLRD - the number of data lines read 29593 NUMVRD - the number of variables read 29594 29595 In addition, the variable names read are saved in the strings 29596 ZZZV1, ZZZV2, ZZZV3, and so on. These parameters and strings are 29597 updated each time a READ is performed. 29598 29599 This capability was added 2014/12. 29600 29601Default: 29602 1) If no file name is specified and a CALL is being executed, then 29603 the data values should be listed directly in the DATAPLOT 29604 sub-program immediately after the READ command (do not forget 29605 the END OF DATA statement). 29606 29607 2) If no file name is specified and the commands are being manually 29608 entered/executed one at a time from the terminal, then the data 29609 should be entered directly from the terminal immediately after 29610 the READ command (also terminated by an END OF DATA statement). 29611 29612Synonyms: 29613 None 29614 29615Related Commands: 29616 READ FUNCTION = Read a function. 29617 READ MATRIX = Read a matrix. 29618 READ PARAMETER = Read a parameter. 29619 READ STRING = Read a string. 29620 READ IMAGE = Read an image format into numeric arrays. 29621 READ STACKED VARIABLE = Read a list of variables into a single 29622 response variable and a group-id variable. 29623 SERIAL READ = Perform a serial read. 29624 SET READ FORMAT = Define a FORTRAN style format for reads. 29625 DATA (LET) = Enter data values into a variable. 29626 CLIPBOARD = Various commands for reading from the 29627 system clipboard. 29628 29629Applications: 29630 Data Input 29631 29632Implementation Date: 29633 Pre-1987 29634 1988/02 Ignore column limits when reading from the terminal 29635 1990/05 Check for comment character in data files 29636 1995/04 Support for unformatted read 29637 1996/04 Ignore SET READ FORMAT for READ STRING 29638 1997/10 Support for SKIP AUTOMATIC 29639 1998/11 Support for more than 100 variable names 29640 1999/12 Support for READ ROWID 29641 2002/07 Support for quotes on file name 29642 2003/02 Maximum number of characters per record user settable 29643 2004/01 Support for reading variable names from file 29644 2004/01 Support for reading character data 29645 2004/11 PACK/DISPERSE options for READ with SUBSET 29646 2014/11 Support for reading from system clipboard 29647 2014/12 Create several automatic parameters/strings for READ 29648 2016/06 Support for SET DATE DELIMITER 29649 2016/06 Support for SET TIME DELIMITER 29650 2016/06 Support for SET READ IP ADDRESSES 29651 2019/03 Support for SET READ ASTERISK IGNORE 29652 2019/12 Support for SET READ PERCENT SIGN IGNORE 29653 Numerous bug fixes over the years 29654 29655Program 1: 29656 SKIP 25 29657 READ BERGER1.DAT Y X BATCH 29658 29659Program 2: 29660 READ X Y 29661 1 1 29662 2 4 29663 3 9 29664 4 16 29665 5 25 29666 END OF DATA 29667 PRINT X Y 29668 29669-----READ DECIMAL POINT (SET)---------------------------------------- 29670 29671READ DECIMAL POINT (SET) 29672 29673Name: 29674 READ DECIMAL POINT (SET) 29675 29676Type: 29677 Subcommand under SET 29678 29679Purpose: 29680 Specifies the character to be interpreted as the decimal 29681 point when reading data. 29682 29683Description: 29684 Dataplot follows the United States convention where the 29685 decimal point is the period ".". Some locales may use a 29686 different character to denote the decimal point. In 29687 particular, some countries use the comma ",". 29688 29689 In order to make it easier for Dataplot to read files which 29690 use a different convention for the decimal point, this command 29691 allows you to specify a different character, such as the comma, 29692 to denote the decimal point. 29693 29694 Note this support is fairly limited. Specifically, it only 29695 applies to free-format reads. 29696 29697 1. This option is not supported for the WRITE command. The 29698 WRITE command will always use a period for the decimal 29699 point. 29700 29701 2. Dataplot alphanumeric output (e.g., the output from the 29702 FIT command) is generated with the period as the decimal 29703 point. 29704 29705 3. If you read your data with a SET READ FORMAT command, the 29706 data must use the period for the decimal point. 29707 29708Syntax: 29709 SET READ DECIMAL POINT <value> 29710 where <value> denotes the character to interpret as the decimal 29711 point. 29712 29713Examples: 29714 SET READ DECIMAL POINT , 29715 SET READ DECIMAL POINT . 29716 29717Default: 29718 The period "." is the default decimal point character. 29719 29720Synonyms: 29721 None 29722 29723Related Commands: 29724 READ = Carries out a column-wise input of data. 29725 ASCII FILES = Provides guidance on reading ASCII files. 29726 29727Applications: 29728 Input/Output 29729 29730Implementation Date: 29731 2005/5 29732 29733Program: 29734 SET READ DECIMAL , 29735 READ FILE.DAT Y X 29736 29737-----READ DELIMITER (SET)---------------------------------------- 29738 29739READ DELIMITER (SET) 29740 29741Name: 29742 READ DELIMITER (SET) 29743 29744Type: 29745 Subcommand under SET 29746 29747Purpose: 29748 Specifies the character that is used as the delimiter to 29749 separate data fields in an ASCII data file. 29750 29751Description: 29752 If Excel writes a comma delimited ASCII file (.CSV), then 29753 missing values are denoted with ",,". In order to interpert 29754 these files correctly, you can enter the command 29755 29756 SET READ DELIMITER <value> 29757 29758 where <value> specifies the desired delimiter. The default 29759 delimiter is a comma. 29760 29761 If Dataplot encounters the delimiter before any valid data 29762 has been found, it interprets this as a missing value. 29763 29764 By default, missing values are set to 0. If you would like 29765 to specify a different value to use for missing values, enter 29766 the command 29767 29768 SET READ MISSING VALUE <value> 29769 29770Syntax: 29771 SET READ DELIMITER <value> 29772 where <value> denotes the value to use as the delimiter. 29773 29774Examples: 29775 SET READ DELIMITER : 29776 SET READ DELIMITER , 29777 SET READ DELIMITER % 29778 29779Default: 29780 Comma 29781 29782Synonyms: 29783 None 29784 29785Related Commands: 29786 READ = Carries out a column-wise input of data. 29787 READ MISSING VALUE = Specify the value to use for missing data. 29788 29789Applications: 29790 Input/Output 29791 29792Implementation Date: 29793 2004/1 29794 29795Program: 29796 SET READ DELIMITER , 29797 SET MISSING VALUE -99 29798 READ DUMMY.CSV Y X 29799 PLOT Y X SUBSET Y > -99 SUBSET X > -99 29800 29801-----READ EXCEL------------------------------------------------- 29802 29803READ EXCEL 29804 29805Name: 29806 READ EXCEL 29807 29808Type: 29809 Support Command 29810 29811Purpose: 29812 Read variables (vectors) from an Excel file. 29813 29814Description: 29815 Spreadsheet programs are a popular method for saving data. Most 29816 spreadsheet programs support the Microsoft Excel file format. 29817 29818 Dataplot does not natively support reading or writing to Excel format 29819 files. The READ EXCEL command works as follows 29820 29821 1. Dataplot writes the name of the Excel file to line 1 29822 of the file "dpst5f.dat". It writes the name of the 29823 Excel sheet to line 2 of "dpst5f.dat". The default 29824 sheet name is "Sheet1". To change the sheet name, enter 29825 the command 29826 29827 SET EXCEL SHEET <sheet-name> 29828 29829 2. Dataplot then invokes a Python script to read the variables 29830 from the specified Excel file and then writes the variables 29831 to the file "dpst1f.dat". 29832 29833 The Python script, "read_excel.py", is located in the 29834 "scripts" subdirectory of the Dataplot auxiliary directory. 29835 This script uses the Pandas function "dataframe.read_excel" 29836 to read the data from the Excel file. It then uses the 29837 Pandas function "pandas.to_csv" to write the variables as 29838 a comma separated file (CSV) to the file "dpst1f.dat". 29839 29840 3. Dataplot reads the contents of the variables from the 29841 file "dpst1f.dat". 29842 29843 This command assumes that Python and the Python package Pandas 29844 are already installed on your local platform. Dataplot does not 29845 check if Python is installed and it does not initiate the 29846 Python installation if it is not already installed. 29847 29848 As Python is used by many popular applications on Linux platforms, 29849 most Linux platforms will already have Python installed. However, 29850 this is not the case for Windows and MacOS platforms. 29851 29852 If you need to install Python, there are a number of Python 29853 distributions (see https://wiki.python.org/moin/PythonDistributions). 29854 However, the most common are ActivePython from ActiveState and 29855 Anaconda from Continuum Analytics. Dataplot does not depend on a 29856 specific Python distribution and we make no recommendation for the 29857 preferred distribution. 29858 29859 This command will typically work well with Excel files that are 29860 clean rectangular data sets. If you have added graphs, formulas, 29861 cross-tabulations, and so on to the Excel sheet, then the 29862 READ EXCEL command is likely to be unsatisfactory. You can either 29863 copy the data portion of the spreadsheet to a new sheet or use 29864 one of the other methods for reading data from spreadsheets 29865 listed below. 29866 29867 If you infrequently need to read Excel files and do not already 29868 have Python installed on your local platform, there are several 29869 additional methods for reading the data from Excel files. However, 29870 if you anticipate the need for frequently reading Excel files, then 29871 going through the Python installation is probably worth the effort. 29872 29873 In addition to READ EXCEL, the following methods can also be used 29874 to read data from Excel files. 29875 29876 1. Spreadsheets typically support writing data to ASCII files. 29877 For example, Excel can write formatted text (space delimited) 29878 (.PRN extension), comma delimited files (.CSV extension), or 29879 tab delimited files (.TXT extension). Enter HELP READ for 29880 details of this. 29881 29882 As with READ EXCEL, this option works best with clean 29883 rectangular data sets. If you do not have a clean Excel 29884 sheet, you will probably need to manually edit the ASCII 29885 file before trying to read it with Dataplot. However, it is 29886 a viable alternative to READ EXCEL when you do not have Python 29887 installed on your platform and do not wish to install it. 29888 29889 2. You can also use Copy and Paste. On Windows platforms, 29890 you can Copy the desired data to the clipboard and then use 29891 the READ CLIPBOARD command. Alternatively, you can paste 29892 the data into an ASCII editor (e.g., Notepad or Wordpad on 29893 Windows, vi or Emacs on Linux), save the file and then use 29894 the Dataplot READ command. 29895 29896 This option is particularly useful when your spreadsheet is 29897 not a clean rectangular data set. 29898 29899Syntax: 29900 READ EXCEL <fname> <variable list> 29901 <SUBSET/EXCEPT/FOR qualification> 29902 where <fname> is the name of the Excel file; 29903 <variable list> is the list of variables to read; 29904 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 29905 29906Examples: 29907 READ EXCEL FILE.XLSX Y1 Y2 Y3 X 29908 29909Note: 29910 The Pandas pandas.to_csv function will typically add a row id 29911 variable to the ASCII file. 29912 29913Note: 29914 The python script will currently read the entire spreadsheet. 29915 Additional commands to specify columns and rows in the spreadsheet 29916 to read are under development but not yet available. 29917 29918 Also, Dataplot will not search for the Excel file in the 29919 Dataplot auxiliary files directories as it does for the 29920 READ for ASCII files. 29921 29922 Note: The 2020/05 version of Dataplot now supports specifying the 29923 first and last rows of the Excel file to read with the following 29924 commands 29925 29926 SET EXCEL START ROW <value> 29927 SET EXCEL STOP ROW <value> 29928 29929 One use of this is to skip over header lines in the Excel file. 29930 29931Note: 29932 Excel (or some other spreadsheet program) does not need to be 29933 installed on your local platform. For example, you can create 29934 the Excel file on a Windows platform and then move the Excel file 29935 to a Linux platform. 29936 29937Note: 29938 If Python is not installed on your default path, you can specify it 29939 using the SET PYTHON PATH command. For example, the following is for 29940 the Anaconda installation of Python 3 under Windows (where Anaconda 29941 is installed for the single user heckert) 29942 29943 set python path c:\Users\heckert\AppData\Local\Continum\anaconda3\ 29944 29945 There are several different Python distributions. The appropriate 29946 Python path will depend on the specific distribution you used to 29947 install Python and whether you choose to install it for a single user 29948 or for all users. 29949 29950Note: 29951 On Windows platforms, the "read_excel.py" script will be copied to 29952 the current directory. 29953 29954Default: 29955 None 29956 29957Synonyms: 29958 None 29959 29960Related Commands: 29961 WRITE EXCEL = Write variables to an Excel file. 29962 PYTHON = Run a user specified Python script from within Dataplot. 29963 READ = Read variables, strings, parameters and matrices. 29964 29965Applications: 29966 Data Input 29967 29968Implementation Date: 29969 2020/02 29970 29971Program: 29972 dimension 40 columns 29973 . Path name for Windows 29974 . read excel "C:\Program Files (x86)\NIST\DATAPLOT\LIB\DATA\FIBERS.XLSX" ... 29975 . rowid breakid xcent ycent xc1 yc1 xc2 yc2 xc3 yc3 xc4 yc4 length 29976 . Path name for Linux 29977 read excel /usr/local/lib/data/FIBERS.XLSX ... 29978 rowid breakid xcent ycent xc1 yc1 xc2 yc2 xc3 yc3 xc4 yc4 length 29979 set write decimals 3 29980 print breakid xcent length 29981 29982-----READ FORMAT (SET)------------------------------------------- 29983 29984READ FORMAT (SET) 29985 29986Name: 29987 READ FORMAT (SET) 29988 29989Type: 29990 Subcommand under SET 29991 29992Purpose: 29993 Sets the (optional) FORTRAN format for the READ and SERIAL READ 29994 commands. Unformatted Fortran files are now also supported (see 29995 NOTE section below). 29996 29997Description: 29998 The default format for the READ and SERIAL READ command is 29999 free-format. This allows the analyst to input data into DATAPLOT 30000 without having to worry about how the data is residing out on the 30001 file. On the other hand, if the data happens to reside on the 30002 file in a structured format, and if the analyst knows what the 30003 format is, then the analyst can optionally specify to DATAPLOT 30004 this format information. The advantage of this is speed since 30005 formatted READs and SERIAL READs are 10 to 15 times faster. For 30006 small data sets (less than a few hundred lines), there is little 30007 to gain. However, if your data file is large (say more than 500 30008 lines) and formatted, then the time for I/O can be drastically 30009 reduced by making use of such format information. Any 30010 FORTRAN-like format must contain only F (floating-point), E 30011 (exponential), and X (blanks) specifications. I (integer), D 30012 (double-precision), H (hollerith), etc. specifications are not 30013 permitted. The restriction against I format is no restriction at 30014 all. Simply use the corresponding F format (e.g., I2 becomes 30015 F2.0, I8 becomes F8.0). 30016 30017Syntax: 30018 SET READ FORMAT <s> 30019 where <s> is a FORTRAN format-like string. 30020 30021Examples: 30022 SET READ FORMAT 4F10.0 30023 SET READ FORMAT 5X,F6.0,F6.2,4X,2F5.0 30024 SET READ FORMAT 10X,3E12.4,5X,F10.0 30025 SET READ FORMAT DEFAULT 30026 30027 SET READ FORMAT 3F10.0 30028 READ CALIB.DAT X Y Z 30029 30030Note: 30031 Support was added for reading Fortran unformatted data files. 30032 This was done primarily for sites that have created "mega" size 30033 versions of DATAPLOT where the time entailed in reading large 30034 data files becomes important. For standard size DATAPLOT 30035 (typically a maximum of 10,000 rows with 10 columns for 100,000 30036 data points total), the use of the SET READ FORMAT command 30037 provides adequate performance. However, the unformatted read 30038 capability is available regardless of the workspace size. The 30039 advantage of unformatted reads is that the data files are much 30040 smaller (typically by a factor of 10 or more) and reading the 30041 data is significantly faster (e.g., reading 10,000 rows of data is 30042 almost instantaneous). The disadvantage is that unformatted 30043 files are binary, and thus cannot be modified or viewed with a 30044 standard text editor. Also, Fortran unformatted files are NOT 30045 transportable across different computer systems. 30046 30047 An unformatted read is accomplished by entering the command: 30048 30049 SET READ FORMAT UNFORMATTED 30050 30051 and then entering a standard READ command. For example, 30052 30053 READ LARGE.DAT X1 X2 X3 30054 30055 There are 2 ways to create the unformatted file in Fortran. For 30056 example, suppose X and Y are to be written to an unformatted 30057 file. The WRITE can be generated by: 30058 30059 a) WRITE(IUNIT) (X(I),Y(I),I=1,N) 30060 b) WRITE(IUNIT) X,Y 30061 30062 The distinction is that (a) stores the data as X(1), Y(1), 30063 X(2), Y(2), ..., X(N), Y(N) while (b) stores all of X then 30064 all of Y. There is no inherent advantage in either method in 30065 terms of performance or file size. The SET READ FORMAT 30066 UNFORMATTED command assumes (a). To specify (b), enter the 30067 command: 30068 30069 SET READ FORMAT COLUMNWISE (or UNFORMATTEDCOLUMNWISE) 30070 30071 Unformatted reading is supported only for variables or matrices 30072 (i.e., not for parameters or strings). Also, it only applies 30073 when reading from a file. The limits for the maximum number of 30074 rows and columns for a matrix still apply (500 rows and 100 30075 columns on most systems). When reading a matrix, the number of 30076 columns must be specified via the SET UNFORMATTED COLUMNS 30077 command. For example, 30078 30079 SET READ FORMAT UNFORMATTED 30080 SET UNFORMATTED COLUMNS 25 30081 READ MATRIX.DAT M 30082 30083 The maximum size of the file that DATAPLOT can read is equal to 30084 the workspace size on your implementation (100,000 or 200,000 30085 points on most installations). For larger files, it will read 30086 up to this number of data values. 30087 30088 The data is assumed to be a rectangular grid of data written in 30089 a single chunk. Only single precision real numbers are 30090 supported. By default, the entire file (up to the maximum number 30091 of points) is read. DATAPLOT does provide 2 commands to allow 30092 some control of what portion of the file is read: 30093 30094 SET UNFORMATTED OFFSET <value> 30095 SET UNFORMATTED RECORDS <value> 30096 30097 The OFFSET specifies the number of data values at the begining of 30098 the file to skip. This is useful for skipping header lines 30099 (similar to a SKIP command for reading ASCII files) and other 30100 miscellaneous values. The RECORDS value is useful for reading 30101 part of a larger file. 30102 30103 Be aware that Fortran unformatted files are NOT transportable 30104 across systems. This is due to the fact that the file contains 30105 various header bytes (the Fortran standard leaves implementation 30106 of this up to vendor) that are not standard. Also, the storage 30107 of real numbers can vary between platforms. This means that 30108 the SET READ FORMAT UNFORMATTED command can NOT be used to read 30109 raw binary files (as might be produced by a C program) and it 30110 cannot, in general, be used to read unformatted Fortran files 30111 created on systems other than the one you are running DATAPLOT on. 30112 30113Default: 30114 Free-format (i.e., no format). 30115 30116Synonyms: 30117 None 30118 30119Related Commands: 30120 READ = Carries out a column-wise input of data. 30121 SERIAL READ = Carries out a line-wise input of data. 30122 30123Applications: 30124 Input/Output 30125 30126Implementation Date: 30127 1988/03 (support for reading unformatted Fortran files added 1995/04) 30128 30129Program: 30130 SET READ FORMAT 2F10.1 30131 READ X Y 30132 21.0 110.7 30133 31.2 120.6 30134 55.4 100.2 30135 END OF DATA 30136 WRITE X Y 30137 30138-----READ FUNCTION-------------------------------------------------- 30139 30140READ FUNCTION 30141 30142Name: 30143 READ FUNCTION 30144 30145Type: 30146 Support Command 30147 30148Purpose: 30149 Reads a function into DATAPLOT: 30150 1) from a mass storage file; 30151 2) from within a CALLed DATAPLOT sub-program; 30152 3) from the terminal. 30153 30154Description: 30155 The rules regarding READ FUNCTION are as follows: 30156 1) Only one line is read. Unlike a READ of variables, no END OF 30157 DATA is searched for. 30158 2) Typically, only one function is read at a time. Reading more 30159 than one function is allowed (but not recommended). If more 30160 than one function is read from the same line, separate the 30161 functions with at least one space and leave no spaces within 30162 a given function. For example, 30163 READ FUNCTION F G 30164 X**2+8X-4 X**3-X+1 30165 3) In scanning for the function, the full line image is scanned 30166 (for reading from a mass storage file, the full line image is 30167 132 columns; for reading from within a sub-program and for 30168 reading from the terminal, the full line image is 80 30169 columns). For variations on this, see the COLUMN LIMITS 30170 command. 30171 4) If one function is read, blanks are ignored in the function. 30172 However, if more than one function is read, blanks are used 30173 to separate the functions (and are therefor significant). 30174 5) Function definitions can be free-format They need not be 30175 aligned in specific columns. 30176 6) All reads start from the beginning of the file (for 30177 variations of this, see the SKIP and ROW LIMITS commands). 30178 30179Syntax 1: 30180 READ FUNCTION <f1> <f2> ... <fk> 30181 where <f1>, <f2>, ..., <fk> are the desired functions (typically 30182 only one is given). 30183 30184 This syntax is used to read a function from the terminal or from 30185 within a DATAPLOT sub-program. 30186 30187Syntax 2: 30188 READ FUNCTION <file> <f1> <f2> ... <fk> 30189 where <file> is the name of the mass storage file where the 30190 function resides; 30191 and <f1>, <f2>, ..., <fk> are the desired functions (typically 30192 only one is given). 30193 30194 This syntax is used to read a function from a file. 30195 30196Examples: 30197 READ FUNCTION CALIB. F 30198 READ FUNCTION F 30199 X**2+4*X-1 30200 30201Default: 30202 1) If no file name is specified, and if a CALL is being executed, 30203 then the function should be listed directly in the DATAPLOT 30204 sub-program immediately after the READ FUNCTION command. 30205 2) If no file name is specified, and if commands are being manually 30206 entered/executed 1-at-a-time from the terminal, then the 30207 function should be entered directly from the terminal 30208 immediately after the READ FUNCTION command. 30209 30210Related Commands: 30211 SERIAL READ = Perform a serial read. 30212 READ = Read variables. 30213 READ PARAMETER = Read a parameter. 30214 READ MATRIX = Read a matrix. 30215 READ STRING = Read a string. 30216 30217Applications: 30218 XX 30219 30220Implementation Date: 30221 XX 30222 30223Program: 30224 READ FUNCTION F 30225 X**2+2*X-6 30226 PLOT F FOR X = -3 .1 3 30227 30228-----READ IMAGE---------------------------------------- 30229 30230READ IMAGE 30231 30232Name: 30233 READ IMAGE 30234 30235Type: 30236 Input Command 30237 30238Purpose: 30239 Reads an image file that is in JPEG, PNG, or GIF format. 30240 30241Description: 30242 Scientific data is increasingly collected in the form of 30243 images. Although Dataplot does not currently support an 30244 explicit image data type, the READ IMAGE command can be used 30245 to read images into Dataplot in the form of real numbers 30246 (i.e., each real number represents the intensity value of 30247 a given pixel in the image). 30248 30249 There are two forms for this command: 30250 30251 1) You can read the image data into a matrix. 30252 30253 2) You can read the image data into a response variable, 30254 a row-id variable, and a column-id variable. 30255 30256 The best choice depends on what analysis you intend to 30257 perform on the data. If you will not be using the matrix 30258 specific commands, the second form is typically more useful. 30259 30260 Images can be either grey scale (i.e., a single color with 30261 varying intensity levels) or color. Color images are 30262 represented with intensity values for red, green, and 30263 blue (RGB). Although RGB is not the only color model used, 30264 it is currently the only one supported in Dataplot. 30265 30266 Dataplot implements the READ IMAGE command using the GD 30267 library. The GD library was developed by the Boutell company. 30268 GD in turn uses three additional libraries: zlib, libpng, and 30269 libjpeg. These libraries are all freely downloadable from the 30270 web. The URL for GD is (this site contains links to the other 30271 three libraries): 30272 30273 http://www.libgd.org/ 30274 30275 The READ IMAGE command depends on the GD library being 30276 integrated into Dataplot. Currently, it should be available 30277 on most Linux and Mac OSX implementations. However, it is 30278 not currently available on the Microsoft Windows 30279 implementation. 30280 30281 Note that the primary purpose of reading images into Dataplot 30282 is in order to perform data analysis on the image data. 30283 Although you can use the LET comamnd to perform some basic 30284 image manipulation tasks, image manipulation is not a primary 30285 goal for the Dataplot developers. 30286 30287Syntax 1: 30288 READ IMAGE <file> <m> 30289 where <file> is the name of the file containing the image; 30290 and <m> is the matrix where the image will be saved. 30291 30292 This syntax is used to save a grey scale image into a matrix. 30293 30294Syntax 2: 30295 READ IMAGE <file> <r> <g> <b> 30296 where <file> is the name of the file containing the image; 30297 <r> is the matrix where the red component of the image 30298 will be saved. 30299 <g> is the matrix where the green component of the image 30300 will be saved. 30301 and <b> is the matrix where the blue component of the image 30302 will be saved. 30303 30304 This syntax is used to save an RGB image into 3 separate matrices 30305 (one matrix for each color). 30306 30307Syntax 3: 30308 READ IMAGE TO VARIABLES <file> <y> <rowid> <colid> 30309 where <file> is the name of the file containing the image; 30310 <y> is the variable where the image data will be saved; 30311 <rowid> is a variable that identifies the row of the image; 30312 and <colid> is a variable that identifies the column of the 30313 image. 30314 30315 This syntax is used to save a grey scale image into a single 30316 response variable and corresponding row-id and column-id 30317 variables. 30318 30319Syntax 4: 30320 READ IMAGE TO VARIABLES <file> <r> <b> <g> <rowid> <colid> 30321 where <file> is the name of the file containing the image; 30322 <r> is the variable where the red component of the image data 30323 will be saved; 30324 <b> is the variable where the blue component of the image data 30325 will be saved; 30326 <g> is the variable where the green component of the image data 30327 will be saved; 30328 <rowid> is a variable that identifies the row of the image; 30329 and <colid> is a variable that identifies the column of the 30330 image. 30331 30332 This syntax is used to save an RGB image into a three response 30333 variables (one for each color component) and corresponding row-id 30334 and column-id variables. 30335 30336Examples: 30337 READ IMAGE TO VARIABLES IMAGE_GREY.JPG Y ROW COL 30338 READ IMAGE TO VARIABLES IMAGE_COLOR.JPG RED BLUE GREEN 30339 READ IMAGE IMAGE_GREY.JPG M 30340 READ IMAGE IMAGE_COLOR.JPG RED BLUE GREEN 30341 30342Note: 30343 The current implementation supports a limited number of image 30344 file formats. If you have image data in some other format 30345 (and there is a long list of available image formats), you will 30346 need to convert the image to either JPEG, PNG, or GIF format. 30347 30348 ImageMagick and Netpbm are two freely downloadable software 30349 suites that are capable of converting image formats for a wide 30350 variety of image formats (they also contains many image 30351 manipulation tools). ImageMagick and Netpbm will often be 30352 installed on Unix/Linux platforms and they are freely 30353 downloadable for most common computer platforms. In addition, 30354 programs such as Perl have integrated the Image Magick libraries 30355 to provide image conversion and manipulation capabilities. 30356 30357 If you need to perform some basic image manipulation tasks, 30358 it is probably easier to use one of these software programs 30359 (or some other image manipulation tool) first before reading the 30360 image into Dataplot. 30361 30362 The ImageMagick software can be downloaded from the following 30363 web site: 30364 30365 http://www.imagemagick.org/ 30366 30367 The Netpbm software can be downloaded from the following 30368 web site: 30369 30370 http://netpbm.sourceforge.net/ 30371 30372 Windows users may find it more convenient to use 30373 30374 http://gnuwin32.sourceforge.net/packages/netpbm.htm 30375 30376 We are investigating the possibility of integrating one or both 30377 of these libraries into a future release of Dataplot in order to 30378 provide direct access to a greater range of image formats and to 30379 provide some basic image manipulation capabilities. 30380 30381Note: 30382 There are some limitations on the size of the images that 30383 Dataplot can handle. 30384 30385 If you use the READ IMAGE TO VARIABLES form of the command, 30386 the limiting factor is the maximum number of rows for a single 30387 variable. On most platforms, the default is to have 10 columns 30388 with a maximum of 1,000,000 rows. You can use the DIMENSION 30389 command to create more columns at the expense of fewer rows. 30390 However, you cannot create more rows (i.e., the minimum number 30391 of columns is 10). 30392 30393 So multiply the number of rows by the number of columns in your 30394 image to see the minimum number of rows you need. For example, 30395 if you have a 512x512 image, you need 262,144 rows of data. If 30396 your version of Dataplot has a maximum of 1,000,000 rows, then 30397 you can accomodate images up to 1,000x1,000. 30398 30399 You may want to do something like the following before using the 30400 READ IMAGE TO VARIABLES command: 30401 30402 LET NUMROW = 512 30403 LET NUMCOL = 512 30404 LET MAXROW = NUMROW*NUMCOL 30405 DIMENSION MAXROW ROWS 30406 30407 If you use the READ IMAGE command, you will typically need to 30408 create a large number of columns (which means you will be able 30409 to accomodate fewer rows in any variables you create). You may 30410 want to do something like the following before using the READ IMAGE 30411 command: 30412 30413 LET NUMROW = 512 30414 LET NUMCOL = 512 30415 DIMENSION NUMROW 30416 MATRIX DIMENSION ROWS NROWS 30417 30418 This will give you the maximum number of columns based on the 30419 number of rows in your image. The MATRIX DIMENSION is used to 30420 dimension temporary matrices in the various Dataplot MATRIX 30421 commands. 30422 30423 The maximum row size is set before Dataplot is built. To see 30424 what it is on your platform, you can enter the command 30425 30426 DIMENSION 10 COLUMNS 30427 30428 The value given for the line MAXIMUM NUMBER OBS/VARIABLE (ROWS) 30429 specifies the maximum number of rows for your implementation. 30430 30431Note: 30432 Unlike most of the other READ commands, the file name argument 30433 is required on the READ IMAGE command. 30434 30435Note: 30436 DATAPLOT has no restrictions on the file name other than it be a 30437 valid file name on the local operating system and that it contain 30438 a period "." in the file name itself or as a trailing character. 30439 DATAPLOT strips off trailing periods on those systems where it is 30440 appropriate to do so. On systems where trailing periods can be a 30441 valid file name (e.g., Unix), DATAPLOT tries to open the file with 30442 the trailing period. If this fails, it then tries to open the file 30443 with the trailing period stripped off. 30444 30445 Although Dataplot does not require specific file extensions for 30446 the other READ commands, it does require them for the READ IMAGE 30447 command. The file extension is used to determine whether a 30448 JPEG, PNG, or GIF file is being read. JPEG files should have 30449 a ".jpeg", ".jpg", ".JPEG", or ".JPG" extension, GIF files should 30450 have a ".gif" or ".GIF" extension, and PNG files should have 30451 a ".png" or ".PNG" extension. 30452 30453Note: 30454 File names are case sensitive on Unix file systems. For Unix, 30455 DATAPLOT attempts to open the file as given. If this fails, it 30456 attempts to open the file as all upper case characters. If this 30457 fails, it attempts to open the file as all lower case characters. 30458 All other currently supported systems are not case sensitive 30459 regarding file names. 30460 30461 As a further caution for Unix hosts, certain expansion characters 30462 (specifically ~ to refer to your home directory) are interpreted 30463 by the shell and are not recognized by the Fortran compiler. These 30464 expansion characters are interpreted as literal characters and do 30465 not yield the intended file name. 30466 30467Default: 30468 None 30469 30470Synonyms: 30471 None 30472 30473Related Commands: 30474 IMAGE PLOT = Display an image. 30475 READ = Read variables. 30476 READ MATRIX = Read matrix data. 30477 READ STACKED VARIABLES = Read a list of variables into a 30478 single response variable and a 30479 group-id variable. 30480 CREATE MATRIX = Create a matrix from a list of 30481 variables. 30482 30483Applications: 30484 Data Input 30485 30486Implementation Date: 30487 2008/3 30488 30489Program: 30490 dimension 10 variables 30491 read image to variables takashi.jpg red blue green rowid colid 30492 . 30493 probe iopsy1 30494 if probeval = 1 30495 device 1 x11 30496 device 1 picture points 600 600 30497 end of if 30498 . 30499 erase 30500 erase 30501 set ipl1na takashi_image.jpg 30502 set gd color true 30503 device 2 gd jpg 30504 device 2 picture points 600 600 30505 . 30506 char size 1 30507 frame off 30508 frame corner coordinates 5 5 95 95 30509 . 30510 title offset 2 30511 title Takashi Image 30512 image plot red rowid colid 30513 . 30514 device 2 close 30515 30516-----READ LINE (SET)------------------------------------------- 30517 30518READ LINE (SET) 30519 30520Name: 30521 READ LINE (SET) 30522 30523Type: 30524 Subcommand under SET 30525 30526Purpose: 30527 Specifies whether or not the GNU READLINE library will be used 30528 to parse commands entered from the terminal. 30529 30530Description: 30531 The GNU READLINE library allows command line editing and 30532 history recall (with editing). This library is available 30533 on most Unix/Linux platforms. Dataplot does not support 30534 this capability for Windows implementations. 30535 30536 By default, this feature is disabled. To specify that 30537 command lines should be parsed by the READLINE library, 30538 enter the command 30539 30540 SET READ LINE ON 30541 30542 This capability is provided as a convenience for those 30543 Unix/Linux users who are familiar with the capabilities 30544 of READLINE from other applications. 30545 30546 This capability only applies to commands that are entered from 30547 the terminal (i.e., commands read from macros or other files 30548 do not use this capability). 30549 30550 When the READLINE capability is supported and the 30551 SET READLINE ON command is entered, then the following is 30552 available: 30553 30554 1) The current command line can be edited. By default, 30555 the editing is performed using EMACS style commands. 30556 Alternatively, you can request vi style editing commands. 30557 30558 2) You can recall previously entered commands (use 30559 Cntrl-r to search the history list starting with the 30560 most recently entered commands and Cntrl-f to search the 30561 history list in the order the commands were entered). 30562 30563 The history list only starts with commands entered 30564 after the SET READ LINE ON command was entered and it 30565 will only include commands entered from the termininal 30566 (i.e., it will not include commands entered from the 30567 macro files). 30568 30569 The editing capabilities supported by readline are extensive 30570 and we do not document them here. They are documented in full 30571 at the readline web site: 30572 30573 http://tiswww.case.edu/php/chet/readline/rltop.html 30574 30575 This documentation lists the editing commands that are 30576 available and shows how you can customize key bindings. 30577 Note that Dataplot does not provide any customized commands 30578 or command completion. 30579 30580Syntax: 30581 SET READ FORMAT <ON/OFF> 30582 where <ON> specifies that the READLINE capability will be used 30583 and <OFF> specifies that it will not. 30584 30585Examples: 30586 SET READ LINE ON 30587 SET READ LINE OFF 30588 30589Note: 30590 Dataplot allows recently entered commands to be listed with 30591 the LIST (or L) command. Selective commands may be re-executed 30592 or saved with the REPEAT (or R) and SAVE (or S) commands, 30593 respectively. However, no editing capability is provided 30594 for the REPEAT and SAVE commands. 30595 30596 The LIST, REPEAT, and SAVE capabilities are independent of the 30597 READLINE capabilities. Commands entered via the READLINE 30598 capability are added to the DATAPLOT command list (i.e., the 30599 commands displayed by the LIST command). 30600 30601Note: 30602 The maximum line length for a command is 255 characters. This 30603 is true whether READLINE is used or not. 30604 30605Default: 30606 The READLINE capability is off. 30607 30608Synonyms: 30609 None 30610 30611Related Commands: 30612 LIST = List previously entered commands. 30613 REPEAT = Execute previously entered commands. 30614 SAVE = Save previously entered commands. 30615 30616Applications: 30617 Input/Output 30618 30619Implementation Date: 30620 2009/4 30621 30622Program: 30623 XX 30624 30625-----READ MISSING VALUE (SET)---------------------------------------- 30626 30627READ MISSING VALUE (SET) 30628 30629Name: 30630 READ MISSING VALUE (SET) 30631 30632Type: 30633 Subcommand under SET 30634 30635Purpose: 30636 Specifies the value to be used when a missing value is 30637 encountered with the array form of the COLUMN LIMITS 30638 command. 30639 30640Description: 30641 The January, 2004 version of Dataplot added support for 30642 an array form of the COLUMN LIMITS command. This form is 30643 used to specify the lower and upper columns to read for 30644 each data field. One specific case this was intended to 30645 handle was data files containing columns of unequal length. 30646 This is a common occurence when Excel files are saved to 30647 ASCII data files. 30648 30649 When the array form of the COLUMN LIMITS comamnd is used, 30650 an empty field is interpreted as a missing value. By default, 30651 Dataplot will assign a value of zero. If you want to assign 30652 a value other than zero, use the SET READ MISSING VALUE command 30653 to specify that value. 30654 30655Syntax: 30656 SET READ MISSING VALUE <value> 30657 where <value> denotes the value to assign when an empty data 30658 field is encoutered. 30659 30660Examples: 30661 SET READ MISSING VALUE -999 30662 SET READ MISSING VALUE 0 30663 SET READ MISSING VALUE -1 30664 30665Note: 30666 This command only applies when the array form of the 30667 COLUMN LIMITS command has been invoked. Otherwise, if the 30668 number of values read is less than the number of variables 30669 specified on the READ command, Dataplot treats this as an 30670 error. 30671 30672Default: 30673 Zero 30674 30675Synonyms: 30676 None 30677 30678Related Commands: 30679 READ = Carries out a column-wise input of data. 30680 COLUMN LIMITS = Specify what columns to read. 30681 30682Applications: 30683 Input/Output 30684 30685Implementation Date: 30686 2004/1 30687 30688Program: 30689 SET READ MISSING VALUE -99 30690 LET LOWLIM = DATA 1 11 30691 LET UPPLIM = DATA 10 20 30692 COLUMN LIMITS LOWLIM UPPLIM 30693 READ DUMMY.DAT Y X 30694 PLOT Y X SUBSET Y > -99 SUBSET X > -99 30695 30696-----READ PAD MISSING COLUMNS (SET)-------------------------------- 30697 30698READ PAD MISSING COLUMNS (SET) 30699 30700Name: 30701 READ PAD MISSING COLUMNS (SET) 30702 30703Type: 30704 Subcommand under SET 30705 30706Purpose: 30707 If the number of variables specified on a READ command is 30708 greater than the number of values read from a data record, 30709 specify whether these extra values will be set to a 30710 "missing value" or this data record will be 30711 considered an error. 30712 30713Description: 30714 Dataplot typically expects all variables to be of equal length. That 30715 is, the data is rectangular with no empty fields. 30716 30717 Dataplot reads the data file one row at a time. When reading a row, 30718 Dataplot assigns the first value read to the first variable name, the 30719 second value read to the second variable name, and so on. By default, 30720 the row with the smallest number of values defines the number of 30721 variables that will be read. For example, if you entered the command 30722 30723 READ FILE.DAT Y X1 X2 X3 30724 30725 and one of the rows has only two values, then only Y and X1 will 30726 be read into Dataplot. 30727 30728 In some cases, it may be more convenient to assign a missing value to 30729 any variables that did not have a corresponding data item. To do 30730 this enter the command 30731 30732 SET READ PAD MISSING COLUMNS ON 30733 30734 You can specify the value to use for missing values (the default is 30735 zero) with the command 30736 30737 SET READ MISSING VALUE <value> 30738 30739 This works well if the empty fields are the end columns. However, 30740 be aware that if your empty fields are the beginning or middle 30741 columns, the data values may not be assigned to the variables 30742 in the way you expect. See the NOTE: section below for alternative 30743 methods for dealing with empty fields are columns of unequal length. 30744 30745 NOTE 2019/04: The default behavior was modifed. Now, Dataplot will 30746 always pad with missing values. The only distinction between ON 30747 and OFF is that OFF is set a warning message will be printed when 30748 a row is encountered with less than the expected number of values. 30749 30750Syntax: 30751 SET READ PAD MISSING COLUMNS <ON/OFF> 30752 where ON specifies that missing columns will be padded with 30753 a missing data value and OFF specifies that missing 30754 columns will be treated as an error. 30755 30756 NOTE 2019/04: Now missing columns will always be padded with the 30757 missing value code. If OFF is specified, a warning 30758 message will be printed when rows with a fewer than 30759 expected number of values are encountered. If ON 30760 is specified, no warning messages will be printed. 30761 30762Examples: 30763 SET READ PAD MISSING COLUMN ON 30764 SET READ PAD MISSING COLUMN OFF 30765 30766Note: 30767 When your data file has columns of unequal length or empty 30768 fields, there are several alternative approaches. 30769 30770 1. Pick some value to represent a missing value and fill in 30771 missing data points with that value. After reading the data, 30772 you can use a RETAIN command to remove them. For example, if 30773 you use -99 to signify a missing value, you can enter 30774 something like 30775 30776 RETAIN Y SUBSET Y > -99 30777 30778 Alternatively, you can use a SUBSET clause on subsequent plot 30779 and analysis commands. 30780 30781 There are two SET commands that pertain to missing values. 30782 30783 SET DATA MISSING VALUE <value> specifies a character string 30784 that will be interpreted as a missing value in the data file 30785 (this character string can be a numeric value). 30786 30787 SET READ MISSING VALUE <value> specifies the numeric value that 30788 will be saved to the Dataplot variable when a missing value (as 30789 defined by the SET DATA MISSING VALUE) is encountered. 30790 30791 Where feasible, this is the recommended solution. 30792 30793 2. If your data file has consistent formats for the rows, then 30794 there are two possible solutions. 30795 30796 If the fields are justified by the decimal point so that a 30797 Fortran format statement can be applied, then you can use the 30798 SET READ FORMAT command. In this case, empty fields are read as 30799 zero. If zero can be a valid data value for one or more of your 30800 variables, then it can be ambiguous whether a zero in your 30801 variable denotes a valid data point or a missing value. The 30802 SET READ MISSING VALUE setting does not apply when the 30803 SET READ FORMAT is used. 30804 30805 Many spreadsheets have an option for saving data to a "fixed 30806 width" ASCII text file. In these cases, the fields are typically 30807 either right or left justified. However, the column for the 30808 decimal point will not be consistent so that the SET READ FORMAT 30809 command cannot be used. In this case, you can use the variable 30810 form of the COLUMN LIMITS command. That is 30811 30812 COLUMN LIMITS LOWLIMIT UPPLIMIT 30813 30814 where LOWLIMIT and UPPLIMIT are variables containing the start 30815 and stop columns, respectively, for each of the variables. By 30816 default, when a blank field is encountered, it is set to zero. 30817 You can specify the value to use by entering the command 30818 30819 SET READ MISSING VALUE <value> 30820 30821 3. If your data has both columns of unequal length (or empty 30822 fields) and inconsistent columns for given data fields, an 30823 alternative is to use a comma delimited data file. If there is 30824 no data between successive commas, this is treated as a missing 30825 value. The default is to assign a value of zero. Alternatively, 30826 you can use the SET READ MISSING VALUE command described above. 30827 30828 You can specify a delimiter other than a comma with the command 30829 30830 SET READ DELIMITER <character> 30831 30832Default: 30833 OFF 30834 30835Synonyms: 30836 None 30837 30838Related Commands: 30839 READ = Carries out a column-wise input of 30840 data. 30841 COLUMN LIMITS = Specify what columns to read. 30842 SET READ MISSING VALUE = Specify the value used to denote a 30843 missing value. 30844 SET DATA MISSING VALUE = Specify the missing value code in a data 30845 file. 30846 SET READ DELIMITER = Specify the character that will be 30847 interperted as a delimiter between 30848 fields on a data record. 30849 30850Applications: 30851 Input/Output 30852 30853Implementation Date: 30854 2004/10 30855 2019/04: The default behavior for empty fields changed. 30856 30857Program: 30858 SET READ MISSING VALUE -99 30859 SET READ PAD MISSING COLUMN ON 30860 READ DUMMY.DAT Y X 30861 RETAIN Y X SUBSET Y > -99 SUBSET X > -99 30862 PLOT Y X 30863 30864-----READ SUBSET (SET)-------------------------------- 30865 30866READ SUBSET (SET) 30867 30868Name: 30869 READ SUBSET (SET) 30870 30871Type: 30872 Subcommand under SET 30873 30874Purpose: 30875 Specify how SUBSET clauses are to be interpreted on 30876 READ commands. 30877 30878Description: 30879 The SUBSET/EXCEPT/FOR clause on a READ command is ambiguous. The 30880 ambiguity aries from the fact that it is not clear whether the 30881 SUBSET/EXCEPT/CLAUSE command refers to the lines in the data file 30882 being read or to the output variables that are created by the 30883 READ command. We address this with the following command: 30884 30885 SET READ SUBSET <PACK/DISPERSE> <PACK/DISPERSE> 30886 30887 In this command, PACK means the SUBSET/EXCEPT/FOR clause does not 30888 apply while DISPERSE means that it does. The first setting applies 30889 to the input file while the second setting applies to the created 30890 data variables. 30891 30892 This is demonstrated with the following example (note that P-D means 30893 the data file is set to PACK and the output variable is set to 30894 DISPERSE). The first column is the data in the file while the 30895 remaining columns show what the resulting data variable should look 30896 like. 30897 30898 LET TAG = 1 FOR I = 1 1 10 30899 LET TAG = 0 FOR I = 2 2 10 30900 READ FILE.DAT X SUBSET TAG = 1 30901 30902 X P-D P-P D-P D-D 30903 =========================================== 30904 1 1 1 1 1 30905 2 0 2 3 0 30906 3 2 3 5 3 30907 4 0 4 7 0 30908 5 3 5 9 5 30909 6 0 6 - 0 30910 7 4 7 - 7 30911 8 0 8 - 0 30912 9 5 9 - 9 30913 10 - 10 - - 30914 30915 The default setting is PACK-DISPERSE (this is the default 30916 because this is the behavior of previous versions of Dataplot). 30917 However, the DISPERSE-PACK option is the one most likely to be 30918 used. The PACK-PACK option is equivalent to not using the 30919 SUBSET clause at all, so is unlikely to be used. 30920 30921Syntax: 30922 SET READ SUBSET <PACK/DISPERSE> <PACK/DISPERSE> 30923 where the first <PACK/DISPERSE> specifies how the SUBSET clause 30924 applies to the data file and second <PACK/DISPERSE> specifies 30925 how the output file is created. 30926 30927Examples: 30928 SET READ SUBSET PACK DISPERSE 30929 SET READ SUBSET PACK PACK 30930 SET READ SUBSET DISPERSE PACK 30931 SET READ SUBSET DISPERSE DISPERSE 30932 30933Note: 30934 This command works as documented for SUBSET clauses. 30935 It is not currently working correctly for FOR clauses. 30936 30937Default: 30938 The default is SET READ SUBSET PACK DISPERSE. 30939 30940Synonyms: 30941 None 30942 30943Related Commands: 30944 READ = Carries out a column-wise input of 30945 data. 30946 COLUMN LIMITS = Specify what columns to read. 30947 SET READ MISSING VALUE = Specify the value used to denote a 30948 missing value. 30949 SET READ DELIMITER = Specify the character that will be 30950 interperted as a delimiter between 30951 fields on a data record. 30952 30953Applications: 30954 Input/Output 30955 30956Implementation Date: 30957 2004/10 30958 30959Program: 30960 . This example shows how to read every other line 30961 . of the input file. 30962 . 30963 SKIP 25 30964 SET READ SUBSET DISPERSE PACK 30965 LET N = 107 30966 LET TAG = 1 FOR I = 1 1 N 30967 LET TAG = 0 FOR I = 2 2 N 30968 READ BERGER1.DAT Y X SUBSET TAG = 1 30969 30970-----READ VARIABLE LABEL (SET)---------------------------------------- 30971 30972READ VARIABLE LABEL (SET) 30973 30974Name: 30975 READ VARIABLE LABEL (SET) 30976 30977Type: 30978 Subcommand under SET 30979 30980Purpose: 30981 Specifies whether variable names will be read from the data 30982 file or not. 30983 30984Description: 30985 Typically, Dataplot reads variable names from the READ 30986 command. For example, 30987 30988 READ BERGER1.DAT Y X BATCH 30989 30990 Alternatively, you can omit the variable names: 30991 30992 READ BERGER1.DAT 30993 30994 In this case, Dataplot will automatically assign the variable 30995 names X1, X2, and X3. 30996 30997 Some data files contain the variable names as the first 30998 line of the data file. In this case, you can enter the 30999 command 31000 31001 SET READ VARIABLE LABEL ON 31002 31003 to instruct Dataplot to read the variable names from the 31004 first line. 31005 31006Syntax: 31007 SET READ VARIABLE LABEL <ON/OFF> 31008 where <ON> specifies that variable labels will be read from 31009 the data file and <OFF> specifies that they will 31010 not. 31011 31012Examples: 31013 SET READ VARIABLE LABEL ON 31014 SET READ VARIABLE LABEL OFF 31015 31016Note: 31017 If the SKIP command has been entered, the variable labels 31018 will be read from the first line after the skipped lines. 31019 For example, SKIP 24 implies that the variable labels will 31020 be read from line 25. 31021 31022Note: 31023 Many of the built-in Dataplot sample files contain the 31024 variable names on line 24 and a line of dashes ("-") on 31025 line 25. These files can be read with 31026 31027 SKIP AUTOMATIC 31028 READ FILE.DAT 31029 31030 31031Default: 31032 OFF (variable labels will not be read from the file) 31033 31034Synonyms: 31035 None 31036 31037Related Commands: 31038 READ = Carries out a column-wise input of data. 31039 SERIAL READ = Carries out a line-wise input of data. 31040 SET CONVERT CHARACTER = Specifies whether character data will 31041 be read. 31042 SKIP = Specifies number of header lines to 31043 bypass. 31044 COLUMN LIMITS = Specify what columns to read. 31045 31046Applications: 31047 Input/Output 31048 31049Implementation Date: 31050 2004/1 31051 31052Program: 31053 SET READ VARIABLE LABEL ON 31054 READ TEST.DAT 31055 31056-----READ MATRIX TO VARIABLES---------------------------------------- 31057 31058READ MATRIX TO VARIABLES 31059 31060Name: 31061 READ MATRIX TO VARIABLES 31062 31063Type: 31064 Input Command 31065 31066Purpose: 31067 Reads matrix data into a response variable, a row-id 31068 variable, and a column-id variable. 31069 31070Description: 31071 The READ MATRIX command is used to read a data file 31072 into a matrix. This is useful for utilizing the Dataplot 31073 commands that explicitly work on matrices. 31074 31075 However, in some cases it may be more convenient to 31076 read the matrix as a single response variable. For 31077 example, you may want to use commands that work on variables 31078 rather than matrices. In these cases, you can use the 31079 READ MATRIX TO VARIABLES command instead of the READ MATRIX 31080 command. This command will create row-id and column-id 31081 variables in addition to the response variable. 31082 31083Syntax: 31084 READ MATRIX TO VARIABLES <file> <y> <rowid> <colid> 31085 where <file> is the name of the file that contains the matrix 31086 data; 31087 <y> is the response variable where the data will be 31088 saved; 31089 <rowid> is a variable that identifies the row of the 31090 matrix for each response variable; 31091 and <colid> is a variable that identifies the column of the 31092 matrix for each response variable. 31093 31094 The <file> argument is optional. If it is omitted, Dataplot 31095 will read the matrix data from the terminal rather than a file. 31096 31097Examples: 31098 READ MATRIX TO VARIABLES FILE.DAT Y ROW COL 31099 31100Note: 31101 By default, DATAPLOT does free format reads. However, it has the 31102 capability for supporting FORTRAN style formats. Formatted reads 31103 can be about 10 times faster on many systems. This can be helpful 31104 for large data files. Enter HELP READ FORMAT for more details. 31105 31106Note: 31107 Blank lines in data files are ignored. 31108 31109Note: 31110 DATAPLOT supports the ability to embed comment lines within 31111 the data file. Enter HELP COMMENT CHECK for details. 31112 31113Note: 31114 In order to determine whether the first argument is a file name or 31115 a variable name, it looks for a period in the name. If it finds 31116 one, it assumes a file name. If it does not, it assumes a variable 31117 name. If your file name does not contain a period, attach a 31118 trailing period (no spaces) to the file name on the 31119 READ MATRIX TO VARIABLES command. 31120 31121Note: 31122 DATAPLOT has no restrictions on the file name other than it be a 31123 valid file name on the local operating system and that it contain 31124 a period "." in the file name itself or as a trailing character. 31125 DATAPLOT strips off trailing periods on those systems where it is 31126 appropriate to do so. On systems where trailing periods can be a 31127 valid file name (e.g., Unix), DATAPLOT tries to open the file with 31128 the trailing period. If this fails, it then tries to open the file 31129 with the trailing period stripped off. 31130 31131 Some users prefer to give all data files a ".DAT" or ".dat" 31132 extension. Although this is a useful method for keeping track of 31133 data files, it is strictly a user convention and is not enforced 31134 by DATAPLOT in any way. 31135 31136Note: 31137 File names are case sensitive on Unix file systems. For Unix, 31138 DATAPLOT attempts to open the file as given. If this fails, it 31139 attempts to open the file as all upper case characters. If this 31140 fails, it attempts to open the file as all lower case characters. 31141 All other currently supported systems are not case sensitive 31142 regarding file names. 31143 31144 As a further caution for Unix hosts, certain expansion characters 31145 (specifically ~ to refer to your home directory) are interpreted 31146 by the shell and are not recognized by the Fortran compiler. These 31147 expansion characters are interpreted as literal characters and do 31148 not yield the intended file name. 31149 31150Default: 31151 None 31152 31153Synonyms: 31154 None 31155 31156Related Commands: 31157 READ MATRIX = Read matrix data. 31158 READ = Read variables. 31159 READ IMAGE TO VARIABLES = Read an image file into one or more 31160 response variables. 31161 READ STACKED VARIABLES = Read a list of variables into a 31162 single response variable and a 31163 group-id variable. 31164 CREATE MATRIX = Create a matrix from a list of 31165 variables. 31166 SERIAL READ = Perform a serial read. 31167 SET READ FORMAT = Define a FORTRAN style format for 31168 reads. 31169 READ PARAMETER = Read a parameter. 31170 READ STRING = Read a string. 31171 31172Applications: 31173 Data Input 31174 31175Implementation Date: 31176 2009/1 31177 31178Program: 31179 READ MATRIX TO VARIABLES Y ROWID COLID 31180 1 3 2 31181 7 3 1 31182 8 1 2 31183 END OF DATA 31184 PRINT Y ROWID COLID 31185 31186 The following output results for Y, ROWID and COLID: 31187 31188 1 1 1 31189 3 1 2 31190 2 1 3 31191 7 2 1 31192 3 2 2 31193 1 2 3 31194 8 3 1 31195 1 3 2 31196 2 3 3 31197 31198-----READ MATRIX------------------------------------------------ 31199 31200READ MATRIX 31201 31202Name: 31203 READ MATRIX 31204 31205Type: 31206 Support Command 31207 31208Purpose: 31209 Reads data into a matrix: 31210 1) from a mass storage file; 31211 2) from within a CALLed DATAPLOT sub-program; 31212 3) from the terminal. 31213 31214Description: 31215 The rules regarding READ MATRIX are as follows: 31216 1) Only one matrix is read for a given READ MATRIX command 31217 (additional matrices on the READ FUNCTION line are ignored). 31218 2) In scanning for the matrix, the full line image is scanned 31219 (for reading from a mass storage file, the full line image 31220 is 132 columns; for reading from within a sub-program and for 31221 reading from the terminal, the full line image is 80 31222 columns). For variations on this, see the COLUMN LIMITS 31223 command. 31224 3) Data values on a line image must be separated by at least 31225 one blank. 31226 4) Data values can be free-format. They need not be aligned in 31227 specific columns. 31228 5) The format of individual data values is general. It can be 31229 integer, floating point, or exponential. It is stored 31230 internally as a single precision real number. 31231 6) All reads start from the beginning of the file (for 31232 variations of this, see the SKIP and ROW LIMITS commands). 31233 7) The analyst need not be concerned about the number of 31234 observations or the number of variables for the matrix. 31235 DATAPLOT automatically determines and reports these values at 31236 the end of the read. 31237 8) The read terminates when a line image is encountered which 31238 consists of 31239 END OF DATA 31240 or 31241 END DATA 31242 or when the end of the file is reached. 31243 9) The individual columns of the matrix are available as 31244 variables (e.g., for matrix M, the columns are M1, M2, and 31245 so on). 31246 31247Syntax 1: 31248 READ MATRIX <mat> 31249 where <mat> is the name for the matrix. 31250 31251 This syntax is used to read a matrix from the terminal or from 31252 within a DATAPLOT sub-program. 31253 31254Syntax 2: 31255 READ MATRIX <file> <mat> 31256 where <file> is the name of the mass storage file where the data 31257 resides; 31258 and <mat> is the name for the matrix. 31259 31260 This syntax is used to read a matrix from a file. 31261 31262Examples: 31263 READ MATRIX CALIB. M 31264 31265Note: 31266 By default, DATAPLOT does free format reads. However, it has the 31267 capability for supporting FORTRAN style formats. Formatted reads 31268 can be about 10 times faster on many systems. This can be helpful 31269 for large data files. Enter HELP READ FORMAT for more details. 31270 31271Note: 31272 Blank lines in data files are ignored. 31273 31274Note: 31275 DATAPLOT supports the ability to embed comment lines within 31276 the data file. Enter HELP COMMENT CHECK for details. 31277 31278Note: 31279 In order to determine whether the first argument is a file name or 31280 a variable name, it looks for a period in the name. If it finds 31281 one, it assumes a file name. If it does not, it assumes a variable 31282 name. If your file name does not contain a period, attach a 31283 trailing period (no spaces) to the file name on the READ command. 31284 31285Note: 31286 DATAPLOT has no restrictions on the file name other than it be a 31287 valid file name on the local operating system and that it contain 31288 a period "." in the file name itself or as a trailing character. 31289 DATAPLOT strips off trailing periods on those systems where it is 31290 appropriate to do so. On systems where trailing periods can be a 31291 valid file name (e.g., Unix), DATAPLOT tries to open the file with 31292 the trailing period. If this fails, it then tries to open the file 31293 with the trailing period stripped off. 31294 31295 Some users prefer to give all data files a ".DAT" or ".dat" 31296 extension. Although this is a useful method for keeping track of 31297 data files, it is strictly a user convention and is not enforced 31298 by DATAPLOT in any way. 31299 31300Note: 31301 File names are case sensitive on Unix file systems. For Unix, 31302 DATAPLOT attempts to open the file as given. If this fails, it 31303 attempts to open the file as all upper case characters. If this 31304 fails, it attempts to open the file as all lower case characters. 31305 All other currently supported systems are not case sensitive 31306 regarding file names. 31307 31308 As a further caution for Unix hosts, certain expansion characters 31309 (specifically ~ to refer to your home directory) are interpreted 31310 by the shell and are not recognized by the Fortran compiler. These 31311 expansion characters are interpreted as literal characters and do 31312 not yield the intended file name. 31313 31314Default: 31315 1) If no file name is specified and a CALL is being executed, then 31316 the data values should be listed directly in the DATAPLOT 31317 sub-program immediately after the READ MATRIX command (do not 31318 forget the END OF DATA statement). 31319 2) If no file name is specified and commands are being manually 31320 entered/executed one at a time from the terminal, then the data 31321 should be entered directly from the terminal immediately after 31322 the READ MATRIX command (also terminated by an END OF DATA 31323 statement). 31324 31325Synonyms: 31326 None 31327 31328Related Commands: 31329 MATRIX DEFINITION = Copy variables into a matrix. 31330 SERIAL READ = Perform a serial read. 31331 SET READ FORMAT = Define a FORTRAN style format for reads. 31332 READ = Read variables. 31333 READ PARAMETER = Read a parameter. 31334 READ STRING = Read a string. 31335 31336Applications: 31337 XX 31338 31339Implementation Date: 31340 XX 31341 31342Program: 31343 READ MATRIX M 31344 1 3 2 31345 7 3 1 31346 8 1 2 31347 END OF DATA 31348 31349-----READ PARAMETER-------------------------------------------------- 31350 31351READ PARAMETER 31352 31353Name: 31354 READ PARAMETER 31355 31356Type: 31357 Support Command 31358 31359Purpose: 31360 Reads a parameter into DATAPLOT: 31361 1) from a mass storage file; or 31362 2) from within a CALLed DATAPLOT sub-program; or 31363 3) from the terminal. 31364 31365Description: 31366 The rules regarding READ PARAMETER are as follows: 31367 1) Only one line is read. Unlike a READ of variables, no END 31368 OF DATA is searched for. 31369 2) If more than one parameter is read, enter them on the same 31370 line separated by one or more spaces. 31371 3) In scanning for the parameter, the full line image is scanned 31372 (for reading from a mass storage file, the full line image is 31373 132 columns; for reading from within a sub-program and for 31374 reading from the terminal, the full line image is 80 31375 columns). For variations on this, see the COLUMN LIMITS 31376 command. 31377 4) Parameters can be free-format. They need not be aligned in 31378 specific columns. 31379 5) All reads start from the beginning of the file (for 31380 variations of this, see the SKIP and ROW LIMITS commands). 31381 31382Syntax 1: 31383 READ PARAMETER <p1> <p2> ... <p3> 31384 where <p1>, <p2>, ..., <pk> are the desired parameters. 31385 31386 This syntax is used to read parameters from the terminal or from a 31387 DATAPLOT sub-program. 31388 31389Syntax 2: 31390 READ PARAMETER <file> <p1> <p2> ... <p3> 31391 where <file> is the name of the mass storage file where the 31392 parameters reside; 31393 and <p1>, <p2>, ..., <pk> are the desired parameters. 31394 31395 This syntax is used to read parameters from a file. 31396 31397Examples: 31398 READ PARAMETER CALIB. P1 P2 31399 READ PARAMETER P 31400 5.2 31401 31402Note: 31403 In order to determine whether the first argument is a file name or 31404 a variable name, it looks for a period in the name. If it finds 31405 one, it assumes a file name. If it does not, it assumes a variable 31406 name. If your file name does not contain a period, attach a 31407 trailing period (no spaces) to the file name on the READ command. 31408 31409Note: 31410 DATAPLOT has no restrictions on the file name other than it be a 31411 valid file name on the local operating system and that it contain 31412 a period "." in the file name itself or as a trailing character. 31413 DATAPLOT strips off trailing periods on those systems where it is 31414 appropriate to do so. On systems where trailing periods can be a 31415 valid file name (e.g., Unix), DATAPLOT tries to open the file with 31416 the trailing period. If this fails, it then tries to open the file 31417 with the trailing period stripped off. 31418 31419 Some users prefer to give all data files a ".DAT" or ".dat" 31420 extension. Although this is a useful method for keeping track of 31421 data files, it is strictly a user convention and is not enforced 31422 by DATAPLOT in any way. 31423 31424Note: 31425 File names are case sensitive on Unix file systems. For Unix, 31426 DATAPLOT attempts to open the file as given. If this fails, it 31427 attempts to open the file as all upper case characters. If this 31428 fails, it attempts to open the file as all lower case characters. 31429 All other currently supported systems are not case sensitive 31430 regarding file names. 31431 31432 As a further caution for Unix hosts, certain expansion characters 31433 (specifically ~ to refer to your home directory) are interpreted 31434 by the shell and are not recognized by the Fortran compiler. These 31435 expansion characters are interpreted as literal characters and do 31436 not yield the intended file name. 31437 31438Default: 31439 1) If no file name is specified, and if a CALL is being 31440 executed, then the parameter should be listed directly 31441 in the DATAPLOT sub-program immediately after the READ 31442 PARAMETER command. 31443 2) If no file name is specified, and if commands are being 31444 manually entered/executed 1-at-a-time from the terminal, 31445 then the parameter should be entered directly from the 31446 terminal immediately after the READ PARAMETER command. 31447 31448Related Commands: 31449 SERIAL READ = Perform a serial read. 31450 READ = Read variables. 31451 READ FUNCTION = Read a function. 31452 READ MATRIX = Read a matrix. 31453 READ STRING = Read a string. 31454 LET = Define a parameter. 31455 31456Applications: 31457 XX 31458 31459Implementation Date: 31460 Pre-1987 31461 31462Program: 31463 READ PARAMETER A B C 31464 10 20 30 31465 31466-----READ ROW--------------------------------------------------- 31467 31468READ ROW 31469 31470Name: 31471 READ ROW 31472 31473Type: 31474 I/O Command 31475 31476Purpose: 31477 Reads row oriented data into variables. 31478 31479Description: 31480 Dataplot is a column oriented system. That is, columns denote 31481 variables while rows denote observations. 31482 31483 Sometimes you may encounter data files that are row oriented, that 31484 is rows denote variables while columns denote observations. This is 31485 often the case when the number of variables is significantly greater 31486 than the number of observations. 31487 31488 The READ ROW command was added to better accomodate these types of 31489 data files. With the ROW READ the file is read one row at a time 31490 and each row is added as a Dataplot variable. Only a single 31491 variable name is given to READ ROW command. This name serves as the 31492 "base name". So if Y is the variable name given and there are 25 31493 rows of data, variables Y1, Y2, ..., Y25 will be created by the 31494 READ ROW command. 31495 31496 The READ ROW command is only supported for numeric data. However, 31497 the rows do not need to contain the same number of data values. 31498 31499 If the maximum number of available columns is reached, the READ ROW 31500 command will be terminated. However, any rows that have already been 31501 successfully read will still be retained. If there in error in 31502 reading a specific row, that row will be skipped and Dataplot will go 31503 to the next row. 31504 31505 The READ ROW command generates a limited amount of feedback. It 31506 prints feedback for the first row read and the last row read only. 31507 If you want to see what variable names were created, you can enter 31508 the command 31509 31510 STATUS VARIABLES (or STATUS V) 31511 31512Syntax 1: 31513 READ ROW <y> 31514 where <y> is the base name for the variables being read. 31515 31516 This syntax is used to read from the terminal or from within a 31517 macro file. All lines are read until an END OF DATA is 31518 encountered. 31519 31520 In practice, READ ROW is not typically used for terminal reads. 31521 However, it does work. 31522 31523Syntax 2: 31524 READ <file> <y> 31525 where <file> is the name of the file where the data resides; 31526 and where <y> is the base name for the variables being read. 31527 31528 This syntax is used to read from a file. All lines are read until an 31529 END OF DATA is encountered, the physical end of file is encountered, 31530 or the maximum number of variables is reached. 31531 31532Examples: 31533 READ ROW FILE.DAT Y 31534 31535Note: 31536 By default, Dataplot does free format reads. However, it has the 31537 capability for supporting Fortran style formats. Formatted reads 31538 can be about 10 times faster on many systems which can be helpful 31539 for large data files. Enter HELP READ FORMAT for more details. 31540 31541 Note that Fortran formats are based on the decimal point lining up 31542 consistenly between rows. Spreadsheet programs such as Excel tend to 31543 generate either right justified or left justified columns when 31544 generating fixed width ASCII files. These are typically not 31545 consistent with Fortran formatted reads. 31546 31547Note: 31548 Blank lines in data files are ignored. 31549 31550Note: 31551 In order to determine whether the first argument is a file name or 31552 a variable name, it looks for a period in the name. If it finds 31553 one, it assumes a file name. If it does not, it assumes a variable 31554 name. If your file name does not contain a period, attach a 31555 trailing period (no spaces) to the file name on the READ command. 31556 31557Note: 31558 Dataplot does not assume specific extensions for file names. Although 31559 using conventions (e.g., ".DAT" or ".TXT" for data files, ".DP" for 31560 Dataplot macros) can be helpful for distinguishing between types of 31561 files, this is more for the analysts convenience. Dataplot itself 31562 does not enforce any conventions. 31563 31564 File names have the following restrictions: 31565 31566 1. The file name should be a valid file name for the local 31567 operating system. 31568 31569 2. The file name should contain a period "." in the file name 31570 itself or as a trailing character. Dataplot strips off trailing 31571 periods on those systems where it is appropriate to do so. On 31572 systems where trailing periods can be a valid file name (e.g., 31573 Unix), Dataplot tries to open the file with the trailing period. 31574 If this fails, it then tries to open the file with the trailing 31575 period stripped off. 31576 31577 3. If the file name contains spaces or hyphens, then it needs to be 31578 enclosed in quotes. 31579 31580 4. File names are currently limited to 80 characters. This can 31581 in particular be a problem if the file name is contained within 31582 a long path name. The following can be helpful in these cases. 31583 31584 a. You can use the CD command to make the path where the file 31585 is stored the current directory. This is most useful for 31586 data files. For example, 31587 31588 pwd 31589 cd <path where data file resided> 31590 read file.dat ... 31591 cd ^CURDIR 31592 31593 The pwd command is used to save the current directory. The 31594 cd command is then used to set the current directory to the 31595 path where the data resides, the read is performed, and then 31596 the cd command is used to restore the original working 31597 directory (the cd command saves the current path in the 31598 string CURDIR). 31599 31600 b. You can use the SEARCH DIRECTORY command to specify an 31601 additional directory to search for file names. 31602 31603Note: 31604 File names are case sensitive on Unix/Linux/Mac OS X systems. For these 31605 systems, Dataplot attempts to open the file as given. If this fails, it 31606 attempts to open the file as all upper case characters. If this fails, it 31607 attempts to open the file as all lower case characters. 31608 31609 As a further caution for Unix/Linux hosts, certain expansion characters 31610 (specifically ~ to refer to your home directory) are interpreted 31611 by the shell and are not recognized by the Fortran compiler. These 31612 expansion characters are interpreted as literal characters and do 31613 not yield the intended file name. 31614 31615Default: 31616 1) If no file name is specified and a CALL is being executed, then 31617 the data values should be listed directly in the DATAPLOT 31618 sub-program immediately after the READ command (do not forget 31619 the END OF DATA statement). 31620 31621 2) If no file name is specified and the commands are being manually 31622 entered/executed one at a time from the terminal, then the data 31623 should be entered directly from the terminal immediately after 31624 the READ command (also terminated by an END OF DATA statement). 31625 31626Synonyms: 31627 None 31628 31629Related Commands: 31630 READ = Read data into variables. 31631 SERIAL READ = Perform a serial read. 31632 READ FUNCTION = Read a function. 31633 READ MATRIX = Read a matrix. 31634 READ PARAMETER = Read a parameter. 31635 READ STRING = Read a string. 31636 READ IMAGE = Read an image format into numeric arrays. 31637 READ STACKED VARIABLE = Read a list of variables into a single 31638 response variable and a group-id variable. 31639 SET READ FORMAT = Define a FORTRAN style format for reads. 31640 DATA (LET) = Enter data values into a variable. 31641 CLIPBOARD = Various commands for reading from the 31642 system clipboard. 31643 31644Applications: 31645 Data Input 31646 31647Implementation Date: 31648 2018/10 31649 31650Program: 31651 READ ROW Y 31652 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 31653 16 17 18 19 20 21 22 23 24 25 31654 END OF DATA 31655 SET WRITE DECIMALS 0 31656 PRINT Y1 Y2 31657 31658-----READ ROW LABEL-------------------------------------------------- 31659 31660READ ROW LABEL 31661 31662Name: 31663 READ ROW LABEL 31664 31665Type: 31666 Support Command 31667 31668Purpose: 31669 Reads row labels into DATAPLOT: 31670 1) from a mass storage file; or 31671 2) from within a CALLed DATAPLOT sub-program; or 31672 3) from the terminal. 31673 31674Description: 31675 Row labels are primarily used for improved labeling. For 31676 this initial implementation, the use of row labels is currently 31677 limited to labeling plot points via the CHARACTER ROWLABEL 31678 command. However, the uses of row labels will expand 31679 in future implementations. 31680 31681Syntax 1: 31682 READ ROW LABEL 31683 31684 This syntax has no file name and no arguments. Row labels 31685 are read from the terminal (one label per row) until an 31686 END OF DATA is entered. 31687 31688Syntax 2: 31689 READ ROW LABEL <file name> 31690 where <file> is the name of the mass storage file where the 31691 row labels reside. 31692 31693 This syntax reads the row label from the specified mass storage 31694 file. 31695 31696Examples: 31697 SKIP 25 31698 COLUMN LIMITS 1 19 31699 READ ROW LABELS AUTO79.DAT 31700 COLUMN LIMITS 31701 31702Note: 31703 The row labels may have up to 32 characters. 31704 31705Note: 31706 The READ ROW LABELS command is almost always preceeded by 31707 a COLUMN LIMITS command. That is, if the data file contains 31708 both a text label and data, then the file is typically read 31709 twice. One read sets the column limits to cover the text 31710 for the row labels and the other sets the column limits 31711 to read the data. Dataplot does not currently allow both 31712 the row labels and data to be read at the same time. 31713 31714Note: 31715 In order to determine whether the first argument is a file name or 31716 a variable name, it looks for a period in the name. If it finds 31717 one, it assumes a file name. If it does not, it assumes a variable 31718 name. If your file name does not contain a period, attach a 31719 trailing period (no spaces) to the file name on the READ command. 31720 31721Note: 31722 DATAPLOT has no restrictions on the file name other than it be a 31723 valid file name on the local operating system and that it contain 31724 a period "." in the file name itself or as a trailing character. 31725 DATAPLOT strips off trailing periods on those systems where it is 31726 appropriate to do so. On systems where trailing periods can be a 31727 valid file name (e.g., Unix), DATAPLOT tries to open the file with 31728 the trailing period. If this fails, it then tries to open the file 31729 with the trailing period stripped off. 31730 31731 Some users prefer to give all data files a ".DAT" or ".dat" 31732 extension. Although this is a useful method for keeping track of 31733 data files, it is strictly a user convention and is not enforced 31734 by DATAPLOT in any way. 31735 31736Note: 31737 File names are case sensitive on Unix file systems. For Unix, 31738 DATAPLOT attempts to open the file as given. If this fails, it 31739 attempts to open the file as all upper case characters. If this 31740 fails, it attempts to open the file as all lower case characters. 31741 All other currently supported systems are not case sensitive 31742 regarding file names. 31743 31744 As a further caution for Unix hosts, certain expansion characters 31745 (specifically ~ to refer to your home directory) are interpreted 31746 by the shell and are not recognized by the Fortran compiler. These 31747 expansion characters are interpreted as literal characters and do 31748 not yield the intended file name. 31749 31750Default: 31751 All row labels are blank. 31752 31753Synonyms: 31754 None 31755 31756Related Commands: 31757 READ = Read data. 31758 READ PARAMETER = Read parameters. 31759 READ STRING = Read strings.. 31760 31761Applications: 31762 Presentation Graphics 31763 31764Implementation Date: 31765 2000/1 31766 31767Program: 31768 SKIP 25 31769 COLUMN LIMITS 1 19 31770 READ ROW LABELS AUTO79.DAT 31771 COLUMN LIMITS 20 80 31772 READ AUTO79.DAT Y1 Y2 31773 CHARACTER ROWLABELS 31774 LINE BLANK 31775 PLOT Y1 VERSUS Y2 31776 31777-----READ REWIND (SET)------------------------------------------- 31778 31779READ REWIND (SET) 31780 31781Name: 31782 READ REWIND (SET) 31783 31784Type: 31785 Subcommand under SET 31786 31787Purpose: 31788 Normally DATAPLOT reads file from the beginning. This command 31789 specifies that files being read are not rewound (more specifically, 31790 when a read is performed, the file is left open at its current 31791 position). 31792 31793Description: 31794 This can be useful when portions of a file are being read (e.g., 31795 the analyst has identifier strings in a file stored one per line). 31796 31797Syntax: 31798 SET READ REWIND <ON/OFF> 31799 where ON specifies that the file is rewound before reading and OFF 31800 specifies that it is not rewound. 31801 31802Examples: 31803 SET READ REWIND ON 31804 SET READ REWIND OFF 31805 31806Default: 31807 Files are rewound before reading (i.e., ON). 31808 31809Synonyms: 31810 None 31811 31812Related Commands: 31813 READ = Carries out a column-wise input of data. 31814 SERIAL READ = Carries out a line-wise input of data. 31815 READ FUNCTION = Read a function. 31816 READ PARAMETER = Read a parameter. 31817 READ MATRIX = Read a matrix. 31818 READ STRING = Read a string. 31819 WRITE REWIND = Specify file rewind when writing to file. 31820 31821Applications: 31822 Input/Output 31823 31824Implementation Date: 31825 88/3 31826 31827Program: 31828 SET READ REWIND OFF 31829 LOOP FOR K = 1 1 50 31830 READ STRING STATES.DAT S^K 31831 END OF LOOP 31832 SET READ REWIND ON 31833 31834-----READ STACKED VARIABLES---------------------------------------- 31835 31836READ STACKED VARIABLES 31837 31838Name: 31839 READ STACKED VARIABLES 31840 31841Type: 31842 Input Command 31843 31844Purpose: 31845 Reads a list of variables into a single response variable 31846 and a corresponding group-id variable. 31847 31848Description: 31849 A number of Dataplot commands expect data in the form 31850 31851 Y X 31852 31853 where Y is a response variable and X is a group-id variable. 31854 For example, 31855 31856 BOX PLOT Y X 31857 MEAN PLOT Y X 31858 31859 However, many data files are in the form where the data for 31860 each group is stored as a separate column. The command 31861 READ STACKED VARIABLES can be used to read these files into 31862 the Y X format needed by many Dataplot commands. 31863 31864Syntax: 31865 READ STACKED VARIABLES <file> <y> <groupid> <var-list> 31866 where <file> is the name of a data file; 31867 <y> is the response variable where the data will be 31868 saved; 31869 <groupid> is a variable that identifies the group for 31870 each row of the response variable; 31871 and <var-list> is a list of one or more variables to read 31872 from the data file. 31873 31874 The file name is optional. If the file name is omitted, the 31875 read will be from the terminal (until an END OF DATA is 31876 entered). 31877 31878 The first variable read will have a group-id value of 1, 31879 the second variable read will have a group-id value of 2 31880 and so on. 31881 31882Examples: 31883 READ STACKED VARIABLES FILE.DAT Y GROUP X1 X2 31884 READ STACKED VARIABLES FILE.DAT Y GROUP X1 X2 X3 31885 READ STACKED VARIABLES FILE.DAT Y GROUP X1 X2 X3 X4 31886 31887Note: 31888 This command is similar to the READ MATRIX TO VARIABLES 31889 command. The distinction is that the READ MATRIX TO VARIABLES 31890 returns both a row-id and a column-id variable. The 31891 READ STACKED VARIABLES just returns a group-id variable 31892 (i.e., a column-id). 31893 31894 The STACK command is also similar. However, it works on 31895 variables that have already been read into Dataplot. 31896 31897Note: 31898 By default, DATAPLOT does free format reads. However, it has the 31899 capability for supporting FORTRAN style formats. Formatted reads 31900 can be about 10 times faster on many systems. This can be helpful 31901 for large data files. Enter HELP READ FORMAT for more details. 31902 31903Note: 31904 Blank lines in data files are ignored. 31905 31906Note: 31907 DATAPLOT supports the ability to embed comment lines within 31908 the data file. Enter HELP COMMENT CHECK for details. 31909 31910Note: 31911 In order to determine whether the first argument is a file name or 31912 a variable name, it looks for a period in the name. If it finds 31913 one, it assumes a file name. If it does not, it assumes a variable 31914 name. If your file name does not contain a period, attach a 31915 trailing period (no spaces) to the file name on the 31916 READ STACKED VARIABLES command. 31917 31918Note: 31919 DATAPLOT has no restrictions on the file name other than it be a 31920 valid file name on the local operating system and that it contain 31921 a period "." in the file name itself or as a trailing character. 31922 DATAPLOT strips off trailing periods on those systems where it is 31923 appropriate to do so. On systems where trailing periods can be a 31924 valid file name (e.g., Unix), DATAPLOT tries to open the file with 31925 the trailing period. If this fails, it then tries to open the file 31926 with the trailing period stripped off. 31927 31928 Some users prefer to give all data files a ".DAT" or ".dat" 31929 extension. Although this is a useful method for keeping track of 31930 data files, it is strictly a user convention and is not enforced 31931 by DATAPLOT in any way. 31932 31933Note: 31934 File names are case sensitive on Unix file systems. For Unix, 31935 DATAPLOT attempts to open the file as given. If this fails, it 31936 attempts to open the file as all upper case characters. If this 31937 fails, it attempts to open the file as all lower case characters. 31938 All other currently supported systems are not case sensitive 31939 regarding file names. 31940 31941 As a further caution for Unix hosts, certain expansion characters 31942 (specifically ~ to refer to your home directory) are interpreted 31943 by the shell and are not recognized by the Fortran compiler. These 31944 expansion characters are interpreted as literal characters and do 31945 not yield the intended file name. 31946 31947Default: 31948 None 31949 31950Synonyms: 31951 None 31952 31953Related Commands: 31954 STACK = Convert a set of response variables to 31955 a single response variable and a 31956 group-id variable. 31957 READ MATRIX TO VARIABLES = Read a matrix into a single response 31958 variable. 31959 READ IMAGE TO VARIABLES = Read an image into variables. 31960 READ = Read variables. 31961 SERIAL READ = Perform a serial read. 31962 READ MATRIX = Read matrix data. 31963 READ PARAMETER = Read a parameter. 31964 READ STRING = Read a string. 31965 SET READ FORMAT = Define a FORTRAN style format for 31966 reads. 31967 31968Applications: 31969 Data Input 31970 31971Implementation Date: 31972 2008/3 31973 31974Program: 31975 SKIP 25 31976 READ STACKED VARIABLES MONTGOME.DAT Y GROUP X1 X2 X3 31977 . 31978 TITLE Mean Plot 31979 TITLE OFFSET 2 31980 TITLE CASE ASIS 31981 XLIMITS 1 3 31982 TIC OFFSET UNITS DATA 31983 XTIC OFFSET 0.5 0.5 31984 MAJOR XTIC MARK NUMBER 3 31985 MINOR XTIC MARK NUMBER 0 31986 XTIC MARK LABEL FORMAT ALPHA 31987 XTIC MARK LABEL CONTENT Large Medium Small 31988 TIC MARK LABEL CASE ASIS 31989 Y1LABEL Mean Percentage 31990 X1LABEL Group 31991 LABEL CASE ASIS 31992 CHARACTER X BLANK 31993 LINE BLANK SOLID 31994 . 31995 MEAN PLOT Y GROUP 31996 31997-----READ STRING-------------------------------------------------- 31998 31999READ STRING 32000 32001Name: 32002 READ STRING 32003 32004Type: 32005 Support Command 32006 32007Purpose: 32008 Reads a string into DATAPLOT: 32009 1) from a mass storage file; or 32010 2) from within a CALLed DATAPLOT sub-program; or 32011 3) from the terminal. 32012 32013Description: 32014 The rules regarding READ STRING are as follows: 32015 1) Only one line is read. Unlike a READ of variables, no 32016 END OF DATA is searched for. 32017 2) Typically, only one string is read at a time. Reading more 32018 than one STRING is allowed (but not recommended). If more 32019 than STRING is read from the same line, separate the strings 32020 with at least one space and leave no spaces within a given 32021 string. For example, 32022 READ STRING S1 S2 32023 String1 String2 32024 3) In scanning for the string, the full line image is scanned 32025 (for reading from a mass storage file, the full line image 32026 is 132 columns; for reading from within a sub-program and 32027 for reading from the terminal, the full line image is 80 32028 columns). For variations on this, see the COLUMN LIMITS 32029 command. 32030 4) If one string is read, embedded blanks are included in the 32031 string. However, if more than one string is read, blanks 32032 are used to separate the strings. 32033 5) All reads start from the beginning of the file (for 32034 variations of this, see the SKIP and ROW LIMITS commands). 32035 32036Syntax 1: 32037 READ STRING <s1> <s2> ... <sk> 32038 where <s1>, <s2>, ..., <sk> are the desired strings (typically 32039 only one is given). 32040 32041 This syntax is used to read strings from the terminal or from a 32042 DATAPLOT sub-program. 32043 32044Syntax 2: 32045 READ STRING <file> <s1> <s2> ... <sk> 32046 where <file> is the name of the mass storage file where the 32047 strings reside; 32048 and <s1>, <s2>, ..., <sk> are the desired strings (typically 32049 only one is given). 32050 32051 This syntax is used to read strings from a file. 32052 32053Examples: 32054 READ STRING CALIB. S 32055 READ STRING S 32056 This is a sample string 32057 32058Note: 32059 The LET command can also be used to define a string (e.g., 32060 LET S = STRING THIS IS A STRING). However, there is one important 32061 distinction. The LET command automatically converts the string to 32062 upper case while the READ STRING command preserves the case that 32063 is read. 32064 32065Note: 32066 In order to determine whether the first argument is a file name or 32067 a variable name, it looks for a period in the name. If it finds 32068 one, it assumes a file name. If it does not, it assumes a variable 32069 name. If your file name does not contain a period, attach a 32070 trailing period (no spaces) to the file name on the READ command. 32071 32072Note: 32073 DATAPLOT has no restrictions on the file name other than it be a 32074 valid file name on the local operating system and that it contain 32075 a period "." in the file name itself or as a trailing character. 32076 DATAPLOT strips off trailing periods on those systems where it is 32077 appropriate to do so. On systems where trailing periods can be a 32078 valid file name (e.g., Unix), DATAPLOT tries to open the file with 32079 the trailing period. If this fails, it then tries to open the file 32080 with the trailing period stripped off. 32081 32082 Some users prefer to give all data files a ".DAT" or ".dat" 32083 extension. Although this is a useful method for keeping track of 32084 data files, it is strictly a user convention and is not enforced 32085 by DATAPLOT in any way. 32086 32087Note: 32088 File names are case sensitive on Unix file systems. For Unix, 32089 DATAPLOT attempts to open the file as given. If this fails, it 32090 attempts to open the file as all upper case characters. If this 32091 fails, it attempts to open the file as all lower case characters. 32092 All other currently supported systems are not case sensitive 32093 regarding file names. 32094 32095 As a further caution for Unix hosts, certain expansion characters 32096 (specifically ~ to refer to your home directory) are interpreted 32097 by the shell and are not recognized by the Fortran compiler. These 32098 expansion characters are interpreted as literal characters and do 32099 not yield the intended file name. 32100 32101Default: 32102 1) If no file name is specified and a CALL is being executed, then 32103 the string should be listed directly in the DATAPLOT 32104 sub-program immediately after the READ STRING command. 32105 2) If no file name is specified and commands are being manually 32106 entered/executed one at a time from the terminal, then the 32107 string should be entered directly from the terminal immediately 32108 after the READ STRING command. 32109 32110Related Commands: 32111 SERIAL READ = Perform a serial read. 32112 READ = Read variables. 32113 READ FUNCTION = Read a function. 32114 READ PARAMETER = Read a parameter. 32115 READ MATRIX = Read a matrix. 32116 LET = Define a string. 32117 32118Applications: 32119 XX 32120 32121Implementation Date: 32122 XX 32123 32124Program: 32125 SET READ REWIND OFF 32126 LOOP FOR K = 1 1 50 32127 READ STRING STATES.DAT S^K 32128 END OF LOOP 32129 SET READ REWIND ON 32130 32131-----RF (LET)---------------------------------------------- 32132 32133RF 32134 32135Name: 32136 RF (LET) 32137 32138Type: 32139 Library Function 32140 32141Purpose: 32142 Compute Carlson's elliptic integral of the first kind. 32143 32144Description: 32145 Carlson's elliptic integral of the first kind is defined as: 32146 RF(x,y,z)=0.5*INTEGRAL[1/SQRT((t+x)*(t+y)*(t+z))]dt 32147 where INTEGRAL is the integral from 0 to infinity. The parameters 32148 x, y, and z must all be non-negative with at most one of them 32149 being zero. 32150 32151Syntax: 32152 LET <a> = RF(<x>,<y>,<z>) <SUBSET/EXCEPT/FOR qualification> 32153 where <x> is a non-negative number, parameter, or variable; 32154 <y> is a non-negative number, parameter, or variable; 32155 <z> is a non-negative number, parameter, or variable; 32156 <a> is a variable or a parameter (depending on what <x>, 32157 <y>, and <z> are) where the computed values are stored; 32158 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 32159 32160Examples: 32161 LET A = RF(2,1,3) 32162 LET A = RF(X,0,4) 32163 LET X2 = RF(1,1,Y) 32164 32165Note: 32166 The Carlson elliptic integrals are computed using the RC, RD, RF, 32167 and RJ routines from the SLATEC Common Mathematical Library. 32168 SLATEC is a large set of high quality, portable, public domain 32169 Fortran routines for various mathematical capabilities maintained 32170 by seven federal laboratories. 32171 32172Note: 32173 DATAPLOT computes Legendre elliptic integrals by computing the 32174 equivalent Carlson elliptic integrals. See the documentation for 32175 the ELLIP1, ELLIP2, ELLIP3, ELLIPC1, and ELLIPC2 functions for 32176 details on computing Legendre elliptic functions in DATAPLOT. 32177 32178Note: 32179 Library functions are distinguished from let subcommands 32180 in the following ways. 32181 1) Functions enclose the input value in parenthesis. Let 32182 subcommands use spaces. 32183 2) Functions can accept (and return) either parameters 32184 (i.e., single values) or variables (i.e., an array of 32185 values) while let subcommands are specific in which they 32186 accept as input and what they return as output. 32187 3) Functions can accept expressions while let subcommands 32188 do not. For example, the following is legal: 32189 LET Y2 = ABS(Y1-INT(Y1)) 32190 For let subcommands, you typically have to do something 32191 like the following: 32192 LET YTEMP = Y**2 + 8 32193 LET A = SUM YTEMP 32194 32195Default: 32196 None 32197 32198Synonyms: 32199 None 32200 32201Related Commands: 32202 RC = Compute the degenerate Carlson elliptic integral. 32203 RD = Compute the Carlson elliptic integral of the second kind. 32204 RF = Compute the Carlson elliptic integral of the first kind. 32205 RJ = Compute the Carlson elliptic integral of the third kind. 32206 ELLIPC1 = Compute the Legendre complete elliptic integral of the 32207 first kind. 32208 ELLIPC2 = Compute the Legendre complete elliptic integral of the 32209 second kind. 32210 ELLIP1 = Compute the Legendre elliptic integral of the first 32211 kind. 32212 ELLIP2 = Compute the Legendre elliptic integral of the second 32213 kind. 32214 ELLIP3 = Compute the Legendre's elliptic integral of the third 32215 kind. 32216 32217Reference: 32218 "Algorithms for Incomplete Elliptic Integrals by Duplication", 32219 Carlson, ACM Transactions on Mathematical Software, 7, 32220 pp. 398-403. 32221 32222 "Handbook of Mathematical Functions, Applied Mathematics Series, 32223 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 32224 1964 (chapter 17). 32225 32226Applications: 32227 Special Functions 32228 32229Implementation Date: 32230 94/9 32231 32232Program: 32233 TITLE CARLSON ELLIPTIC FUNCTIONS 32234 PLOT RF(X,1,2) FOR X = 0.1 0.1 10 AND 32235 PLOT RF(1,X,2) FOR X = 0.1 0.1 10 AND 32236 PLOT RF(1,2,X) FOR X = 0.1 0.1 10 32237 32238 32239-----RECCDF (LET)-------------------------------- 32240 32241RECCDF 32242 32243Name: 32244 RECCDF (LET) 32245 32246Type: 32247 Library Function 32248 32249Purpose: 32250 Compute the reciprocal probability density function. 32251 32252Description: 32253 The probability density function is: 32254 f(x.b) = 1/(x*LOG(b)) for 1/b <= x < 1, b > 1 32255 where b is the shape parameter. The formula for the cumulative 32256 distribution function is: 32257 F(x,b) = (LOG(x) + LOG(b))/LOG(b) for 1/b <= x < 1, b > 1 32258 32259Syntax: 32260 LET <y> = RECCDF(<x>,<b>) <SUBSET/EXCEPT/FOR qualification> 32261 where <x> is a variable, a number, or a parameter; 32262 <y> is a variable or a parameter (depending on what <x> is) 32263 where the computed reciprocal cdf value is saved; 32264 <b> is a number, parameter, or variable that specifies 32265 the shape parameter; 32266 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 32267 32268Examples: 32269 LET A = RECCDF(0.5,1.5) 32270 LET X2 = RECCDF(X1,B) 32271 32272Note: 32273 Library functions are distinguished from let subcommands 32274 in the following ways. 32275 1) Functions enclose the input value in parenthesis. Let 32276 subcommands use spaces. 32277 2) Functions can accept (and return) either parameters 32278 (i.e., single values) or variables (i.e., an array of 32279 values) while let subcommands are specific in which they 32280 accept as input and what they return as output. 32281 3) Functions can accept expressions while let subcommands 32282 do not. For example, the following is legal: 32283 LET Y2 = ABS(Y1-INT(Y1)) 32284 For let subcommands, you typically have to do something 32285 like the following: 32286 LET YTEMP = Y**2 + 8 32287 LET A = SUM YTEMP 32288 32289Default: 32290 None 32291 32292Synonyms: 32293 None 32294 32295Related Commands: 32296 RECPDF = Compute the reciprocal probability density function. 32297 RECPPF = Compute the reciprocal percent point function. 32298 BRACDF = Compute the Bradford cumulative distribution function. 32299 BRAPDF = Compute the Bradford probability density function. 32300 BRAPPF = Compute the Bradford percent point function. 32301 BETCDF = Compute the beta cumulative distribution function. 32302 BETPDF = Compute the beta probability density function. 32303 BETPPF = Compute the beta percent point function. 32304 32305Reference: 32306 "Numerical Methods for Scientists and Engineers", 2nd. Ed., 32307 Hamming, Dover Publications, 1973. 32308 32309Applications: 32310 Data Analysis 32311 32312Implementation Date: 32313 96/5 32314 32315Program: 32316 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 32317 TITLE AUTOMATIC 32318 X1LABEL X 32319 Y1LABEL PROBABILITY 32320 LET B = 10 32321 X1LABEL BETA = ^B 32322 PLOT RECCDF(X,B) FOR X = 0.1 0.01 0.99 32323 LET B = 100 32324 X1LABEL BETA = ^B 32325 PLOT RECCDF(X,B) FOR X = 0.01 0.01 0.99 32326 LET B = 5 32327 X1LABEL BETA = ^B 32328 PLOT RECCDF(X,B) FOR X = 0.2 0.01 0.99 32329 LET B = 2 32330 X1LABEL BETA = ^B 32331 PLOT RECCDF(X,B) FOR X = 0.5 0.01 0.99 32332 END OF MULTIPLOT 32333 32334-----RECIPE--------------------------------------------- 32335 32336RECIPE 32337 32338Name: 32339 RECIPE 32340 32341Type: 32342 Analysis Command 32343 32344Purpose: 32345 Compute REgression Confidence Intervals on PErcentiles 32346 (RECIPE). 32347 32348Description: 32349 RECIPE is used to compute approximate one-sided tolerance 32350 limits (or equivalently, confidence intervals on 32351 percentiles) for a wide range of situations where one is 32352 able to assume a normal probability model. Arbitrary 32353 regression models with or without a random effect can be 32354 analyzed. It is this ability to accomodate between batch 32355 variability that makes the RECIPE code perhaps unique. 32356 32357 The development of RECIPE was motivated for use in 32358 determining design allowables for composite materials in 32359 aircraft applications, particularly in the prescence of 32360 between-batch variability. 32361 32362 Note that an A-basis value is a (0.99,0.95) lower tolerance 32363 limit and a B-basis value is a (0.90,0.95) lower tolerance 32364 limit. Alternatively A- and B-basis values can be 32365 interpreted to be 95% lower confidence bounds on the 1st 32366 and 10th population percentiles respectively. 32367 32368 In Dataplot, the A BASIS and B BASIS commands can be used 32369 to compute A-basis and B-basis values for univariate 32370 data for normal, lognormal, and Weibull distributions. 32371 32372 RECIPE is used to calculate basis values for regression 32373 models with or without a random batch effect. This 32374 methodology was developed by NIST statistician Mark Vangel 32375 as part of his involvement with MIL-HDBK-17E (or MIL-17 32376 Handbook). Dataplot adapted source code provided by 32377 Mark Vangel to implement this command within Dataplot. 32378 32379 More formally, let 32380 32381 y = X*theta + Z*b + e 32382 32383 denote a mixed model with two components of variance. The 32384 fixed part of the model is X*theta, where X is an nxr 32385 known matrix having l <= n distinct rows and theta is an 32386 unkown rXl vector. The random part is Z*b + e where Z 32387 is an nxm known matrix of zeros and ones, 32388 b follows a normal distribution with mean zero and standard 32389 deviation sigma(b)**2*I(m), and e follows a normal 32390 distribution with mean zero and standard deviation 32391 sigma(e)**2*I(n). Let w be an arbitrary rx1 vector, and 32392 assume (w**T)*theta, sigma(b)**2, and sigma(e)**2 are 32393 estimable. RECIPE uses y to obtain approximate one-sided 32394 beta-content tolerance intervals for the population 32395 U where U follows a normal distribution with mean 32396 (w**T)*theta and standard deviation 32397 sigma(b)**2 + sigma(e)**2. 32398 32399 A complete discussion of this methodolgy is available at 32400 the following web site (including the original Fortran 32401 source code): 32402 32403 http://www.itl.nist.gov/div898/software/recipe/ 32404 32405 These web pages discuss both the mathematical model 32406 for RECIPE and its application to real problems. 32407 Additional discussion is contained in the papers listed 32408 in the Reference section. The example programs below 32409 give some typical applications of RECIPE. 32410 32411 Note that the input model for the original Fortran 32412 implementation of RECIPE is different than the Dataplot 32413 implementation. 32414 32415 RECIPE is typically preceeded by a regression or ANOVA 32416 analysis. RECIPE is then typically applied to the final 32417 regression or ANOVA model. RECIPE supports the following 32418 types of models: 32419 32420 1) 1-factor regression (including polynomial models) 32421 2) multi-factor regression 32422 3) multi-factor ANOVA 32423 32424 RECIPE is generally used in the context of the MIL-17 32425 Handbook standards for obtaining A- and B-basis material 32426 property values. 32427 32428 The primary output from the RECIPE command is a set of 32429 tolerance values. 32430 32431Syntax 1: 32432 RECIPE FIT <y> <x> <batch> <xpred> 32433 <SUBSET/EXCEPT/FOR qualification> 32434 where <y> is the response (= dependent) variable; 32435 <x> is the independent variable; 32436 <batch> is a batch identifier variable; 32437 <xpred> is a variable containing the points at 32438 which the tolerances are calculated; 32439 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 32440 32441 This syntax is used for linear regression and polynomial 32442 models. 32443 32444 The degree of the fit can be specified by entering the 32445 following command before the RECIPE FIT command: 32446 32447 RECIPE FIT DEGREE <N> 32448 where <N> is a positive integer that specifies the degree 32449 polynomial to fit (usually 1 or 2, but higher degrees 32450 are allowed). 32451 32452 If the RECIPE FIT DEGREE command is not entered, a linear 32453 fit is assumed. 32454 32455Syntax 2: 32456 RECIPE FIT <y> <x1 ... xk> <batch> <xpred1 ... xpredk> 32457 <SUBSET/EXCEPT/FOR qualification> 32458 where <y> is the response (= dependent) variable; 32459 <x1 ... xk> is a list of one or more independent 32460 variables; 32461 <batch> is a batch identifier variable; 32462 <xpred1 ... xpredk> is a list of one or more variables 32463 containing the points at which the tolerances are 32464 calculated; 32465 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 32466 32467 This syntax is used for the multilinear regression case. 32468 32469Syntax 3: 32470 RECIPE ANOVA <y> <x1> ... <xk> <batch> 32471 <SUBSET/EXCEPT/FOR qualification> 32472 where <y> is the response (= dependent) variable; 32473 <x1> ... <xk> are the k independent variables; 32474 <batch> is a batch identifier variable; 32475 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 32476 32477 This syntax is used for multilinear and ANOVA models. 32478 32479 The <batch> variable is optional. To specify whether or not 32480 the last variable is a batch variable or one of the factor 32481 variables, enter the following command: 32482 32483 RECIPE FACTORS <N> 32484 where <N> is a positive integer that specifies the number 32485 of factor (indpendent) variables on the RECIPE ANOVA 32486 command. 32487 32488Examples: 32489 RECIPE ANOVA Y X BATCH 32490 RECIPE ANOVA Y X BATCH SUBSET BATCH = 1 TO 3 32491 32492 RECIPE FIT Y X BATCH X2 32493 RECIPE FIT Y X1 X2 BATCH X1P X2P 32494 32495Note: 32496 By default, Dataplot compute a 95% confidence interval for the 32497 90% coverage interval (i.e., the 10th percentile). 32498 32499 To change the confidence interval calculated, enter 32500 32501 RECIPE CONFIDENCE <val> 32502 32503 where <val> defines the desired confidence. Typical values 32504 are 0.95, 0.90, or 0.99. 32505 32506 To change the coverage interval, enter 32507 32508 RECIPE PROBABILITY CONTENT <val> 32509 32510 where <val> defines the desired coverage. Typical values are 32511 0.90 and 0.99. 32512 32513Note: 32514 By default, the tolerance values outout from the RECIPE commands 32515 are automatically saved in the internal variable TOL. If you 32516 want to save these values in a variable with a different name, 32517 then enter the following command before the RECIPE FIT or 32518 RECIPE ANOVA command: 32519 32520 RECIPE OUTPUT <varname> 32521 32522 where <varname> is the desired variable name. Note that after 32523 the RECIPE FIT or RECIPE ANOVA command, this variable can be 32524 used like any other Dataplot variable. 32525 32526Note: 32527 If the between batch variance is zero, then tolerance limits 32528 produced by RECIPE are exact. However, when between batch 32529 variability exists, the actual confidence level will depend on 32530 the ratio of between batch variability and to within batch 32531 variability sigma(b)**2/sigma(e)**2, or equivalently, to 32532 the intraclass correlation 32533 32534 p = sigma(b)**2/(sigma(b)**2 + sigma(e)**2) 32535 32536 The intraclass correlation is the correlation between 32537 observations from the same batch. 32538 32539 The nuisance parameter p is unknown and typically the number 32540 of batches is too small to even estimate it well. We would 32541 like to have a tolerance limit procedure for which the 32542 actual confidence interval equals the nominal level, whatever 32543 p might be. Although this goal is probably unobtainable in 32544 general, one can come extremely close for certain simple 32545 regression models. RECIPE provides tolerance intervals for 32546 which the confidence levels do not depend strongly on p, 32547 and for which the actual confidence is generally fairly close 32548 to the nominal level. 32549 32550 In order to determine how close the actual and nominal 32551 confidence levels are, it is necessary to simulate. The 32552 following commands 32553 32554 RECIPE SIMCOV FIT 32555 RECIPE SIMCOV ANOVA 32556 32557 correspond to the RECIPE FIT and RECIPE ANOVA commands and 32558 can be used to simulate the actual confidence. The 32559 RECIPE SIMCOV commands have the same syntax as the RECIPE 32560 commands. 32561 32562 The output from the RECIPE SIMCOV commands is a column of 32563 values for p with the corresponding actual confidence 32564 level. One can expect this command to show that the RECIPE 32565 intervals are conservative when p is near zero, somewhat 32566 anticonservative for intermediate values of p, and nearly 32567 exact for p near 1. For highly unbalanced data, the 32568 confidence may vary substatially from the nominal level 32569 when p=1. 32570 32571 If the actual confidence levels differ too substantially 32572 from the nominal levels, this indicates that a 32573 Satterthwaite approximation used by RECIPE is not 32574 adequate and can be improved upon by replacing the 32575 Satterthwaite approximation with the appropriate quantile 32576 of a simulated pivotal random variable. By doing this, 32577 one can obtain an actual confidence level that is nearly 32578 exact for p=1 and typically better than Satterthwaite 32579 approximation for intermediate values of p as well. 32580 32581 If the RECIPE SIMCOV command shows that the Satterthwaite 32582 approximation is not adequate, enter the following command 32583 to use simulated pivotal values instead: 32584 32585 RECIPE SATTERTHWAITE NO 32586 32587 To restore the use of Satterthwaite approximation, enter 32588 32589 RECIPE SATTERTHWAITE NO 32590 32591 To control the number of correlation values at which to 32592 compute SIMCOV probabilites, enter 32593 32594 RECIPE CORRELATION <n> 32595 32596 where <n> is the desired number of values. The default 32597 is 11 (that is, p = 0, 0.1, 0.2, 0.3, ... , 0.9 1.0). 32598 32599 To control the number of replicates used in computing the 32600 SIMCOV confidence levels, enter 32601 32602 RECIPE SIMCOV REPLICATES <n> 32603 32604 where <n> is the number of replicates. The default is 10,000. 32605 32606 If Satterthwaite approximation is turned off (and simulated 32607 pivotal values are used instead), the number of replicates used 32608 in computing the simulated pivotal values can be specified 32609 by entering the command 32610 32611 RECIPE SIMPVT REPLICATES <n> 32612 32613 where <n> is the number of replicates. The default is 10,000. 32614 32615Default: 32616 None 32617 32618Synonyms: 32619 None 32620 32621Related Commands: 32622 FIT = Perform a lest squares fit. 32623 ANOVA = Perform an ANOVA. 32624 BASIS TOLERANCE LIMITS = Generate A- and B-basis tolerance 32625 limits. 32626 TOLERANCE LIMITS = Generate tolerance limits for the mean. 32627 ANDERSON-DARLING K = Perform an Anderson-Darling k sample 32628 SAMPLE TEST test. 32629 ANDERSON-DARLING TEST = Perform an Anderson-Darling goodness 32630 of fit test. 32631 GRUBBS TEST = Perform Grubbs test for outliers. 32632 32633References: 32634 "MIL-HDBK-17 Volume 1: Guidelines for Characterization of 32635 Structural Materials", Depeartment of Defense, chapter 8. 32636 The URL for MIL-HDBK-17 is http://mil-17.udel.edu/. 32637 32638 "A User's Guide to RECIPE: A FORTRAN Program for Determining 32639 One-Sided Tolerance Limits for Mixed Models With Two 32640 Components of Variance Version 1.0", Mark Vangel, 32641 unpublished document available online at 32642 http://www.itl.nist.gov/div898/software/recipe/recidoc.pdf. 32643 32644 "New Methods for One-Sided Tolerance Limits for a One-Way 32645 Balanced Random Effects ANOVA Model", Mark Vangel, 32646 Technometrics, Vol. 34, 1992, pp. 176-185. 32647 32648 "One-Sided B-Content Tolerance Limits for Mixed Models 32649 with Two Components of Variance", Mark Vangel, 32650 Technometrics, submitted. 32651 32652 "Design Allowables From Regression Models Using Data From 32653 Several Batches", Mark Vangel, 12th Symposium on Composite 32654 Materials: Testing and Design, American Society of Testing 32655 and Materials, 1996. 32656 32657Applications: 32658 Materials Science 32659 32660Implementation Date: 32661 1997/9 32662 32663Program 1: (UNIVARIATE EXAMPLE) 32664 . The complete analysis can be viewed by: 32665 . LIST VANGEL31.DP 32666 . RECIPE Tolerance Limits Analysis of Graphite/Epoxy Tape Strength 32667 . Univariate Case 32668 . ------------------------ 32669 . Step 1--Read in the data 32670 . 32671 skip 25 32672 read vangel31.dat y 32673 . ------------------------------------------------ 32674 . Step 6--Compute (recipe/normal) tolerance limits 32675 . 32676 recipe content 90 32677 recipe confidence 95 32678 recipe factors 1 32679 let n = size y 32680 let x = 1 for i = 1 1 n 32681 let b = 1 for i = 1 1 n 32682 recipe anova y x b 32683 . 32684 let tol1 = tol(1) 32685 relative histogram y 32686 drawdata tol1 0 tol1 +.01 32687 32688Program 2: (NON-LINEAR EXAMPLE) 32689 . The complete analysis can be viewed by: 32690 . LIST VANGEL32.DP 32691 . RECIPE Tolerance Limits Analysis of Graphite/Epoxy Tape Strength 32692 . Regression Case 32693 . Date--September 1997 32694 . 32695 . ------------------------ 32696 . Step 1--Read in the data 32697 . 32698 skip 25 32699 read vangel32.dat y x b 32700 . 32701 . ------------------------------------------------ 32702 . Step 6--Compute (recipe/normal) tolerance limits 32703 . 32704 recipe content 90 32705 recipe confidence 95 32706 recipe degree 1 32707 let x2 = sequence -75 25 200 32708 recipe fit y x b x2 32709 . 32710 . 32711 characters x blank box 32712 lines blank solid dotted 32713 plot y pred versus x and 32714 plot tol versus x2 32715 32716Program 3: (ANOVA EXAMPLE) 32717 . The complete analysis can be viewed by: 32718 . LIST VANGEL33.DP 32719 . RECIPE Tolerance Limits Analysis of Graphite/Epoxy Fabric Strength 32720 . ANOVA Case 32721 . Date--September 1997 32722 . 32723 . ------------------------ 32724 . Step 1--Read in the data 32725 . 32726 skip 25 32727 read vangel33.dat y x b 32728 . 32729 . ------------------------------------------------ 32730 . Step 6--Compute (recipe/normal) tolerance limits 32731 . 32732 recipe content 90 32733 recipe confidence 95 32734 recipe factors 1 32735 recipe anova y x b 32736 . 32737 characters x blank box 32738 lines blank blank blank 32739 xtic offset 0.3 0.3 32740 major xtic mark number 2 32741 minor xtic mark number 0 32742 plot y pred versus x and 32743 plot tol versus x 32744 32745-----RECPDF (LET)-------------------------------- 32746 32747RECPDF 32748 32749Name: 32750 RECPDF (LET) 32751 32752Type: 32753 Library Function 32754 32755Purpose: 32756 Compute the reciprocal probability density function. 32757 32758Description: 32759 The probability density function is: 32760 f(x.b) = 1/(x*LOG(b)) for 1/b <= x < 1, b > 1 32761 where b is the shape parameter. 32762 32763Syntax: 32764 LET <y> = RECPDF(<x>,<b>) <SUBSET/EXCEPT/FOR qualification> 32765 where <x> is a variable, a number, or a parameter; 32766 <y> is a variable or a parameter (depending on what <x> is) 32767 where the computed reciprocal pdf value is saved; 32768 <b> is a number, parameter, or variable that specifies 32769 the shape parameter; 32770 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 32771 32772Examples: 32773 LET A = RECPDF(0.5,1.5) 32774 LET X2 = RECPDF(X1,B) 32775 32776Note: 32777 Library functions are distinguished from let subcommands 32778 in the following ways. 32779 1) Functions enclose the input value in parenthesis. Let 32780 subcommands use spaces. 32781 2) Functions can accept (and return) either parameters 32782 (i.e., single values) or variables (i.e., an array of 32783 values) while let subcommands are specific in which they 32784 accept as input and what they return as output. 32785 3) Functions can accept expressions while let subcommands 32786 do not. For example, the following is legal: 32787 LET Y2 = ABS(Y1-INT(Y1)) 32788 For let subcommands, you typically have to do something 32789 like the following: 32790 LET YTEMP = Y**2 + 8 32791 LET A = SUM YTEMP 32792 32793Default: 32794 None 32795 32796Synonyms: 32797 None 32798 32799Related Commands: 32800 RECCDF = Compute the reciprocal cumulative distribution function. 32801 RECPPF = Compute the reciprocal percent point function. 32802 BRACDF = Compute the Bradford cumulative distribution function. 32803 BRAPDF = Compute the Bradford probability density function. 32804 BRAPPF = Compute the Bradford percent point function. 32805 BETCDF = Compute the beta cumulative distribution function. 32806 BETPDF = Compute the beta probability density function. 32807 BETPPF = Compute the beta percent point function. 32808 32809Reference: 32810 "Numerical Methods for Scientists and Engineers", 2nd. Ed., 32811 Hamming, Dover Publications, 1973. 32812 32813Applications: 32814 Data Analysis 32815 32816Implementation Date: 32817 96/5 32818 32819Program: 32820 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 32821 TITLE AUTOMATIC 32822 X1LABEL X 32823 Y1LABEL PROBABILITY 32824 LET B = 10 32825 X1LABEL BETA = ^B 32826 PLOT RECPDF(X,B) FOR X = 0.1 0.01 0.99 32827 LET B = 100 32828 X1LABEL BETA = ^B 32829 PLOT RECPDF(X,B) FOR X = 0.01 0.01 0.99 32830 LET B = 5 32831 X1LABEL BETA = ^B 32832 PLOT RECPDF(X,B) FOR X = 0.2 0.01 0.99 32833 LET B = 2 32834 X1LABEL BETA = ^B 32835 PLOT RECPDF(X,B) FOR X = 0.5 0.01 0.99 32836 END OF MULTIPLOT 32837 32838-----RECPPF (LET)-------------------------------- 32839 32840RECPPF 32841 32842Name: 32843 RECPPF (LET) 32844 32845Type: 32846 Library Function 32847 32848Purpose: 32849 Compute the reciprocal probability density function. 32850 32851Description: 32852 The probability density function is: 32853 f(x.b) = 1/(x*LOG(b)) for 1/b <= x < 1, b > 1 32854 where b is the shape parameter. The formula for the percent 32855 point function is: 32856 G(p,b) = EXP(LOG(b)*(p-1)) for 0 <= p < 1, b > 1 32857 32858Syntax: 32859 LET <y> = RECPPF(<p>,<b>) <SUBSET/EXCEPT/FOR qualification> 32860 where <p> is a variable, a number, or a parameter in the 32861 range (0,1); 32862 <y> is a variable or a parameter (depending on what <p> is) 32863 where the computed reciprocal ppf value is saved; 32864 <b> is a number, parameter, or variable that specifies 32865 the shape parameter; 32866 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 32867 32868Examples: 32869 LET A = RECPPF(0.5,1.5) 32870 LET X2 = RECPPF(P,B) 32871 32872Note: 32873 Library functions are distinguished from let subcommands 32874 in the following ways. 32875 1) Functions enclose the input value in parenthesis. Let 32876 subcommands use spaces. 32877 2) Functions can accept (and return) either parameters 32878 (i.e., single values) or variables (i.e., an array of 32879 values) while let subcommands are specific in which they 32880 accept as input and what they return as output. 32881 3) Functions can accept expressions while let subcommands 32882 do not. For example, the following is legal: 32883 LET Y2 = ABS(Y1-INT(Y1)) 32884 For let subcommands, you typically have to do something 32885 like the following: 32886 LET YTEMP = Y**2 + 8 32887 LET A = SUM YTEMP 32888 32889Default: 32890 None 32891 32892Synonyms: 32893 None 32894 32895Related Commands: 32896 RECCDF = Compute the reciprocal cumulative distribution function. 32897 RECPDF = Compute the reciprocal probability density function. 32898 BRACDF = Compute the Bradford cumulative distribution function. 32899 BRAPDF = Compute the Bradford probability density function. 32900 BRAPPF = Compute the Bradford percent point function. 32901 BETCDF = Compute the beta cumulative distribution function. 32902 BETPDF = Compute the beta probability density function. 32903 BETPPF = Compute the beta percent point function. 32904 32905Reference: 32906 "Numerical Methods for Scientists and Engineers", 2nd. Ed., 32907 Hamming, Dover Publications, 1973. 32908 32909Applications: 32910 Data Analysis 32911 32912Implementation Date: 32913 96/5 32914 32915Program: 32916 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 32917 TITLE AUTOMATIC 32918 Y1LABEL X 32919 X1LABEL PROBABILITY 32920 LET B = 10 32921 X1LABEL BETA = ^B 32922 PLOT RECPPF(P,B) FOR P = 0 0.01 0.99 32923 LET B = 100 32924 X1LABEL BETA = ^B 32925 PLOT RECPPF(P,B) FOR P = 0 0.01 0.99 32926 LET B = 5 32927 X1LABEL BETA = ^B 32928 PLOT RECPPF(P,B) FOR P = 0 0.01 0.99 32929 LET B = 2 32930 X1LABEL BETA = ^B 32931 PLOT RECPPF(P,B) FOR P = 0 0.01 0.99 32932 END OF MULTIPLOT 32933 32934-----REGION BASE------------------------------------------------------- 32935 32936REGION BASE 32937 32938Name: 32939 REGION BASE 32940 32941Type: 32942 Plot Control Command 32943 32944Purpose: 32945 Specifies the base location for regions on plots. 32946 32947Description: 32948 On a plot, a region is defined as the figure formed by the line 32949 connecting points belonging to a common trace and a region base 32950 (typically zero). The REGION FILL command can be used to generate 32951 a solid fill or a cross-hatch fill of this region. The attributes 32952 of the fill are set with additional REGION commands (see the 32953 RELATED COMMANDS section below). The attributes of the region 32954 border are set with LINE, LINE COLOR, and LINE THICKNESS commands. 32955 32956 There are 3 special cases for the region base. Specifying REGION 32957 BASE POLYGON specifies that the points in the trace form a closed 32958 polygon. DATAPLOT automatically connects the first and last point 32959 if they are not already the same. This option is useful for 32960 drawing filled 2d polygons with the standard PLOT command. Drawing 32961 statistical maps is one application of this. The PROGRAM 2 example 32962 demonstrates this case. 32963 32964 The REGION BASE AUTOMATIC and REGION BASE INTERPOLATE commands 32965 are typically used together to fill in the area between 2 curves. 32966 The REGION BASE AUTOMATIC command specifies a variable to be used 32967 as arguments for the REGION BASE command which allows a moving 32968 region base between points. However, in the case of filling the 32969 area between curves, the base is not horizontal between points. 32970 The REGION BASE INTERPOLATE command specifies that the base should 32971 be drawn to connect pairs of base points. The PROGRAM 3 example 32972 shows how these two commands can be used to draw two curves with 32973 the are between them filled. The key trick in this macro is to 32974 define each consecutive pair of points on the second curve as a 32975 single trace. Generally, it is better practice to explicitly plot 32976 differences than it is to draw filled area curves. 32977 32978 The REGION AUTOMATIC and REGION BASE INTERPOLATE commands are 32979 actually not needed because the REGION BASE POLY command supports 32980 the capability they provide in a simpler manner. The PROGRAM 4 32981 example generates the same plot as the PROGRAM 3 example, but it 32982 uses the REGION BASE POLY command. 32983 32984Syntax 1: 32985 REGION BASE <number> <number> <number> etc. 32986 where <number> is a decimal number or trace that specifies the 32987 desired region base. Up to 100 region bases can be 32988 specified. 32989 32990Syntax 2: 32991 REGION BASE POLYGON <ON/OFF> <ON/OFF> etc. 32992 where ON specifies that the trace is treated as a closed polygon 32993 while OFF specifies that it is not. Up to 100 region 32994 bases can be specified. 32995 32996Syntax 3: 32997 REGION BASE AUTOMATIC <var> 32998 where <var> is a variable whose elements are used as arguments to 32999 the REGION BASE command. 33000 33001Syntax 2: 33002 REGION BASE INTERPOLATE <ON/OFF> <ON/OFF> etc. 33003 where ON specifies that the region base is drawn between the 33004 entered values for 2 consecutive bases while OFF 33005 specifies that it is not. Up to 100 region bases can be 33006 specified. 33007 33008Examples: 33009 REGION BASES 0. 0. 10. 33010 REGION BASES 20. 20. 20. 33011 REGION BASES 0. ALL 33012 REGION BASES ALL 0. 33013 REGION BASES 33014 REGION BASE POLYGON ON 33015 REGION BASE INTERPOLATE ON 33016 REGION BASE AUTOMATIC Y1 33017 33018Note: 33019 The REGION BASE command with no arguments sets the region base to 33020 zero for all regions. The REGION BASE command with the word ALL 33021 before or after the specified base assigns that region base to all 33022 regions; thus REGION BASE 0. ALL or REGION BASE ALL 0. uses a base 33023 of 0. for all regions. The REGION, BAR, SPIKE, CHARACTER, and LINE 33024 switch all work independently of each other. That is, a plot point 33025 can be a line, a character, a region, a spike or a bar or any 33026 combination of the above. 33027 33028Default: 33029 All region bases are 0.0. 33030 33031Synonyms: 33032 None 33033 33034Related Commands: 33035 PLOT = Generates a data or function plot. 33036 REGION FILL = Sets the on/off switches for region fills. 33037 REGION FILL COLOR = Sets the color for solid region fills. 33038 REGION PATTERN = Sets the types for region fill patterns. 33039 REGION PATTERN COLOR = Sets the color for hatched region fills. 33040 REGION PATTERN LINE = Sets the line types for region fill 33041 patterns. 33042 REGION PATTERN SPACING = Sets the line spacing for region fill 33043 patterns. 33044 REGION PATTERN THICK = Sets the line thickness for region fill 33045 patterns. 33046 LINE BORDER COLOR = Sets the color for region border lines. 33047 LINE BORDER LINE = Sets the types for region border lines. 33048 LINE BORDER THICKNESS = Sets the line thickness for region border 33049 lines. 33050 33051Applications: 33052 Presentation Graphics 33053 33054Implementation Date: 33055 XX 33056 33057 The REGION BASE POLYGON option was added 94/4. 33058 33059 The REGION BASE AUTOMATIC and REGION BASE INTERPOLATE commands and 33060 the ability to do hatch fills of non-rectangular regions were 33061 added 93/10. 33062 33063Program 1: 33064 LET FUNCTION F = SHIFT + AMPL*SIN(PERIOD*X+PHASE) 33065 LET SHIFT = 3 33066 LET AMPL = 2 33067 LET PERIOD = 0.5 33068 LET PHASE = PI 33069 . 33070 REGION FILL ON 33071 REGION BASE SHIFT 33072 . 33073 TITLE SINE WAVE 33074 LET MIN = -2*PI 33075 LET MAX = 2*PI 33076 XLIMITS -7 7 33077 PLOT F FOR X = MIN 0.1 MAX 33078 33079Program 2: 33080 SKIP 25 33081 READ TEXAS.DAT X Y 33082 . 33083 FRAME OFF 33084 FRAME CORNER COORDINATES 5 5 95 95 33085 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 33086 PRE-SORT OFF 33087 PLOT Y X 33088 PRE-SORT ON 33089 REGION BASE POLYGON 33090 REGION FILL ON 33091 PLOT Y X 33092 REGION PATTERN COLOR G25 33093 PLOT Y X 33094 REGION PATTERN D1D2 33095 REGION PATTERN SPACING 5 33096 PLOT Y X 33097 END OF MULTIPLOT 33098 33099Program 3: 33100 . PERCENTAGE BELOW POVERTY LEVEL 33101 . SOURCE: "SOCIAL INDICATORS 1976", US CENSUS BUREAU 33102 . Y1 = AGES 22-42 Y2 = AGES 65+ 33103 . 33104 LET Y1 = DATA 9.8 9.1 8.2 7.7 8.3 8.5 8.2 7.6 7.7 8.8 33105 LET Y2 = DATA 28.5 29.5 25.0 25.3 24.5 21.6 18.6 16.3 14.6 15.3 33106 LET N = SIZE Y1 33107 . 33108 XLIMITS 1 N; XTIC OFFSET 1 1 33109 MAJOR X1TIC MARK NUMBER N; MINOR X1TICMARK NUMBER 0 33110 X1TIC MARK FORMAT ALPHA 33111 X1TIC MARK CONTENT 66 67 68 69 70 71 72 73 74 75 33112 YLIMITS 0 30 33113 . 33114 PLOT Y1 33115 PRE-ERASE OFF 33116 LET N1 = N - 1 33117 LET N2 = N + 1 33118 . 33119 REGION BASE INTERPOLATION ON 33120 REGION BASE AUTOMATIC Y1 33121 REGION FILL ON ALL 33122 . CREATE X AND TAG VARIABLES 33123 LET X = SEQUENCE 1 1 N1 33124 LET NLAST = 2*N1 33125 LET X = SEQUENCE 2 1 N FOR I = N 1 NLAST 33126 LET TAG = SEQUENCE 1 1 N1 FOR I = 1 1 NLAST 33127 . CREATE Y VARIABLE 33128 LET JUNK = Y2 33129 DELETE JUNK(1) 33130 DELETE Y2(^N) 33131 EXTEND Y2 JUNK 33132 PLOT Y2 X TAG 33133 33134Program 4: 33135 . PERCENTAGE BELOW POVERTY LEVEL 33136 . SOURCE: "SOCIAL INDICATORS 1976", US CENSUS BUREAU 33137 . Y1 = 22-42 Y2 = 65+ 33138 . 33139 LET Y1 = DATA 9.8 9.1 8.2 7.7 8.3 8.5 8.2 7.6 7.7 8.8 33140 LET Y2 = DATA 28.5 29.5 25.0 25.3 24.5 21.6 18.6 16.3 14.6 15.3 33141 LET X = SEQUENCE 1966 1 1975 33142 LET XREV = X 33143 LET N = SIZE Y1 33144 LET INDX = SEQUENCE N -1 1 33145 LET INDX = SORTC INDX XREV Y2 33146 . 33147 EXTEND Y1 Y2 33148 EXTEND X XREV 33149 REGION BASE POLYGON 33150 REGION FILL ON ALL 33151 XLIMITS 1966 1975; XTIC OFFSET 1 1 33152 MAJOR X1TIC MARK NUMBER N; MINOR X1TICMARK NUMBER 0 33153 TITLE FILLED AREA PLOT 33154 PLOT Y1 X 33155 33156-----REGION FILL-------------------------------------------------- 33157 33158REGION FILL 33159 33160Name: 33161 REGION FILL 33162 33163Type: 33164 Plot Control Command 33165 33166Purpose: 33167 Specifies whether or not regions on subsequent plots are filled. 33168 Additionally, it is used to specify whether or not certain types 33169 of diagrammatic graphics are filled. 33170 33171Description: 33172 On a plot, a region is defined as the figure formed by the line 33173 connecting points belonging to a common trace and a region base 33174 (typically zero). The REGION FILL command can be used to generate 33175 a solid fill or a cross-hatch fill of this region. The attributes 33176 of the fill are set with additional REGION commands (see the 33177 RELATED COMMANDS section below). The attributes of the region 33178 border are set with LINE, LINE COLOR, and LINE THICKNESS commands. 33179 33180 The diagrammatic graphics commands CIRCLE, CUBE, DIAMOND, ELLIPSE, 33181 HEXAGON, PYRAMID, SEMI-CIRCLE, and TRIANGLE can be filled using the 33182 REGION FILL command. The BOX command has its own attribute 33183 setting commands. 33184 33185Syntax: 33186 REGION FILL <ON/OFF> <ON/OFF> <ON/OFF> etc. 33187 where ON specifies that the region is filled while OFF specifies 33188 that it is not. Up to 100 region fill switches can be 33189 specified. 33190 33191Examples: 33192 REGION FILL ON OFF ON OFF 33193 REGION FILL OFF OFF ON 33194 REGION FILL ON ALL 33195 REGION FILL ALL ON 33196 REGION 33197 33198Note: 33199 The diagrammatic graphics commands use the first setting of the 33200 REGION FILL command only. 33201 33202Note: 33203 Regions can be used for the following applications in DATAPLOT: 33204 1) They can be used to draw filled or cross-hatched 2d 33205 polygons. These polygons are not limited to convex polygons. 33206 2) Statistical maps can be generated. The boundary for each 33207 area (e.g., state or county) should be defined as a common 33208 trace. This area can then be treated as a polygon. At this 33209 time, DATAPLOT does not provide map files. Hopefully, some 33210 will be added in the future. 33211 3) Area plots can be generated or the area between curves can 33212 be filled. Although this type of plot is possible with 33213 DATAPLOT, it is generally not a recommended graphical 33214 technique. 33215 33216Note: 33217 At this time, the region fill capability should not be used for 33218 3d plots. The results will be unpredictable. 33219 33220Note: 33221 The REGION FILL command with no arguments sets the region fill to 33222 OFF for all traces. The REGION FILL command with the word ALL 33223 before or after the specified fill switch assigns that region type 33224 to all traces; thus REGION FILL ON ALL or REGION FILL ALL ON plots 33225 regions for all traces. 33226 33227Note: 33228 The BAR, REGION, SPIKE, CHARACTER, and LINE switch all work 33229 independently of each other. That is, a plot point can be a line, 33230 a character, a bar, a spike or a region or any combination of the 33231 above. 33232 33233Default: 33234 All regions off 33235 33236Synonyms: 33237 None 33238 33239Related Commands: 33240 PLOT = Generates a data or function plot. 33241 REGION BASE = Sets the base locations for plot regions. 33242 REGION FILL COLOR = Sets the color for solid region fills. 33243 REGION PATTERN = Sets the types for region fill patterns. 33244 REGION PATTERN COLOR = Sets the color for region hatched fills. 33245 REGION PATTERN LINE = Sets the line types for region fill 33246 patterns. 33247 REGION PATTERN SPACING = Sets the line spacing for region fill 33248 patterns. 33249 REGION PATTERN THICK = Sets the line thickness for region fill 33250 patterns. 33251 LINE BORDER COLOR = Sets the color for region border lines. 33252 LINE BORDER LINE = Sets the types for region border lines. 33253 LINE BORDER THICKNESS = Sets the line thickness for region border 33254 lines. 33255 33256Applications: 33257 Presentation Graphics 33258 33259Implementation Date: 33260 XX 33261 33262Program 1: 33263 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 33264 TITLE SIZE 3 33265 . 33266 REGION FILL ON OFF 33267 REGION BASE 0 ALL 33268 TITLE NORPDF FROM -1.5 TO -1 33269 PLOT NORPDF(X) FOR X = -1.5 0.01 -1 AND 33270 PLOT NORPDF(X) FOR X = -3 0.01 3 33271 . 33272 TITLE PLOT OF SINE CURVE 33273 PLOT SIN(X) FOR X = -6.28 0.1 6.28 33274 . 33275 LET X = DATA 81 82 83 84 85 33276 LET Y = DATA 2 5 9 15 28 33277 TITLE AREA CURVE 33278 PLOT Y X 33279 . 33280 TITLE PIE CHART 33281 LINE THICKNESS 0.3 ALL 33282 REGION FILL ON ALL 33283 REGION BASE 33284 REGION FILL COLOR G10 G30 G50 G70 G90 33285 PIE CHART Y X 33286 END OF MULTIPLOT 33287 33288Program 2: 33289 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 33290 TITLE SIZE 3 33291 . 33292 READ X2 Y2 33293 .6255459213E+002 .4360801888E+002 33294 .6408000851E+002 .4019557142E+002 33295 .7055372143E+002 .3765282536E+002 33296 .7249774456E+002 .3541294813E+002 33297 .7415955067E+002 .3788125515E+002 33298 .7837881279E+002 .3731980515E+002 33299 .8329592896E+002 .3269992304E+002 33300 .8584967327E+002 .2901664400E+002 33301 .9298062229E+002 .3339557743E+002 33302 .9053282833E+002 .3760073233E+002 33303 .8058299351E+002 .4461946392E+002 33304 .7574584389E+002 .4518656731E+002 33305 .7132878590E+002 .4718765020E+002 33306 .6534696388E+002 .4567384863E+002 33307 .6277094793E+002 .4543599606E+002 33308 END OF DATA 33309 REGION FILL ON 33310 REGION BASE POLYGON 33311 TITLE PLOT A POLYGON 33312 PLOT Y2 X2 33313 . 33314 SKIP 25 33315 READ TEXAS.DAT X Y 33316 REGION FILL ON 33317 REGION BASE POLYGON 33318 FRAME OFF 33319 TITLE MAP OF TEXAS 33320 PLOT Y X 33321 REGION BASE 0 33322 . 33323 TITLE; PLOT 33324 MOVE 50 97; JUSTIFICATION CENTER 33325 TEXT FILLED DIAGRAMMATIC GRAPHICS REGION FILL ON 33326 CIRCLE 10 10 20 20 33327 REGION FILL ONTS 33328 CUBE 40 70 48 78 33329 REGION FILL ON 33330 ELLIPSE 10 90 15 80 20 90 33331 DIAMOND 80 70 84 65 88 70 33332 HEXAGON 60 10 80 30 33333 END OF MULTIPLOT 33334 33335-----REGION FILL COLOR--------------------------------------------- 33336 33337REGION FILL COLOR 33338 33339Name: 33340 REGION FILL COLOR 33341 33342Type: 33343 Plot Control Command 33344 33345Purpose: 33346 Specifies the color used for solid fill regions on subsequent 33347 plots or for certain types of diagrammatic graphics. 33348 33349Description: 33350 On a plot, a region is defined as the figure formed by the line 33351 connecting points belonging to a common trace and a region base 33352 (typically zero). The REGION FILL command can be used to generate 33353 a solid fill or a cross-hatch fill of this region. The REGION FILL 33354 command is used to set the color for solid fill regions (the REGION 33355 PATTERN COLOR command is used to set the color for hatch fill 33356 regions). Other attributes of the fill are set with additional 33357 REGION commands (see the RELATED COMMANDS section below). The 33358 attributes of the region border are set with LINE, LINE COLOR, and 33359 LINE THICKNESS commands. 33360 33361 The diagrammatic graphics commands CIRCLE, CUBE, DIAMOND, ELLIPSE, 33362 HEXAGON, PYRAMID, SEMI-CIRCLE, and TRIANGLE can be filled using the 33363 REGION FILL command. The BOX command has its own attribute 33364 setting commands. 33365 33366Syntax: 33367 REGION FILL COLOR <color> <color> <color> etc. 33368 where <color> is a character string or index number that specifies 33369 the desired color. Up to 100 region fill colors can 33370 be specified. 33371 33372Examples: 33373 REGION FILL COLOR RED BLUE GREEN 33374 REGION FILL COLOR BLACK ALL 33375 REGION FILL COLOR ALL BLACK 33376 REGION FILL COLOR 33377 33378Default: 33379 All solid region fills are black. 33380 33381Synonyms: 33382 None 33383 33384Note: 33385 The diagrammatic graphics commands use the first setting of the 33386 REGION FILL COLOR command only. 33387 33388Note: 33389 The REGION FILL COLOR command with no arguments sets the region 33390 fill color to default for all regions. The REGION FILL COLOR 33391 command with the word ALL before or after the specified color 33392 assigns that region fill color to all regions; thus REGION FILL 33393 COLOR BLACK ALL or REGION FILL COLOR ALL BLACK plots all region 33394 fills in black. 33395 33396Note: 33397 The REGION, BAR, SPIKE, CHARACTER, and LINE switch all work 33398 independently of each other. That is, a plot point can be a line, 33399 a character, a spike a region, a bar or any combination of the 33400 above. 33401 33402Related Commands: 33403 PLOT = Generates a data or function plot. 33404 REGION BASE = Sets the base locations for plot regions. 33405 REGION FILL = Sets the on/off switches for region fills. 33406 REGION PATTERN = Sets the types for region fill patterns. 33407 REGION PATTERN COLOR = Sets the color for region hatched fills. 33408 REGION PATTERN LINE = Sets the line types for region fill 33409 patterns. 33410 REGION PATTERN SPACING = Sets the line spacing for region fill 33411 patterns. 33412 REGION PATTERN THICK = Sets the line thickness for region fill 33413 patterns. 33414 LINE BORDER COLOR = Sets the color for region border lines. 33415 LINE BORDER LINE = Sets the types for region border lines. 33416 LINE BORDER THICKNESS = Sets the line thickness for region border 33417 lines. 33418 33419Applications: 33420 Presentation Graphics 33421 33422Implementation Date: 33423 XX 33424 33425Program: 33426 SKIP 25 33427 READ TEXAS.DAT X Y 33428 . 33429 FRAME OFF 33430 FRAME CORNER COORDINATES 5 5 95 95 33431 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 33432 REGION BASE POLYGON 33433 REGION FILL ON 33434 TITLE BLACK 33435 PLOT Y X 33436 REGION FILL COLOR G75 33437 TITLE G75 33438 PLOT Y X 33439 REGION FILL COLOR G50 33440 TITLE G50 33441 PLOT Y X 33442 REGION FILL COLOR G25 33443 TITLE G25 33444 PLOT Y X 33445 END OF MULTIPLOT 33446 33447-----REGION PATTERN--------------------------------------------------- 33448 33449REGION PATTERN 33450 33451Name: 33452 REGION PATTERN 33453 33454Type: 33455 Plot Control Command 33456 33457Purpose: 33458 Specifies the type of fill pattern for regions on subsequent plots 33459 or for certain types of diagrammatic graphics. 33460 33461Description: 33462 On a plot, a region is defined as the figure formed by the line 33463 connecting points belonging to a common trace and a region base 33464 (typically zero). The REGION FILL command can be used to generate 33465 a solid fill or a cross-hatch fill of this region. The REGION 33466 PATTERN command can be used to specify the type of pattern fill. 33467 Other attributes of the fill are set with additional REGION 33468 commands (see the RELATED COMMANDS section below). The attributes 33469 of the region border are set with LINE, LINE COLOR, and LINE 33470 THICKNESS commands. 33471 33472 The diagrammatic graphics commands CIRCLE, CUBE, DIAMOND, ELLIPSE, 33473 HEXAGON, PYRAMID, SEMI-CIRCLE, and TRIANGLE can be filled using the 33474 REGION FILL command. The BOX command has its own attribute 33475 setting commands. 33476 33477Syntax: 33478 REGION PATTERN <pattern> <pattern> <pattern> etc. 33479 where <pattern> is a character string that specifies the desired 33480 fill pattern. 33481 33482Examples: 33483 REGION PATTERN SOLID VERTICAL HORIZONTAL BLANK 33484 REGION PATTERN D1 D2 D1D2 HOD1 VED2 VEDD 33485 REGION PATTERN D1 ALL 33486 REGION PATTERN ALL D1 33487 REGION PATTERN 33488 33489Note: 33490 The following region fill patterns are available: 33491 BLANK - no fill 33492 EMPTY - no fill 33493 OFF - no fill 33494 SOLID - solid fill 33495 ON - solid fill 33496 HORI - horizontal lines 33497 VERT - vertical lines 33498 D1 - up diagonals 33499 D2 - down diagonals 33500 D1D2 - both up and down diagonals 33501 VED1 - both vertical lines and up diagonals 33502 VED2 - both vertical lines and down diagonals 33503 HOD1 - both horizontal lines and up diagonals 33504 HOD2 - both vertical lines and down diagonals 33505 VEDD - both horizontal and vertical lines, and 33506 both up and down diagonals 33507 In practice, the first 7 (OFF, ON, HORI, VERT, D1, D2, D1D2) are 33508 heavily used and the last 5 (VED1, VED2, HOD1, HOD2, VEDD) are 33509 rarely used. 33510 33511Note: 33512 The diagrammatic graphics commands use the first setting of the 33513 REGION PATTERN command only. 33514 33515Note: 33516 The REGION PATTERN command with no arguments sets the region 33517 pattern type to blank for all regions. The REGION PATTERN command 33518 with the word ALL before or after the specified pattern type 33519 assigns that region pattern type to all regions; thus REGION 33520 PATTERN D1 ALL or REGION PATTERN ALL D1 fills all regions with 33521 pattern D1. 33522 33523Note: 33524 The REGION, SPIKE, CHARACTER, BAR, and LINE switch all work 33525 independently of each other. That is, a plot point can be a line, 33526 a region, a character, a spike, a region, or any combination of the 33527 above. 33528 33529Default: 33530 All region patterns are blank. 33531 33532Synonyms: 33533 None 33534 33535Related Commands: 33536 PLOT = Generates a data or function plot. 33537 REGION BASE = Sets the base locations for plot regions. 33538 REGION FILL = Sets the on/off switches for region fills. 33539 REGION FILL COLOR = Sets the color for region solid fills. 33540 REGION PATTERN COLOR = Sets the color for region hatched fills. 33541 REGION PATTERN LINE = Sets the line types for region fill 33542 patterns. 33543 REGION PATTERN SPACING = Sets the line spacing for region fill 33544 patterns. 33545 REGION PATTERN THICK = Sets the line thickness for region fill 33546 patterns. 33547 LINE COLOR = Sets the color for region border lines. 33548 LINE = Sets the types for region border lines. 33549 LINE THICKNESS = Sets the line thickness for region border 33550 lines. 33551 33552Applications: 33553 Presentation Graphics 33554 33555Implementation Date: 33556 The ability to generate hatch fills for non-rectangular regions 33557 was added 93/10. 33558 33559Program: 33560 LET C = 1 33561 LET FUNCTION F1 = C 33562 LET FUNCTION F2 = -1.5*X + 9 33563 LET FUNCTION F3 = 6 33564 LET FUNCTION F4 = 1+0.3*X**2 33565 . 33566 XMINIMUM 0; YLIMITS 0 10 33567 TITLE PLOT INEQUALITY REGIONS 33568 . 33569 REGION FILL ON ALL 33570 REGION BASE 0 10 10 0 33571 REGION PATTERN D1 HORI D2 VERT 33572 REGION PATTERN SPACING 5 ALL 33573 . 33574 LINE THICKNESS 0.3 33575 LINE SOLID DASH SOLID DASH 33576 X1LABEL SOLID = EQUALITY 33577 X2LABEL DASH = INEQUALITY 33578 . 33579 PLOT F1 FOR X = 0 5 5 AND 33580 PLOT F2 FOR X = 0 5 5 AND 33581 PLOT F3 FOR X = 0 5 5 AND 33582 PLOT F4 FOR X = 0 0.01 5 33583 33584-----REGION PATTERN COLOR--------------------------------------------- 33585 33586REGION PATTERN COLOR 33587 33588Name: 33589 REGION PATTERN COLOR 33590 33591Type: 33592 Plot Control Command 33593 33594Purpose: 33595 Specifies the color used for cross-hatch fill regions on subsequent 33596 plots or for certain types of diagrammatic graphics. 33597 33598Description: 33599 On a plot, a region is defined as the figure formed by the line 33600 connecting points belonging to a common trace and a region base 33601 (typically zero). The REGION FILL and REGION PATTERN commands can 33602 be used to generate a solid or cross-hatch fill of this region. 33603 The REGION FILL COLOR command specifies the color for solid fill 33604 regions while the REGION PATTERN COLOR command specifies the color 33605 for cross-hatch lines. Other attributes of the fill are set with 33606 additional REGION commands (see the RELATED COMMANDS section 33607 below). The attributes of the region border are set with LINE, 33608 LINE COLOR, and LINE THICKNESS commands. 33609 33610 The diagrammatic graphics commands CIRCLE, CUBE, DIAMOND, ELLIPSE, 33611 HEXAGON, PYRAMID, SEMI-CIRCLE, and TRIANGLE can be filled using the 33612 REGION FILL command. The BOX command has its own attribute 33613 setting commands. 33614 33615Syntax: 33616 REGION PATTERN COLOR <color> <color> <color> etc. 33617 where <color> is a character string or index number that specifies 33618 the desired color. Up to 100 region pattern colors can 33619 be specified. 33620 33621Examples: 33622 REGION PATTERN COLOR RED BLUE GREEN 33623 REGION PATTERN COLOR BLACK ALL 33624 REGION PATTERN COLOR ALL BLACK 33625 REGION PATTERN COLOR 33626 33627Note: 33628 The diagrammatic graphics commands use the first setting of the 33629 REGION FILL command only. 33630 33631Note: 33632 The REGION PATTERN COLOR command with no arguments sets the region 33633 pattern color to default for all regions. The REGION PATTERN COLOR 33634 command with the word ALL before or after the specified color 33635 assigns that region pattern color to all regions; thus REGION 33636 PATTERN COLOR BLACK ALL or REGION PATTERN COLOR ALL BLACK plots all 33637 region fills in black. 33638 33639Note: 33640 The REGION, BAR, SPIKE, CHARACTER, and LINE switch all work 33641 independently of each other. That is, a plot point can be a line, 33642 a character, a spike, a region, a bar, or any combination of the 33643 above. 33644 33645Default: 33646 All region pattern colors are black. 33647 33648Synonyms: 33649 None 33650 33651Related Commands: 33652 PLOT = Generates a data or function plot. 33653 REGION BASE = Sets the base locations for plot regions. 33654 REGION FILL = Sets the on/off switches for region fills. 33655 REGION FILL COLOR = Sets the color for region solid fills. 33656 REGION PATTERN = Sets the types for region fill patterns. 33657 REGION PATTERN LINE = Sets the line types for region fill 33658 patterns. 33659 REGION PATTERN SPACING = Sets the line spacing for region fill 33660 patterns. 33661 REGION PATTERN THICK = Sets the line thickness for region fill 33662 patterns. 33663 LINE COLOR = Sets the color for region border lines. 33664 LINE = Sets the types for region border lines. 33665 LINE THICKNESS = Sets the line thickness for region border 33666 lines. 33667 33668Applications: 33669 Presentation Graphics 33670 33671Implementation Date: 33672 The capability to do cross-hatch fills for non-rectangular regions 33673 was added 93/10. 33674 33675Program: 33676 LET C = 1 33677 LET FUNCTION F1 = C 33678 LET FUNCTION F2 = -1.5*X + 9 33679 LET FUNCTION F3 = 6 33680 LET FUNCTION F4 = 1+0.3*X**2 33681 . 33682 XMINIMUM 0; YLIMITS 0 10 33683 TITLE PLOT INEQUALITY REGIONS 33684 . 33685 REGION FILL ON ALL 33686 REGION BASE 0 10 10 0 33687 REGION PATTERN D1 HORI D2 VERT 33688 REGION PATTERN SPACING 5 ALL 33689 REGION PATTERN THICKNESS 0.5 0.5 0.5 0.5 33690 REGION PATTERN COLOR G10 G30 G50 G80 33691 . 33692 PLOT F1 FOR X = 0 5 5 AND 33693 PLOT F2 FOR X = 0 5 5 AND 33694 PLOT F3 FOR X = 0 5 5 AND 33695 PLOT F4 FOR X = 0 0.01 5 33696 33697-----REGION PATTERN LINE---------------------------------------------- 33698 33699REGION PATTERN LINE 33700 33701Name: 33702 REGION PATTERN LINES 33703 33704Type: 33705 Plot Control Command 33706 33707Purpose: 33708 Specifies the line patterns used to do region fills on subsequent 33709 plots and certain types of diagrammatic graphics. 33710 33711Description: 33712 On a plot, a region is defined as the figure formed by the line 33713 connecting points belonging to a common trace and a region base 33714 (typically zero). The REGION FILL and REGION PATTERN commands can 33715 be used to generate a solid fill or a cross-hatch fill of this 33716 region. The REGION PATTERN LINE command is used to specify the 33717 line type (i.e., solid, dashed) when generating cross-hatch fills. 33718 The attributes of the fill are set with additional REGION commands 33719 (see the RELATED COMMANDS section below). The attributes of the 33720 region border are set with LINE, LINE COLOR, and LINE THICKNESS 33721 commands. 33722 33723 The diagrammatic graphics commands CIRCLE, CUBE, DIAMOND, ELLIPSE, 33724 HEXAGON, PYRAMID, SEMI-CIRCLE, and TRIANGLE can be filled using the 33725 REGION FILL command. The BOX command has its own attribute 33726 setting commands. 33727 33728 The line type (e.g., solid or dashed) is distinct from the pattern 33729 type (e.g., solid or horizontal). 33730 33731Syntax: 33732 REGION PATTERN LINE <type> <type> <type> etc. 33733 where <type> is a character string that specifies the desired line 33734 type. Up to 100 region pattern line types can be 33735 specified. 33736 33737Examples: 33738 REGION PATTERN LINE SOLID DASH DOT 33739 REGION PATTERN LINES SOLID ALL 33740 REGION PATTERN LINES ALL SOLID 33741 REGION PATTERN LINES 33742 33743Note: 33744 The REGION PATTERN LINE command with no arguments sets the region 33745 type to default for all regions. The REGION PATTERN LINE command 33746 with the word ALL before or after the specified type assigns that 33747 pattern line type to all regions; thus REGION PATTERN LINE SOLID 33748 ALL or REGION PATTERN LINE ALL SOLID plots region patterns with 33749 solid lines for all regions. 33750 33751Note: 33752 The REGION, BAR, SPIKE, CHARACTER, and LINE switch all work 33753 independently of each other. That is, a plot point can be a line, 33754 a character, a region, a spike, a bar, or any combination of the 33755 above. 33756 33757Default: 33758 All region pattern line types are solid. 33759 33760Synonyms: 33761 None 33762 33763Related Commands: 33764 PLOT = Generates a data or function plot. 33765 REGION BASE = Sets the base locations for plot regions. 33766 REGION FILL = Sets the on/off switches for region fills. 33767 REGION FILL COLOR = Sets the color for region solid fills. 33768 REGION PATTERN = Sets the types for region fill patterns. 33769 REGION PATTERN COLOR = Sets the color for region hatched fills. 33770 REGION PATTERN SPACING = Sets the line spacing for region fill 33771 patterns. 33772 REGION PATTERN THICK = Sets the line thickness for region fill 33773 patterns. 33774 LINE COLOR = Sets the color for region border lines. 33775 LINE = Sets the types for region border lines. 33776 LINE THICKNESS = Sets the line thickness for region border 33777 lines. 33778 33779Applications: 33780 Presentation Graphics 33781 33782Implementation Date: 33783 The ability to generate cross-hatch fills of non-rectangular 33784 regions was added 93/10. 33785 33786Program: 33787 LET C = 1 33788 LET FUNCTION F1 = C 33789 LET FUNCTION F2 = -1.5*X + 9 33790 LET FUNCTION F3 = 6 33791 LET FUNCTION F4 = 1+0.3*X**2 33792 . 33793 XMINIMUM 0; YLIMITS 0 10 33794 TITLE PLOT INEQUALITY REGIONS 33795 . 33796 REGION FILL ON ALL 33797 REGION BASE 0 10 10 0 33798 REGION PATTERN D1 HORI D2 VERT 33799 REGION PATTERN SPACING 5 ALL 33800 LINE SOLID DASH SOLID DASH 33801 REGION PATTERN LINE SOLID DASH SOLID DASH 33802 . 33803 X1LABEL SOLID = EQUALITY 33804 X2LABEL DASH = INEQUALITY 33805 . 33806 PLOT F1 FOR X = 0 5 5 AND 33807 PLOT F2 FOR X = 0 5 5 AND 33808 PLOT F3 FOR X = 0 5 5 AND 33809 PLOT F4 FOR X = 0 0.01 5 33810 33811-----REGION PATTERN SPACING------------------------------------------ 33812 33813REGION PATTERN SPACING 33814 33815Name: 33816 REGION PATTERN SPACING 33817 33818Type: 33819 Plot Control Command 33820 33821Purpose: 33822 Specifies the spacing to be used between lines when doing 33823 cross-hatch pattern fills of regions on subsequent plots or for 33824 certain types of diagrammatic graphics. 33825 33826Description: 33827 On a plot, a region is defined as the figure formed by the line 33828 connecting points belonging to a common trace and a region base 33829 (typically zero). The REGION FILL and REGION PATTERN commands can 33830 be used to generate a solid fill or a cross-hatch fill of this 33831 region. The REGION PATTERN SPACING controls the spacing between 33832 lines for cross-hatch fills. Other attributes of the fill are set 33833 with additional REGION commands (see the RELATED COMMANDS section 33834 below). The attributes of the region border are set with LINE, 33835 LINE COLOR, and LINE THICKNESS commands. 33836 33837 The diagrammatic graphics commands CIRCLE, CUBE, DIAMOND, ELLIPSE, 33838 HEXAGON, PYRAMID, SEMI-CIRCLE, and TRIANGLE can be filled using the 33839 REGION FILL command. The BOX command has its own attribute 33840 setting commands. 33841 33842 The region pattern spacing is given in 0.0 to 100.0 DATAPLOT units. 33843 A value of 0.1 gives a solid fill on most devices. Typical values 33844 are between 1 and 5. 33845 33846Syntax: 33847 REGION PATTERN SPACINGS <number> <number> <number> etc. 33848 where <number> is a number or parameter that specifies the desired 33849 region pattern spacing. Up to 100 region pattern 33850 spacings can be specified. 33851 33852Examples: 33853 REGION PATTERN SPACINGS 1.0 0.5 3.0 5.0 33854 REGION PATTERN SPACINGS 1.0 ALL 33855 REGION PATTERN SPACINGS ALL 1.0 33856 REGION PATTERN SPACINGS 33857 33858Note: 33859 The diagrammatic graphics commands use the first setting of the 33860 REGION FILL command only. 33861 33862Note: 33863 The REGION PATTERN SPACING command with no arguments sets the 33864 region pattern spacing to default for all regions. The REGION 33865 PATTERN SPACING command with the word ALL before or after the 33866 specified pattern spacing assigns that pattern spacing to all 33867 regions; thus REGION PATTERN SPACING 1.0 ALL or REGION PATTERN 33868 SPACING ALL 1.0 uses a pattern spacing of 1.0 for all regions on 33869 the plot. 33870 33871Note: 33872 The REGION, SPIKE, BAR, CHARACTER, and LINE switch all work 33873 independently of each other. That is, a plot point can be a bar, a 33874 line, a character, a spike, a region, or any combination of the 33875 above. 33876 33877Default: 33878 All region pattern spacings are 1.0. 33879 33880Synonyms: 33881 None 33882 33883Related Commands: 33884 PLOT = Generates a data or function plot. 33885 REGION BASE = Sets the base locations for plot regions. 33886 REGION FILL = Sets the on/off switches for region fills. 33887 REGION FILL COLOR = Sets the color for region solid fills. 33888 REGION PATTERN = Sets the types for region fill patterns. 33889 REGION PATTERN COLOR = Sets the color for region hatched fills. 33890 REGION PATTERN LINE = Sets the line types for region fill 33891 patterns. 33892 REGION PATTERN THICK = Sets the line thickness for region fill 33893 patterns. 33894 LINE COLOR = Sets the color for region border lines. 33895 LINE = Sets the types for region border lines. 33896 LINE THICKNESS = Sets the line thickness for region border 33897 lines. 33898 33899Applications: 33900 Presentation Graphics 33901 33902Implementation Date: 33903 The ability to generate cross-hatch fills for non-rectangular 33904 regions was added 93/10. 33905 33906Program: 33907 LET C = 1 33908 LET FUNCTION F1 = C 33909 LET FUNCTION F2 = -1.5*X + 9 33910 LET FUNCTION F3 = 6 33911 LET FUNCTION F4 = 1+0.3*X**2 33912 . 33913 XMINIMUM 0; YLIMITS 0 10 33914 TITLE PLOT INEQUALITY REGIONS 33915 . 33916 REGION FILL ON ALL 33917 REGION BASE 0 10 10 0 33918 REGION PATTERN D1 HORI D2 VERT 33919 REGION PATTERN SPACING 5 2 4 3 33920 . 33921 PLOT F1 FOR X = 0 5 5 AND 33922 PLOT F2 FOR X = 0 5 5 AND 33923 PLOT F3 FOR X = 0 5 5 AND 33924 PLOT F4 FOR X = 0 0.01 5 33925 33926-----REGION PATTERN THICKNESS----------------------------------------- 33927 33928REGION PATTERN THICKNESS 33929 33930Name: 33931 REGION PATTERN THICKNESS 33932 33933Type: 33934 Plot Control Command 33935 33936Purpose: 33937 Specifies the thickness of lines used when generating cross-hatch 33938 pattern fills of regions on subsequent plots or for certain 33939 diagrammatic graphics. 33940 33941Description: 33942 On a plot, a region is defined as the figure formed by the line 33943 connecting points belonging to a common trace and a region base 33944 (typically zero). The REGION FILL and REGION PATTERN commands can 33945 be used to generate a solid or cross-hatch fill of this region. 33946 The REGION PATTERN THICKNESS command is used to specify the line 33947 thickness for a cross-hatch pattern. Other attributes of the fill 33948 are set with additional REGION commands (see the RELATED COMMANDS 33949 section below). The attributes of the region border are set with 33950 LINE, LINE COLOR, and LINE THICKNESS commands. 33951 33952 The diagrammatic graphics commands CIRCLE, CUBE, DIAMOND, ELLIPSE, 33953 HEXAGON, PYRAMID, SEMI-CIRCLE, and TRIANGLE can be filled using the 33954 REGION FILL command. The BOX command has its own attribute 33955 setting commands. 33956 33957 The line thickness is specified in 0.0 to 100.0 DATAPLOT units. 33958 Typical values are between 0.05 and 0.3. 33959 33960Syntax: 33961 REGION PATTERN THICKNESSS <thick> <thick> <thick> etc. 33962 where <thick> is a number or parameter that specifies the desired 33963 thickness. Up to 100 region pattern line thicknesses 33964 can be specified. 33965 33966Examples: 33967 REGION PATTERN THICKNESSS 0.1 0.2 0.1 0.2 33968 REGION PATTERN THICKNESSS 0.2 0.2 0.1 33969 REGION PATTERN THICKNESSS 0.1 ALL 33970 REGION PATTERN THICKNESSS ALL 0.1 33971 REGION PATTERN THICKNESSS 33972 33973Note: 33974 The diagrammatic graphics commands use the first setting of the 33975 REGION FILL command only. 33976 33977Note: 33978 The REGION PATTERN THICKNESS command with no arguments sets 33979 the region pattern line thickness to default for all regions. 33980 The REGION PATTERN THICKNESS command with the word ALL before 33981 or after the specified thickness assigns that region pattern 33982 line thickness to all regions; thus REGION PATTERN THICKNESS 33983 0.1 ALL or REGION PATTERN THICKNESS ALL 0.1 plots region 33984 pattern fills with a line thickness of 0.1 for all regions 33985 on the plot. 33986 33987Note: 33988 The REGION, SPIKE, CHARACTER, BAR, and LINE switches all work 33989 independently of each other. That is, a plot point can be a line, 33990 a bar, a character, a spike, a region, or any combination of the 33991 above. 33992 33993Default: 33994 All region pattern line thicknesses are 0.1. 33995 33996Synonyms: 33997 None 33998 33999Related Commands: 34000 PLOT = Generates a data or function plot. 34001 REGION BASE = Sets the base locations for plot regions. 34002 REGION FILL = Sets the on/off switches for region fills. 34003 REGION FILL COLOR = Sets the color for region solid fills. 34004 REGION PATTERN = Sets the types for region fill patterns. 34005 REGION PATTERN COLOR = Sets the color for region hatched fills. 34006 REGION PATTERN LINE = Sets the line types for region fill 34007 patterns. 34008 REGION PATTERN SPACING = Sets the line spacing for region fill 34009 patterns. 34010 LINE COLOR = Sets the color for region border lines. 34011 LINE = Sets the types for region border lines. 34012 LINE THICKNESS = Sets the line thickness for region border 34013 lines. 34014 34015Applications: 34016 Presentation Graphics 34017 34018Implementation Date: 34019 The ability to generate cross-hatch fills of non-rectangular 34020 regions was added 93/10. 34021 34022Program: 34023 LET C = 1 34024 LET FUNCTION F1 = C 34025 LET FUNCTION F2 = -1.5*X + 9 34026 LET FUNCTION F3 = 6 34027 LET FUNCTION F4 = 1+0.3*X**2 34028 . 34029 XMINIMUM 0; YLIMITS 0 10 34030 TITLE PLOT INEQUALITY REGIONS 34031 . 34032 REGION FILL ON ALL 34033 REGION BASE 0 10 10 0 34034 REGION PATTERN D1 HORI D2 VERT 34035 REGION PATTERN SPACING 5 ALL 34036 REGION PATTERN THICKNESS 0.1 0.3 0.1 0.5 34037 . 34038 PLOT F1 FOR X = 0 5 5 AND 34039 PLOT F2 FOR X = 0 5 5 AND 34040 PLOT F3 FOR X = 0 5 5 AND 34041 PLOT F4 FOR X = 0 0.01 5 34042 34043-----REGIS------------------------------------------------------- 34044 34045REGIS 34046 34047Name: 34048 REGIS 34049 34050Type: 34051 Output Device Command 34052 34053Purpose: 34054 The REGIS command is used to direct graphical output to a REGIS 34055 device. 34056 34057Description: 34058 This is the protocol supported on many DEC terminals (e.g., the 34059 VT-240 and VT-340). 34060 34061Syntax 1: 34062 REGIS <model> 34063 where <model> is 240 for VT-240 class terminals and 340 for VT-340 34064 class terminals. 34065 34066 This form designates device 1 (the terminal) as a Regis device. 34067 34068Syntax 2: 34069 DEVICE <1/2/3> REGIS <model> 34070 where <model> is 240 for VT-240 class terminals and 340 for VT-340 34071 class terminals. 34072 34073 This form designates one of of DATAPLOT's 3 devices (it will 34074 typically be device 1) as a Regis device. 34075 34076Examples: 34077 REGIS 34078 DEVICE 1 REGIS 34079 DEVICE 1 REGIS 340 34080 34081Note: 34082 Regis supports both monochrome and color terminals. By default, 34083 the Regis driver is monochrome. To specify color Regis, enter 34084 the command DEVICE 1 COLOR ON after the REGIS command. 34085 34086Note: 34087 Regis terminals support 64 colors. However, only a subset of these 34088 can be active at a given time. For the VT-240 type terminals, 4 34089 colors can be active. For the VT-340 type terminals, 16 colors 34090 can be active. One color is reserved for the background and the 34091 rest for the foreground. The command REGIS COLORS can be used to 34092 specify the active colors. If this command is not used, then the 34093 3 (or 15 for the VT-340) foreground colors are assigned in the 34094 order requested. Any additional colors are assigned to the last 34095 position (which can cause current colors on the screen to change 34096 when the new one is assigned). 34097 34098Default: 34099 Off 34100 34101Synonyms: 34102 None 34103DEVICE NOTES 34104 1) HARDWARE TEXT - Regis supports 17 hardware characters, although 34105 only the first few are generally useful. The first size is 34106 9x10 pixels, the second is 9x15. The rest are integer multiples 34107 of the 9x15 pixel size. This means there is a fairly large 34108 jump between successive character strings. Regis hardware 34109 characters are of low quality. They are not rotated. 34110 2) COLOR - Some Regis terminals support color. Regis defines a 34111 database of 64 fixed colors. The VT-240 allows 4 of these 34112 colors to be active (1 background color, 3 foreground colors) at 34113 one time. The VT-340 allows 15 foreground colors to be active. 34114 3) HARDWARE FILL - Solid area fills are done in hardware. 34115 4) DASH PATTERNS - The Regis driver supports unique dash patterns 34116 for DASH, DOT, DASH2, DASH3, and DASH4. DASH5 is the same 34117 as DASH4. 34118 5) LINE WIDTH - Thick lines are generated as multiple lines. 34119 6) GRAPHICS INPUT - The CROSS-HAIR command is supported for this 34120 device. 34121 34122Related Commands: 34123 POSTSCRIPT = Direct graphical output to a Postscript device. 34124 HPGL = Direct graphical output to an HPGL device. 34125 TEKTRONIX = Direct graphical output to a Tektronix device. 34126 X11 = Direct graphical output to an X11 device. 34127 DEVICE = Specify certain actions for the graphics 34128 output. 34129 SHOW REGIS COLOR = Show the available colors on the Regis device. 34130 34131Applications: 34132 XX 34133 34134Implementation Date: 34135 XX 34136 34137Program: 34138 XX 34139 34140-----REGIS COLORS-------------------------------------------------- 34141 34142REGIS COLORS 34143 34144Name: 34145 REGIS COLORS 34146 34147Type: 34148 Output Devices Command 34149 34150Purpose: 34151 Assign the active colors for a Regis graphics device. 34152 34153Description: 34154 Regis color devices support 64 colors. However, only 4 (for VT-240 34155 class terminals) or 16 (for VT-340 class terminals) colors can be 34156 active at a given time. This command allows the analyst to specify 34157 the active colors. 34158 34159Syntax: 34160 REGIS COLORS <color> <index> 34161 where <color> is a character string that specifies the desired 34162 color; 34163 and <index> is an integer number or parameter between 1 and 16. 34164 34165Examples: 34166 REGIS COLORS SHOW 34167 REGIS COLORS RED 4 34168 34169Default: 34170 The following is the default for VT-240 class terminals 34171 1 WHITE 34172 2 YELLOW 34173 3 RED 34174 The following is the default for VT-340 class terminals 34175 1 WHITE 34176 2 YELLOW 34177 3 RED 34178 4 BLACK 34179 5 GREEN 34180 6 CYAN 34181 7 BLUE 34182 8 ORANGE 34183 9 TURQUOISE 34184 10 MAGENTA 34185 11 YELLOW GREEN 34186 12 TAN 34187 13 GOLD 34188 14 VIOLET RED 34189 15 LIGHT GRAY 34190 34191Synonyms: 34192 REGIS PEN MAP 34193 34194Related Commands: 34195 SHOW COLORS = Print the available colors for various devices. 34196 REGIS = Direct graphical output to a Regis device. 34197 34198Applications: 34199 XX 34200 34201Implementation Date: 34202 90/6 34203 34204Program: 34205 DEVICE 1 REGIS 340 34206 DEVICE 1 COLOR ON 34207 REGIS COLORS BLACK 1 34208 REGIS COLORS BLUE 2 34209 REGIS COLORS GREEN 3 34210 REGIS COLORS RED 4 34211 34212-----RJ (LET)---------------------------------------------- 34213 34214RJ 34215 34216Name: 34217 RJ (LET) 34218 34219Type: 34220 Library Function 34221 34222Purpose: 34223 Compute Carlson's elliptic integral of the third kind. 34224 34225Description: 34226 Carlson's elliptic integral of the third kind is defined as: 34227 RJ(x,y,z,p)=1.5*INTEGRAL[1/((t+p)*SQRT((t+x)*(t+y)*(t+z)))]dt 34228 where INTEGRAL is the integral from 0 to infinity. The parameters 34229 x, y, and z must all be non-negative with at most one of them 34230 being zero. The p parameter must be non-zero. 34231 34232Syntax: 34233 LET <a> = RJ(<x>,<y>,<z>,<p>) <SUBSET/EXCEPT/FOR qualification> 34234 where <x> is a non-negative number, parameter, or variable; 34235 <y> is a non-negative number, parameter, or variable; 34236 <z> is a non-negative number, parameter, or variable; 34237 <p> is a non-zero number, parameter, or variable; 34238 <a> is a variable or a parameter (depending on what, <p>, 34239 <x>, <y>, and <z> are) where the computed values are 34240 stored; 34241 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 34242 34243Examples: 34244 LET A = RJ(2,1,3,1) 34245 LET A = RJ(X,0,4,1) 34246 LET X2 = RJ(1,1,Y,P) 34247 34248Note: 34249 The Carlson elliptic integrals are computed using the RC, RD, RF, 34250 and RJ routines from the SLATEC Common Mathematical Library. 34251 SLATEC is a large set of high quality, portable, public domain 34252 Fortran routines for various mathematical capabilities maintained 34253 by seven federal laboratories. 34254 34255Note: 34256 DATAPLOT computes Legendre elliptic integrals by computing the 34257 equivalent Carlson elliptic integrals. See the documentation for 34258 the ELLIP1, ELLIP2, ELLIP3, ELLIPC1, and ELLIPC2 functions for 34259 details on computing Legendre elliptic functions in DATAPLOT. 34260 34261Note: 34262 Library functions are distinguished from let subcommands 34263 in the following ways. 34264 1) Functions enclose the input value in parenthesis. Let 34265 subcommands use spaces. 34266 2) Functions can accept (and return) either parameters 34267 (i.e., single values) or variables (i.e., an array of 34268 values) while let subcommands are specific in which they 34269 accept as input and what they return as output. 34270 3) Functions can accept expressions while let subcommands 34271 do not. For example, the following is legal: 34272 LET Y2 = ABS(Y1-INT(Y1)) 34273 For let subcommands, you typically have to do something 34274 like the following: 34275 LET YTEMP = Y**2 + 8 34276 LET A = SUM YTEMP 34277 34278Default: 34279 None 34280 34281Synonyms: 34282 None 34283 34284Related Commands: 34285 RF = Compute the Carlson elliptic integral of the first kind. 34286 RC = Compute the degenerate Carlson elliptic integral. 34287 RD = Compute the Carlson elliptic integral of the second kind. 34288 ELLIPC1 = Compute the Legendre complete elliptic integral of the 34289 first kind. 34290 ELLIPC2 = Compute the Legendre complete elliptic integral of the 34291 second kind. 34292 ELLIP1 = Compute the Legendre elliptic integral of the first 34293 kind. 34294 ELLIP2 = Compute the Legendre elliptic integral of the second 34295 kind. 34296 ELLIP3 = Compute the Legendre's elliptic integral of the third 34297 kind. 34298 34299Reference: 34300 "Algorithms for Incomplete Elliptic Integrals by Duplication", 34301 Carlson, ACM Transactions on Mathematical Software, 7, 34302 pp. 398-403. 34303 34304 "Handbook of Mathematical Functions, Applied Mathematics Series, 34305 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 34306 1964 (chapter 17). 34307 34308Applications: 34309 Special Functions 34310 34311Implementation Date: 34312 94/9 34313 34314Program: 34315 TITLE CARLSON ELLIPTIC FUNCTIONS 34316 PLOT RJ(X,1,2,1) FOR X = 0.1 0.1 10 AND 34317 PLOT RJ(1,X,2,2) FOR X = 0.1 0.1 10 AND 34318 PLOT RJ(1,2,2,P) FOR P = 0.1 0.1 10 34319 34320-----RELATIVE DISPERSION INDEX (LET)----------------------------------------- 34321 34322RELATIVE DISPERSION INDEX 34323 34324Name: 34325 RELATIVE DISPERSION INDEX (LET) 34326 34327Type: 34328 Let Subcommand 34329 34330Purpose: 34331 Given a vector of counts, compute the difference from uniformity 34332 based on a transformation of the variational distance. 34333 34334Description: 34335 In spatial analysis, it is sometimes desired to determine if the 34336 points in the given space are consistent with a uniform 34337 distribution. One such measure is based on the variational distance 34338 which is defined as 34339 34340 d = 0.5*SUM[k=0 to infinity][|P(Unif=k) - P(data=k)|] 34341 34342 Given that the points have been converted to a set of N counts, X(k), 34343 this formula becomes 34344 34345 34346 d = 0.5*SUM[k=1 to N][|((1/N) - X(k))/SUM[k=1 to N][X(k)]|] 34347 34348 The value of the variational distance is between zero and one with 34349 values closer to zero indicating greater consistency with a uniform 34350 distribution. 34351 34352 The relative dispersion index is a scaled version of the variational 34353 distance 34354 34355 RDI = 100*(1 - d) 34356 34357 where d is the variational distance statistic. This transforms the 34358 zero to one scale to a zero to 100 scale. Values close to 100 indicate 34359 consistency with a uniform distribution. 34360 34361Syntax: 34362 LET <a> = RELATIVE DISPERSION INDEX <y> 34363 <SUBSET/EXCEPT/FOR qualification> 34364 where <y> is the response variable; 34365 <a> is a parameter where the computed statistic is saved; 34366 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 34367 34368Examples: 34369 LET A = RELATIVE DISPERSION INDEX Y1 34370 LET A = RELATIVE DISPERSION INDEX Y1 SUBSET TAG > 2 34371 34372Note: 34373 Dataplot statistics can be used in a number of commands. For 34374 details, enter 34375 34376 HELP STATISTICS 34377 34378Default: 34379 None 34380 34381Synonyms: 34382 None 34383 34384Related Commands: 34385 VARIATIONAL DISTANCE = Compute the variational distance of 34386 a variable containing a set of counts. 34387 UNIFORM CHISQUARE STAT = Compute the chi-square statistic for 34388 uniformity for a variable containing a 34389 set of counts. 34390 GOODNESS OF FIT = Perform a goodness of fit test. 34391 34392Reference: 34393 Kashiwagi, Fagan, Douglas, Yamamoto, Heckert, Leigh, Obrzut, Du, Lin-Gibson, 34394 Mu, Winey, Haggennueller (2007), "Relationship between dispersion metric and 34395 properties of PMMA/SWNT nanocomposites", Polymer Journal, Vol. 48, 34396 pp. 4855 - 4866. 34397 34398Applications: 34399 Spatial Statistics 34400 34401Implementation Date: 34402 2014/3 34403 34404Program: 34405 LET Y = UNIFORM RANDOM NUMBERS FOR I = 1 1 1000 34406 LET Y1 X1 = BINNED Y 34407 LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 1000 34408 LET Y2 X2 = BINNED Y 34409 LET Y = EXPONENTIAL RANDOM NUMBERS FOR I = 1 1 1000 34410 LET Y3 X3 = BINNED Y 34411 LET A1 = RELATIVE DISPERSION INDEX Y1 34412 LET A2 = RELATIVE DISPERSION INDEX Y2 34413 LET A3 = RELATIVE DISPERSION INDEX Y3 34414 SET WRITE DECIMALS 4 34415 PRINT A1 A2 A3 34416 34417-----RELATIVE RISK (LET)-------------------------------- 34418 34419RELATIVE RISK 34420 34421Name: 34422 RELATIVE RISK (LET) 34423 34424Type: 34425 Let Subcommand 34426 34427Purpose: 34428 Compute the relative risk between two binary variables. 34429 34430Description: 34431 Given two variables with n parired observations where each 34432 variable has exactly two possible outcomes, we can generate 34433 the following 2x2 table: 34434 34435 | Variable 2 | 34436 Variable 1 | Success Failure | Row Total 34437 ==================================================== 34438 Success | N11 N12 | N11 + N12 34439 Failure | N21 N22 | N21 + N22 34440 ==================================================== 34441 Column Total | Success Failure | Total 34442 34443 The parameters N11, N12, N21, and N22 denote the counts 34444 for each category. 34445 34446 Success and failure can denote any binary response. 34447 Dataplot expects "success" to be coded as "1" and "failure" 34448 to be coded as "0". Some typical examples would be: 34449 34450 1) Variable 1 denotes whether or not a patient has a 34451 disease (1 denotes disease is present, 0 denotes 34452 disease not present). Variable 2 denotes the result 34453 of a test to detect the disease (1 denotes a positive 34454 result and 0 denotes a negative result). 34455 34456 2) Variable 1 denotes whether an object is present or 34457 not (1 denotes present, 0 denotes absent). Variable 2 34458 denotes a detection device (1 denotes object detected 34459 and 0 denotes object not detected). 34460 34461 In these examples, the "ground truth" is typically given 34462 as variable 1 while some estimator of the ground truth is 34463 given as variable 2. 34464 34465 The relative risk is defined as the ratio of the 34466 probability of "success" probabilities, that is 34467 34468 relative risk = {N11/(N11+N21)}/{N12/(N12+N22)} 34469 34470 The relative risk is a useful statistic when comparing the 34471 difference in two binomial proportions when the probabilities 34472 of success are close to zero. For example, page 21 of 34473 Agresti gives the example where the absolute difference of 34474 proportions between 0.410, 0.401 and 0.010, 0.001 are both 34475 0.09. However the relative risks are 0.410/0.401 = 1.02 34476 and 0.010/0.001 = 10. 34477 34478Syntax: 34479 LET <par> = RELATIVE RISK <y1> <y2> 34480 <SUBSET/EXCEPT/FOR qualification> 34481 where <y1> is the first response variable; 34482 <y2> is the second response variable; 34483 <par> is a parameter where the computed relative risk 34484 proportion is stored; 34485 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 34486 34487Examples: 34488 LET A = RELATIVE RISK Y1 Y2 34489 LET A = RELATIVE RISK Y1 Y2 SUBSET TAG > 2 34490 34491Note: 34492 The two variables need not have the same number of elements. 34493 34494Note: 34495 Dataplot statistics can be used in 20+ commands. For details, enter 34496 34497 HELP STATISTICS 34498 34499Note: 34500 There are two ways you can define the response variables: 34501 34502 1) Raw data - in this case, the variables contain 34503 0's and 1's. 34504 34505 If the data is not coded as 0's and 1's, Dataplot 34506 will check for the number of distinct values. If 34507 there are two distinct values, the minimum value 34508 is converted to 0's and the maximum value is 34509 converted to 1's. If there is a single distinct 34510 value, it is converted to 0's if it is less than 34511 0.5 and to 1's if it is greater than or equal to 34512 0.5. If there are more than two distinct values, 34513 an error is returned. 34514 34515 2) Summary data - if there are two observations, the 34516 data is assummed to be the 2x2 summary table. 34517 That is, 34518 34519 Y1(1) = N11 34520 Y1(2) = N21 34521 Y2(1) = N12 34522 Y2(2) = N22 34523 34524 Note that the above commands expect the variables to have 34525 the same number of observations. If the two samples are 34526 in fact of different sizes, there are two ways to address 34527 the issue: 34528 34529 1) Y1 and Y2 can contain the summary data. That is, 34530 34531 Y1(1) = N11 34532 Y1(2) = N21 34533 Y2(1) = N12 34534 Y2(2) = N22 34535 34536 This is a useful option in that the data is sometimes 34537 only available in summary form. Note that this will 34538 not work for the BOOTSTRAP PLOT and JACKNIFE PLOT 34539 commands (these require raw data). 34540 34541 2) You can specify a missing value for the smaller 34542 sample. For example, if Y1 has 100 observations and 34543 Y2 has 200 observations, you can do something like 34544 34545 SET STATISTIC MISSING VALUE -99 34546 LET Y1 = -99 FOR I = 101 1 200 34547Default: 34548 None 34549 34550Synonyms: 34551 None 34552 34553Related Commands: 34554 ODDS RATIO = Compute the bias corrected 34555 log(odds ratio). 34556 ODDS RATIO STANDARD ERROR = Compute the standard error of the 34557 bias corrected log(odds ratio). 34558 FALSE POSITIVES = Compute the proportion of 34559 false positives. 34560 FALSE NEGATIVES = Compute the proportion of 34561 false negatives. 34562 TRUE NEGATIVES = Compute the proportion of 34563 true negatives. 34564 TRUE POSITIVES = Compute the proportion of 34565 true positives. 34566 TEST SENSITIVITY = Compute the test sensitivity. 34567 TEST SPECIFICITY = Compute the test specificity. 34568 TABULATE = Compute a statistic for data with 34569 a single grouping variable. 34570 CROSS TABULATE = Compute a statistic for data with 34571 two grouping variables. 34572 STATISTIC PLOT = Generate a plot of a statistic for 34573 data with a single grouping 34574 variable. 34575 CROSS TABULATE PLOT = Generate a plot of a statistic for 34576 data with two grouping variables. 34577 BOOTSTRAP PLOT = Generate a bootstrap plot for a 34578 given statistic. 34579 34580References: 34581 Fleiss, Levin, and Paik (2003), "Statistical Methods for 34582 Rates and Proportions", Third Edition, Wiley, chapter 1. 34583 34584 Agresti (2007), "Introduction to Categorical Data Analysis", 34585 Second Edition, Wiley. 34586 34587Applications: 34588 Categorical Data Analysis 34589 34590Implementation Date: 34591 2007/4 34592 34593Program: 34594 let n = 1 34595 . 34596 let p = 0.2 34597 let y1 = binomial rand numb for i = 1 1 100 34598 let p = 0.1 34599 let y2 = binomial rand numb for i = 1 1 100 34600 . 34601 let p = 0.4 34602 let y1 = binomial rand numb for i = 101 1 200 34603 let p = 0.08 34604 let y2 = binomial rand numb for i = 101 1 200 34605 . 34606 let p = 0.15 34607 let y1 = binomial rand numb for i = 201 1 300 34608 let p = 0.18 34609 let y2 = binomial rand numb for i = 201 1 300 34610 . 34611 let p = 0.6 34612 let y1 = binomial rand numb for i = 301 1 400 34613 let p = 0.45 34614 let y2 = binomial rand numb for i = 301 1 400 34615 . 34616 let p = 0.3 34617 let y1 = binomial rand numb for i = 401 1 500 34618 let p = 0.1 34619 let y2 = binomial rand numb for i = 401 1 500 34620 . 34621 let x = sequence 1 100 1 5 34622 . 34623 let a = relative risk y1 y2 subset x = 1 34624 tabulate relative risk y1 y2 x 34625 . 34626 label case asis 34627 xlimits 1 5 34628 major xtic mark number 5 34629 minor xtic mark number 0 34630 xtic mark offset 0.5 0.5 34631 y1label Relative Risk 34632 x1label Group ID 34633 character x blank 34634 line blank solid 34635 . 34636 relative risk plot y1 y2 x 34637 34638-----RELATIVE STANDARD DEVIATION (LET)------------------------------ 34639 34640RELATIVE STANDARD DEVIATION 34641 34642Name: 34643 RELATIVE STANDARD DEVIATION (LET) 34644 34645Type: 34646 Let Subcommand 34647 34648Purpose: 34649 Compute the relative standard deviation of a variable. 34650 34651Description: 34652 The relative standard deviation is: 34653 relsd = 100*(standard deviation/abs(mean)) 34654 Some analysts prefer to call this the percent relative standard 34655 deviation and the value obtained without multiplying by 100 the 34656 relative standard deviation. If this is your preference, simply 34657 divide the obtained value by 100 with the LET command. 34658 34659Syntax: 34660 LET <par> = RELATIVE STANDARD DEVIATION <x1> 34661 <SUBSET/EXCEPT/FOR qualification> 34662 where <x1> is a response variable; 34663 <par> is a parameter where the relative standard deviation 34664 value is saved; 34665 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 34666 34667Examples: 34668 LET RSD = RELATIVE STANDARD DEVIATION Y1 34669 LET RSD = RELATIVE STANDARD DEVIATION Y1 SUBSET TAG > 2 34670 34671Note: 34672 Versions prior to 94/2 use the mean rather than the absolute value 34673 of the mean. 34674 34675Default: 34676 None 34677 34678Synonyms: 34679 COEFFICIENT OF VARIATION 34680 COEFFICIENT VARIATION 34681 RELATIVE SD 34682 34683Related Commands: 34684 MEAN (LET) = Compute the mean of a variable. 34685 STAND DEVI (LET) = Compute the standard deviation of a variable. 34686 RELATIVE SD PLOT = Generate a relative standard deviation (versus 34687 subset) plot. 34688 34689Applications: 34690 XX 34691 34692Implementation Date: 34693 XX 34694 34695Program: 34696 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 34697 LET RSD = RELATIVE STANDARD DEVIATION X1 34698 34699-----RELATIVE VARIANCE (LET)------------------------------ 34700 34701RELATIVE VARIANCE 34702 34703Name: 34704 RELATIVE VARIANCE (LET) 34705 34706Type: 34707 Let Subcommand 34708 34709Purpose: 34710 Compute the relative variance of a variable. 34711 34712Description: 34713 The relative variance is: 34714 relvar = 100*(variance/mean) 34715 Some analysts prefer to call this the percent relative variance and 34716 the value obtained without multiplying by 100 the relative variance. 34717 If this is your preference, simply divide the obtained value by 100 34718 with the LET command. If you prefer to use the absolute value of 34719 the mean, use the LET command to calculate the absolute value of 34720 the value (e.g., LET RELVAR = ABS(RELVAR)). 34721 34722Syntax: 34723 LET <par> = RELATIVE VARIANCE <y> <SUBSET/EXCEPT/FOR qualification> 34724 where <y> is a response variable; 34725 <par> is a parameter where the relative variance value is 34726 stored; 34727 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 34728 34729Examples: 34730 LET RELVAR = RELATIVE VARIANCE Y1 34731 LET RELVAR = RELATIVE VARIANCE Y1 SUBSET TAG > 2 34732 34733Default: 34734 None 34735 34736Synonyms: 34737 None 34738 34739Related Commands: 34740 MEAN = Compute the mean of a variable. 34741 VARIANCE = Compute the variance of a variable. 34742 STANDARD DEVIATION = Compute the standard deviation of a 34743 variable. 34744 RELATIVE VARIANCE PLOT = Generate a relative variance versus 34745 subset plot. 34746 RELATIVE STANDARD DEVI = Compute the relative standard deviation 34747 of a variable. 34748 34749Applications: 34750 XX 34751 34752Implementation Date: 34753 XX 34754 34755Program: 34756 SKIP 25 34757 READ GEAR.DAT DIAMETER 34758 LET RELVAR = RELATIVE VARIANCE DIAMETER 34759 34760-----RELATIVE VARIANCE PLOT----------------------------------------- 34761 34762RELATIVE VARIANCE PLOT 34763 34764Name: 34765 RELATIVE VARIANCE PLOT 34766 34767Type: 34768 Graphics Command 34769 34770Purpose: 34771 Generates a relative variance plot. 34772 34773Description: 34774 A relative variance plot is a plot consisting of subsample relative 34775 variances versus subsample index. The relative variance is the 34776 variance divided by the mean times 100. The subsample relative 34777 variance is the relative variance of the data in the subsample. The 34778 relative variance plot is used to answer the question--"Does the 34779 subsample spread change over different subsamples?". The plot 34780 consists of: 34781 Vertical axis = subsample relative variance; 34782 Horizontal axis = subsample index. 34783 The relative variance plot yields 2 traces: 34784 1. a subsample relative variance trace; and 34785 2. a full-sample relative variance reference line. 34786 Like usual, the appearance of these 2 traces is controlled by 34787 the first 2 settings of the LINES, CHARACTERS, SPIKES, BARS, 34788 and similar attributes. 34789 34790Syntax: 34791 RELATIVE VARIANCE PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 34792 where <y> is the response (= dependent) variable; 34793 <x> is the subsample identifier variable (this variable 34794 appears on the horizontal axis); 34795 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 34796 34797Examples: 34798 RELATIVE VARIANCE PLOT Y X 34799 RELATIVE VARIANCE PLOT Y TAG SUBSET TAG > 2 34800 34801Default: 34802 None 34803 34804Synonyms: 34805 None 34806 34807Related Commands: 34808 RELATIVE VARIANCE = Compute the relative variance of a variable. 34809 RELSD PLOT = Generates a relative standard deviation plot. 34810 CHARACTERS = Sets the type for plot characters. 34811 LINES = Sets the type for plot lines. 34812 MEAN PLOT = Generates a mean plot. 34813 SD PLOT = Generates a standard deviation plot. 34814 BOX PLOT = Generates a box plot. 34815 XBAR CHART = Generates a mean control chart. 34816 PLOT = Generates a data or function plot. 34817 34818Applications: 34819 Exploratory Data Analysis 34820 34821Implementation Date: 34822 88/2 34823 34824Program: 34825 SKIP 25 34826 READ GEAR.DAT DIAMETER BATCH 34827 LINE BLANK DASH 34828 CHARACTER X BLANK 34829 XTIC OFFSET 0.2 0.2 34830 Y1LABEL RELATIVE VARIANCE 34831 X1LABEL SAMPLE BATCH 34832 TITLE AUTOMATIC 34833 RELATIVE VARIANCE PLOT DIAMETER BATCH 34834 34835-----RELDIF (LET)-------------------------------- 34836 34837RELDIF 34838 34839Name: 34840 RELDIF (LET) 34841 34842Type: 34843 Library Function 34844 34845Purpose: 34846 Return the relative difference of two numbers. 34847 34848Description: 34849 The definition of the relative difference between X1 and X2 used 34850 by Dataplot is: 34851 34852 Relative Difference = ABS(X1 - X2)/MAX(ABS(X1),ABS(X2)) 34853 34854 Dataplot also supports the alternative formula 34855 34856 Relative Difference = ABS((X1 - X2)/((X1 + X2)/2)) 34857 34858Syntax 1: 34859 LET <y> = RELDIF(<y1>,<y2>) <SUBSET/EXCEPT/FOR qualification> 34860 where <y1> is a variable or a parameter; 34861 <y2> is a variable or a parameter; 34862 <y> is a variable or a parameter (depending on what <y1> and 34863 <y2> are) where the computed relative difference values 34864 are stored; 34865 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 34866 34867 This syntax implements the first formula given above (the 34868 denominator is the maximum of the two values). 34869 34870Syntax 2: 34871 LET <y> = RELDIF2(<y1>,<y2>) <SUBSET/EXCEPT/FOR qualification> 34872 where <y1> is a variable or a parameter; 34873 <y2> is a variable or a parameter; 34874 <y> is a variable or a parameter (depending on what <y1> and 34875 <y2> are) where the computed relative difference values 34876 are stored; 34877 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 34878 34879 This syntax implements the second formula given above (the 34880 denominator is the average of the two values). 34881 34882Examples: 34883 LET A = RELDIF(14,10) 34884 LET A = RELDIF(A1,A2) 34885 LET X2 = RELDIF(X1,X4) 34886 LET X2 = RELDIF(X1-4,X2+6) 34887 34888Note: 34889 Library functions are distinguished from let subcommands 34890 in the following ways. 34891 1) Functions enclose the input value in parenthesis. Let 34892 subcommands use spaces. 34893 2) Functions can accept (and return) either parameters 34894 (i.e., single values) or variables (i.e., an array of 34895 values) while let subcommands are specific in which they 34896 accept as input and what they return as output. 34897 3) Functions can accept expressions while let subcommands 34898 do not. For example, the following is legal: 34899 LET Y2 = ABS(Y1-INT(Y1)) 34900 For let subcommands, you typically have to do something 34901 like the following: 34902 LET YTEMP = Y**2 + 8 34903 LET A = SUM YTEMP 34904 34905Default: 34906 None 34907 34908Synonyms: 34909 None 34910 34911Related Commands: 34912 RELERR = Compute the relative error of two numbers. 34913 PERCDIF = Compute the percent difference of two numbers. 34914 PERCERR = Compute the percent error of two numbers. 34915 MIN = Compute the minimum of two numbers. 34916 MAX = Compute the maximum of two numbers. 34917 ABS = Compute the absolute value of a number. 34918 34919Applications: 34920 Data Management 34921 34922Implementation Date: 34923 2010/12 34924 34925Program: 34926 LET X = SEQUENCE 0.1 0.1 3 34927 LET Y1 = X**2 34928 LET Y2 = X**(1/2) 34929 LET Y3 = RELDIF(Y1,Y2) 34930 SET WRITE DECIMALS 5 34931 PRINT Y1 Y2 Y3 34932 34933-----RELERR (LET)-------------------------------- 34934 34935RELERR 34936 34937Name: 34938 RELERR (LET) 34939 34940Type: 34941 Library Function 34942 34943Purpose: 34944 Return the relative error of two numbers. 34945 34946Description: 34947 The definition of the relative error between a "true" value 34948 X(t) and an observed value X(o) used by Dataplot is: 34949 34950 Relative Error = (X(t) - X(o))/X(t) 34951 34952 There may be some slight differences for this formula in other 34953 sources. Specifically, 34954 34955 1) Some sources take the absolute value of the above 34956 quantity. In Dataplot, you can use the ABS function 34957 to obtain this form. 34958 34959 2) Some sources may reverse the order of the X(t) and X(o) values. 34960 This changes the sign of the result, but not the magnitude. 34961 34962 34963Syntax: 34964 LET <y> = RELERR(<y1>,<y2>) <SUBSET/EXCEPT/FOR qualification> 34965 where <y1> is a variable or a parameter; 34966 <y2> is a variable or a parameter; 34967 <y> is a variable or a parameter (depending on what <y1> and 34968 <y2> are) where the computed relative error values 34969 are stored; 34970 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 34971 34972Examples: 34973 LET A = RELERR(14,10) 34974 LET A = RELERR(A1,A2) 34975 LET X2 = RELERR(X1,X4) 34976 LET X2 = RELERR(X1-4,X2+6) 34977 34978Note: 34979 Library functions are distinguished from let subcommands 34980 in the following ways. 34981 1) Functions enclose the input value in parenthesis. Let 34982 subcommands use spaces. 34983 2) Functions can accept (and return) either parameters 34984 (i.e., single values) or variables (i.e., an array of 34985 values) while let subcommands are specific in which they 34986 accept as input and what they return as output. 34987 3) Functions can accept expressions while let subcommands 34988 do not. For example, the following is legal: 34989 LET Y2 = ABS(Y1-INT(Y1)) 34990 For let subcommands, you typically have to do something 34991 like the following: 34992 LET YTEMP = Y**2 + 8 34993 LET A = SUM YTEMP 34994 34995Default: 34996 None 34997 34998Synonyms: 34999 None 35000 35001Related Commands: 35002 RELDIF = Compute the relative difference of two numbers. 35003 PERCDIF = Compute the percent difference of two numbers. 35004 PERCERR = Compute the percent error of two numbers. 35005 MIN = Compute the minimum of two numbers. 35006 MAX = Compute the maximum of two numbers. 35007 ABS = Compute the absolute value of a number. 35008 35009Applications: 35010 Data Management 35011 35012Implementation Date: 35013 2010/12 35014 35015Program: 35016 LET X = SEQUENCE 0.1 0.1 3 35017 LET Y1 = X**2 35018 LET Y2 = X**(1/2) 35019 LET Y3 = RELERR(Y1,Y2) 35020 SET WRITE DECIMALS 5 35021 PRINT Y1 Y2 Y3 35022 35023-----RELIABILITY TRENDS TEST--------------------------------- 35024 35025RELIABILITY TRENDS TEST 35026 35027Name: 35028 RELIABILITY TRENDS TEST 35029 35030Type: 35031 Analysis Command 35032 35033Purpose: 35034 Compute tests to determine whether or not the repair times of 35035 a system show significant trend. The trend may be either an 35036 improvement or a degradation. 35037 35038 Specifically, it computes the following three tests 35039 35040 1) The reverse arrangement test. 35041 2) The military handbook test. 35042 3) The Laplace test. 35043 35044Description: 35045 Determining if repair times exhibit a trend is necessary for 35046 choosing an appropriate reliability model. These formal tests 35047 for trend in repair times are a compliment to the Duane plot 35048 for detecting trend. 35049 35050 Each of these tests will be described separately. 35051 35052 1) The Reverse Arrangement Test 35053 35054 Given r repairs, T1, T2, ...., Tr, the interarrival 35055 times I2=R2-T1, I3=T3-T2, ...., Ir=Tr-T(r-1), and the 35056 censoring time T(end) > Tr, we calculate how many instances 35057 we have of a later interarrival time being strictly greater 35058 than an earlier interarrival time. These are called 35059 reversals. Too many reversals indicates a significant 35060 improving trend and too few reversals indicates a 35061 significant degradation trend. More formally, 35062 35063 1) Count a reversal every time I(j) < I(k) for some 35064 j and k with j < k. 35065 35066 2) Compute the total number of reversals, R. 35067 35068 3) For r repair times, the maximum possible number of 35069 reversals is r(r-1)/2. 35070 35071 4) If there are no trends, the expected number of 35072 reversals is r(r-1)/4. 35073 35074 5) For r > 12, the following approximation can be 35075 used to determine if the number of reversals is 35076 statistically significant. 35077 35078 z = R - C1 + 0.5/SQRT(C2) 35079 35080 where 35081 35082 C1 = r(r-1)/4 35083 C2 = (2r+5)(r-1)r/72 35084 35085 The test statistic is compared to a standard 35086 normal distribution. That is, if |z| > 1.96, we 35087 have statistical significance at the 95% level. 35088 35089 For r <= 12, tabled values are used. 35090 35091 The advantage of this test is that it is simple and it 35092 makes no assumptions about a model for the possible trend. 35093 35094 2) The Military Handbook Test 35095 35096 Given r repairs, T1, T2, ...., Tr and the censoring time 35097 T(end) > Tr, we calculate the test statistic 35098 35099 T = 2*SUM(ln(T(end)/T(i))) 35100 35101 where the summation is from i=1 to r. 35102 35103 This test statistic follows a chi-square distribution with 35104 2*r degrees of freedom. 35105 35106 This test is recommended for the case when the choice is 35107 between no trend and a non-homogeneous Poisson process 35108 (NHPP) power law (Duane) model. 35109 35110 3) The Laplace Test 35111 35112 Given r repairs, T1, T2, ...., Tr and the censoring time 35113 T(end) > Tr, we calculate the test statistic 35114 35115 z = SQRT(12*r)*SUM(T(i) - T(end)/2)/r*T(end) 35116 35117 where the summation is from i=1 to r. 35118 35119 This test statistic follows a standard normal distribution. 35120 35121 This test is recommended for the case when the choice is 35122 between no trend and a non-homogeneous Poisson process 35123 (NHPP) exponential law model. 35124 35125 If you have internet access, you can enter the following 35126 command to see a discussion of the power law model 35127 35128 WEB HANDBOOK NHPP POWER LAW 35129 35130Syntax: 35131 RELIABILITY TREND TEST <y> <SUBSET/EXCEPT/FOR qualification> 35132 where <y> is the response variable; 35133 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 35134 35135Examples: 35136 RELIABILITY TREND TEST Y 35137 RELIABILITY TREND TEST Y SUBSET TAG > 0 35138 35139Note: 35140 These commands require a censoring time. Enter the following 35141 command before the RELIABILITY TREND TEST command to 35142 specify the censoring time: 35143 35144 LET TEND = <censor time> 35145 35146Default: 35147 None 35148 35149Synonyms: 35150 None 35151 35152Related Commands: 35153 DUANE PLOT = Generate a Duane plot. 35154 POWER LAW RANDOM NUMBERS = Generate random number from a 35155 NHPP power law model. 35156 INTERARRIVAL TIME = Compute interarrival times of a 35157 variable. 35158 35159Applications: 35160 Reliability 35161 35162Implementation Date: 35163 1998/5 35164 35165Program: 35166 skip 25 35167 read hahn.dat y tag 35168 . 35169 LET TEND = 135000 35170 RELIABILITY TREND TEST Y SUBSET TAG = 1 35171 35172 The following output is generated: 35173 35174 35175 ***** NOTE-- 35176 SUBSET VARIABLE = TAG 35177 SUBSET MINIMUM = 0.9999989867E+00 35178 SUBSET MAXIMUM = 0.1000000954E+01 35179 INPUT NUMBER OF OBSERVATIONS = 96 35180 NUMBER OF OBSERVATIONS IGNORED = 59 35181 OUTPUT NUMBER OF OBSERVATIONS = 37 35182 35183 REVERSE ARRANGEMENTS TEST: 35184 NUMBER OF FAILURE TIMES = 37 35185 OBSERVED NUMBER OF REVERSALS = 215 35186 MAXIMUM POSSIBLE NUMBER OF REVERSALS = 666 35187 EXPECTED NUMBER OF REVERSALS = 333 35188 VALUE OF TEST STATISTIC = -21.40790 35189 90% CRITICAL VALUE FOR NO IMPROVEMENT = 1.282 35190 95% CRITICAL VALUE FOR NO IMPROVEMEMT = 1.645 35191 99% CRITICAL VALUE FOR NO IMPROVEMENT = 2.33 35192 35193 35194 MILITARY HANDBOOK TEST: 35195 NUMBER OF FAILURE TIMES = 37 35196 CHI-SQUARE TEST STATISTIC VALUE = 35.72037 35197 CHI-SQUARE TEST STATISTIC CDF VALUE = 0.4925163E-04 35198 35199 IMPROVEMENT TEST 35200 HYPOTHESIS ACCEPTANCE INTERVAL CONCLUSION 35201 NO TREND (0.000,0.900) ACCEPT 35202 NO TREND (0.000,0.950) ACCEPT 35203 NO TREND (0.000,0.990) ACCEPT 35204 35205 35206 DEGRADATION TEST 35207 HYPOTHESIS ACCEPTANCE INTERVAL CONCLUSION 35208 NO TREND (0.100,1) REJECT 35209 NO TREND (0.050,1) REJECT 35210 NO TREND (0.010,1) REJECT 35211 35212 35213 35214 LAPLACE TEST: 35215 NUMBER OF FAILURE TIMES = 37 35216 NORMAL TEST STATISTIC VALUE = 3.416969 35217 NORMAL TEST STATISTIC CDF VALUE = 0.9996833 35218 35219 IMPROVEMENT TEST 35220 HYPOTHESIS ACCEPTANCE INTERVAL CONCLUSION 35221 NO TREND (0.000,0.900) REJECT 35222 NO TREND (0.000,0.950) REJECT 35223 NO TREND (0.000,0.990) REJECT 35224 35225 35226 DEGRADATION TEST 35227 HYPOTHESIS ACCEPTANCE INTERVAL CONCLUSION 35228 NO TREND (0.100,1) ACCEPT 35229 NO TREND (0.050,1) ACCEPT 35230 NO TREND (0.010,1) ACCEPT 35231 35232 35233-----RELSD PLOT------------------------------------------------ 35234 35235RELSD PLOT 35236 35237Name: 35238 RELSD PLOT 35239 35240Type: 35241 Graphics Command 35242 35243Purpose: 35244 Generates a relative standard deviation plot. 35245 35246Description: 35247 A relative standard deviation plot is a plot consisting of 35248 subsample relative standard deviations versus subsample index. 35249 The subsample relative standard deviation is the relative standard 35250 deviation of the data in the subsample. The relative standard 35251 deviation plot is used to answer the question--"Does the subsample 35252 spread change over different subsamples?". It consists of: 35253 Vertical axis = subsample relative standard deviation; 35254 Horizontal axis = subsample index. 35255 The relative standard deviation plot yields 2 traces: 35256 1. a subsample relative standard deviation trace; and 35257 2. a full-sample relative standard deviation reference line. 35258 Like usual, the appearance of these 2 traces is controlled by 35259 the first 2 settings of the LINES, CHARACTERS, SPIKES, BARS, 35260 and similar attributes. 35261 35262Syntax: 35263 RELSD PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 35264 where <y> is the response (= dependent) variable; 35265 <x> is the subsample identifier variable (this variable 35266 appears on the horizontal axis); 35267 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 35268 35269Examples: 35270 RELSD PLOT Y X 35271 RELSD PLOT Y TAG SUBSET TAG > 2 35272 35273Default: 35274 None 35275 35276Synonyms: 35277 None 35278 35279Related Commands: 35280 CHARACTERS = Sets the type for plot characters. 35281 LINES = Sets the type for plot lines. 35282 MEAN PLOT = Generates a mean plot. 35283 SD PLOT = Generates a standard deviation plot. 35284 BOX PLOT = Generates a box plot. 35285 XBAR CHART = Generates a xbar control chart. 35286 PLOT = Generates a data or function plot. 35287 35288Applications: 35289 Exploratory Data Analysis 35290 35291Implementation Date: 35292 88/2 35293 35294Program: 35295 SKIP 25 35296 READ GEAR.DAT DIAMETER BATCH 35297 LINE BLANK DASH 35298 CHARACTER X BLANK 35299 XTIC OFFSET 0.2 0.2 35300 Y1LABEL RELATIVE STANDARD DEVIATION 35301 X1LABEL SAMPLE BATCH 35302 TITLE AUTOMATIC 35303 RELSD PLOT DIAMETER BATCH 35304 35305-----RENAME------------------------------------------------------- 35306 35307RENAME 35308 RENAME 35309 35310Type: 35311 Support Command 35312 35313Purpose: 35314 Specifies an additional name to be assigned to an already-existing 35315 variable. 35316 35317Description: 35318 This is useful, for example, if the analyst has written a generic 35319 sub-program which makes reference to, say, X and Y, while the 35320 variable names in the main program are, say, PRESSURE and TEMP. 35321 The RENAME command is efficient in that it does not duplicate the 35322 data. Thus RENAME X PRESSURE will not duplicate the data already 35323 existing in the variable PRESSURE (as would LET X = PRESSURE). It 35324 merely adds the additional name X by which that same data in 35325 PRESSURE can be subsequently referred. 35326 35327Syntax: 35328 RENAME <name 1> <name 2> 35329 where <name 1> is the name of an already-existing variable; 35330 and <name 2> is the desired additional name by which that 35331 variable can be referred. 35332 35333Examples: 35334 RENAME PRESSURE Y 35335 35336Note: 35337 The name list can be extended in pairs; thus 35338 RENAME PRESSURE Y TEMP X CONC Z 35339 is equivalent to 35340 RENAME PRESSURE Y 35341 RENAME TEMP X 35342 RENAME CONC Y 35343 35344Default: 35345 None 35346 35347Synonyms: 35348 NAME 35349 35350Related Commands: 35351 LET = Copies variables (and many other operations). 35352 STATUS = Displays dimension, variables, parameters, functions, 35353 etc. 35354 DELETE = Deletes (all or part of) a variable. 35355 DIMENSION = Changes internal workspace size. 35356 CALL = Executes the commands in a "macro" file. 35357 35358Applications: 35359 Data Management 35360 35361Implementation Date: 35362 Pre-1987 35363 35364Program: 35365 XX 35366 35367-----REPAIR PLOT-------------------------------------- 35368 35369REPAIR PLOT 35370 35371Name: 35372 REPAIR PLOT 35373 35374Type: 35375 Graphics Command 35376 35377Purpose: 35378 Generates a plot of repair times where there may be 35379 multiple groups and a censoring time for each group. 35380 35381Description: 35382 In reliability studies, it is often necessary to 35383 analyze repair times. A first step in analyzing these 35384 repair times is to simply plot the repair data. 35385 35386 The repair data consists of the following: 35387 35388 1) The repair times. 35389 35390 2) A system id corresponding to each of the repair 35391 times. 35392 35393 3) If the test continued to run after the last failure 35394 time, then a censoring time needs to be included. 35395 Note that there should be at most one censoring time 35396 for each system. 35397 35398 The Dataplot convention is to code the repair times 35399 as 1 and censoring times as 0. 35400 35401 The vertical coordinate is the system id and the horizontal 35402 coordinates are the repair/censoring times. 35403 35404 The appearance of the plot can be controlled by appropriate 35405 settings for the LINE and CHARACTER commands. The traces 35406 (i.e., curves) are defined as follows: 35407 35408 1) The first trace consists of all the repair times. 35409 For this trace, the line setting is typically set to 35410 a blank value while the character is set to some 35411 non-blank value. 35412 35413 2) If there are N systems, traces 2 through N+1 correspond 35414 to the repair and censoring times for each of these 35415 systems. The line settings are typically set to a 35416 non-blank value while the character settings are 35417 typically set to blank. 35418 35419 A typical sequence of commands to set the character and 35420 line settings would be 35421 35422 LINES SOLID ALL 35423 CHARACTER BLANK ALL 35424 LINE BLANK 35425 CHARACTER * 35426 35427 35428 The system id and censoring variables are optional. If you 35429 specify a censoring variable, a group variable must be 35430 given. If you have a single system with a censoring time, 35431 simply create a variable the same length as the response 35432 variable that has all values equal to 1. For example, 35433 35434 LET N = SIZE Y 35435 LET GROUPID = 1 FOR I = 1 1 N 35436 35437Syntax 1: 35438 REPAIR PLOT <y> <x> <cens> <SUBSET/EXCEPT/FOR qualification> 35439 where <y> is a variable containing repair times; 35440 <x> is a variable containing the group id's; 35441 <cens> is a variable containing the censoring values; 35442 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 35443 35444 This syntax is used to plot repair times for the case where 35445 there multiple systems, but there are no censoring times. 35446 35447Syntax 2: 35448 REPAIR PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 35449 where <y> is a variable containing repair times; 35450 <x> is a variable containing the group id's; 35451 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 35452 35453 This syntax is used to plot repair times for the case where 35454 there multiple systems, but there are no censoring times. 35455 35456Syntax 3: 35457 REPAIR PLOT <y> <SUBSET/EXCEPT/FOR qualification> 35458 where <y> is a variable containing repair times; 35459 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 35460 35461 This syntax is used to plot repair times for the case where 35462 there is only a single system and there is no censoring time. 35463 35464Examples: 35465 REPAIR PLOT Y BATCH CENSOR 35466 REPAIR PLOT Y BATCH 35467 REPAIR PLOT Y BATCH CENSOR SUBSET BATCH > 1 35468 35469Default: 35470 None 35471 35472Synonyms: 35473 None 35474 35475Related Commands: 35476 LINES = Sets the type for plot lines. 35477 CHARACTERS = Sets the type for plot characters. 35478 MEAN REPAIR FUNCTION PLOT = Generates a mean repair function 35479 plot. 35480 DUANE PLOT = Generates a Duane plot. 35481 KAPLAN-MEIER PLOT = Generates a Kaplan-Meier plot. 35482 PLOT = Generates a data or function plot. 35483 35484Applications: 35485 Reliability (Repairable Systems) 35486 35487Implementation Date: 35488 2006/10 35489 35490Program: 35491 skip 25 35492 read tob312.dat y x cens 35493 . 35494 tic offset units screen 35495 tic offset 5 5 35496 ylimits 1 3 35497 major ytic mark number 3 35498 minor ytic mark number 0 35499 line blank 35500 char * 35501 title Repair Plot 35502 y1label System ID 35503 x1label System Age 35504 title case asis 35505 title offset 2 35506 label case asis 35507 . 35508 repair plot y x cens 35509 35510-----REPDF------------------------------------------------------- 35511 35512REPDF 35513 35514Name: 35515 REPDF 35516 35517Type: 35518 Keyword 35519 35520Purpose: 35521 An internal DATAPLOT parameter into which the replication 35522 degrees of freedom is automatically placed whenever the FIT, 35523 SPLINE FIT, EXACT RATIONAL FIT, LOWESS, ANOVA, SMOOTH, YATES 35524 ANALYSIS, PRE-FIT, and MEDIAN POLISH commands are executed. 35525 35526Description: 35527 In general, the replication degrees of freedom is computable only 35528 when replication exists in the data. The formula is: 35529 REPDF = total number of observations - number of subsets 35530 REPDF may be used by the analyst in whatever fashion desired. 35531 35532Syntax: 35533 None 35534 35535Examples: 35536 WRITE RESDF REPSD RESDF RESSD LOGCDF 35537 LET SSQD = RESDF*(REPSD**2) 35538 WRITE CALIB. RESDF REPSD RESDF RESSD LOGCDF 35539 35540Default: 35541 None 35542 35543Synonyms: 35544 None 35545 35546Related Commands: 35547 PRED = A variable where predicted values are stored. 35548 RES = A variable where residuals are stored. 35549 RESSD = A parameter where the residual standard 35550 deviation is stored. 35551 RESDF = A parameter where the residual degrees of 35552 freedom is stored. 35553 REPSD = A parameter where the replication standard 35554 deviation is stored. 35555 LOFCDF = A parameter where the lack of fit cdf is 35556 stored. 35557 FIT = Carries out a least squares linear or 35558 non-linear fit. 35559 EXACT RATIONAL FIT = Carries out an exact rational fit. 35560 PRE-FIT = Carries out a least squares pre-fit. 35561 SPLINE FIT = Carries out a spline fit. 35562 YATES ANALYSIS = Carries out an analysis of a Yates design. 35563 LOWESS = Carries out a locally weighted least squares 35564 fit. 35565 SMOOTH = Carries out a smoothing. 35566 ANOVA = Carries out an ANOVA. 35567 MEDIAN POLISH = Carries out a median polish. 35568 PLOT = Generates a data/function plot. 35569 35570Applications: 35571 Fitting 35572 35573Implementation Date: 35574 Pre-1987 35575 35576Program: 35577 XX 35578 35579-----REPLACE (LET)------------------------------------- 35580 35581REPLACE 35582 35583Name: 35584 REPLACE (LET) 35585 35586Type: 35587 Let Subcommand 35588 35589Purpose: 35590 Match two columns (typically group-id vaues) and use 35591 the indices of any matching rows to replace the 35592 values in one array with the values in another array. 35593 35594Description: 35595 Given the command 35596 35597 LET Y2 = REPLACE GROUPID GROUP2 Y1 35598 35599 This command does the following: 35600 35601 1) It matches the values in GROUP2 against GROUPID 35602 and returns the indices of the matching rows for 35603 the GROUPID array. 35604 35605 2) The indices are used to access the corresponding 35606 value in the Y1 array. 35607 35608 3) The corresponding row of Y2 is replaced with the 35609 Y1 value. 35610 35611 The motivation for adding this command was to address 35612 the problem where you have two sets of labs (each data set 35613 contains a lab-id and a corresponding measurement) and you 35614 need to create a new data set that contains the data for 35615 the labs that are common to both sets. The program example 35616 below demonstrates how the REPLACE command can help 35617 accomplish this. 35618 35619Syntax 1: 35620 LET <y2> = REPLACE <groupid> <group2> <y1> 35621 <SUBSET/EXCEPT/FOR qualification> 35622 where <groupid> is a variable (typically a group-id variable); 35623 <group2> is a variable (typically a group-id variable); 35624 <y1> is a variable containing the values to be 35625 extracted; 35626 <y2> is a variable where the extracted values from 35627 <y1> are placed; 35628 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 35629 35630 The <groupid> and <group2> variable do not need to be the 35631 same length. The <y2> variable should be a previously 35632 existing variable. 35633 35634Syntax 2: 35635 LET <y2> = REPLACE <groupid> <group2> 35636 <SUBSET/EXCEPT/FOR qualification> 35637 where <groupid> is a variable (typically a group-id variable); 35638 <group2> is a variable (typically a group-id variable); 35639 <y2> is the returned variable; 35640 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 35641 35642 This is an abbreviated syntax where the <y1> variable is 35643 assummed to be all 1's. 35644 35645 The <groupid> and <group2> variable do not need to be the 35646 same length. The <y2> variable should be a previously 35647 existing variable. 35648 35649Examples: 35650 LET Y2 = REPLACE LAB1 LAB2 Y1 35651 LET Y2 = REPLACE LAB1 LAB2 35652 LET Y2 = REPLACE LAB1 LAB2 Y1 SUBSET LAB1 > 2 35653 35654Default: 35655 None 35656 35657Synonyms: 35658 None 35659 35660Related Commands: 35661 MATCH = Compare two column of numbers and return the 35662 indices of any matching values. 35663 SORT = Sort a column of numbers. 35664 RANK = Rank a column of numbers. 35665 CODE = Code a column of numbers. 35666 35667Applications: 35668 Data Transformation 35669 35670Implementation Date: 35671 2006/3 35672 35673Program: 35674 . 35675 . Problem: 35676 . 35677 . We have 2 sets of labs and we want to create a new 35678 . data set that contains the labs common to both sets 35679 . (for each set, there is a lab-id and a measurement). 35680 . 35681 . Step 1: Create some data 35682 . 35683 let lab1 = data 1 3 4 5 7 8 11 13 15 16 18 19 35684 let n1 = size lab1 35685 let y1 = norm rand numb for i = 1 1 n1 35686 . 35687 let lab2 = data 1 2 5 6 8 12 15 18 20 35688 let n2 = size lab2 35689 let y2 = norm rand numb for i = 1 1 n2 35690 . 35691 . Step 2: Identify the common labs 35692 . 35693 let labint = set intersection lab1 lab2 35694 . 35695 . Step 3: Create the tag variables for 35696 . each lab 35697 . 35698 let tag1 = 0 for i = 1 1 n1 35699 let tag1 = replace lab1 labint 35700 . 35701 let tag3 = 0 for i = 1 1 n2 35702 let tag3 = replace lab2 labint 35703 . 35704 . Step 5: Retain the common labs 35705 . 35706 set write decimals 2 35707 retain y1 lab1 subset tag1 = 1 35708 retain y2 lab2 subset tag3 = 1 35709 print lab1 y1 y2 35710 35711-----REPLICATED STACK--------------------------------------------- 35712 35713REPLICATED STACK 35714 35715Name: 35716 REPLICATED STACK 35717 35718Type: 35719 Support Command 35720 35721Purpose: 35722 Convert a set of response variables and a single group-id 35723 variable to a single response variable and two group-id 35724 variables. 35725 35726Description: 35727 Many commands in Dataplot expect the data to be in the 35728 form of a single response variable and two group-id variables 35729 (specifically, the INTERLAB E691 command). However, many 35730 data files will contain this data in column form. That is, 35731 each column contains the response for one value of the first 35732 group-id variable. One of the columns will contain the value 35733 of the second group-id variable. 35734 35735 That is, the data is the form 35736 35737 X1 X2 X3 ... XK LABID 35738 35739 The REPLICATED STACK command will convert this to 35740 35741 X1(1) 1 LAB(1) 35742 . . . 35743 X1(n) 1 LAB(n) 35744 X2(1) 2 LAB(1) 35745 . . . 35746 X2(n) 2 LAB(n) 35747 ... 35748 Xk(1) k LAB(1) 35749 . . . 35750 Xk(n) k LAB(n) 35751 35752 35753Syntax: 35754 LET <y> <matid> <labid> = REPLICATED STACK <x1> ... <xk> <lab> 35755 <SUBSET/EXPCEPT/FOR qualification> 35756 where <x1> ... <xk> is a set of one or more response variables; 35757 <lab> is the first group-id variable (often a lab-id); 35758 <y> is the variable to contain <x1> ... <xk> in a 35759 single response variable; 35760 <matid> is the variable that contain the value of the 35761 second group-id variable (i.e., the column number); 35762 <labid> is the variable that contain the value of the 35763 first group-id variable (i.e., the value of <lab>); 35764 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 35765 35766Examples: 35767 LET Y MATID LABID = REPLICATED STACK Z1 Z2 Z3 Z4 Z5 LAB 35768 35769Default: 35770 None. 35771 35772Synonyms: 35773 None 35774 35775Related Commands: 35776 STACK = Convert column data to a single response 35777 variable and a group-id variable; 35778 EXTEND = Extends a variable by another variable. 35779 LET = Creates, transforms, etc. a variable. 35780 E691 INTERLAB = Peform an interlab analysis based on the 35781 E691 standard. 35782 35783Applications: 35784 Data Management 35785 35786Implementation Date: 35787 2005/4 35788 35789Program: 35790 SKIP 25 35791 READ GLUCOSE2.DAT LAB X1 TO X5 35792 . 35793 LET Y MATID LABID = REPLICATED STACK X1 X2 X3 X4 X5 LAB 35794 . 35795 E691 INTERLAB Y MATID LABID 35796 35797-----REPLOT------------------------------------------------------- 35798 35799REPLOT 35800 35801Name: 35802 REPLOT 35803 35804Type: 35805 Support Command 35806 35807Purpose: 35808 This command regenerates the most recently created plot. 35809 35810Syntax: 35811 REPLOT 35812 35813Examples: 35814 PLOT SIN(X) FOR X = 0 0.1 6.28 35815 TITLE SIN FUNCTION 35816 REPLOT 35817 35818Default: 35819 None 35820 35821Synonyms: 35822 None 35823 35824Related Commands: 35825 SAVE = Save one or more commands for later execution. 35826 LIST = List previously entered commands. 35827 REPEAT = Re-execute previously entered commands. 35828 / = Re-execute previously saved commands. 35829 35830Applications: 35831 Interactive Usage 35832 35833Implementation Date: 35834 1997/12 35835 35836Program: 35837 PLOT SIN(X) FOR X = 0 0.1 6.28 35838 TITLE SIN FUNCTION 35839 REPLOT 35840 35841-----REPRODUCIBILITY STANDARD DEVIATION (LET)-------------------------- 35842 35843REPRODUCIBILITY STANDARD DEVIATION 35844 35845Name: 35846 REPRODUCIBILITY STANDARD DEVIATION (LET) 35847 35848Type: 35849 Let Subcommand 35850 35851Purpose: 35852 Compute the reproducibility standard deviation of a variable 35853 as defined by the ASTM E 691 - 99 standard. 35854 35855Description: 35856 The reproducibility standard deviation is a core concept 35857 defined in the ASTM E 691 - 99 standard. This standard 35858 is described in detail in the following document: 35859 35860 "Standard Practice for Conducting an Interlaboratory Study 35861 to Determine the Precision of a Test Method", ASTM 35862 International, 100 Barr Harbor Drive, PO BOX C700, 35863 West Conshohoceken, PA 19428-2959, USA. 35864 35865 This document describes reproducibility in the following way. 35866 35867 Reproducability is the variability between single test 35868 results obtained in different laboratories, each of which 35869 has applied the test method to test specimens taken at 35870 random from a single quantity of homogeneous material. 35871 35872 The reproducibility standard deviation is computed as 35873 35874 s(R) = MAX(s(R)*,s(r)) 35875 35876 with 35877 35878 s(R)* = SQRT(s(xbar)**2 + (S(r)**2*(n-1)/n) 35879 35880 s(xbar) = Standard deviation of the cell averages 35881 n = cell sample size (currently, equal cell sizes 35882 expected) 35883 35884 and S(r) denoting the repeatability standard deviation 35885 35886 Sr = SQRT(SUM[i=1 to p][s(i)**2/p] 35887 35888 with 35889 35890 p = number of labs 35891 s(i) = Standard deviation of group i. 35892 35893 In an interlaboratory study, the reproducibility standard 35894 deviation is computed for each material. 35895 35896Syntax: 35897 LET <par> = REPRODUCIBILITY STANDARD DEVIATION <y> <labid> 35898 <SUBSET/EXCEPT/FOR qualification> 35899 where <y> is a response variable; 35900 <labid> is a lab-id variable; 35901 <par> is a parameter where the reproducibility standard 35902 deviation value is saved; 35903 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 35904 35905Examples: 35906 LET RSD = REPRODUCIBILITY STANDARD DEVIATION Y LAB 35907 LET RSD = REPRODUCIBILITY STANDARD DEVIATION Y LAB SUBSET MAT = 1 35908 35909Note: 35910 The reproducibility standard deviation can be computed for 35911 multiple materials with the command 35912 35913 TABULATE REPRODUCIBILITY STANDARD DEVIATION Y LABID MATID 35914 35915 The reproducibility standard deviation can be plotted for 35916 multiple materials with the command 35917 35918 REPRODUCIBILITY STANDARD DEVIATION PLOT Y LABID MATID 35919 35920Default: 35921 None 35922 35923Synonyms: 35924 REPRODUCIBILITY SD 35925 35926Related Commands: 35927 E691 INTERLAB = Perform an E691 interlab 35928 analysis. 35929 REPEATABILITY STANDARD DEVIATION = Compute the repeatability 35930 standard deviation. 35931 35932Reference: 35933 "Standard Practice for Conducting an Interlaboratory Study 35934 to Determine the Precision of a Test Method", ASTM 35935 International, 100 Barr Harbor Drive, PO BOX C700, 35936 West Conshohoceken, PA 19428-2959, USA. 35937 35938Applications: 35939 Interlaboratory Analysis 35940 35941Implementation Date: 35942 2005/4 35943 35944Program: 35945 SKIP 25 35946 READ GLUCOSE.DAT Y LABID MATID 35947 . 35948 LET MATDIST = DISTINCT MATID 35949 LET NMAT = SIZE MATDIST 35950 XLIMITS 1 NMAT 35951 MAJOR XTIC MARK NUMBER NMAT 35952 MINOR XTIC MARK NUMBER 0 35953 XTIC OFFSET 0.5 0.5 35954 Y1LABEL REPRODUCIBILITY SD 35955 X1LABEL MATERIAL 35956 LINE BLANK 35957 CHARACTER X 35958 . 35959 REPRODUCIBILITY SD PLOT Y LABID MATID 35960 35961-----REPSD------------------------------------------------------- 35962 35963REPSD 35964 35965Name: 35966 REPSD 35967 35968Type: 35969 Keyword 35970 35971Purpose: 35972 An internal DATAPLOT parameter into which the replication standard 35973 deviation is automatically placed whenever the FIT, PRE-FIT, SPLINE 35974 FIT, YATES ANALYSIS, LOWESS, ANOVA, and MEDIAN POLISH commands are 35975 executed. 35976 35977Description: 35978 The replication standard deviation is a model-free estimate of the 35979 population standard deviation and is computable only when 35980 replication exists in the data. REPSD may be used by the analyst 35981 in whatever fashion desired. 35982 35983Syntax: 35984 None 35985 35986Examples: 35987 WRITE RESDF REPSD RESDF RESSD LOGCDF 35988 LET SSQD = RESDF*(REPSD**2) 35989 WRITE CALIB. RESDF REPSD RESDF RESSD LOGCDF 35990 35991Default: 35992 None 35993 35994Synonyms: 35995 None 35996 35997Related Commands: 35998 PRED = A variable where predicted values are stored. 35999 RES = A variable where residuals are stored. 36000 RESSD = A parameter where the residual standard 36001 deviation is stored. 36002 RESDF = A parameter where the residual degrees of 36003 freedom is stored. 36004 REPDF = A parameter where the replication degrees of 36005 freedom is stored. 36006 LOFCDF = A parameter where the lack of fit cdf is 36007 stored. 36008 FIT = Carries out a least squares linear or 36009 non-linear fit. 36010 EXACT RATIONAL FIT = Carries out an exact rational fit. 36011 PRE-FIT = Carries out a least squares pre-fit. 36012 SPLINE FIT = Carries out a spline fit. 36013 YATES ANALYSIS = Carries out an analysis of a Yates design. 36014 LOWESS = Carries out a locally weighted least squares 36015 fit. 36016 SMOOTH = Carries out a smoothing. 36017 ANOVA = Carries out an ANOVA. 36018 MEDIAN POLISH = Carries out a median polish. 36019 PLOT = Generates a data/function plot. 36020 36021Applications: 36022 XX 36023 36024Implementation Date: 36025 XX 36026 36027Program: 36028 XX 36029 36030-----REPEAT------------------------------------------------------- 36031 36032REPEAT 36033 36034Name: 36035 REPEAT 36036 36037Type: 36038 Support Command 36039 36040Purpose: 36041 Selectively re-execute one of, or a set of, the last 20 DATAPLOT 36042 commands that had been entered. 36043 36044Syntax: 36045 REPEAT <id of first command> <id of last command> 36046 where <id1> is the line number of the first command to re-execute; 36047 and <id2> is the line number of the last command to re-execute. 36048 36049 The line numbers are obtained by preceding the REPEAT command by 36050 a LIST command with no arguments. All the commands between the 36051 first and last line are re-executed as well. 36052 36053Examples: 36054 REPEAT 6 3 --to repeat commands 6, 5, 4, and 3 ago 36055 REPEAT 3 6 --to repeat commands 6, 5, 4, and 3 ago 36056 REPEAT 6 6 --to repeat command 6 ago 36057 REPEAT 6 --to repeat command 6 ago 36058 REPEAT 1 --to repeat the last command 36059 REPEAT --to repeat the last command 36060 36061Note: 36062 The REPEAT command is almost always preceded by the LIST command 36063 (with no arguments). LIST will print the last 20 commands that 36064 were entered. Based on that list, the analyst can then enter the 36065 REPEAT command to selectively execute one or more of those 36066 commands. For example, 36067 36068 LIST 36069 REPEAT 6 3 36070 36071 would list the last 20 commands and then re-execute the sixth, 36072 fifth, fourth, and third commands ago. See the documentation for 36073 the LIST command for details. 36074 36075Note: 36076 DATAPLOT actually saves the last 200 (50 in earlier versions) 36077 commands. Enter the command SET LIST LINES <n> where <n> is 36078 between 1 and 200 to control the number of commands that LIST 36079 prints. 36080 36081Note: 36082 The REPEAT command is commonly used for the re-execution of long 36083 complicated commands (e.g., PLOT with a complicated mathematical 36084 expression). 36085 36086Note: 36087 The R synonym for the REPEAT command is heavily used. 36088 36089Note: 36090 At this time, there is no way to edit the re-executed commands 36091 with the REPEAT command. You can use SAVE to a file and then use 36092 the built-in editor (EDIT command). However, this may be more 36093 trouble than it is worth. 36094 36095Default: 36096 If only one argument is entered, then only that command is 36097 re-executed. 36098 If no arguments are entered, then the last command is re-executed. 36099 36100Synonyms: 36101 R 36102 36103Related Commands: 36104 LIST = List the previously entered commands. 36105 SAVE = Select previously entered commands to be re-executed 36106 with the "/" command. 36107 36108Applications: 36109 XX 36110 36111Implementation Date: 36112 XX 36113 36114Program: 36115 XX 36116 36117-----REPEATABILITY STANDARD DEVIATION (LET)-------------------------- 36118 36119REPEATABILITY STANDARD DEVIATION 36120 36121Name: 36122 REPEATABILITY STANDARD DEVIATION (LET) 36123 36124Type: 36125 Let Subcommand 36126 36127Purpose: 36128 Compute the repeatability standard deviation of a variable 36129 as defined by the ASTM E 691 - 99 standard. 36130 36131Description: 36132 The repeatability standard deviation is a core concept 36133 defined in the ASTM E 691 - 99 standard. This standard 36134 is described in detail in the following document: 36135 36136 "Standard Practice for Conducting an Interlaboratory Study 36137 to Determine the Precision of a Test Method", ASTM 36138 International, 100 Barr Harbor Drive, PO BOX C700, 36139 West Conshohoceken, PA 19428-2959, USA. 36140 36141 This document describes repeatability in the following way. 36142 36143 Repeatability concerns the variability between independent 36144 test results obtained within a single laboratory in the 36145 shortest practical period of time by a single operator with 36146 a specific set of test apparatus using test specimens taken 36147 at random from a single quantity of homogeneous material. 36148 36149 The repeatability standard deviation is computed as 36150 36151 Sr = SQRT(SUM[i=1 to p][s(i)**2/p] 36152 36153 with 36154 36155 p = number of labs 36156 s(i) = Standard deviation of group i. 36157 36158 In an interlaboratory study, the repeatability standard 36159 deviation is computed for each material. 36160 36161Syntax: 36162 LET <par> = REPEATABILITY STANDARD DEVIATION <y> <labid> 36163 <SUBSET/EXCEPT/FOR qualification> 36164 where <y> is a response variable; 36165 <labid> is a lab-id variable; 36166 <par> is a parameter where the repeatability standard 36167 deviation value is saved; 36168 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 36169 36170Examples: 36171 LET RSD = REPEATABILITY STANDARD DEVIATION Y LAB 36172 LET RSD = REPEATABILITY STANDARD DEVIATION Y LAB SUBSET MAT = 1 36173 36174Note: 36175 The repeatability standard deviation can be computed for 36176 multiple materials with the command 36177 36178 TABULATE REPEATABILITY STANDARD DEVIATION Y LABID MATID 36179 36180 The repeatability standard deviation can be plotted for 36181 multiple materials with the command 36182 36183 REPEATABILITY STANDARD DEVIATION PLOT Y LABID MATID 36184 36185Default: 36186 None 36187 36188Synonyms: 36189 REPEATABILITY SD 36190 36191Related Commands: 36192 E691 INTERLAB = Perform an E691 interlab 36193 analysis. 36194 REPRODUCIBILITY STANDARD DEVIATION = Compute the reproducibility 36195 standard deviation. 36196 36197Reference: 36198 "Standard Practice for Conducting an Interlaboratory Study 36199 to Determine the Precision of a Test Method", ASTM 36200 International, 100 Barr Harbor Drive, PO BOX C700, 36201 West Conshohoceken, PA 19428-2959, USA. 36202 36203Applications: 36204 Interlaboratory Analysis 36205 36206Implementation Date: 36207 2005/4 36208 36209Program: 36210 SKIP 25 36211 READ GLUCOSE.DAT Y LABID MATID 36212 . 36213 LET MATDIST = DISTINCT MATID 36214 LET NMAT = SIZE MATDIST 36215 XLIMITS 1 NMAT 36216 MAJOR XTIC MARK NUMBER NMAT 36217 MINOR XTIC MARK NUMBER 0 36218 XTIC OFFSET 0.5 0.5 36219 Y1LABEL REPEATABILITY SD 36220 X1LABEL MATERIAL 36221 LINE BLANK 36222 CHARACTER X 36223 . 36224 REPEATABILITY SD PLOT Y LABID MATID 36225 36226-----RES------------------------------------------------------- 36227 36228RES 36229 36230Name: 36231 RES 36232 36233Type: 36234 Keyword 36235 36236Purpose: 36237 An internal DATAPLOT variable into which the residuals are 36238 automatically placed whenever the FIT, PRE-FIT, SPLINE FIT, LOWESS, 36239 YATES ANALYSIS, SMOOTH, ANOVA, and MEDIAN POLISH commands are 36240 executed. 36241 36242Description: 36243 In general, the residuals are defined as 36244 raw data - predicted values 36245 where the predicted values are the "fitted values" from fitting, 36246 pre-fitting, spline fitting, smoothing, ANOVA, locally weighted 36247 least squares fitting, Yates analysis, and median polish. RES can 36248 be used by the analyst in whatever fashion desired. Residuals are 36249 extremely important because they serve as the base for testing 36250 model adequacy via the battery of techniques known as residual 36251 analysis. Typical operations with these residuals include: 36252 1) plotting the residuals versus any independent variable to check 36253 for latent relationships (e.g., PLOT RES X); 36254 2) generating a lag plot of the residuals to check for 36255 autocorrelation (e.g., LAG PLOT RES); 36256 3) generating a histogram of the residuals to check for general 36257 distributional structure (e.g., HISTOGRAM RES); 36258 4) generating a normal probability plot of the residuals to check 36259 for normality (e.g., NORMAL PROBABILITY PLOT RES). 36260 36261Syntax: 36262 None 36263 36264Examples: 36265 WRITE X Y PRED RES 36266 PLOT RES X 36267 LET RES2=ABS(RES) 36268 36269Default: 36270 None 36271 36272Synonyms: 36273 None 36274 36275Related Commands: 36276 PRED = A variable where predicted values are stored. 36277 RESSD = A parameter where the residual standard 36278 deviation is stored. 36279 RESDF = A parameter where the residual degrees of 36280 freedom is stored. 36281 REPSD = A parameter where the replication standard 36282 deviation is stored. 36283 REPDF = A parameter where the replication degrees of 36284 freedom is stored. 36285 LOFCDF = A parameter where the lack of fit cdf is 36286 stored. 36287 FIT = Carries out a least squares linear or 36288 non-linear fit. 36289 EXACT RATIONAL FIT = Carries out an exact rational fit. 36290 PRE-FIT = Carries out a least squares pre-fit. 36291 SPLINE FIT = Carries out a spline fit. 36292 YATES ANALYSIS = Carries out an analysis of a Yates design. 36293 LOWESS = Carries out a locally weighted least squares 36294 fit. 36295 SMOOTH = Carries out a smoothing. 36296 ANOVA = Carries out an ANOVA. 36297 MEDIAN POLISH = Carries out a median polish. 36298 PLOT = Generates a data/function plot. 36299 36300Applications: 36301 Fitting 36302 36303Implementation Date: 36304 Pre-1987 36305 36306Program: 36307 SKIP 25 36308 READ BERGER.DAT Y X 36309 FIT Y X 36310 4-PLOT RES 36311 36312-----RESCALED SUM (LET)----------------------------------------- 36313 36314RESCALED SUM 36315 36316Name: 36317 RESCALED SUM (LET) 36318 36319Type: 36320 Let Subcommand 36321 36322Purpose: 36323 Compute the rescaled sum of a variable. 36324 36325Description: 36326 The rescaled sum has the formula: 36327 36328 RS = SUM[i=1 to N][X(i)]/SQRT(N) 36329 36330 with N denoting the number of observations. This statistic has 36331 application in the ISO 13528 proficiency testing. 36332 36333Syntax 1: 36334 LET <par> = RESCALED SUM <y> <SUBSET/EXCEPT/FOR qualification> 36335 where <y> is the response variable; 36336 <par> is a parameter where the computed rescaled sum is saved; 36337 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 36338 36339Syntax 2: 36340 LET <par> = DIFFERENCE OF RESCALED SUM <y1> <y2> 36341 <SUBSET/EXCEPT/FOR qualification> 36342 where <y1> is the first response variable; 36343 <y2> is the second response variable; 36344 <par> is a parameter where the computed difference of 36345 the rescaled sums is saved; 36346 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 36347 36348 This syntax computes the recaled sum of <y1> and <y2> and then 36349 computes the difference of the two sums. 36350 36351Examples: 36352 LET A = RESCALED SUM Y1 36353 LET A = RESCALED SUM Y1 SUBSET TAG > 2 36354 LET A = DIFFERENCE OF RESCALED SUM Y1 Y2 36355 36356Note: 36357 The rescaled sum is sometimes used in the context of ISO 13528 36358 proficiency studies for the case where there are multiple rounds 36359 of the proficiency study. Specifcally, the following two plots 36360 are sometimes generated 36361 36362 1) A plot of the rescaled sum versus the laboratory where the 36363 summation is over all rounds and all materials for a given 36364 laboratory. Laboratories with an absolute value greater than 36365 2 are of possible concern (i.e., warning) and those with an 36366 absolute value greater than 3 are of concern (i.e., action 36367 signal). The advantage of this statistic is that it has the 36368 same interpretation as the z-scores. The disadvantage is that 36369 large magnitude z-scores of opposite sign can cancel each other. 36370 36371 2) A plot of the relative laboratory performance (RLP) versus the 36372 rescaled sum for all laboratories. A box is formed for 36373 the rescaled sum between -2 and 2 and for RLP between 0 and 1.5. 36374 Laboratories outside this box are identified as needing 36375 attention. 36376 36377Note: 36378 In some applications it may be desired to cap the value 36379 of outliers. This is most common when the response variable 36380 is a z-score or some other standardized score. 36381 36382 To specify this value, enter the command 36383 36384 LET CAPVALUE = <value> 36385 36386 where <value> is typically 3 or 4 (if the reponse data are 36387 z-scores or z-score type data). Note that the value represents 36388 an absolute value. For example, if CAPVALUE is 4, values greater 36389 than 4 will be set to 4 and values less than -4 will be set to -4. 36390 36391Note: 36392 Dataplot statistics can be used in a number of commands. For 36393 details, enter 36394 36395 HELP STATISTICS 36396 36397Default: 36398 None 36399 36400Synonyms: 36401 None 36402 36403Related Commands: 36404 MEAN = Compute the mean of a variable. 36405 STANDARD DEVIATION = Compute the standard deviation of a variable. 36406 SUM OF SQUARES = Compute the sum of squares of a variable. 36407 ROOT MEAN SQUARE = Compute the root mean square error of a 36408 variable. 36409 36410Applications: 36411 ISO 13528 Proficiency Testing 36412 36413Implementation Date: 36414 2012/2 36415 2012/6: Added DIFFERENCE OF RESCALED SUM 36416 36417Program 1: 36418 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 36419 LET RSUM = RESCALED SUM Y1 36420 36421Program 2: 36422 SKIP 25 36423 READ GEAR.DAT Y X 36424 LET Y = ZSCORE Y 36425 . 36426 CHARACTER X BLANK 36427 LINE BLANK SOLID 36428 TIC MARK OFFSET UNITS DATA 36429 X1TIC MARK OFFSET 0.5 0.5 36430 . 36431 LABEL CASE ASIS 36432 Y1LABEL Rescaled Sum 36433 X1LABEL Batch 36434 RESCALED SUM PLOT Y X 36435 36436-----RESDF------------------------------------------------------- 36437 36438RESDF 36439 36440Name: 36441 RESDF 36442 36443Type: 36444 Keyword 36445 36446Purpose: 36447 An internal DATAPLOT parameter into which the residual degrees of 36448 freedom is automatically placed whenever the FIT, PRE-FIT, SPLINE 36449 FIT, SMOOTH, ANOVA, YATES ANALYSIS, LOWESS, and MEDIAN POLISH 36450 commands are executed. 36451 36452Description: 36453 In general, the formula is: 36454 RESDF = total number of observations - number of parameters 36455 + the number of constraints. 36456 RESDF can be used by the analyst in whatever fashion desired. 36457 36458Syntax: 36459 None 36460 36461Examples: 36462 WRITE RESDF REPSD RESDF RESSD LOGCDF 36463 LET SSQD = RESDF*(REPSD**2) 36464 WRITE CALIB. RESDF REPSD RESDF RESSD LOGCDF 36465 36466Default: 36467 None 36468 36469Synonyms: 36470 None 36471 36472Related Commands: 36473 PRED = A variable where predicted values are stored. 36474 RES = A variable where residuals are stored. 36475 RESSD = A parameter where the residual standard 36476 deviation is stored. 36477 REPSD = A parameter where the replication standard 36478 deviation is stored. 36479 REPDF = A parameter where the replication degrees of 36480 freedom is stored. 36481 LOFCDF = A parameter where the lack of fit cdf is 36482 stored. 36483 FIT = Carries out a least squares linear or 36484 non-linear fit. 36485 EXACT RATIONAL FIT = Carries out an exact rational fit. 36486 PRE-FIT = Carries out a least squares pre-fit. 36487 SPLINE FIT = Carries out a spline fit. 36488 YATES ANALYSIS = Carries out an analysis of a Yates design. 36489 LOWESS = Carries out a locally weighted least squares 36490 fit. 36491 SMOOTH = Carries out a smoothing. 36492 ANOVA = Carries out an ANOVA. 36493 MEDIAN POLISH = Carries out a median polish. 36494 PLOT = Generates a data/function plot. 36495 36496Applications: 36497 XX 36498 36499Implementation Date: 36500 XX 36501 36502Program: 36503 XX 36504 36505-----RESET------------------------------------------------------- 36506 36507RESET 36508 36509Name: 36510 RESET 36511 36512Type: 36513 Support Command 36514 36515Purpose: 36516 Resets all internal Dataplot parameters, variables, functions, and 36517 switches to default sign-on conditions. 36518 36519Description: 36520 The RESET command allows the analyst to clear all of Dataplot's 36521 internal settings so as to start afresh. 36522 36523 You can also selectively reset internal settings based on a 36524 keyword (see Syntax 2). You can also specifiy names that will 36525 not be reset for the DATA, VARIABLES, PARAMETERS, FUNCTIONS, and 36526 MATRICES options (see Syntax 3). 36527 36528Syntax 1: 36529 RESET 36530 36531 This resets all internal settings. 36532 36533Syntax 2: 36534 RESET <keyword> 36535 where <keyword is one of the following: 36536 ALL - reset all internal settings 36537 CONTROL - reset the plot control settings 36538 DATA - reset the data settings 36539 SUPPORT - resets the support settings 36540 GRAPHICS - resets the graphics settings 36541 I/O - resets the I/O settings 36542 CLSB - resets the CLSB (CHARACTER, LINE, SPIKE, BAR) 36543 settings 36544 LIMITS - resets the LIMITS settings 36545 VARIABLES - reset variable settings 36546 PARAMETERS - reset parameter settings 36547 FUNCTIONS - reset function settings 36548 MATRICES - reset matrix settings. 36549 36550Syntax 3: 36551 RESET NO RESET <name> <ON/OFF> 36552 where <name> identifies a single name; 36553 and where ON specifies the name will be added to the list and 36554 OFF specifies the name will be removed from the list. 36555 36556 Dataplot maintains a list of 1 to 30 names that will not be 36557 reset by the RESET DATA, RESET VARIABLES, RESET PARAMETERS, 36558 RESET FUNCTIONS, and RESET MATRICES commands. You can use this 36559 syntax to add or remove names from the list. The ON switch is 36560 optional for adding a name. However, the OFF switch is required to 36561 delete a name from the list. 36562 36563Syntax 4: 36564 RESET COMMAND LINE ARGUMENTS 36565 36566 This syntax can be used to clear the argument list for macros. 36567 Enter HELP MACRO SUBSTITUTION CHARACTER for details. 36568 36569Examples: 36570 RESET 36571 RESET DATA 36572 RESET LIMITS 36573 RESET VARIABLES 36574 RESET NO RESET Y 36575 36576Default: 36577 None 36578 36579Synonyms: 36580 CLEAR 36581 36582Related Commands: 36583 SAVE MEMORY = Dumps all of DATAPLOT' interal parameters, 36584 variables, functions, and switches to a file. 36585 DIMENSION = Set the number of columns and rows for 36586 DATAPLOT's work array. 36587 36588Applications: 36589 Data Management 36590 36591Implementation Date: 36592 Pre-1987 36593 1993/09: Added RESET LIMITS and RESET CLSB 36594 2015/12: For Windows, do not reset the QuickWin device 36595 2016/09: Added RESET NO RESET option 36596 2016/09: Added RESET COMMAND LINE ARGUMENTS 36597 36598Program: 36599 SKIP 25 36600 READ BERGER1.DAT Y X BATCH 36601 FIT Y X 36602 RESET VARIABLES 36603 READ LEW.DAT Y 36604 4-PLOT Y 36605 36606-----RESISTOR------------------------------------------------------- 36607 36608RESISTOR 36609 36610Name: 36611 RESISTOR 36612 36613Type: 36614 Diagrammatic Graphics Command 36615 36616Purpose: 36617 Draws a (fixed value) resistor (a component used in electronic 36618 circuit diagrams). 36619 36620Description: 36621 The 2 pairs of coordinates define the (x,y) values for the start 36622 point and the end point (respectively) of the resistor. Note that 36623 the height of the wrinkles in the resistor is controlled by the 36624 HEIGHT command. 36625 36626Syntax: 36627 RESISTOR <x1> <y1> <x2> <y2> 36628 where <x1> is a decimal number or parameter in the range 0 to 100 36629 that specifies the x coordinate of the start point; 36630 <y1> is a decimal number or parameter in the range 0 to 100 36631 that specifies the y coordinate of the start point; 36632 <x2> is a decimal number or parameter in the range 0 to 100 36633 that specifies the x coordinate of the end point; 36634 and <y2> is a decimal number or parameter in the range 0 to 100 36635 that specifies the y coordinate of the end point. 36636 36637Examples: 36638 RESISTOR 50 50 60 50 36639 RESISTOR 50 50 60 60 36640 RESISTOR 20 20 25 20 36641 RESISTOR 20 70 25 70 36642 RESISTOR 30.55 50.7 40.23 50.7 36643 RESISTOR X1 Y1 X2 Y2 36644 36645Note: 36646 The line style (i.e., solid, dash), color, and thickness are 36647 controlled by the LINE, LINE COLOR, and LINE THICKNESS commands. 36648 36649Default: 36650 None 36651 36652Synonyms: 36653 None 36654 36655Related Commands: 36656 GROUND = Draws a ground. 36657 AMPLIFIER = Draws an amplifier. 36658 CAPACITOR = Draws a capacitor. 36659 INDUCTOR = Draws an inductor. 36660 RESISTOR = Draws a resistor. 36661 DRAW = Draws a line. 36662 MOVE = Moves to a point. 36663 LINES = Sets the line type for figures and plot lines. 36664 LINE THICKNESSES = Sets the line thickness for figures and plot 36665 lines. 36666 LINE COLOR = Sets the line colors for figures and plot lines. 36667 CROSS-HAIR = Activates and reads the cross-hair. 36668 TEXT = Writes a text string. 36669 36670Applications: 36671 XX 36672 36673Implementation Date: 36674 XX 36675 36676Program: 36677 LINE SOLID 36678 LINE COLOR BLACK 36679 LINE THICKNESS 0.2 36680 RESISTOR 20 70 50 70 36681 MOVE 20 90 36682 TEXT RESISTOR COORDINATES (20,70), (50,70) 36683 36684-----RESSD------------------------------------------------------- 36685 36686RESSD 36687 36688Name: 36689 RESSD 36690 36691Type: 36692 Keyword 36693 36694Purpose: 36695 An internal DATAPLOT parameter into which the residual standard 36696 deviation is automatically placed whenever the FIT, PRE-FIT, SPLINE 36697 FIT, SMOOTH, ANOVA, LOWESS, YATES ANALYSIS, and MEDIAN POLISH 36698 commands are executed. 36699 36700Description: 36701 The residual standard deviation is a model-dependent estimate of 36702 the population standard deviation. It is a measure of the 36703 variability that remains after the model has been accounted for. 36704 It is the single most important number in the output from the above 36705 commands. RESSD can be used by the analyst in whatever fashion 36706 desired. 36707 36708Syntax: 36709 None 36710 36711Examples: 36712 WRITE RESDF RESSD RESDF RESSD LOGCDF 36713 LET SSQD = RESDF*(RESSD**2) 36714 WRITE CALIB. RESDF RESSD RESDF RESSD LOGCDF 36715 36716Default: 36717 None 36718 36719Synonyms: 36720 None 36721 36722Related Commands: 36723 PRED = A variable where predicted values are stored. 36724 RES = A variable where residuals are stored. 36725 RESDF = A parameter where the residual degrees of 36726 freedom is stored. 36727 REPSD = A parameter where the replication standard 36728 deviation is stored. 36729 REPDF = A parameter where the replication degrees of 36730 freedom is stored. 36731 LOFCDF = A parameter where the lack of fit cdf is 36732 stored. 36733 FIT = Carries out a least squares linear or 36734 non-linear fit. 36735 EXACT RATIONAL FIT = Carries out an exact rational fit. 36736 PRE-FIT = Carries out a least squares pre-fit. 36737 SPLINE FIT = Carries out a spline fit. 36738 YATES ANALYSIS = Carries out an analysis of a Yates design. 36739 LOWESS = Carries out a locally weighted least squares 36740 fit. 36741 SMOOTH = Carries out a smoothing. 36742 ANOVA = Carries out an ANOVA. 36743 MEDIAN POLISH = Carries out a median polish. 36744 PLOT = Generates a data/function plot. 36745 36746Applications: 36747 XX 36748 36749Implementation Date: 36750 XX 36751 36752Program: 36753 XX 36754 36755-------------RESTORE MEMORY------------------------------------ 36756 36757RESTORE MEMORY 36758 36759Name: 36760 RESTORE MEMORY 36761 36762Type: 36763 Support Command 36764 36765Purpose: 36766 Reloads all internal DATAPLOT parameters, variables, functions, 36767 and switches that were previously dumped to a file via the SAVE 36768 MEMORY command. 36769 36770Description: 36771 The RESTORE MEMORY command thus allows the analyst to restore all 36772 of DATAPLOT's internal settings so that a run my be resumed after 36773 being interrupted by a meeting, lunch, etc. 36774 36775Syntax: 36776 RESTORE MEMORY <file name> 36777 where <file name> is the name of a file where the internal 36778 settings were previously saved. 36779 36780 If the file name does not contain a period, place a period (no 36781 spaces) at the end of the file name. 36782 36783Examples: 36784 RESTORE MEMORY OUT. 36785 RESTORE MEMORY SCRATCH. 36786 RESTORE MEMORY TEMP. 36787 36788Note: 36789 DATAPLOT has no restrictions on the file name other than it be a 36790 valid file name on the local operating system and that it contain 36791 a period "." in the file name itself or as a trailing character. 36792 DATAPLOT strips off trailing periods on those systems where it is 36793 appropriate to do so. On systems where trailing periods can be a 36794 valid file name (e.g., Unix), DATAPLOT tries to open the file with 36795 the trailing period. If this fails, it then tries to open the file 36796 with the trailing period stripped off. 36797 36798Note: 36799 File names are case sensitive on Unix file systems. For Unix, 36800 DATAPLOT attempts to open the file as given. If this fails, it 36801 attempts to open the file as all upper case characters. If this 36802 fails, it attempts to open the file as all lower case characters. 36803 All other currently supported systems are not case sensitive 36804 regarding file names. 36805 36806 As a further caution for Unix hosts, certain expansion characters 36807 (specifically ~ to refer to your home directory) are interpreted 36808 by the shell and are not recognized by the Fortran compiler. These 36809 expansion characters are interpreted as literal characters and do 36810 not yield the intended file name. 36811 36812Default: 36813 None 36814 36815Synonyms: 36816 None 36817 36818Related Commands: 36819 SAVE MEMORY = Dump all internal DATAPLOT settings to a file. 36820 RESET = Reset internal DATAPLOT settings to their default 36821 values. 36822 36823Applications: 36824 XX 36825 36826Implementation Date: 36827 XX 36828 36829Program: 36830 XX 36831 36832-----RETAIN------------------------------------------------------- 36833 36834RETAIN 36835 36836Name: 36837 RETAIN 36838 36839Type: 36840 Support Command 36841 36842Purpose: 36843 Retains (keeps) the specified rows or subset of a variable, 36844 deletes the unspecified rows or subset, and packs the kept 36845 elements into the "top" of the variable. 36846 36847Syntax 1: 36848 RETAIN <list> <SUBSET/EXCEPT/FOR qualification> 36849 where <list> is a list of variables; 36850 and where the <SUBSET/EXCEPT/FOR qualification> is required. 36851 36852Syntax 2: 36853 RETAIN <list> 36854 where <list> is a list of elements of a variable. 36855 36856Examples: 36857 RETAIN Y SUBSET X 2 TO 4 36858 RETAIN Y1 Y2 X SUBSET X 8 TO INFINITY 36859 RETAIN X Y Z FOR I = 11 1 20 36860 RETAIN X(100) 36861 RETAIN X(2) Y(7) Z(15) 36862 RETAIN X(2) Y(2) PRED(2) RES(2) 36863 36864Default: 36865 None 36866 36867Synonyms: 36868 KEEP 36869 36870Related Commands: 36871 DELETE = Deletes rows or subsets of a variable. 36872 LET = Transforms rows or subsets of a variable (plus other 36873 capabilities). 36874 SUBSET = Allows specification of a subset. 36875 EXCEPT = Allows exclusion-specification of a subset. 36876 FOR = Allows row-specification of a subset. 36877 36878Applications: 36879 Data Manipulation 36880 36881Implementation Date: 36882 Pre-1987 36883 36884Program: 36885 SKIP 25 36886 READ AUTO83B.DAT Y1 Y2 36887 RETAIN Y2 > -998 36888 BIHISTOGRAM Y1 Y2 36889 36890-----REVERSE (LET)-------------------------------- 36891 36892REVERSE 36893 36894Name: 36895 REVERSE (LET) 36896 36897Type: 36898 Let Subcommand 36899 36900Purpose: 36901 Reverse the order of the elements in a variable. 36902 That is, if Y has N elements, Y(1) = Y(N), Y(2)=Y(N-1), ... , 36903 Y(N)=Y(1). 36904 36905Syntax: 36906 LET <y2> = REVERSE <y1> <SUBSET/EXCEPT/FOR qualification> 36907 where <y1> is a response variable; 36908 <y2> is a variable where the reversed data is stored; 36909 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 36910 36911Examples: 36912 LET Y2 = REVERSE Y 36913 LET Y2 = REVERSE Y FOR I = 1 1 30 36914 36915Default: 36916 None 36917 36918Synonyms: 36919 FLIP is a synonym for REVERSE. 36920 36921Related Commands: 36922 SORT = Sort the elements in a variable. 36923 RANK = Rank the elements in a variable. 36924 SORT DIRECTION = Specify whether sorting is done in a 36925 descending or ascending order. 36926 36927Applications: 36928 Data Manipulation 36929 36930Implementation Date: 36931 1998/5 36932 36933Program: 36934 LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 100 36935 LET Y2 = RANK Y 36936 LET Y3 = REVERSE Y2 36937 36938-----RF SPREAD PLOT-------------------------------------- 36939 36940RF SPREAD PLOT 36941 36942Name: 36943 RF SPREAD PLOT 36944 36945Type: 36946 Graphics Command 36947 36948Purpose: 36949 Generates a residuals-fitted (r-f) spread plot. 36950 36951Description: 36952 The residuals-fitted (r-f) spread plot is a graphical measure 36953 of the goodness of fit. That is, this command is preceeded 36954 by some type of fit. It plots percent point (or quantile) 36955 plots of the fitted values minus their mean and the residuals 36956 arranged side by side with a common vertical scale. 36957 36958 The vertical spread of the residuals compared to the vertical 36959 spread of the fitted values gives an indication of how much 36960 of the variation is explained by the fit. 36961 36962 Dataplot assumes that some type of fit has already been 36963 performed and that the predicted values are stored in the 36964 internal variable PRED and the residuals are stored in the 36965 internal variable RES. If you want to generate the rf 36966 spread plot for variables that are not automatically 36967 stored on PRED and RES, then simply copy the desired variables 36968 into PRED and RES before entering the RF SPREAD PLOT (e.g., 36969 LET PRED = Y). 36970 36971Syntax: 36972 RF SPREAD PLOT <SUBSET/EXCEPT/FOR qualification> 36973 where the <SUBSET/EXCEPT/FOR qualification> is optional. 36974 36975Examples: 36976 FIT Y X 36977 RF SPREAD PLOT 36978 36979 LOWESS Y X 36980 RF SPREAD PLOT 36981 36982 SPLINE FIT Y X 36983 RF SPREAD PLOT 36984 36985Default: 36986 None 36987 36988Synonyms: 36989 None 36990 36991Related Commands: 36992 LINES = Sets the type for plot lines. 36993 CHARACTER = Sets the type for plot characters. 36994 PERCENT POINT PLOT = Generates a percent point plot. 36995 PLOT = Generates a data or function plot. 36996 36997References: 36998 "Visualizing Data", Cleveland, William S., Hobart Press, 1993. 36999 37000Applications: 37001 Exploratory Data Analysis 37002 37003Implementation Date: 37004 2000/1 37005 37006Program: 37007 SKIP 25 37008 READ BERGER1.DAT Y X 37009 FIT Y X 37010 CHARACTER CIRCLE 37011 LINE BLANK 37012 RF SPREAD PLOT 37013 37014-----RGTCDF (LET)-------------------------------- 37015 37016RGTCDF 37017 37018Name: 37019 RGTCDF (LET) 37020 37021Type: 37022 Library Function 37023 37024Purpose: 37025 Compute the reflected generalized Topp and Leone cumulative 37026 distribution function with shape parameters alpha and beta. 37027 37028Description: 37029 The reflected generalized Topp and Leone distribution has 37030 the following cumulative distribution function: 37031 37032 F(x;alpha,beta,a,b) = 1 - 37033 ((b - x)/(b-a))**beta* 37034 {alpha - (alpha-1)*((b-x)/(b-a))}**beta 37035 a <= x <= b, beta > 0, 0 < alpha <= 2 37036 37037 with alpha and beta denoting the shape parameters and 37038 a and b the lower and upper limits, respectively. 37039 37040 The case where a = 0 and b = 1 is referred to as the 37041 standard reflected generalized Topp and Leone distribution. 37042 37043 The lower and upper limits are related to the location 37044 and scale parameters as follows: 37045 37046 location = a 37047 scale = b - a 37048 37049 Kotz and van Dorp have proposed this distribution as an 37050 alternative to the beta distribution. It is distinguished 37051 from the beta distribution in that it can have positive 37052 density at the lower limit with a strict positive mode. 37053 37054Syntax: 37055 LET <y> = RGTCDF(<x>,<alpha>,<beta>,<a>,<b>) 37056 <SUBSET/EXCEPT/FOR qualification> 37057 where <x> is a number, parameter, or variable containing 37058 values in the interval (a,b); 37059 <y> is a variable or a parameter (depending on what 37060 <x> is) where the computed reflected generalized 37061 topp and leone cdf value is stored; 37062 <alpha> is a number, parameter, or variable in the 37063 interval (0, 2) that specifies the first shape 37064 parameter; 37065 <beta> is a positive number, parameter, or variable that 37066 specifies the second shape parameter; 37067 <a> is a number, parameter, or variable that 37068 specifies the lower limit; 37069 <b> is a number, parameter, or variable that 37070 specifies the upper limit; 37071 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 37072 37073 If <a> and <b> are omitted, they default to 0 and 1, 37074 respectively. 37075 37076Examples: 37077 LET A = RGTCDF(0.3,0.2,1.2) 37078 LET Y = RGTCDF(X,0.5,2) 37079 PLOT RGTCDF(X,2,3) FOR X = 0 0.01 1 37080 37081Note: 37082 Library functions are distinguished from let subcommands 37083 in the following ways. 37084 1) Functions enclose the input value in parenthesis. Let 37085 subcommands use spaces. 37086 2) Functions can accept (and return) either parameters 37087 (i.e., single values) or variables (i.e., an array of 37088 values) while let subcommands are specific in which they 37089 accept as input and what they return as output. 37090 3) Functions can accept expressions while let subcommands 37091 do not. For example, the following is legal: 37092 LET Y2 = ABS(Y1-INT(Y1)) 37093 For let subcommands, you typically have to do something 37094 like the following: 37095 LET YTEMP = Y**2 + 8 37096 LET A = SUM YTEMP 37097 37098Default: 37099 None 37100 37101Synonyms: 37102 None 37103 37104Related Commands: 37105 RGTPDF = Compute the reflected generalized Topp and Leone 37106 probability density function. 37107 RGTPPF = Compute the reflected generalized Topp and Leone 37108 percent point function. 37109 GTLCDF = Compute the generalized Topp and Leone probability 37110 density function. 37111 TOPPDF = Compute the Topp and Leone probability density 37112 function. 37113 TSPPDF = Compute the two-sided power probability density 37114 function. 37115 BETPDF = Compute the beta probability density function. 37116 TRIPDF = Compute the triangular probability density function. 37117 TRAPDF = Compute the trapezoid probability density function. 37118 UNIPDF = Compute the uniform probability density function. 37119 POWPDF = Compute the power probability density function. 37120 JSBPDF = Compute the Johnson SB probability density function. 37121 37122Reference: 37123 Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Beta: 37124 Other Continuous Families of Distributions with Bounded 37125 Support and Applications", World Scientific, chapter 7. 37126 37127Applications: 37128 Distributional Modeling 37129 37130Implementation Date: 37131 2007/2 37132 37133Program: 37134 LABEL CASE ASIS 37135 TITLE CASE ASIS 37136 TITLE OFFSET 2 37137 . 37138 MULTIPLOT 3 3 37139 MULTIPLOT CORNER COORDINATES 0 0 100 95 37140 MULTIPLOT SCALE FACTOR 3 37141 . 37142 LET ALPHA = 2 37143 LET BETA = 3 37144 TITLE Alpha = ^alpha, Beta = ^beta 37145 PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37146 . 37147 LET ALPHA = 1.5 37148 LET BETA = 6 37149 TITLE Alpha = ^alpha, Beta = ^beta 37150 PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37151 . 37152 LET ALPHA = 1.5 37153 LET BETA = 2 37154 TITLE Alpha = ^alpha, Beta = ^beta 37155 PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37156 . 37157 LET ALPHA = 1.5 37158 LET BETA = 1 37159 TITLE Alpha = ^alpha, Beta = ^beta 37160 PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37161 . 37162 LET ALPHA = 0.5 37163 LET BETA = 2 37164 TITLE Alpha = ^alpha, Beta = ^beta 37165 PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37166 . 37167 LET ALPHA = 0.5 37168 LET BETA = 1 37169 TITLE Alpha = ^alpha, Beta = ^beta 37170 PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37171 . 37172 LET ALPHA = 0.5 37173 LET BETA = 0.75 37174 TITLE Alpha = ^alpha, Beta = ^beta 37175 PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37176 . 37177 LET ALPHA = 0.5 37178 LET BETA = 0.25 37179 TITLE Alpha = ^alpha, Beta = ^beta 37180 PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37181 . 37182 LET ALPHA = 1 37183 LET BETA = 1 37184 TITLE Alpha = ^alpha, Beta = ^beta 37185 PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37186 . 37187 END OF MULTIPLOT 37188 . 37189 JUSTIFICATION CENTER 37190 MOVE 50 97 37191 TEXT Reflected Generalized Topp and Leone CDF Functions 37192 37193-----RGTPDF (LET)-------------------------------- 37194 37195RGTPDF 37196 37197Name: 37198 RGTPDF (LET) 37199 37200Type: 37201 Library Function 37202 37203Purpose: 37204 Compute the reflected generalized Topp and Leone probability 37205 density function with shape parameters alpha and beta. 37206 37207Description: 37208 The reflected generalized Topp and Leone distribution has 37209 the following probability density function: 37210 37211 f(x;alpha,beta,a,b) = (beta/(b-a))* 37212 ((b-x)/(b-a))**(beta-1)* 37213 {alpha - (alpha-1)*((b-x)/(b-a))}**(beta-1)* 37214 {alpha - 2*(alpha-1)*((b-x)/(b-a))} 37215 a <= x <= b, beta > 0, 0 < alpha <= 2 37216 37217 with alpha and beta denoting the shape parameters and 37218 a and b the lower and upper limits, respectively. 37219 37220 The case where a = 0 and b = 1 is referred to as the 37221 standard reflected generalized Topp and Leone distribution. 37222 37223 The lower and upper limits are related to the location 37224 and scale parameters as follows: 37225 37226 location = a 37227 scale = b - a 37228 37229 Kotz and van Dorp have proposed this distribution as an 37230 alternative to the beta distribution. It is distinguished 37231 from the beta distribution in that it can have positive 37232 density at the lower limit with a strict positive mode. 37233 37234Syntax: 37235 LET <y> = RGTPDF(<x>,<alpha>,<beta>,<a>,<b>) 37236 <SUBSET/EXCEPT/FOR qualification> 37237 where <x> is a number, parameter, or variable containing 37238 values in the interval (a,b); 37239 <y> is a variable or a parameter (depending on what 37240 <x> is) where the computed reflected generalized 37241 topp and leone pdf value is stored; 37242 <alpha> is a number, parameter, or variable in the 37243 interval (0, 2) that specifies the first shape 37244 parameter; 37245 <beta> is a positive number, parameter, or variable that 37246 specifies the second shape parameter; 37247 <a> is a number, parameter, or variable that 37248 specifies the lower limit; 37249 <b> is a number, parameter, or variable that 37250 specifies the upper limit; 37251 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 37252 37253 If <a> and <b> are omitted, they default to 0 and 1, 37254 respectively. 37255 37256Examples: 37257 LET A = RGTPDF(0.3,0.2,1.2) 37258 LET Y = RGTPDF(X,0.5,2) 37259 PLOT RGTPDF(X,2,3) FOR X = 0 0.01 1 37260 37261Note: 37262 Reflected generalized Topp and Leone random numbers, 37263 probability plots, and goodness of fit tests can be 37264 generated with the commands: 37265 37266 LET ALPHA = <value> 37267 LET BETA = <value> 37268 LET A = <value> 37269 LET B = <value> 37270 LET Y = REFLECTED GENERALIZED TOPP LEONE ... 37271 RANDOM NUMBERS FOR I = 1 1 N 37272 REFLECTED GENERALIZED TOPP LEONE PROBABILITY PLOT Y 37273 REFLECTED GENERALIZED TOPP LEONE PROBABILITY PLOT Y2 X2 37274 REFLECTED GENERALIZED TOPP LEONE PROBABILITY PLOT ... 37275 Y3 XLOW XHIGH 37276 REFLECTED GENERALIZED TOPP LEONE KOLMOGOROV SMIRNOV ... 37277 GOODNESS OF FIT Y 37278 REFLECTED GENERALIZED TOPP LEONE CHI-SQUARE ... 37279 GOODNESS OF FIT Y2 X2 37280 REFLECTED GENERALIZED TOPP LEONE CHI-SQUARE ... 37281 GOODNESS OF FIT Y3 XLOW XHIGH 37282 37283 The following commands can be used to estimate the alpha 37284 and beta shape parameters for the reflected generalized 37285 Topp and Leone distribution: 37286 37287 LET ALPHA1 = <value> 37288 LET ALPHA2 = <value> 37289 LET BETA1 = <value> 37290 LET BETA2 = <value> 37291 REFLECTED GENERALIZED TOPP LEONE PPCC PLOT Y 37292 REFLECTED GENERALIZED TOPP LEONE PPCC PLOT Y2 X2 37293 REFLECTED GENERALIZED TOPP LEONE PPCC PLOT Y3 XLOW XHIGH 37294 REFLECTED GENERALIZED TOPP LEONE KS PLOT Y 37295 REFLECTED GENERALIZED TOPP LEONE KS PLOT Y2 X2 37296 REFLECTED GENERALIZED TOPP LEONE KS PLOT Y3 XLOW XHIGH 37297 37298 The default values for ALPHA1 and ALPHA2 are 0.1 and 2. 37299 The default values for BETA1 and BETA2 are 0.5 and 10. 37300 37301 The probability plot can then be used to estimate the 37302 lower and upper limits (lower limit = PPA0, 37303 upper limit = PPA0 + PPA1). 37304 37305 The following options may be useful for these commands. 37306 37307 1) Instead of generating the ppcc plot or ks plot on 37308 the original data, we can generate them on 37309 selected percentiles of the data. For example, 37310 if we have 1,000 points, we can choose to generate 37311 the plots on 100 evenly spaced percentiles with 37312 the command 37313 37314 SET PPCC PLOT DATA POINTS 100 37315 37316 This can be used to speed up the generation of 37317 the plot for larger data sets. 37318 37319 2) For the ks plot, we can fix the location and scale. 37320 This is equivalent to assuming that the lower and 37321 upper limits are known (e.g., we could use the 37322 data minimum and maximum as the lower and upper 37323 limit values). Given that the lower and upper 37324 limits are LOWLIM and UPPLIM, enter the commands 37325 37326 LET KSLOC = LOWLIM 37327 LET KSSCALE = UPPLIM 37328 37329 The ppcc plot is invariant to location and scale, 37330 so we cannot fix the lower and upper limits. 37331 37332 Kotz and Van Dorp describe an approximate maximum likelihood 37333 method for estimating the alpha and beta parameters of the standard 37334 reflected generalized Topp and Leone distribution. It is assumed 37335 that the data are grouped into m intervals [x(i)-1,x(i)] where the 37336 ith interval has n(i) observations. The midpoint of the interval is 37337 denoted as xbar(i). For unbinned data, the intervals consist of the 37338 individual observations (and the frequency is equal to 1). The total 37339 sample size, N, is the sum of the n(i). 37340 37341 The parameter alpha is the solution to the following equation: 37342 37343 G(alpha) = {N/SUM[i=1 to m][n(i)*LOG(1/(alpha*y(i) - 37344 (alpha - 1)*y(i)**2)]) - 1}* 37345 SUM[i=1 to m][n(i)*(1 - y(i)/(alpha - (alpha - 1)*y(i))] 37346 + SUM[i=1 to m] 37347 [n(i)*(1 - 2*y(i)/(alpha - 2*(alpha - 1)*y(i))] 37348 37349 where 37350 37351 y(i) = 1 - xbar(i) 37352 37353 The maximum likelihood estimate of beta is then: 37354 37355 betahat = N/ 37356 SUM[i=1 to m][n(i)*LOG(1/(alpha*y(i)-(alpha-1)*y(i)**2))] 37357 37358 If the data lie outside the (0,1) interval, then we first apply the 37359 transformation 37360 37361 X'(i) = (X(i) - Lower Limit)/(Upper Limit - Lower Limit) 37362 37363 To generate the approximate maximum likelihood estimates for 37364 ungrouped data in Dataplot, enter the command 37365 37366 REFLECTED GENERALIZED TOPP AND LEONE MLE Y 37367 37368 For grouped data, enter one of the following commands 37369 37370 REFLECTED GENERALIZED TOPP AND LEONE MLE Y X 37371 REFLECTED GENERALIZED TOPP AND LEONE MLE Y XLOW XHIGH 37372 37373 In the first case, X denotes the mid-points of the bins and Y 37374 denotes the corresponding frequency. In the second case, 37375 XLOW denotes the lower end-points of the bins and XHIGH denotes 37376 the upper end-points of the bins. 37377 37378 If the lower and upper limits are fixed and known, you 37379 can enter the following commands: 37380 37381 LET LOWLIMIT = <value> 37382 LET UPPLIMIT = <value> 37383 37384 For the unknown case, the minimum and maximum of the data 37385 will be used (an epsilon value will be subtracted/added 37386 to the minimum/maximum). Alternatively, you can use 37387 the estimates of the lower/upper limits generated by 37388 either the PPCC plot method or the KS plot methods and 37389 specify the LOWLIMIT and UPPLIMIT as above. 37390 37391 To specify starting values for alpha and beta, enter 37392 the commands 37393 37394 LET ALPHASV = <value> 37395 LET BETASV = <value> 37396 37397 For example, the estimates obtained from the PPCC plot or the 37398 KS plot can be used as starting values for the maximum likelihood 37399 estimates. 37400 37401Note: 37402 Library functions are distinguished from let subcommands 37403 in the following ways. 37404 1) Functions enclose the input value in parenthesis. Let 37405 subcommands use spaces. 37406 2) Functions can accept (and return) either parameters 37407 (i.e., single values) or variables (i.e., an array of 37408 values) while let subcommands are specific in which they 37409 accept as input and what they return as output. 37410 3) Functions can accept expressions while let subcommands 37411 do not. For example, the following is legal: 37412 LET Y2 = ABS(Y1-INT(Y1)) 37413 For let subcommands, you typically have to do something 37414 like the following: 37415 LET YTEMP = Y**2 + 8 37416 LET A = SUM YTEMP 37417 37418Default: 37419 None 37420 37421Synonyms: 37422 None 37423 37424Related Commands: 37425 RGTCDF = Compute the reflected generalized Topp and Leone 37426 cumulative distribution function. 37427 RGTPPF = Compute the reflected generalized Topp and Leone 37428 percent point function. 37429 GTLPDF = Compute the generalized Topp and Leone probability 37430 density function. 37431 TOPPDF = Compute the Topp and Leone probability density 37432 function. 37433 TSPPDF = Compute the two-sided power probability density 37434 function. 37435 BETPDF = Compute the beta probability density function. 37436 TRIPDF = Compute the triangular probability density function. 37437 TRAPDF = Compute the trapezoid probability density function. 37438 UNIPDF = Compute the uniform probability density function. 37439 POWPDF = Compute the power probability density function. 37440 JSBPDF = Compute the Johnson SB probability density function. 37441 37442Reference: 37443 Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Beta: 37444 Other Continuous Families of Distributions with Bounded 37445 Support and Applications", World Scientific, chapter 7. 37446 37447Applications: 37448 Distributional Modeling 37449 37450Implementation Date: 37451 2007/2 37452 37453Program 1: 37454 LABEL CASE ASIS 37455 TITLE CASE ASIS 37456 TITLE OFFSET 2 37457 . 37458 MULTIPLOT 3 3 37459 MULTIPLOT CORNER COORDINATES 0 0 100 95 37460 MULTIPLOT SCALE FACTOR 3 37461 . 37462 LET ALPHA = 2 37463 LET BETA = 3 37464 TITLE Alpha = ^alpha, Beta = ^beta 37465 PLOT RGTPDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37466 . 37467 LET ALPHA = 1.5 37468 LET BETA = 6 37469 TITLE Alpha = ^alpha, Beta = ^beta 37470 PLOT RGTPDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37471 . 37472 LET ALPHA = 1.5 37473 LET BETA = 2 37474 TITLE Alpha = ^alpha, Beta = ^beta 37475 PLOT RGTPDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37476 . 37477 LET ALPHA = 1.5 37478 LET BETA = 1 37479 TITLE Alpha = ^alpha, Beta = ^beta 37480 PLOT RGTPDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37481 . 37482 LET ALPHA = 0.5 37483 LET BETA = 2 37484 TITLE Alpha = ^alpha, Beta = ^beta 37485 PLOT RGTPDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37486 . 37487 LET ALPHA = 0.5 37488 LET BETA = 1 37489 TITLE Alpha = ^alpha, Beta = ^beta 37490 PLOT RGTPDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37491 . 37492 LET ALPHA = 0.5 37493 LET BETA = 0.75 37494 TITLE Alpha = ^alpha, Beta = ^beta 37495 PLOT RGTPDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37496 . 37497 LET ALPHA = 0.5 37498 LET BETA = 0.25 37499 TITLE Alpha = ^alpha, Beta = ^beta 37500 PLOT RGTPDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37501 . 37502 LET ALPHA = 1 37503 LET BETA = 1 37504 TITLE Alpha = ^alpha, Beta = ^beta 37505 PLOT RGTPDF(X,ALPHA,BETA) FOR X = 0 0.01 1 37506 . 37507 END OF MULTIPLOT 37508 37509Program 2: 37510 let alpha = 1.5 37511 let beta = 2 37512 . 37513 let y = reflected generalized topp leone rand numb for i = 1 1 200 37514 . 37515 let alphsav = alpha 37516 let betasav = beta 37517 reflected generalized topp leone ppcc plot y 37518 just center 37519 move 50 5 37520 let alpha = shape1 37521 let beta = shape2 37522 text maxppcc = ^maxppcc, Alpha = ^alpha, Beta = ^beta 37523 move 50 2 37524 text Alphasav = ^alphsav, Betasav = ^betasav 37525 . 37526 char x 37527 line blank 37528 reflected generalized topp leone prob plot y 37529 move 50 5 37530 text PPA0 = ^ppa0, PPA1 = ^ppa1 37531 move 50 2 37532 let upplim = ppa0 + ppa1 37533 text Lower Limit = ^ppa0, Upper Limit = ^upplim 37534 char blank 37535 line solid 37536 . 37537 let ksloc = ppa0 37538 let ksscale = upplim 37539 reflected generalized topp leone kolm smir goodness of fit y 37540 . 37541 bootstrap reflected generalized topp leone plot y 37542 . 37543 37544-----RGTPPF (LET)-------------------------------- 37545 37546RGTPPF 37547 37548Name: 37549 RGTPPF (LET) 37550 37551Type: 37552 Library Function 37553 37554Purpose: 37555 Compute the reflected generalized Topp and Leone percent 37556 point function with shape parameters alpha and beta. 37557 37558Description: 37559 The standard reflected generalized Topp and Leone 37560 distribution has the following percent point function: 37561 37562 G(p;alpha,beta,a,b) = 37563 1-{alpha-SQRT(alpha**2-4*(alpha-1)*(1-p)**(1/beta)}/ 37564 {2*(alpha-1)} for 1 < alpha <= 2 37565 37566 1 - (1-p)**(1/beta) for alpha = 1 37567 37568 1-{alpha+SQRT(alpha**2-4*(alpha-1)*(1-p)**(1/beta)}/ 37569 {2*(alpha-1)} for 0 < alpha < 1 37570 37571 0 <= p <= 1, beta > 0 37572 37573 with alpha and beta denoting the shape parameters. 37574 37575 The standard distribution can be generalized with 37576 lower and upper bound parameters, a and b respectively, 37577 by utilizing the following relation: 37578 37579 G(p;alpha,beta,a,b) = a + (b-a)*G(p;alpha,beta,0,1) 37580 37581 The lower and upper limits are related to the location 37582 and scale parameters as follows: 37583 37584 location = a 37585 scale = b - a 37586 37587Syntax: 37588 LET <y> = RGTPPF(<p>,<alpha>,<beta>,<a>,<b>) 37589 <SUBSET/EXCEPT/FOR qualification> 37590 where <p> is a number, parameter, or variable containing 37591 values in the interval (0,1); 37592 <y> is a variable or a parameter (depending on what 37593 <x> is) where the computed reflected generalized 37594 topp and leone ppf value is stored; 37595 <alpha> is a number, parameter, or variable in the 37596 interval (0, 2) that specifies the first shape 37597 parameter; 37598 <beta> is a positive number, parameter, or variable that 37599 specifies the second shape parameter; 37600 <a> is a number, parameter, or variable that 37601 specifies the lower limit; 37602 <b> is a number, parameter, or variable that 37603 specifies the upper limit; 37604 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 37605 37606 If <a> and <b> are omitted, they default to 0 and 1, 37607 respectively. 37608 37609Examples: 37610 LET A = RGTPPF(0.95,0.2,1.2) 37611 LET Y = RGTPPF(P,0.5,2) 37612 PLOT RGTPPF(P,2,3) FOR P = 0 0.01 1 37613 37614Note: 37615 Library functions are distinguished from let subcommands 37616 in the following ways. 37617 1) Functions enclose the input value in parenthesis. Let 37618 subcommands use spaces. 37619 2) Functions can accept (and return) either parameters 37620 (i.e., single values) or variables (i.e., an array of 37621 values) while let subcommands are specific in which they 37622 accept as input and what they return as output. 37623 3) Functions can accept expressions while let subcommands 37624 do not. For example, the following is legal: 37625 LET Y2 = ABS(Y1-INT(Y1)) 37626 For let subcommands, you typically have to do something 37627 like the following: 37628 LET YTEMP = Y**2 + 8 37629 LET A = SUM YTEMP 37630 37631Default: 37632 None 37633 37634Synonyms: 37635 None 37636 37637Related Commands: 37638 RGTCDF = Compute the reflected generalized Topp and Leone 37639 cumulative distribution function. 37640 RGTPDF = Compute the reflected generalized Topp and Leone 37641 probability density function. 37642 GTLPPF = Compute the generalized Topp and Leone probability 37643 density function. 37644 TOPPDF = Compute the Topp and Leone probability density 37645 function. 37646 TSPPDF = Compute the two-sided power probability density 37647 function. 37648 BETPDF = Compute the beta probability density function. 37649 TRIPDF = Compute the triangular probability density function. 37650 TRAPDF = Compute the trapezoid probability density function. 37651 UNIPDF = Compute the uniform probability density function. 37652 POWPDF = Compute the power probability density function. 37653 JSBPDF = Compute the Johnson SB probability density function. 37654 37655Reference: 37656 Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Beta: 37657 Other Continuous Families of Distributions with Bounded 37658 Support and Applications", World Scientific, chapter 7. 37659 37660Applications: 37661 Distributional Modeling 37662 37663Implementation Date: 37664 2007/2 37665 37666Program: 37667 LABEL CASE ASIS 37668 TITLE CASE ASIS 37669 TITLE OFFSET 2 37670 . 37671 MULTIPLOT 3 3 37672 MULTIPLOT CORNER COORDINATES 0 0 100 95 37673 MULTIPLOT SCALE FACTOR 3 37674 . 37675 LET ALPHA = 2 37676 LET BETA = 3 37677 TITLE Alpha = ^alpha, Beta = ^beta 37678 PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 37679 . 37680 LET ALPHA = 1.5 37681 LET BETA = 6 37682 TITLE Alpha = ^alpha, Beta = ^beta 37683 PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 37684 . 37685 LET ALPHA = 1.5 37686 LET BETA = 2 37687 TITLE Alpha = ^alpha, Beta = ^beta 37688 PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 37689 . 37690 LET ALPHA = 1.5 37691 LET BETA = 1 37692 TITLE Alpha = ^alpha, Beta = ^beta 37693 PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 37694 . 37695 LET ALPHA = 0.5 37696 LET BETA = 2 37697 TITLE Alpha = ^alpha, Beta = ^beta 37698 PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 37699 . 37700 LET ALPHA = 0.5 37701 LET BETA = 1 37702 TITLE Alpha = ^alpha, Beta = ^beta 37703 PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 37704 . 37705 LET ALPHA = 0.5 37706 LET BETA = 0.75 37707 TITLE Alpha = ^alpha, Beta = ^beta 37708 PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 37709 . 37710 LET ALPHA = 0.5 37711 LET BETA = 0.25 37712 TITLE Alpha = ^alpha, Beta = ^beta 37713 PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 37714 . 37715 LET ALPHA = 1 37716 LET BETA = 1 37717 TITLE Alpha = ^alpha, Beta = ^beta 37718 PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 37719 . 37720 END OF MULTIPLOT 37721 . 37722 JUSTIFICATION CENTER 37723 MOVE 50 97 37724 TEXT Reflected Generalized Topp and Leone PPF Functions 37725 37726-----RIGCDF (LET)-------------------------------- 37727 37728RIGCDF 37729 37730Name: 37731 RIGCDF (LET) 37732 37733Type: 37734 Library Function 37735 37736Purpose: 37737 Compute the reciprocal inverse Gaussian cumulative distribution 37738 function with shape parameters gamma and mu. 37739 37740Description: 37741 The reciprocal inverse Gaussian distribution is the distribution 37742 of (1/X) when X has an inverse Gaussian distribution. It has 37743 the following cumulative distribution function: 37744 37745 F(x;gamma,mu) = NORCDF[-(1/(mu*x) - 1)*SQRT(gamma*x)] - 37746 EXP(2/gamma**2)* 37747 NORCDF[-(1/(mu*x) - 1)*SQRT(gamma*x)] 37748 x >= 0; gamma, mu > 0 37749 37750 with gamma and mu denoting the shape parameters and NORCDF denoting 37751 the cumulative distribution function of the standard normal 37752 distribution. 37753 37754 The reciprocal inverse Gaussian distribution can be computed 37755 in terms of the inverse Gaussian distribution by 37756 37757 RIGCDF(x;gamma,mu) = IGCDF((1/x);gamma,mu)/(x**2) 37758 37759 The reciprocal inverse Gaussian distribution can be generalized 37760 with location and scale parameters in the usual way. 37761 37762Syntax: 37763 LET <y> = RIGCDF(<x>,<gamma>,<mu>,<loc>,<scale>) 37764 <SUBSET/EXCEPT/FOR qualification> 37765 where <x> is a variable or a parameter; 37766 <gamma> is number or parameter that specifies the first 37767 shape parameter; 37768 <mu> is number or parameter that specifies the second 37769 shape parameter; 37770 <loc> is number or parameter that specifies the location 37771 parameter; 37772 <scale> is number or parameter that specifies the scale 37773 parameter; 37774 <y> is a variable or a parameter (depending on what <x> is) 37775 where the computed reciprocal inverse Gaussian cdf 37776 value is stored; 37777 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 37778 37779 Note that the location and scale parameters are optional. 37780 37781Examples: 37782 LET A = RIGCDF(3,2,1) 37783 LET A = RIGCDF(A1,2,1) 37784 LET X2 = RIGCDF(X1,2,3) 37785 PLOT RIGCDF(X,2,1.5) FOR X = 0.1 0.1 5 37786 37787Note: 37788 Library functions are distinguished from let subcommands 37789 in the following ways. 37790 1) Functions enclose the input value in parenthesis. Let 37791 subcommands use spaces. 37792 2) Functions can accept (and return) either parameters 37793 (i.e., single values) or variables (i.e., an array of 37794 values) while let subcommands are specific in which they 37795 accept as input and what they return as output. 37796 3) Functions can accept expressions while let subcommands 37797 do not. For example, the following is legal: 37798 LET Y2 = ABS(Y1-INT(Y1)) 37799 For let subcommands, you typically have to do something 37800 like the following: 37801 LET YTEMP = Y**2 + 8 37802 LET A = SUM YTEMP 37803 37804Default: 37805 None 37806 37807Synonyms: 37808 None 37809 37810Related Commands: 37811 RIGPDF = Compute the reciprocal inverse Gaussian probability 37812 density function. 37813 RIGCHAZ = Compute the reciprocal inverse Gaussian cumulative 37814 hazard function. 37815 RIGHAZ = Compute the reciprocal inverse Gaussian hazard 37816 function. 37817 RIGPPF = Compute the reciprocal inverse Gaussian percent point 37818 function. 37819 IGPDF = Compute the reciprocal inverse Gaussian probability 37820 density function. 37821 CHSPDF = Compute the chi-square probability density function. 37822 FPDF = Compute the F probability density function. 37823 NORPDF = Compute the normal probability density function. 37824 TPDF = Compute the t probability density function. 37825 WEIPDF = Compute the Weibull probability density function. 37826 WALPDF = Compute the Wald probability density function. 37827 FLPDF = Compute the fatigue life probability density function. 37828 37829Reference: 37830 "Continuous Univariate Distributions--Volume 1", Second Edition, 37831 Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 15. 37832 37833 "Statistical Distributions", Third Edition, Evans, Hastings, 37834 and Peacock, Wiley, 2000, pp. 114-116. 37835 37836Applications: 37837 Distributional Modeling 37838 37839Implementation Date: 37840 1990/5: Original implementation 37841 2003/12: Modified to treat mu as a shape parameter instead of 37842 a location parameter 37843 37844Program: 37845 Y1LABEL Probability 37846 X1LABEL X 37847 LABEL CASE ASIS 37848 X1LABEL DISPLACEMENT 12 37849 Y1LABEL DISPLACEMENT 12 37850 MULTIPLOT SCALE FACTOR 2 37851 MULTIPLOT 2 2 37852 MULTIPLOT CORNER COORDINATES 0 0 100 95 37853 TITLE GAMMA = 2, MU = 1 37854 PLOT RIGCDF(X,2,1) FOR X = 0.01 0.01 5 37855 TITLE GAMMA = 5, MU = 1 37856 PLOT RIGCDF(X,5,1) FOR X = 0.01 0.01 5 37857 TITLE GAMMA = 2, MU = 2 37858 PLOT RIGCDF(X,2,2) FOR X = 0.01 0.01 5 37859 TITLE GAMMA = 5, MU = 2 37860 PLOT RIGCDF(X,5,2) FOR X = 0.01 0.01 5 37861 END OF MULTIPLOT 37862 JUSTIFICATION CENTER 37863 MOVE 50 97 37864 CASE ASIS 37865 TEXT Reciprocal Inverse Gaussian CDF 37866 37867-----RIGCHAZ (LET)-------------------------------- 37868 37869RIGCHAZ 37870 37871Name: 37872 RIGCHAZ (LET) 37873 37874Type: 37875 Library Function 37876 37877Purpose: 37878 Compute the reciprocal inverse Gaussian cumulative hazard 37879 function with shape parameters gamma and mu. 37880 37881Description: 37882 The reciprocal inverse Gaussian distribution is the distribution 37883 of (1/X) when X has an inverse Gaussian distribution. It has 37884 the following cumulative hazard function: 37885 37886 H(x;gamma,mu) = -LOG[1 - RIGCDF(x;gamma,mu)] 37887 x >= 0; gamma, mu > 0 37888 37889 with gamma and mu denoting the shape parameters and RIGCDF 37890 denoting the reciprocal inverse Gaussian cumulative 37891 distribution function. 37892 37893 The reciprocal inverse Gaussian distribution can be generalized 37894 with location and scale parameters in the usual way. 37895 37896Syntax: 37897 LET <y> = RIGCHAZ(<x>,<gamma>,<mu>,<loc>,<scale>) 37898 <SUBSET/EXCEPT/FOR qualification> 37899 where <x> is a variable or a parameter; 37900 <gamma> is number or parameter that specifies the first 37901 shape parameter; 37902 <mu> is number or parameter that specifies the second 37903 shape parameter; 37904 <loc> is number or parameter that specifies the location 37905 parameter; 37906 <scale> is number or parameter that specifies the scale 37907 parameter; 37908 <y> is a variable or a parameter (depending on what <x> is) 37909 where the computed reciprocal inverse Gaussian 37910 cumulative hazard value is stored; 37911 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 37912 37913 Note that the location and scale parameters are optional. 37914 37915Examples: 37916 LET A = RIGCHAZ(3,2,1) 37917 LET A = RIGCHAZ(A1,2,1) 37918 LET X2 = RIGCHAZ(X1,2,3) 37919 PLOT RIGCHAZ(X,2,1.5) FOR X = 0.1 0.1 5 37920 37921Note: 37922 Library functions are distinguished from let subcommands 37923 in the following ways. 37924 1) Functions enclose the input value in parenthesis. Let 37925 subcommands use spaces. 37926 2) Functions can accept (and return) either parameters 37927 (i.e., single values) or variables (i.e., an array of 37928 values) while let subcommands are specific in which they 37929 accept as input and what they return as output. 37930 3) Functions can accept expressions while let subcommands 37931 do not. For example, the following is legal: 37932 LET Y2 = ABS(Y1-INT(Y1)) 37933 For let subcommands, you typically have to do something 37934 like the following: 37935 LET YTEMP = Y**2 + 8 37936 LET A = SUM YTEMP 37937 37938Default: 37939 None 37940 37941Synonyms: 37942 None 37943 37944Related Commands: 37945 RIGCDF = Compute the reciprocal inverse Gaussian cumulative 37946 distribution function. 37947 RIGHAZ = Compute the reciprocal inverse Gaussian hazard 37948 function. 37949 RIGPDF = Compute the reciprocal inverse Gaussian probability 37950 density function. 37951 RIGPPF = Compute the reciprocal inverse Gaussian percent point 37952 function. 37953 IGPDF = Compute the reciprocal inverse Gaussian probability 37954 density function. 37955 CHSPDF = Compute the chi-square probability density function. 37956 FPDF = Compute the F probability density function. 37957 NORPDF = Compute the normal probability density function. 37958 TPDF = Compute the t probability density function. 37959 WEIPDF = Compute the Weibull probability density function. 37960 WALPDF = Compute the Wald probability density function. 37961 FLPDF = Compute the fatigue life probability density function. 37962 37963Reference: 37964 "Continuous Univariate Distributions--Volume 1", Second Edition, 37965 Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 15. 37966 37967 "Statistical Distributions", Third Edition, Evans, Hastings, 37968 and Peacock, Wiley, 2000, pp. 114-116. 37969 37970Applications: 37971 Distributional Modeling 37972 37973Implementation Date: 37974 1990/5: Original implementation 37975 2003/12: Modified to treat mu as a shape parameter instead of 37976 a location parameter 37977 37978Program: 37979 Y1LABEL Cumulative Hazard 37980 X1LABEL X 37981 LABEL CASE ASIS 37982 X1LABEL DISPLACEMENT 12 37983 Y1LABEL DISPLACEMENT 12 37984 MULTIPLOT SCALE FACTOR 2 37985 MULTIPLOT 2 2 37986 MULTIPLOT CORNER COORDINATES 0 0 100 95 37987 TITLE GAMMA = 2, MU = 1 37988 PLOT RIGCHAZ(X,2,1) FOR X = 0.01 0.01 5 37989 TITLE GAMMA = 5, MU = 1 37990 PLOT RIGCHAZ(X,5,1) FOR X = 0.01 0.01 5 37991 TITLE GAMMA = 2, MU = 2 37992 PLOT RIGCHAZ(X,2,2) FOR X = 0.01 0.01 5 37993 TITLE GAMMA = 5, MU = 2 37994 PLOT RIGCHAZ(X,5,2) FOR X = 0.01 0.01 5 37995 END OF MULTIPLOT 37996 JUSTIFICATION CENTER 37997 MOVE 50 97 37998 CASE ASIS 37999 TEXT Reciprocal Inverse Gaussian Cumulative Hazard 38000 38001-----RIGHAZ (LET)-------------------------------- 38002 38003RIGHAZ 38004 38005Name: 38006 RIGHAZ (LET) 38007 38008Type: 38009 Library Function 38010 38011Purpose: 38012 Compute the reciprocal inverse Gaussian hazard function with 38013 shape parameters gamma and mu. 38014 38015Description: 38016 The reciprocal inverse Gaussian distribution is the distribution 38017 of (1/X) when X has an inverse Gaussian distribution. It has 38018 the following hazard function: 38019 38020 h(x;gamma,mu) = RIGPDF(x;gamma/mu)/[1 - RIGCDF(x;gamma,mu)] 38021 x >= 0; gamma, mu > 0 38022 38023 with gamma and mu denoting the shape parameters and RIGPDF and 38024 RIGCDF denoting the reciprocal inverse Gaussian probability 38025 density and cumulative distribution functions, respectively. 38026 38027 The reciprocal inverse Gaussian distribution can be generalized 38028 with location and scale parameters in the usual way. 38029 38030Syntax: 38031 LET <y> = RIGHAZ(<x>,<gamma>,<mu>,<loc>,<scale>) 38032 <SUBSET/EXCEPT/FOR qualification> 38033 where <x> is a variable or a parameter; 38034 <gamma> is number or parameter that specifies the first 38035 shape parameter; 38036 <mu> is number or parameter that specifies the second 38037 shape parameter; 38038 <loc> is number or parameter that specifies the location 38039 parameter; 38040 <scale> is number or parameter that specifies the scale 38041 parameter; 38042 <y> is a variable or a parameter (depending on what <x> is) 38043 where the computed reciprocal inverse Gaussian cdf 38044 value is stored; 38045 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 38046 38047 Note that the location and scale parameters are optional. 38048 38049Examples: 38050 LET A = RIGHAZ(3,2,1) 38051 LET A = RIGHAZ(A1,2,1) 38052 LET X2 = RIGHAZ(X1,2,3) 38053 PLOT RIGHAZ(X,2,1.5) FOR X = 0.1 0.1 5 38054 38055Note: 38056 Library functions are distinguished from let subcommands 38057 in the following ways. 38058 1) Functions enclose the input value in parenthesis. Let 38059 subcommands use spaces. 38060 2) Functions can accept (and return) either parameters 38061 (i.e., single values) or variables (i.e., an array of 38062 values) while let subcommands are specific in which they 38063 accept as input and what they return as output. 38064 3) Functions can accept expressions while let subcommands 38065 do not. For example, the following is legal: 38066 LET Y2 = ABS(Y1-INT(Y1)) 38067 For let subcommands, you typically have to do something 38068 like the following: 38069 LET YTEMP = Y**2 + 8 38070 LET A = SUM YTEMP 38071 38072Default: 38073 None 38074 38075Synonyms: 38076 None 38077 38078Related Commands: 38079 RIGPDF = Compute the reciprocal inverse Gaussian probability 38080 density function. 38081 RIGCDF = Compute the reciprocal inverse Gaussian cumulative 38082 distribution function. 38083 RIGCHAZ = Compute the reciprocal inverse Gaussian cumulative 38084 hazard function. 38085 RIGPPF = Compute the reciprocal inverse Gaussian percent point 38086 function. 38087 IGPDF = Compute the reciprocal inverse Gaussian probability 38088 density function. 38089 CHSPDF = Compute the chi-square probability density function. 38090 FPDF = Compute the F probability density function. 38091 NORPDF = Compute the normal probability density function. 38092 TPDF = Compute the t probability density function. 38093 WEIPDF = Compute the Weibull probability density function. 38094 WALPDF = Compute the Wald probability density function. 38095 FLPDF = Compute the fatigue life probability density function. 38096 38097Reference: 38098 "Continuous Univariate Distributions--Volume 1", Second Edition, 38099 Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 15. 38100 38101 "Statistical Distributions", Third Edition, Evans, Hastings, 38102 and Peacock, Wiley, 2000, pp. 114-116. 38103 38104Applications: 38105 Distributional Modeling 38106 38107Implementation Date: 38108 1990/5: Original implementation 38109 2003/12: Modified to treat mu as a shape parameter instead of 38110 a location parameter 38111 38112Program: 38113 Y1LABEL Hazard 38114 X1LABEL X 38115 LABEL CASE ASIS 38116 X1LABEL DISPLACEMENT 12 38117 Y1LABEL DISPLACEMENT 12 38118 MULTIPLOT SCALE FACTOR 2 38119 MULTIPLOT 2 2 38120 MULTIPLOT CORNER COORDINATES 0 0 100 95 38121 TITLE GAMMA = 2, MU = 1 38122 PLOT RIGHAZ(X,2,1) FOR X = 0.01 0.01 5 38123 TITLE GAMMA = 5, MU = 1 38124 PLOT RIGHAZ(X,5,1) FOR X = 0.01 0.01 5 38125 TITLE GAMMA = 2, MU = 2 38126 PLOT RIGHAZ(X,2,2) FOR X = 0.01 0.01 5 38127 TITLE GAMMA = 5, MU = 2 38128 PLOT RIGHAZ(X,5,2) FOR X = 0.01 0.01 5 38129 END OF MULTIPLOT 38130 JUSTIFICATION CENTER 38131 MOVE 50 97 38132 CASE ASIS 38133 TEXT Reciprocal Inverse Gaussian Hazard 38134 38135-----RIGPDF (LET)-------------------------------- 38136 38137RIGPDF 38138 38139Name: 38140 RIGPDF (LET) 38141 38142Type: 38143 Library Function 38144 38145Purpose: 38146 Compute the reciprocal inverse Gaussian probability density 38147 function with shape parameters gamma and mu. 38148 38149Description: 38150 The reciprocal inverse Gaussian distribution is the distribution 38151 of (1/X) when X has an inverse Gaussian distribution. It has 38152 the following probability density function: 38153 38154 f(x;gamma,mu) = SQRT(gamma/(2*PI*x))* 38155 EXP(-gamma*(1-mu*x)**2/(2*mu**2*x)) 38156 x >= 0; gamma, mu > 0 38157 38158 with gamma and mu denoting the shape parameters. 38159 38160 The reciprocal inverse Gaussian distribution can be computed 38161 in terms of the inverse Gaussian distribution by 38162 38163 RIGPDF(x;gamma,mu) = IGPDF((1/x);gamma,mu)/(x**2) 38164 38165 The reciprocal inverse Gaussian distribution has mean 38166 (gamma + mu)/(gamma*mu) and standard deviation 38167 SQRT((gamma + 2*mu)/(gamma**2*mu)). 38168 38169 The reciprocal inverse Gaussian distribution can be generalized 38170 with location and scale parameters in the usual way. 38171 38172 The reciprocal inverse Gaussian distribution is also known as 38173 the random walk distribution. 38174 38175Syntax: 38176 LET <y> = RIGPDF(<x>,<gamma>,<mu>,<loc>,<scale>) 38177 <SUBSET/EXCEPT/FOR qualification> 38178 where <x> is a variable or a parameter; 38179 <gamma> is number or parameter that specifies the first 38180 shape parameter; 38181 <mu> is number or parameter that specifies the second 38182 shape parameter; 38183 <loc> is number or parameter that specifies the location 38184 parameter; 38185 <scale> is number or parameter that specifies the scale 38186 parameter; 38187 <y> is a variable or a parameter (depending on what <x> is) 38188 where the computed reciprocal inverse Gaussian pdf 38189 value is stored; 38190 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 38191 38192 Note that the location and scale parameters are optional. 38193 38194Examples: 38195 LET A = RIGPDF(3,2,1) 38196 LET A = RIGPDF(A1,2,1) 38197 LET X2 = RIGPDF(X1,2,3) 38198 PLOT RIGPDF(X,2,1.5) FOR X = 0.1 0.1 5 38199 38200Note: 38201 Random numbers, probability plots, and Kolmogorov-Smirnov and 38202 chi-square goodness of fit tests can be generated with the 38203 commands: 38204 38205 LET GAMMA = <value> 38206 LET MU = <value> 38207 LET Y = RECIPROCAL INVERSE GAUSSIAN RANDOM NUMBERS FOR I = 1 1 N 38208 RECIPROCAL INVERSE GAUSSIAN PROBABILITY PLOT Y 38209 RECIPROCAL INVERSE GAUSSIAN KOLMOGOROV-SMIRNOV GOODNESS OF FIT Y 38210 RECIPROCAL INVERSE GAUSSIAN CHI-SQUARE FIT Y 38211 38212 The following commands can be used to generate estimates for the 38213 shape parameters of the reciprocal inverse Gaussian distribution: 38214 38215 LET GAMMA1 = <value> 38216 LET GAMMA2 = <value> 38217 LET MU1 = <value> 38218 LET MU2 = <value> 38219 RECIPROCAL INVERSE GAUSSIAN PPCC PLOT Y 38220 RECIPROCAL INVERSE GAUSSIAN KS PLOT Y 38221 38222 The default values for GAMMA1 and GAMMA2 are 0.5 and 25. The 38223 default values for MU1 and MU2 are 0.5 and 25. 38224 38225Note: 38226 Library functions are distinguished from let subcommands 38227 in the following ways. 38228 1) Functions enclose the input value in parenthesis. Let 38229 subcommands use spaces. 38230 2) Functions can accept (and return) either parameters 38231 (i.e., single values) or variables (i.e., an array of 38232 values) while let subcommands are specific in which they 38233 accept as input and what they return as output. 38234 3) Functions can accept expressions while let subcommands 38235 do not. For example, the following is legal: 38236 LET Y2 = ABS(Y1-INT(Y1)) 38237 For let subcommands, you typically have to do something 38238 like the following: 38239 LET YTEMP = Y**2 + 8 38240 LET A = SUM YTEMP 38241 38242Default: 38243 None 38244 38245Synonyms: 38246 None 38247 38248Related Commands: 38249 RIGCDF = Compute the reciprocal inverse Gaussian cumulative 38250 distribution function. 38251 RIGCHAZ = Compute the reciprocal inverse Gaussian cumulative 38252 hazard function. 38253 RIGHAZ = Compute the reciprocal inverse Gaussian hazard 38254 function. 38255 RIGPPF = Compute the reciprocal inverse Gaussian percent point 38256 function. 38257 IGPDF = Compute the reciprocal inverse Gaussian probability 38258 density function. 38259 CHSPDF = Compute the chi-square probability density function. 38260 FPDF = Compute the F probability density function. 38261 NORPDF = Compute the normal probability density function. 38262 TPDF = Compute the t probability density function. 38263 WEIPDF = Compute the Weibull probability density function. 38264 WALPDF = Compute the Wald probability density function. 38265 FLPDF = Compute the fatigue life probability density function. 38266 38267Reference: 38268 "Continuous Univariate Distributions--Volume 1", Second Edition, 38269 Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 15. 38270 38271 "Statistical Distributions", Third Edition, Evans, Hastings, 38272 and Peacock, Wiley, 2000, pp. 114-116. 38273 38274Applications: 38275 Distributional Modeling 38276 38277Implementation Date: 38278 1990/5: Original implementation 38279 2003/12: Modified to treat mu as a shape parameter instead of 38280 a location parameter 38281 38282Program: 38283 Y1LABEL Probability 38284 X1LABEL X 38285 LABEL CASE ASIS 38286 X1LABEL DISPLACEMENT 12 38287 Y1LABEL DISPLACEMENT 12 38288 MULTIPLOT SCALE FACTOR 2 38289 MULTIPLOT 2 2 38290 MULTIPLOT CORNER COORDINATES 0 0 100 95 38291 TITLE GAMMA = 2, MU = 1 38292 PLOT RIGPDF(X,2,1) FOR X = 0.01 0.01 5 38293 TITLE GAMMA = 5, MU = 1 38294 PLOT RIGPDF(X,5,1) FOR X = 0.01 0.01 5 38295 TITLE GAMMA = 2, MU = 2 38296 PLOT RIGPDF(X,2,2) FOR X = 0.01 0.01 5 38297 TITLE GAMMA = 5, MU = 2 38298 PLOT RIGPDF(X,5,2) FOR X = 0.01 0.01 5 38299 END OF MULTIPLOT 38300 JUSTIFICATION CENTER 38301 MOVE 50 97 38302 CASE ASIS 38303 TEXT Reciprocal Inverse Gaussian PDF 38304 38305-----RIGPPF (LET)-------------------------------- 38306 38307RIGPPF 38308 38309Name: 38310 RIGPPF (LET) 38311 38312Type: 38313 Library Function 38314 38315Purpose: 38316 Compute the reciprocal inverse Gaussian percent point function 38317 with shape parameters gamma and mu. 38318 38319Description: 38320 The reciprocal inverse Gaussian distribution is the distribution 38321 of (1/X) when X has an inverse Gaussian distribution. It has 38322 the following cumulative distribution function: 38323 38324 F(x;gamma,mu) = NORCDF[-(1/(mu*x) - 1)*SQRT(gamma*x)] - 38325 EXP(2/gamma**2)* 38326 NORCDF[-(1/(mu*x) - 1)*SQRT(gamma*x)] 38327 x >= 0; gamma, mu > 0 38328 38329 with gamma and mu denoting the shape parameters and NORCDF denoting 38330 the cumulative distribution function of the standard normal 38331 distribution. 38332 38333 The percent point function is the inverse of the cumulative 38334 distribution function. The percent point function for the 38335 reciprocal inverse Gaussian distribution does not exist in 38336 simple, closed form. 38337 38338 The reciprocal inverse Gaussian percent point function can be 38339 computed in terms of the inverse Gaussian percent point 38340 function by 38341 38342 RIGPPF(p;gamma,mu) = 1/IGPPF(1-p;gamma,mu) 38343 38344 Dataplot uses this relationship to compute the reciprocal 38345 inverse gaussian percent point function. 38346 38347 The reciprocal inverse Gaussian distribution can be generalized 38348 with location and scale parameters in the usual way. 38349 38350Syntax: 38351 LET <y> = RIGPPF(<p>,<gamma>,<mu>,<loc>,<scale>) 38352 <SUBSET/EXCEPT/FOR qualification> 38353 where <p> is a variable or a parameter in the interval (0,1); 38354 <gamma> is number or parameter that specifies the first 38355 shape parameter; 38356 <mu> is number or parameter that specifies the second 38357 shape parameter; 38358 <loc> is number or parameter that specifies the location 38359 parameter; 38360 <scale> is number or parameter that specifies the scale 38361 parameter; 38362 <y> is a variable or a parameter (depending on what <x> is) 38363 where the computed reciprocal inverse Gaussian ppf 38364 value is stored; 38365 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 38366 38367 Note that the location and scale parameters are optional. 38368 38369Examples: 38370 LET A = RIGPPF(0.95,2,1) 38371 LET A = RIGPPF(P1,2,1) 38372 PLOT RIGPPF(P,2,1.5) FOR P = 0 0.01 0.99 38373 38374Note: 38375 Library functions are distinguished from let subcommands 38376 in the following ways. 38377 1) Functions enclose the input value in parenthesis. Let 38378 subcommands use spaces. 38379 2) Functions can accept (and return) either parameters 38380 (i.e., single values) or variables (i.e., an array of 38381 values) while let subcommands are specific in which they 38382 accept as input and what they return as output. 38383 3) Functions can accept expressions while let subcommands 38384 do not. For example, the following is legal: 38385 LET Y2 = ABS(Y1-INT(Y1)) 38386 For let subcommands, you typically have to do something 38387 like the following: 38388 LET YTEMP = Y**2 + 8 38389 LET A = SUM YTEMP 38390 38391Default: 38392 None 38393 38394Synonyms: 38395 None 38396 38397Related Commands: 38398 RIGCDF = Compute the reciprocal inverse Gaussian cumulative 38399 distribution function. 38400 RIGCHAZ = Compute the reciprocal inverse Gaussian cumulative 38401 hazard function. 38402 RIGHAZ = Compute the reciprocal inverse Gaussian hazard 38403 function. 38404 RIGPDF = Compute the reciprocal inverse Gaussian probability 38405 density function. 38406 IGPDF = Compute the reciprocal inverse Gaussian probability 38407 density function. 38408 CHSPDF = Compute the chi-square probability density function. 38409 FPDF = Compute the F probability density function. 38410 NORPDF = Compute the normal probability density function. 38411 TPDF = Compute the t probability density function. 38412 WEIPDF = Compute the Weibull probability density function. 38413 WALPDF = Compute the Wald probability density function. 38414 FLPDF = Compute the fatigue life probability density function. 38415 38416Reference: 38417 "Continuous Univariate Distributions--Volume 1", Second Edition, 38418 Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 15. 38419 38420 "Statistical Distributions", Third Edition, Evans, Hastings, 38421 and Peacock, Wiley, 2000, pp. 114-116. 38422 38423Applications: 38424 Distributional Modeling 38425 38426Implementation Date: 38427 1990/5: Original implementation 38428 2003/12: Modified to treat mu as a shape parameter instead of 38429 a location parameter 38430 38431Program: 38432 X1LABEL Probability 38433 Y1LABEL X 38434 LABEL CASE ASIS 38435 X1LABEL DISPLACEMENT 12 38436 Y1LABEL DISPLACEMENT 12 38437 MULTIPLOT SCALE FACTOR 2 38438 MULTIPLOT 2 2 38439 MULTIPLOT CORNER COORDINATES 0 0 100 95 38440 TITLE GAMMA = 2, MU = 1 38441 PLOT RIGPPF(P,2,1) FOR P = 0 0.01 0.99 38442 TITLE GAMMA = 5, MU = 1 38443 PLOT RIGPPF(P,5,1) FOR P = 0 0.01 0.99 38444 TITLE GAMMA = 2, MU = 2 38445 PLOT RIGPPF(P,2,2) FOR P = 0 0.01 0.99 38446 TITLE GAMMA = 5, MU = 2 38447 PLOT RIGPPF(P,5,2) FOR P = 0 0.01 0.99 38448 END OF MULTIPLOT 38449 JUSTIFICATION CENTER 38450 MOVE 50 97 38451 CASE ASIS 38452 TEXT Reciprocal Inverse Gaussian Percent Point 38453 38454-----RING BELL------------------------------------------------------- 38455 38456RING BELL 38457 38458Name: 38459 RING BELL 38460 38461Type: 38462 Diagrammatic Graphics Command 38463 38464Purpose: 38465 Rings the bell (immediately). 38466 38467Syntax: 38468 RING BELL <number> 38469 where <number> is an integer number or parameter that specifies 38470 the number of times to ring the bell. 38471 38472Examples: 38473 RING BELL 38474 RING BELL 3 38475 38476Note: 38477 RING BELL with no arguments is equivalent ot RING BELL 1. 38478 38479Default: 38480 None 38481 38482Synonyms: 38483 None 38484 38485Related Commands: 38486 ERASE = Erases the screen (immediately). 38487 COPY = Copies the screen (immediately). 38488 BELL = Sets the automatic bell switch for plots. 38489 PRE-ERASE = Sets the automatic pre-erase switch for plots. 38490 HARDCOPY = Sets the automatic copy switch for plots. 38491 SEQUENCE = Sets the automatic sequence switch for plots. 38492 38493Applications: 38494 XX 38495 38496Implementation Date: 38497 Pre-1987 38498 38499Program: 38500 XX 38501 38502-----RLP (LET)----------------------------------------- 38503 38504RLP 38505 38506Name: 38507 RLP (LET) 38508 38509Type: 38510 Let Subcommand 38511 38512Purpose: 38513 Given a response variable containing z-scores and an associated 38514 variable containing the material-id, compute the relative laboratory 38515 performance (RLP) of a variable. 38516 38517Description: 38518 One scenario for proficiency testing described in the ISO 13528 38519 standard is for the case where there are multiple rounds of testing. 38520 The proficiency data typically consists of 38521 38522 Z - a variable containing the response data in z-score 38523 units 38524 MATID - a variable containing the material-id 38525 ROUNDID - a variable containing the round-id 38526 LABID - a variable containing the lab-id 38527 38528 For ISO 13528 multi-round proficiency studies, the relative 38529 laboratory performance (RLP) for a given laboratory with N z-scores 38530 (Z(i)) is defined as 38531 38532 RLP = SQRT{SUM[i=1 to N][Z(I)**2]/NMAT} 38533 38534 where NMAT is the number of materials. An RLP near 1 indicates 38535 average performance and an RLP greater than 1.5 indicates that 38536 the laboratory may be problematic. An advantage of this 38537 statistic is that z-scores of opposite sign do not cancel each 38538 other out. A disadvantage is that this statistic is suspectible 38539 to outliers in the z-scores. 38540 38541 The RLP statistic is discussed in Uhlig and Lischer (1998). The RLP 38542 statistic is an examples of a combination score (i.e., the statistic 38543 is a combination of many individual z-scores). Although the 38544 ISO 13528 standard recommends against using combination scores, these 38545 can be helpful in judging the overall performance of a 38546 laboratory. These combination scores can be used to identify 38547 laboratories that are potentially problematic. These 38548 laboratories can then be examined more carefully. For 38549 example: is the poor performance due to one or a few outliers? 38550 is the lab consistently high or consistently low? does the 38551 laboratory need to carefully examine their procedures? 38552 38553 This statistic is used to compute the RLP for a single 38554 laboratory. Note that the material-id variable is only 38555 used to determine the number of materials (NMAT in the 38556 above formula). 38557 38558 The most typical use of this statistic is with the 38559 TABULATE command or the STATISTIC PLOT command where the 38560 group-id variable is the laboratory-id variable. For 38561 example, the command 38562 38563 RLP PLOT Z MATID LABID 38564 38565 can be used to generate a plot of the RLP values for each 38566 laboratory. 38567 38568Syntax: 38569 LET <par> = RLP <z> <matid> <SUBSET/EXCEPT/FOR qualification> 38570 where <z> is the response variable containing z-scores; 38571 <matid> is a variable containing the material-id's; 38572 <par> is a parameter where the computed rlp is saved; 38573 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 38574 38575 The SUBSET clause can be used to specify a specific laboratory 38576 for which to compute the statistic. 38577 38578Examples: 38579 LET A = RLP Z MAT 38580 LET A = RLP Z MAT SUBSET LAB = 23 38581 TABULATE RLP Z MATID LABID 38582 RLP PLOT Z MATID LABID 38583 38584Note: 38585 The ISO 13528 standard defines a number of methods for computing the 38586 z-scores (enter HELP ISO 13528 ZSCORE, HELP ISO 13528 ZPRIME SCORE, 38587 and HELP ISO 13528 ZETA SCORE for details). For this reason, the 38588 ISO 13528 RLP PLOT command does not automatically compute the 38589 z-scores from the original response data. 38590 38591Note: 38592 In some applications it may be desired to cap the value 38593 of outliers. This is most common when the response variable 38594 is a z-score or some other standardized score. 38595 38596 To specify this value, enter the command 38597 38598 LET CAPVALUE = <value> 38599 38600 where <value> is typically 3 or 4 (if the reponse data are 38601 z-scores or z-score type data). Note that the value represents 38602 an absolute value. For example, if CAPVALUE is 4, values greater 38603 than 4 will be set to 4 and values less than -4 will be set to -4. 38604 38605Note: 38606 Dataplot statistics can be used in a number of commands. For 38607 details, enter 38608 38609 HELP STATISTICS 38610 38611Default: 38612 None 38613 38614Synonyms: 38615 None 38616 38617Related Commands: 38618 ISO 13528 RLP PLOT = Generate a plot of relative laboratory 38619 performance against the rescaled sums. 38620 ISO 13528 PLOT = Generate an ISO 13528 plot. 38621 ISO 13528 ZSCORE PLOT = Generate an ISO 13528 zscore plot. 38622 ISO 13528 CONTROL CHART = Generate an ISO 13528 control chart. 38623 ISO 13528 ZSCORE = Compute z-scores as defined in the 38624 ISO 13528 standard. 38625 ISO 13528 ZPRIME SCORE = Compute z-prime scores as defined in the 38626 ISO 13528 standard. 38627 ISO 13528 ZETA SCORE = Compute zeta scores as defined in the 38628 ISO 13528 standard. 38629 TABULATE = Compute a statistic for one or more 38630 group variables. 38631 STATISTIC PLOT = Generate a statistic versus index plot. 38632 38633References: 38634 Uhlig and Lischer (1998), "Statistically-based Performance 38635 Characteristics in Laboratory Performance Studies", Analyst, 38636 123, pp. 167-172. 38637 38638 ISO 13528 (2005), "Statistical Methods for use in proficiency 38639 testing by interlaboratory comparisons," First Edition, 38640 2005-09-01. 38641 38642Applications: 38643 Multiple Round Proficiency Testing 38644 38645Implementation Date: 38646 2015/2 38647 38648Program 1: 38649 . Step 1: Read the data 38650 . 38651 dimension 40 columns 38652 skip 25 38653 read turner.dat labid z year quarter matid matave 38654 skip 0 38655 let labcoded = code labid 38656 . 38657 . Step 2: Set plot control setting 38658 . 38659 case asis 38660 title case asis 38661 title offset 2 38662 label case asis 38663 y1label Relative Laboratory Performance 38664 x1label Laboratory 38665 title RLP Versus Laboratory for TURNER.DAT 38666 y1tic mark label decimal 1 38667 tic mark offset units data 38668 x1tic mark offset 2 0 38669 y1tic mark offset 0.2 0.5 38670 ylimits 0 3 38671 . 38672 line blank 38673 character circle 38674 character hw 0.5 0.375 38675 character fill on 38676 . 38677 . Step 3: Generate plot of RLP vs Lab 38678 . 38679 rlp plot z matid labcoded 38680 line dash 38681 line color blue 38682 drawsdsd 15 1.5 85 1.5 38683 line color red 38684 drawsdsd 15 3.0 85 3.0 38685 . 38686 . Step 4: Tabulate RLP values for each laboratory 38687 . 38688 set write decimals 4 38689 tabulate rlp z matid labid 38690 38691-----RM------------------------------------------------------- 38692 38693RM 38694RMDIR 38695 38696Name: 38697 RM 38698 RMDIR 38699 38700Type: 38701 Support Command 38702 38703Purpose: 38704 This command deletes one or more files or directories. 38705 38706Description: 38707 This command uses an operating system command to delete 38708 one or more files or one or more directories. 38709 38710 For Unix/Linux/MacOS systems, the RM command issues a 38711 38712 rm .... 38713 38714 command to the operating system and the RMDIR command issues a 38715 38716 rm -r ... 38717 38718 command to the operating system. 38719 38720 For Windows systems, the RM command issues an 38721 38722 ERASE .... 38723 38724 command to the operating system and the RMDIR command issues a 38725 38726 DELTRE ... 38727 38728 command to the operating system. 38729 38730 The RMDIR command will remove any files or sub-directories 38731 under the directory being removed. 38732 38733 The string that follows the RM or RMDIR on the command line 38734 is passed to the operating system as is. Dataplot does no 38735 error checking of this string. 38736 38737 This command should be used with caution so that files 38738 are not accidentally deleted. 38739 38740 This is a system dependent command. It is currently supported 38741 for Unix/Linux/MacOS and Windows platforms. 38742 38743Syntax 1: 38744 RM <file-list> 38745 where <file-list> is a string containing a list of one or more 38746 files to delete. 38747 38748Syntax 2: 38749 RMDIR <file-list> 38750 where <file-list> is a string containing a list of one or more 38751 directories to delete. 38752 38753Examples: 38754 RM *.ps 38755 RM macro.out macro.ps macro.pdf 38756 RMDIR macros tmp 38757 38758Note: 38759 The RM capability can be implemented by direct use of the 38760 SYSTEM command. For example, under Linux do something like 38761 38762 system rm junk*.out 38763 38764 The motivation for adding this as a separate command is to 38765 allow the capability to be implemented in an operating 38766 system independent way. This can be useful when writing 38767 general purpose macros that may be used on different 38768 operating systems. 38769 38770Default: 38771 None 38772 38773Synonyms: 38774 None (we have not added DELETE or ERASE as synonyms as these 38775 commands are already used in Dataplot) 38776 38777Note: 38778 Dataplot does no checking to ensure that a valid file name 38779 or directory name was specified. The entered string is 38780 passed to the operating system as entered. 38781 38782Note: 38783 File names are case sensitive on Unix/Linux/MacOS file 38784 systems. For this reason, case is preserved in passing the 38785 file list to the operating system. 38786 38787Related Commands: 38788 SYSTEM = Enter an operating system command within a 38789 Dataplot session. 38790 CD = Change the current working directory. 38791 PWD = Retrieve the current working directory. 38792 CAT = List the contents of a file. 38793 MKDIR = Create a new directory. 38794 DIR = List the contents of a directory. 38795 38796Applications: 38797 Interactive Usage 38798 38799Implementation Date: 38800 2019/09 38801 38802Program: 38803 . Automatically convert Postscript output to PDF and then 38804 . delete the original Postscript file 38805 . 38806 SKIP 25 38807 READ BERGER1.DAT Y X 38808 . 38809 SET POSTSCRIPT CONVERT PDF 38810 SET IPL1NA PLOT.PS 38811 CHARACTER X 38812 LINE BLANK 38813 . 38814 PLOT Y X 38815 . 38816 DEVICE 2 CLOSE 38817 RM PLOT.PS 38818 38819-----ROBUST POOLED STANDARD DEVIATION (LET)----------------------------- 38820 38821ROBUST POOLED STANDARD DEVIATION 38822 38823Name: 38824 ROBUST POOLED STANDARD DEVIATION (LET) 38825 38826Type: 38827 Let Subcommand 38828 38829Purpose: 38830 Compute the robust pooled standard deviation of a variable. 38831 38832Description: 38833 The definition for the robust pooled standard deviation from 38834 the ISO 13528 standard. It is computed as follows. 38835 38836 Let w1, w2, ... , wp be the standard deviations from the p labs. 38837 The degrees of freedom for w(i) = n(i) - 1 where n(i) is the number 38838 of replications for lab i. 38839 38840 Compute 38841 38842 Limit Factor = LF = SQRT(CHSPPF(0.9,nu)/nu) 38843 38844 Adjustment Factor = AF = 1/SQRT(CHSCDF(nu*LF**2),nu+2) + 0.1*LF**2) 38845 38846 The limit factor and adjustment factor assume that each lab has the 38847 same number of replications. If the number of replications are not 38848 equal, Dataplot will use the average number of replications. 38849 38850 The initual value of w* is set to the median of the w(i)'s. 38851 38852 To update the value of w*, compute 38853 38854 psi = limit factor times w* 38855 38856 For each w(i), 38857 38858 w(i)* = psi if w(i) > psi 38859 = w(i) if w(i) <= psi 38860 38861 The updated value of w* is 38862 38863 w* = Adjustment Factor * SQRT(SUM[i=1 to p][(w(i))**2]/p) 38864 38865 The value of w* is iterated until the difference between two 38866 successive values of w* is sufficiently small. 38867 38868 The ISO 13528 standard also allows this computation to be performed 38869 on the lab ranges. In this case, the robust pooled range uses the 38870 same computation as above with the exception that the degrees of 38871 freedom, nu, is set to 1. 38872 38873Syntax 1: 38874 LET <par> = ROBUST POOLED STANDARD DEVIATION <y> <x> 38875 <SUBSET/EXCEPT/FOR qualification> 38876 where <y> is the response variable; 38877 <x> is the lab-id variable; 38878 <par> is a parameter where the computed robust pooled sd 38879 is saved; 38880 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 38881 38882Syntax 2: 38883 LET <par> = ROBUST POOLED RANGE <y> <x> 38884 <SUBSET/EXCEPT/FOR qualification> 38885 where <y> is the response variable; 38886 <x> is the lab-id variable; 38887 <par> is a parameter where the computed robust pooled range 38888 is saved; 38889 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 38890 38891Examples: 38892 LET SD = ROBUST POOLED STANDARD DEVIATION Y X 38893 LET SD = ROBUST POOLED STANDARD DEVIATION Y X SUBSET TAG > 2 38894 LET SD = ROBUST POOLED RANGE Y X 38895 38896Note: 38897 Dataplot statistics can be used in a number of commands. For 38898 details, enter 38899 38900 HELP STATISTICS 38901 38902Default: 38903 None 38904 38905Synonyms: 38906 ROBUST POOLED SD is a synonym for ROBUST POOLED STANDARD DEVIATION 38907 38908Related Commands: 38909 MEAN = Compute the mean of a variable. 38910 MEDIAN = Compute the median of a variable. 38911 RANGE = Compute the range of a variable. 38912 STANDARD DEVIATION = Compute the standard deviation of a variable. 38913 H15 SCALE = Compute the H15 scale estimate of a variable. 38914 WEIGHTED STAND DEVI = Compute the weighted standard deviation of 38915 a variable. 38916 HOMOSCEDASTICITY PLOT = Compute the standard deviation of a variable. 38917 38918Applications: 38919 Data Analysis, Proficiency Analysis 38920 38921Reference: 38922 ISO 13528 (2005), "Statistical Methods for use in proficiency 38923 testing by interlaboratory comparisons," Section C.2 Algorithm S. 38924 38925Implementation Date: 38926 2010/12 38927 38928Program: 38929 SKIP 25 38930 READ GEAR.DAT Y X 38931 . 38932 SET LET CROSS TABULATE COLLAPSE 38933 LET YSD = CROSS TABULATE SD Y X 38934 LET NSIZE = CROSS TABULATE SIZE X 38935 LET NREPL = MEAN NSIZE 38936 . 38937 LET A = ROBUST POOLED STANDARD DEVIATION Y X 38938 38939-----ROC CURVE (LET)-------------------------------- 38940 38941ROC CURVE 38942 38943Name: 38944 ROC CURVE (LET) 38945 38946Type: 38947 Graphics Command 38948 38949Purpose: 38950 Generate a Reciever Operating Characterisitc (ROC) curve. 38951 38952Description: 38953 Given two variables with n parired observations where each 38954 variable has exactly two possible outcomes, we can generate 38955 the following 2x2 table: 38956 38957 | Variable 2 | 38958 Variable 1 | Success Failure | Row Total 38959 ==================================================== 38960 Success | N11 N12 | N11 + N12 38961 Failure | N21 N22 | N21 + N22 38962 ==================================================== 38963 Column Total | N11+N21 N12+N22 | N11+N12+N21+N22 38964 38965 The parameters N11, N12, N21, and N22 denote the counts 38966 for each category. 38967 38968 Success and failure can denote any binary response. 38969 Dataplot expects "success" to be coded as "1" and "failure" 38970 to be coded as "0". Some typical examples would be: 38971 38972 1) Variable 1 denotes whether or not a patient has a 38973 disease (1 denotes disease is present, 0 denotes 38974 disease not present). Variable 2 denotes the result 38975 of a test to detect the disease (1 denotes a positive 38976 result and 0 denotes a negative result). 38977 38978 2) Variable 1 denotes whether an object is present or 38979 not (1 denotes present, 0 denotes absent). Variable 2 38980 denotes a detection device (1 denotes object detected 38981 and 0 denotes object not detected). 38982 38983 In these examples, the "ground truth" is typically given 38984 as variable 1 while some estimator of the ground truth is 38985 given as variable 2. 38986 38987 In the above table, we can define the following 38988 quantities: 38989 38990 1) True Positives = N11 (i.e., number of cases where 38991 disease present and test detects it) 38992 38993 2) True Negatives = N22 (i.e., number of cases where 38994 disease not present and test did not 38995 detect it) 38996 38997 3) False Positives = N21 (i.e., number of cases where 38998 disease not present and test detects 38999 it) 39000 39001 4) False Negatives = N12 (i.e., number of cases where 39002 disease is present and test does not 39003 detect it) 39004 39005 5) Sensitivity = N11/(N11+N12) (i.e., the probability 39006 that the test detects the disease 39007 given that the disease is present) 39008 39009 6) Specificity = N21/(N21+N22) (i.e., the probability 39010 that the test detects the disease 39011 given that the disease is not 39012 present) 39013 39014 The ROC curve is a plot of the sensitivity versus 39015 1 - the specificity. Points in the upper left corner 39016 (i.e., high sensitivity and high specificity) are 39017 desirable. 39018 39019 We have two typical scenarios for generating the 39020 ROC curve. 39021 39022 1) We have a medical test and we want to determine 39023 an optimal level for deciding whether the disease 39024 is present. Setting the level too low results 39025 in too many false negatives (i.e., we fail to 39026 detect the disease when it is in fact present). 39027 This is low sensitivity. On the other hand, if 39028 we set the level too high we may obtain too many 39029 false positives (i.e., we detect the disease when 39030 it is in fact not present). This is low specificity. 39031 39032 In this case, we typically want to generate the 39033 ROC curve as a connected line to show the 39034 tradeoff between sensitivity and specificity 39035 as we change the threshold level. 39036 39037 2) We are testing sensors to determine which provides 39038 the best performance in detecting some substances. 39039 39040 Since these are distinct devices, we would typically 39041 want to plot these as distinct points rather than 39042 as a connected curve. 39043 39044 You can also combine these scenarios. That is, we may 39045 testing multiple devices (scenario 2) where each device 39046 may have multiple settings. 39047 39048Syntax 1: 39049 ROC CURVE <y1> <y2> <x> <SUBSET/EXCEPT/FOR qualification> 39050 where <y1> is the first response variable; 39051 <y2> is the second response variable; 39052 <x> is a group-id variable; 39053 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 39054 39055 This syntax is used for the cases where 39056 39057 a) we have multiple settings for a single machine 39058 b) we have multiple machines each with a single setting 39059 39060Syntax 2: 39061 ROC CURVE <y1> <y2> <x1> <x2> <SUBSET/EXCEPT/FOR qualification> 39062 where <y1> is the first response variable; 39063 <y2> is the second response variable; 39064 <x1> is a group-id variable; 39065 <x2> is a variable that identifies the setting within 39066 the group; 39067 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 39068 39069 This syntax is used for the case where we have multiple 39070 settings for multiple machines. 39071 39072Examples: 39073 ROC CURVE Y1 Y2 X 39074 ROC CURVE Y1 Y2 X SUBSET X > 2 39075 ROC CURVE Y1 Y2 X1 X2 39076 ROC CURVE Y1 Y2 X1 X2 SUBSET X1 > 2 39077 39078Note: 39079 Some guidelines for interperting the ROC curve are: 39080 39081 1) Points in the upper left corner denote high 39082 accuracy. 39083 39084 2) Dataplot draws a line from the (0,0) point to the 39085 (1,1) point. This is referred to as the no 39086 discrimination line. Points falling on this line 39087 indicate a test that is no better than flipping a 39088 coin. 39089 39090 For the case where we are changing the threshold of a 39091 test, the ROC curves does an excellent job of demonstrating 39092 the tradeoff between specificity and sensitivity. That is, 39093 as we decrease the chance of a false negative (i.e., we do 39094 not miss detection), we inevitably increase the chance of 39095 a false positive. So what we are looking for is a test 39096 that follows the left x-axis and then the top y-axis. In 39097 other words, the closer the curve is to the no discrimination 39098 line, the poorer the test. 39099 39100Note: 39101 The three (or four) variables must have the same number of 39102 elements. 39103 39104Note: 39105 There are two ways you can define the response variables: 39106 39107 1) Raw data - in this case, the variables contain 39108 0's and 1's. 39109 39110 If the data is not coded as 0's and 1's, Dataplot 39111 will check for the number of distinct values. If 39112 there are two distinct values, the minimum value 39113 is converted to 0's and the maximum value is 39114 converted to 1's. If there is a single distinct 39115 value, it is converted to 0's if it is less than 39116 0.5 and to 1's if it is greater than or equal to 39117 0.5. If there are more than two distinct values, 39118 an error is returned. 39119 39120 2) Summary data - if there are two observations for 39121 a group, the data is assummed to be the 2x2 summary 39122 table. That is, 39123 39124 Y1(1) = N11 39125 Y1(2) = N21 39126 Y2(1) = N12 39127 Y2(2) = N22 39128 39129Note: 39130 As noted above, there are two distinct cases for which ROC 39131 curves can be used. Consider the example where we are testing 39132 whether an instrument can detect some specified object. 39133 39134 1) In one case, we may want to compare instruments from 39135 different vendors. In this case, the ROC curve 39136 would be used to help determine which vendor 39137 has the best instrument. 39138 39139 2) In the other case, we may be able to change the 39140 level at which we determine whether or not we 39141 have detected the object. In this case, the 39142 ROC curve can be used to help determine an 39143 optimal setting for the instrument. In this case, 39144 there is typically a trade-off between sensitivity 39145 and specificity (i.e., as our instrument becomes 39146 more sensitive to the prescence of the object, 39147 we also increase the probability of a false 39148 positive). 39149 39150 Of course, we can have a combination of these cases 39151 (i.e., multiple instruments each with multiple possible 39152 settings). 39153 39154Note: 39155 You can control the appearance of the plot using the 39156 LINE and CHARACTER (and their various attribute setting 39157 commands). 39158 39159 For Syntax 1, the following traces are generated for the 39160 plot: 39161 39162 1) trace 1 - a line from (0,0) to (1,1). This is the 39163 "no discrimination line". 39164 39165 2) trace 2 - a curve containing all the points on the 39166 ROC curve. 39167 39168 3) trace 3 and above - each point is drawn as a separate 39169 trace. This is useful for the case 39170 when each point represents a distinct 39171 instrument. 39172 39173 For Syntax 2, the following traces are generated for the 39174 plot: 39175 39176 1) trace 1 - a line from (0,0) to (1,1). This is the 39177 "no discrimination line". 39178 39179 2) trace 2 and above - each curve contains all the settings 39180 for one group (i.e., trace 2 contains 39181 the settings for group 1, trace 3 39182 contains the settings for group 2, and 39183 so on). 39184 39185Note: 39186 Dataplot automatically returns the area under the curve 39187 as the parameter AUC (points are added at (0,0) and (1,1)). 39188 This area is determined by numerical integration. 39189 39190 This statistic is only meaningful for the case where we 39191 are plotting different settings of the same instrument. 39192 39193 For the case where we have multiple settings for multiple 39194 vendors, we write the AUC statistic to the file 39195 dpst1f.dat (in the current directory). Column 1 contains 39196 the group-id value and column 2 contains the value of the 39197 AUC statistic for that group. 39198 39199Default: 39200 None 39201 39202Synonyms: 39203 None 39204 39205Related Commands: 39206 ROSE PLOT = Generate a Rose plot. 39207 BINARY TABULATION PLOT = Generate a binary tabulation plot. 39208 TEST SPECIFICITY = Compute the test specificity. 39209 TEST SENSITIVITY = Compute the test sensitivity. 39210 FALSE NEGATIVES = Compute the proportion of 39211 false negatives. 39212 FALSE POSITIVES = Compute the proportion of 39213 false positives. 39214 TRUE NEGATIVES = Compute the proportion of 39215 true negatives. 39216 TRUE POSITIVES = Compute the proportion of 39217 true positives. 39218 ODDS RATIO = Compute the bias corrected 39219 log(odds ratio). 39220 ODDS RATIO STANDARD ERROR = Compute the standard error of the 39221 bias corrected log(odds ratio). 39222 RELTIVE RISK = Compute the relative risk. 39223 39224Reference: 39225 Hosmer and Lemeshow (2000), "Applied Logistic Regression", 39226 Second Edition, Wiley, pp. 160-164. 39227 39228Applications: 39229 Categorical Data Analysis 39230 39231Implementation Date: 39232 2007/7: Support for syntax 2 added 39233 39234Program 1: 39235 let n = 1 39236 . 39237 let p = 0.2 39238 let y1 = binomial rand numb for i = 1 1 100 39239 let p = 0.1 39240 let y2 = binomial rand numb for i = 1 1 100 39241 . 39242 let p = 0.4 39243 let y1 = binomial rand numb for i = 101 1 200 39244 let p = 0.08 39245 let y2 = binomial rand numb for i = 101 1 200 39246 . 39247 let p = 0.15 39248 let y1 = binomial rand numb for i = 201 1 300 39249 let p = 0.18 39250 let y2 = binomial rand numb for i = 201 1 300 39251 . 39252 let p = 0.6 39253 let y1 = binomial rand numb for i = 301 1 400 39254 let p = 0.45 39255 let y2 = binomial rand numb for i = 301 1 400 39256 . 39257 let p = 0.3 39258 let y1 = binomial rand numb for i = 401 1 500 39259 let p = 0.1 39260 let y2 = binomial rand numb for i = 401 1 500 39261 . 39262 let x = sequence 1 100 1 5 39263 . 39264 limits 0 1 39265 major xtic mark number 6 39266 minor xtic mark number 1 39267 tic mark offset 0.05 0.05 39268 . 39269 label case asis 39270 title case asis 39271 title offset 2 39272 x1label 1 - Specificity 39273 y1label Sensitivity 39274 character blank blank 1 2 3 4 5 39275 line blank all 39276 line dotted 39277 roc curve y1 y2 x 39278 39279Program 2: 39280 . Following sample data from Wikipedia site 39281 read y1 y2 x 39282 63 37 1 39283 28 72 1 39284 77 23 2 39285 77 23 2 39286 24 76 3 39287 88 12 3 39288 88 12 4 39289 24 76 4 39290 end of data 39291 . 39292 character blank blank A B C D 39293 line blank all 39294 line dotted 39295 limits 0 1 39296 major tic mark number 6 39297 minor tic mark number 1 39298 tic mark offset 0.05 0.05 39299 . 39300 label case asis 39301 title case asis 39302 title offset 2 39303 title ROC Curve 39304 y1label Sensitivity 39305 x1label 1 - Specificity 39306 . 39307 roc curve y1 y2 x 39308 39309-----ROOTS (LET)------------------------------------------------- 39310 39311ROOTS 39312 39313Name: 39314 ROOTS (LET) 39315 39316Type: 39317 Let Subcommand 39318 39319Purpose: 39320 Determine the real roots of a function. 39321 39322Syntax: 39323 LET <resp> = ROOTS <func> WRT <var> FOR <var> = <lower> <upper> 39324 where <func> is the name of a previously defined function or a 39325 functional expression; 39326 <var> is the variable for which the roots are being computed; 39327 <lower> is a number or parameter defining the lower limit for 39328 finding roots; 39329 <upper> is a number or parameter defining the upper limit for 39330 finding roots; 39331 <resp> is a parameter where the computed roots are stored. 39332 39333Examples: 39334 LET A = ROOTS X**2+2*X**2-4*X+5 WRT X FOR X = -10 10 39335 LET A = ROOTS F1 WRT X FOR X = 0 B 39336 39337Note: 39338 DATAPLOT uses an inward bracketing followed by bisection algorithm 39339 to find roots. The Numerical Recipes book listed in the REFERENCE 39340 gives a description of these methods (although DATAPLOT does not 39341 use their implementation). 39342 39343Note: 39344 DATAPLOT uses the following convergence test: 39345 value = delta x / x 39346 where delta x is the difference between two iterations in the root 39347 finding algorithm and x is the current value of the root. 39348 Convergence is assumed when this value is smaller than a specified 39349 cutoff (hard-coded to 0.000001). 39350 39351Default: 39352 None 39353 39354Synonyms: 39355 None 39356 39357Related Commands: 39358 POLYNOMIAL ROOTS = Compute the roots of a polynomial. 39359 DERIVATIVE = Compute the derivative of a function. 39360 INTEGRAL = Compute the integral of a function. 39361 RUNGE KUTTA = Runge Kutta differential equation solver. 39362 INTERPOLATE = Interpolate a function. 39363 39364Reference: 39365 "A First Course in Numerical Analysis", 2nd ed., Ralston and 39366 Rabinowitz, 1978, McGraw-Hill. 39367 39368 "Numerical Recipes: The Art of Scientific Computing (FORTRAN 39369 Version)", Press, Flannery, Teukolsky, and Vetterling. Cambridge 39370 University Press, 1989 (chapter 9). 39371 39372Applications: 39373 XX 39374 39375Implementation Date: 39376 XX 39377 39378Program: 39379 LET FUNCTION F1 = X**3+2*X**2-4*X+5 39380 PLOT F1 FOR X = -10 0.1 10 39381 LET A1 = ROOTS F1 WRT X FOR X = -10 10 39382 39383-----ROOT ACCURACY--------------------------------------------------- 39384 39385ROOT ACCURACY 39386 39387Note: 39388 This command is currently ignored by the ROOTS command. The ROOTS 39389 command uses a hard-coded value of 0.000001. 39390 39391Name: 39392 ROOT ACCURACY 39393 39394Type: 39395 Support Command 39396 39397Purpose: 39398 Specify the root accuracy for the ROOTS command. 39399 39400Description: 39401 When DATAPLOT finds roots, it computes 39402 delta x / x 39403 where delta x is the difference between two iterations in the root 39404 finding algorithm and x is the current value of the root. If this 39405 value is less than the root accuracy, then convergence is assumed. 39406 39407Syntax: 39408 ROOT ACCURACY <val> 39409 where <val> is a number or parameter that specifies the root 39410 accuracy. 39411 39412Examples: 39413 ROOT ACCURACY 0.001 39414 ROOT ACCURACY 0.00001 39415 39416Default: 39417 0.000001 39418 39419Synonyms: 39420 XX 39421 39422Related Commands: 39423 ROOTS = Find the real roots of an equation. 39424 COMPLEX ROOTS = Find the complex roots of a polynomial. 39425 39426Applications: 39427 Mathematics 39428 39429Implementation Date: 39430 Pre-1987 39431 39432Program: 39433 XX 39434 39435-----ROOT MEAN SQUARE ERROR (LET)----------------------------------------- 39436 39437ROOT MEAN SQUARE ERROR 39438 39439Name: 39440 ROOT MEAN SQUARE ERROR (LET) 39441 39442Type: 39443 Let Subcommand 39444 39445Purpose: 39446 Compute the root means square error of a variable. 39447 39448Description: 39449 The root mean square error has the formula: 39450 39451 RMS = SQRT(SUM[i=1 to N][X(i)**2]/N) 39452 39453Syntax 1: 39454 LET <par> = ROOT MEAN SQUARE ERROR <y> 39455 <SUBSET/EXCEPT/FOR qualification> 39456 where <y> is the response variable; 39457 <par> is a parameter where the computed root mean square error 39458 is saved; 39459 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 39460 39461Syntax 2: 39462 LET <par> = DIFFERENCE OF ROOT MEAN SQUARE ERROR <y1> <y2> 39463 <SUBSET/EXCEPT/FOR qualification> 39464 where <y1> is the first response variable; 39465 <y2> is the second response variable; 39466 <par> is a parameter where the computed difference of 39467 root mean square errors is saved; 39468 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 39469 39470 This syntax computes the root mean square error of <y1> and 39471 <y2> and then computes the difference of the two root mean 39472 square error values. 39473 39474Examples: 39475 LET A = ROOT MEAN SQUARE ERROR Y1 39476 LET A = ROOT MEAN SQUARE ERROR Y1 SUBSET TAG > 2 39477 LET A = DIFFERENCE OF ROOT MEAN SQUARE ERROR Y1 Y2 39478 39479Note: 39480 Dataplot statistics can be used in a number of commands. For 39481 details, enter 39482 39483 HELP STATISTICS 39484 39485Default: 39486 None 39487 39488Synonyms: 39489 ROOT MEAN SQUARE 39490 RMS 39491 39492Related Commands: 39493 MEAN = Compute the mean of a variable. 39494 RANGE = Compute the range of a variable. 39495 STANDARD DEVIATION = Compute the standard deviation of a variable. 39496 VARIANCE = Compute the variance of a variable. 39497 39498Applications: 39499 Statistics 39500 39501Implementation Date: 39502 2010/1 39503 39504Program: 39505 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 39506 LET RMS = ROOT MEAN SQUARE ERROR Y1 39507 39508-----ROOTOGRAM------------------------------------------------------- 39509 39510ROOTOGRAM 39511 39512Name: 39513 ... ROOTOGRAM 39514 39515Type: 39516 Graphics Command 39517 39518Purpose: 39519 Generates a rootogram. 39520 39521Description: 39522 A rootogram is a graphical data analysis technique for summarizing 39523 the distributional information of a variable. It consists of: 39524 Vertical axis = square root of frequencies or relative 39525 frequencies; 39526 Horizontal axis = response variable. 39527 There are 4 types of rootograms: 39528 1) rootogram (absolute counts); 39529 2) relative rootogram (converts counts to proportions); 39530 3) cumulative rootogram; 39531 4) cumulative relative rootogram. 39532 The rootogram is a modified version of a histogram. It plots the 39533 square roots of the frequencies rather than the raw frequencies. 39534 Many univariate data sets can be normalized with a square root 39535 transformation (particularly counts or measurement data that have 39536 a lower bound and tend to be skewed at the upper tail). 39537 39538Syntax 1: 39539 ROOTOGRAM <x> <SUBSET/EXCEPT/FOR qualification> 39540 RELATIVE ROOTOGRAM <x> <SUBSET/EXCEPT/FOR qualification> 39541 CUMULATIVE ROOTOGRAM <x> <SUBSET/EXCEPT/FOR qualification> 39542 CUMULATIVE RELATIVE ROOTOGRAM <x> <SUBSET/EXCEPT/FOR qualification> 39543 where <x> is the variable of raw data values which will appear on 39544 the horizontal axis; 39545 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 39546 39547 This syntax is used when you have raw data only. 39548 39549Syntax 2: 39550 ROOTOGRAM <y> <x> <SUBSET/EXCEPT/FOR qualification> 39551 RELATIVE ROOTOGRAM <y> <x> <SUBSET/EXCEPT/FOR qualification> 39552 CUMULATIVE ROOTOGRAM <y> <x> <SUBSET/EXCEPT/FOR qualification> 39553 CUMULATIVE RELATIVE ROOTOGRAM <y> <x> 39554 <SUBSET/EXCEPT/FOR qualification> 39555 where <y> is the variable of pre-computed frequencies to appear on 39556 the vertical axis; 39557 <x> is the variable of raw data values which will appear on 39558 the horizontal axis; 39559 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 39560 39561 This syntax is used when you have pre-computed frequencies at each 39562 horizontal axis value. 39563 39564Examples: 39565 ROOTOGRAM TEMP 39566 RELATIVE ROOTOGRAM TEMP 39567 CUMULATIVE ROOTOGRAM TEMP 39568 CUMULATIVE RELATIVE ROOTOGRAM TEMP 39569 ROOTOGRAM COUNTS STATE 39570 RELATIVE ROOTOGRAM COUNTS STATE 39571 CUMULATIVE ROOTOGRAM COUNTS STATE 39572 CUMULATIVE RELATIVE ROOTOGRAM COUNTS STATE 39573 39574Note: 39575 The appearance of the bars on the rootogram (i.e., whether they are 39576 filled or not, the line width of the bar border, etc.) are 39577 controlled by the various bar attribute commands. A few are listed 39578 in the RELATED COMMANDS section below. See the documentation for 39579 the BAR command for a complete list of the bar attribute commands. 39580 39581Note: 39582 Although DATAPLOT does not have a FREQUENCY TABLE command, one can 39583 be generated with the following commands: 39584 HISTOGRAM Y 39585 LET YFREQ = YPLOT 39586 LET XVAL = XPLOT 39587 Then the variables YFREQ and XVAL essentially contain a frequency 39588 table. There is a LET subcommand called FREQUENCY. However, it 39589 does not generate a frequency table in the sense that a histogram 39590 or a frequency plot does. The frequency table can also be 39591 generated by replacing HISTOGRAM with ROOTOGRAM in the above 39592 sequence. However, be aware that this generates the square roots 39593 of the frequencies, not the raw frequencies. 39594 39595Note: 39596 By default, DATAPLOT uses a class width of 0.3 X the standard 39597 deviation of the variable. Use the CLASS WIDTH command to override 39598 this default. DATAPLOT also tends to generate a large number of 39599 zero frequency classes at the lower and upper tails. This tends to 39600 compress the histogram on the horizontal axis. Use the XLIMITS 39601 command or the CLASS LOWER and CLASS UPPER commands to avoid 39602 plotting these zero frequency classes. 39603 39604Default: 39605 None 39606 39607Synonyms: 39608 A synonym for CUMULATIVE RELATIVE ROOTOGRAM is RELATIVE CUMULATIVE 39609 ROOTOGRAM 39610 39611Related Commands: 39612 HISTOGRAM = Generate a histogram. 39613 FREQUENCY PLOT = Generates a frequency plot. 39614 PIE CHART = Generates a pie chart. 39615 PERCENT POINT PLOT = Generates a percent point plot. 39616 PROBABILITY PLOT = Generates a probability plot. 39617 PPCC PLOT = Generates probability plot correlation 39618 coefficient plot. 39619 CLASS LOWER = Sets the lower class minimum for histograms, 39620 frequency plots, and pie charts. 39621 CLASS UPPER = Sets the upper class maximum for histograms, 39622 frequency plots, and pie charts. 39623 CLASS WIDTH = Sets the class width for histograms, frequency 39624 plots, and pie charts. 39625 MINIMUM = Sets the frame minima for all plots. 39626 MAXIMUM = Sets the frame maxima for all plots. 39627 LIMITS = Sets the frame limits for all plots. 39628 PLOT = Generates a data or function plot. 39629 BARS = Sets the on/off switches for plot bars. 39630 BAR WIDTH = Sets the widths for plot bars. 39631 BAR FILL = Sets the on/off switches for plot bar fills. 39632 BAR PATTERN = Sets the types for bar fill patterns. 39633 BAR BORDER LINE = Sets the types for bar border lines. 39634 39635Reference: 39636 Most introductory statistics book discuss frequency polygons and 39637 histograms. The rootogram is described in "Exploratory Data 39638 Analysis", John Tukey, Addison-Wesley, 1977. 39639 39640Applications: 39641 XX 39642 39643Implementation Date: 39644 XX 39645 39646Program: 39647 LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 1000 39648 MULTIPLOT 2 2 39649 MULTIPLOT CORNER COORDINATES 0 0 100 100 39650 XLIMITS -5 5 39651 ROOTOGRAM Y 39652 BAR FILL ON 39653 RELATIVE ROOTOGRAM Y 39654 BAR FILL OFF 39655 BAR BORDER THICKNESS 0.3 39656 CUMULATIVE ROOTOGRAM Y 39657 BAR FILL ON 39658 BAR PATTERN D1 39659 BAR PATTERN SPACING 3 39660 CUMULATIVE RELATIVE ROOTOGRAM Y 39661 END OF MULTIPLOT 39662 39663-----ROSE PLOT------------------------------------------------------- 39664 39665ROSE PLOT 39666 39667Name: 39668 ROSE PLOT 39669 39670Type: 39671 Graphics Command 39672 39673Purpose: 39674 Generate a rose plot. 39675 39676Description: 39677 The rose plot is a variation of the common pie chart. For 39678 both, we have k data points where each point denotes a 39679 frequency or a count. Pie charts and rose plots both use 39680 the area of segments of a circle to convey amounts. The 39681 pie chart uses a common radius and varies the central angle 39682 according to the data. That is, the angle is proportional 39683 to the frequency. So if the ith point has count X and the 39684 total count is N, the ith angle is 360*(X/N). For the rose 39685 plot, the angle is constant (i.e., divide 360 by the number 39686 of groups, k) and it is the square root of the radius that is 39687 proportional to the data. 39688 39689 According to Wainer (1997), the use of a common angle is the 39690 strength of the rose plot since it allows us to easily compare 39691 a sequence of rose plots (i.e., the corresponding segments in 39692 different rose plots are always in the same relative 39693 position). In particular, this makes rose plots an effective 39694 technique for displaying the data in contingency tables. 39695 39696 Friendly (2000) refers to the special case of 2x2 tables as 39697 the fourfold plot. As with the general case, an effective 39698 use of these plots is when we have a sequence of related 2x2 39699 tables. Using the MULTIPLOT command, Dataplot can easily 39700 generate the sequence of rose plots or fourfold plots on a 39701 single page. 39702 39703 As an interesting historical note, Wainer points out that 39704 rose plots were used by Florence Nightingale (she referred to 39705 them as coxcombs). 39706 39707Syntax 1: 39708 ROSE PLOT <x> <SUBSET/EXCEPT/FOR qualification> 39709 where <x> is the variable containing counts; 39710 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 39711 39712 Use this syntax when you have a single variable of 39713 counts (or proportions). 39714 39715Syntax 2: 39716 ROSE PLOT <y1> <y2> <SUBSET/EXCEPT/FOR qualification> 39717 where <y1> is the first response variable; 39718 <y2> is the second response variable; 39719 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 39720 39721 With this syntax, the <y1> and <y2> variables are 39722 cross-tabulated to generate a 2x2 table. The rose plot 39723 is then generated from this 2x2 table. 39724 39725Examples: 39726 ROSE PLOT X 39727 ROSE PLOT X SUBSET TAG > 2 39728 ROSE PLOT Y1 Y2 39729 39730Note: 39731 Each wedge is drawn with a common set of attributes. The 39732 attributes of the wedge borders are set with the LINE, 39733 LINE COLOR, and LINE THICKNESS commands (typically they are 39734 all set the same). The attributes of the interior are set 39735 with the various REGION commands. Any labels for the wedges 39736 must be set with the LEGEND or TEXT commands. The CROSS HAIR 39737 command can help in positioning labels. The program example 39738 below shows how to set the attributes. Dataplot does not 39739 support features such as 3d rose plots or exploding slices 39740 that are common in many business graphics programs. 39741 39742Note: 39743 You can use the CONDITION PLOT command for the case where 39744 you want to generate rose plots for a series of 2x2 tables. 39745 This is demomstrated in the program examples below. 39746 39747Default: 39748 None 39749 39750Synonyms: 39751 None 39752 39753Related Commands: 39754 PIE CHART = Generates a pie chart. 39755 HISTOGRAM = Generates a histogram. 39756 PERCENT POINT PLOT = Generates a percent point plot. 39757 PLOT = Generates a plot (including bar plots). 39758 LINE = Sets the types for plot lines. 39759 LINE COLOR = Sets the colors for plot lines. 39760 LINE THICKNESS = Sets the thicknesses for plot lines. 39761 REGION = Sets the types for plot regions. 39762 REGION FILL = Sets on/off switches for region fills. 39763 39764Reference: 39765 Wainer (1997), "Visual Revelations: Graphical Tales of Fate 39766 and Deception from Napolean Bonaporte to Ross Perot", 39767 Copernicus, Chapter 11. 39768 39769 Friendly (2000), "Visualizing Categorical Data", SAS Institute 39770 Inc., p. 90. 39771 39772Applications: 39773 Categorical Data Analysis 39774 39775Implementation Date: 39776 2007/4 39777 39778Program 1: 39779 let y = data 48 12 53 7 39780 . 39781 region fill on on on on 39782 region fill color black blue red green 39783 rose plot y 39784 . 39785 case asis 39786 justification left 39787 move 15 90 39788 text Truecr()Positives 39789 move 15 10 39790 text Falsecr()Positives 39791 move 75 90 39792 text Falsecr()Negatives 39793 move 75 10 39794 text Truecr()Negatives 39795 39796Program 2: 39797 let n = 1 39798 let x = sequence 1 100 1 5 39799 . 39800 let p = 0.8 39801 let y1 = binomial rand numb for i = 1 1 100 39802 let p = 0.92 39803 let y2 = binomial rand numb for i = 1 1 100 39804 . 39805 let p = 0.6 39806 let y1 = binomial rand numb for i = 101 1 200 39807 let p = 0.95 39808 let y2 = binomial rand numb for i = 101 1 200 39809 . 39810 let p = 0.96 39811 let y1 = binomial rand numb for i = 201 1 300 39812 let p = 0.98 39813 let y2 = binomial rand numb for i = 201 1 300 39814 . 39815 let p = 0.3 39816 let y1 = binomial rand numb for i = 301 1 400 39817 let p = 0.2 39818 let y2 = binomial rand numb for i = 301 1 400 39819 . 39820 let p = 0.9 39821 let y1 = binomial rand numb for i = 401 1 500 39822 let p = 0.2 39823 let y2 = binomial rand numb for i = 401 1 500 39824 . 39825 region fill on on on on 39826 region color black blue red green 39827 rose plot y1 y2 subset x = 5 39828 . 39829 set conditioning plot type two variable rose 39830 region fill off on on on on 39831 region color white black blue red green 39832 condition plot y1 y2 x 39833 39834Program 3: 39835 orientation square 39836 . 39837 . Berkeley Admissions Data from p. 391 of 39838 . Friendly (2000), "Visualizing Categorical Data", 39839 . SAS Institute Inc. 39840 . 39841 read y1 y2 x 39842 512 313 1 39843 353 207 1 39844 89 19 2 39845 17 8 2 39846 120 205 3 39847 138 279 3 39848 202 391 4 39849 131 244 4 39850 53 138 5 39851 22 351 5 39852 94 299 6 39853 24 317 6 39854 end of data 39855 . 39856 multiplot corner coordinates 0 0 100 95 39857 multiplot scale factor 2 39858 multiplot 3 3 39859 . 39860 legend case asis 39861 legend justification left 39862 legend 2 justification right 39863 legend 4 justification right 39864 legend 1 coordinates 17 83 39865 legend 2 coordinates 83 83 39866 legend 3 coordinates 17 22 39867 legend 4 coordinates 83 22 39868 . 39869 region fill on on on on 39870 region fill color black blue red green 39871 box shadow hw 0 0 39872 . 39873 label case asis 39874 title case asis 39875 y1label Admit = Yes 39876 y2label Admit = No 39877 x1label Sex: Female 39878 x2label Sex: Male 39879 x2label displacement -74 39880 . 39881 let string t1 = Department A 39882 let string t2 = Department B 39883 let string t3 = Department C 39884 let string t4 = Department D 39885 let string t5 = Department E 39886 let string t6 = Department F 39887 . 39888 let icnt = 0 39889 let icnt2 =0 39890 loop for k = 1 1 6 39891 let icnt = icnt+1 39892 let atemp = y1(icnt) 39893 legend 1 ^atemp 39894 let atemp = y2(icnt) 39895 legend 2 ^atemp 39896 let icnt = icnt+1 39897 let atemp = y1(icnt) 39898 legend 3 ^atemp 39899 let atemp = y2(icnt) 39900 legend 4 ^atemp 39901 title ^t^k 39902 let icnt2 = icnt2 + 1 39903 if k = 3 39904 let icnt2 = icnt2 + 1 39905 end of if 39906 if k = 5 39907 let icnt2 = icnt2 + 1 39908 end of if 39909 multiplot 3 3 icnt2 39910 rose plot y1 y2 subset x = k 39911 box 15 20 85 90 39912 end of loop 39913 . 39914 end of multiplot 39915 . 39916 case asis 39917 justification center 39918 move 30 97 39919 text Rose Plots for Berkeley Admissions Data 39920 39921-----ROTATE EYE-------------------------------------------------- 39922 39923ROTATE EYE 39924 39925Name: 39926 ROTATE EYE 39927 39928Type: 39929 Plot Control Command 39930 39931Purpose: 39932 Specifies a direction and angle to rotate the current eye 39933 coordinates for 3-d plots. 39934 39935Description: 39936 Changing the viewing position allows you to view a 3-d plot from 39937 a different perspective. This can sometimes allow you to see more 39938 clearly certain structures that are hidden in the default viewing 39939 position. The ROTATE EYE command can be used to do this 39940 automatically. It is often used in conjunction with the LOOP 39941 command. 39942 39943 The rotation has both a direction and an angle. The direction can 39944 be one of the following: 39945 LEFT - rotate left (in the XY plane); 39946 RIGHT - rotate right (in the XY plane); 39947 UP - rotate up (this case not implemented yet); 39948 DOWN - rotate down (this case not implemented yet); 39949 XY - rotate in the XY plane (equivalent to RIGHT); 39950 XZ - rotate in the XZ plane; 39951 YZ - rotate in the YZ plane. 39952 The angle is specified in degrees. 39953 39954Syntax: 39955 ROTATE EYE <dir> <angle> 39956 where <dir> is one of the character strings listed above that 39957 specifies the desired direction; 39958 and <angle> is a number or parameter that specifies the number of 39959 degrees to rotate the eye coordinates. 39960 39961Examples: 39962 ROTATE 39963 ROTATE EYE 39964 ROTATE EYE 20 39965 ROTATE EYE RIGHT 39966 ROTATE EYE RIGHT 40 39967 39968Default: 39969 If the <dir> argument is omitted, LEFT is used. If the <angle> 39970 argument is omitted, 10 degrees is used. 39971 39972Synonyms: 39973 ROTATE is a synonym for ROTATE EYE. 39974 39975Related Commands: 39976 EYE COORDINATES = Specifies the eye coordinates for a 3d plot. 39977 3D-PLOT = Generates a 3-d data or function plot. 39978 3D-FRAME = Specifies what type of 3D frame is drawn. 39979 39980Applications: 39981 XX 39982 39983Implementation Date: 39984 93/10 39985 39986Program: 39987 LET FUNCTION F = SIN(X+COS(Y)) 39988 3DFRAME 3PLANE 39989 FEEDBACK OFF 39990 . 39991 MULTIPLOT 4 4; MULTIPLOT CORNER COORDINATES 0 0 100 100 39992 LOOP FOR K = 1 1 16 39993 ROTATE 39994 3DPLOT F FOR X = -2 .2 2 FOR Y = -2 .2 2 39995 END LOOP 39996 39997-----ROUND (LET)-------------------------------- 39998 39999ROUND 40000 40001Name: 40002 ROUND (LET) 40003 40004Type: 40005 Library Function 40006 40007Purpose: 40008 Compute the rounded value of a number to a user specified number of 40009 decimal places. 40010 40011Syntax: 40012 LET <y2> = ROUND(<y1>,<n>) <SUBSET/EXCEPT/FOR qualification> 40013 where <y1> is a variable or a parameter containing decimal numbers 40014 to be rounded; 40015 <n> is a number or parameter that specifies the number of 40016 decimal places to use for the rounding; 40017 <y2> is a variable or a parameter (depending on what <y1> is) 40018 where the computed rounded values are stored; 40019 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 40020 40021Examples: 40022 LET A = ROUND(14.2835,1) 40023 LET A = ROUND(A1,2) 40024 LET X2 = ROUND(X1,1) 40025 LET X2 = ROUND(X1-4,2) 40026 40027Note: 40028 Library functions are distinguished from let subcommands 40029 in the following ways. 40030 1) Functions enclose the input value in parenthesis. Let 40031 subcommands use spaces. 40032 2) Functions can accept (and return) either parameters 40033 (i.e., single values) or variables (i.e., an array of 40034 values) while let subcommands are specific in which they 40035 accept as input and what they return as output. 40036 3) Functions can accept expressions while let subcommands 40037 do not. For example, the following is legal: 40038 LET Y2 = ABS(Y1-INT(Y1)) 40039 For let subcommands, you typically have to do something 40040 like the following: 40041 LET YTEMP = Y**2 + 8 40042 LET A = SUM YTEMP 40043 40044Default: 40045 None 40046 40047Synonyms: 40048 None 40049 40050Related Commands: 40051 INT = Compute the integer portion of number. 40052 FRACT = Compute the fractional portion of number. 40053 OCTDEC = Perform an octal to decimal conversion. 40054 MOD = Compute the modulo function. 40055 40056Applications: 40057 Data Transformations 40058 40059Implementation Date: 40060 Pre-1987 40061 40062Program: 40063 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 40064 LET Y2 = ROUND(Y1,1) 40065 PRINT Y1 Y2 40066 40067-----ROWLABEL------------------------------------------------- 40068 40069ROWLABEL 40070 40071Name: 40072 ROWLABEL (LET) 40073 40074Type: 40075 Subcommand under LET 40076 40077Purpose: 40078 Converts previously read character data to row labels. 40079 40080Description: 40081 The command READ ROW LABELS can be used to read the row labels 40082 from a file. Alternatively, Dataplot can read character data 40083 using the 40084 40085 SET CONVERT CHARACTER ON 40086 40087 command. This command stores the character fields in the 40088 file "dpchzf.dat". 40089 40090 The two primary uses of character data are: 40091 40092 1) Provide a row identifier for the data. 40093 40094 2) Define a group (or factor) variable. For example, we 40095 can identify sex by coding males as M and females as F. 40096 40097 The ROWLABEL command (Syntax 1) is used to convert one of the 40098 previosuly read character variables to a row label. 40099 40100 You can also copy a string to a specific row (Syntax 2 or 40101 Syntax 3). 40102 40103 Once a row label has been defined, you can use the 40104 40105 CHARACTER ROWLABEL 40106 40107 command to label plot points. Additional uses for row labels 40108 are anticipated in future releases of Dataplot. 40109 40110Syntax 1: 40111 LET ROWLABEL = <ix> 40112 where <ix> specifies the name of the character variable in 40113 the file dpzchf.dat. 40114 40115 The character variable is originally created with a READ 40116 command where the SET CONVERT CHARACTER ON was entered prior 40117 to the READ. 40118 40119Syntax 2: 40120 LET ROWLABEL = STRING TO ROW LABEL <irow> <s> 40121 where <s> is a previously defined string; 40122 and <irow> is a parameter that identifies which row to set. 40123 40124 This syntax is used to set a specific row of the row labels to 40125 a previously defined string. 40126 40127Syntax 3: 40128 LET ROWLABEL <ival> = <string> 40129 where <string> is a literal string; 40130 and <ival> is a parameter which specifies the row number. 40131 40132 This syntax copies <string> into the <ival>-th row of the row 40133 labels. 40134 40135Syntax 4: 40136 LET ROWLABEL = DELETE 40137 40138 This syntax re-initializes all row labels to blank. 40139 labels. 40140 40141Syntax 5: 40142 LET ROWLABEL = SHIFT LEFT <ival> 40143 where <ival> is a parameter. 40144 40145 This syntax shifts all row labels left (= down) by <ival> rows. 40146 Vacated row labels will be set blank. 40147 40148Syntax 6: 40149 LET ROWLABEL = SHIFT RIGHT <ival> 40150 where <ival> is a parameter. 40151 40152 This syntax shifts all row labels right (= up) by <ival> rows. 40153 Vacated row labels will be set blank. 40154 40155Examples: 40156 SET CONVERT CHARACTER ON 40157 READ TEST.DAT Y X IX 40158 LET IG = ROW LABEL IX 40159 40160Note: 40161 Row labels can be up to 24 characters long. 40162 40163Note: 40164 Row labels can also be defined using the READ ROW LABELS 40165 command. 40166 40167Default: 40168 None 40169 40170Synonyms: 40171 None 40172 40173Related Commands: 40174 READ = Carries out a column-wise input of 40175 data. 40176 CONVERT CHARACTER = Specify how Dataplot will handle 40177 character data. 40178 CHARACTER CODE = Converts character data to a coded 40179 numeric variable. 40180 GROUP LABELS = Define row labels from character 40181 data. 40182 40183Applications: 40184 Input/Output 40185 40186Implementation Date: 40187 2004/1 40188 2012/08: Support for Syntax 2 - Syntax 6 added. 40189 40190Program 1: 40191 let rowlabel 1 = 100101 40192 let rowlabel 2 = 100102 40193 let rowlabel 3 = 100103 40194 let rowlabel 4 = 100104 40195 let rowlabel 5 = 100105 40196 let rowlabel 6 = 100106 40197 let rowlabel 7 = 100107 40198 let rowlabel 8 = 100108 40199 let rowlabel 9 = 100109 40200 let rowlabel 10 = 100110 40201 . 40202 tic mark offset units screen 40203 tic mark offset 5 5 40204 character rowlabel 40205 plot x**2 for x = 1 1 10 40206 40207Program 2: 40208 skip 25 40209 read antibody.dat lab ymean ysd nrep 40210 . 40211 title case asis 40212 label case asis 40213 x1label Mean 40214 y1label Standard Deviation 40215 . 40216 xlimits 0.8 2.4 40217 major xtic mark number 9 40218 minor xtic mark number 1 40219 ylimits 0 1.6 40220 major ytic mark number 9 40221 minor ytic mark number 1 40222 . 40223 system rm dpzchf.dat 40224 let rowlabel = lab 40225 character blank all 40226 character blank blank blank rowlabel 40227 line blank all 40228 line solid dash dotted 40229 . 40230 title Highlight/Summary Form of Homoscedasticity Plot with Contour Linescr() ... 40231 for ANTIBODY.DAT 40232 set homo plot circle technique on 40233 summary homoscedasticity plot ymean ysd nrep 40234 40235-----ROW LIMITS------------------------------------------------------- 40236 40237ROW LIMITS 40238 40239Name: 40240 ROW LIMITS 40241 40242Type: 40243 Support Command 40244 40245Purpose: 40246 Specifies the row limits in a file between which the read scan is 40247 restricted during subsequent READ and SERIAL READ commands. 40248 40249Description: 40250 The specified rows and all rows in between are included in the 40251 data read. 40252 40253Syntax: 40254 ROW LIMITS <row 1> <row 2> 40255 where <row 1> is a number or parameter that specifies the desired 40256 starting row; 40257 and <row 2> is a number or parameter that specifies the desired 40258 ending row; 40259 40260Examples: 40261 ROW LIMITS 10 30 40262 ROW LIMITS 1 15 40263 ROW LIMITS 50 63 40264 40265Note: 40266 The NLIST command can be used to list a file with row numbers. 40267 This can sometimes be useful when setting row limits. 40268 40269Default: 40270 All rows in the file are read. 40271 40272Synonyms: 40273 None 40274 40275Related Commands: 40276 READ = Reads data (column-wise) into variables. 40277 SERIAL READ = Reads data (row-wise) into variables. 40278 COLUMN LIMITS = Sets the file columns to be included in the read. 40279 SKIP = Sets the number of lines to skip over before the 40280 read. 40281 WRITE = Writes variables, parameters, and functions to 40282 the screen or to a file. 40283 LIST = Lists a file or the last 20 commands. 40284 NLIST = Lists a file with row numbers. 40285 40286Applications: 40287 Data Input 40288 40289Implementation Date: 40290 Pre-1987 40291 40292Program: 40293 XX 40294 40295-----RPOCDF (LET)-------------------------------- 40296 40297RPOCDF 40298 40299Name: 40300 RPOCDF (LET) 40301 40302Type: 40303 Library Function 40304 40305Purpose: 40306 Compute the reflected power cumulative distribution function 40307 with shape parameter c. 40308 40309Description: 40310 The standard reflected power distribution has the 40311 following cumulative distribution function: 40312 40313 F(x;c) = 1 - (1-x)**c 40314 0 <= x <= 1, c > 0 40315 40316 with c denoting the shape parameter. 40317 40318 This distribution can be extended with lower and upper 40319 bound parameters. If a and b denote the lower and upper 40320 bounds, respectively, then the location and scale 40321 parameters are: 40322 40323 location = a 40324 scale = b - a 40325 40326 The general form of the distribution can then be found 40327 by using the relation 40328 40329 F(x;c,a,b) = F((x-a)/(b-a);c,0,1) 40330 40331 The reflected power distribution is a special case of the 40332 beta distribution where the first shape parameter = 1 40333 (the power distribution is a special case of beta 40334 distribution where the second shape parameter = 1). 40335 40336Syntax: 40337 LET <y> = RPOCDF(<x>,<c>,<a>,<b>) 40338 <SUBSET/EXCEPT/FOR qualification> 40339 where <x> is a number, parameter, or variable containing 40340 values in the interval (a,b); 40341 <y> is a variable or a parameter (depending on what 40342 <x> is) where the computed reflected power cdf value 40343 is stored; 40344 <c> is a positive number, parameter, or variable that 40345 specifies the shape parameter; 40346 <a> is a number, parameter, or variable that 40347 specifies the lower limit; 40348 <b> is a number, parameter, or variable that 40349 specifies the upper limit; 40350 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 40351 40352 If <a> and <b> are omitted, they default to 0 and 1, 40353 respectively. 40354 40355Examples: 40356 LET A = RPOCDF(0.3,0.2) 40357 LET Y = RPOCDF(X,0.5,0,5) 40358 PLOT RPOCDF(X,2.3) FOR X = 0 0.01 1 40359 40360Note: 40361 Library functions are distinguished from let subcommands 40362 in the following ways. 40363 1) Functions enclose the input value in parenthesis. Let 40364 subcommands use spaces. 40365 2) Functions can accept (and return) either parameters 40366 (i.e., single values) or variables (i.e., an array of 40367 values) while let subcommands are specific in which they 40368 accept as input and what they return as output. 40369 3) Functions can accept expressions while let subcommands 40370 do not. For example, the following is legal: 40371 LET Y2 = ABS(Y1-INT(Y1)) 40372 For let subcommands, you typically have to do something 40373 like the following: 40374 LET YTEMP = Y**2 + 8 40375 LET A = SUM YTEMP 40376 40377Default: 40378 None 40379 40380Synonyms: 40381 None 40382 40383Related Commands: 40384 RPOPDF = Compute the reflected power probability density 40385 function. 40386 RPOPPF = Compute the reflected power percent point function. 40387 RPOHAZ = Compute the reflected power hazard function. 40388 RPOCHAZ = Compute the reflected power cumulative hazard 40389 function. 40390 POWPDF = Compute the power probability density function. 40391 BETPDF = Compute the beta probability density function. 40392 TOPPDF = Compute the Topp and Leone probability density 40393 function. 40394 RGTPDF = Compute the generalized reflected Topp and Leone 40395 probability density function. 40396 GTLPDF = Compute the generalized Topp and Leone probability 40397 density function. 40398 TSPPDF = Compute the two-sided power probability density 40399 function. 40400 TRIPDF = Compute the triangular probability density function. 40401 TRAPDF = Compute the trapezoid probability density function. 40402 UNIPDF = Compute the uniform probability density function. 40403 JSBPDF = Compute the Johnson SB probability density function. 40404 40405Reference: 40406 Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Beta: 40407 Other Continuous Families of Distributions with Bounded 40408 Support and Applications", World Scientific, pp. 199-201. 40409 40410Applications: 40411 Distributional Modeling 40412 40413Implementation Date: 40414 2007/12 40415 40416Program: 40417 LABEL CASE ASIS 40418 TITLE CASE ASIS 40419 TITLE OFFSET 2 40420 . 40421 MULTIPLOT 2 2 40422 MULTIPLOT CORNER COORDINATES 0 0 100 95 40423 MULTIPLOT SCALE FACTOR 40424 . 40425 LET C = 0.5 40426 TITLE C = ^c 40427 PLOT RPOCDF(X,C) FOR X = 0 0.01 1 40428 . 40429 LET C = 1 40430 TITLE C = ^c 40431 PLOT RPOCDF(X,C) FOR X = 0 0.01 1 40432 . 40433 LET C = 1.5 40434 TITLE C = ^c 40435 PLOT RPOCDF(X,C) FOR X = 0 0.01 1 40436 . 40437 LET C = 2 40438 TITLE C = ^c 40439 PLOT RPOCDF(X,C) FOR X = 0 0.01 1 40440 . 40441 END OF MULTIPLOT 40442 . 40443 JUSTIFICATION CENTER 40444 MOVE 50 97 40445 TEXT Reflected Power Cumulative Distribution Functions 40446 40447-----RPOCHAZ (LET)-------------------------------- 40448 40449RPOCHAZ 40450 40451Name: 40452 RPOCHAZ (LET) 40453 40454Type: 40455 Library Function 40456 40457Purpose: 40458 Compute the reflected power cumulative hazard function 40459 with shape parameter c. 40460 40461Description: 40462 The standard reflected power distribution has the 40463 following cumulative hazard function: 40464 40465 H(x;c) = -LOG((1-x)**c) 40466 0 <= x <= 1, c > 0 40467 40468 with c denoting the shape parameter. 40469 40470 This distribution can be extended with lower and upper 40471 bound parameters. If a and b denote the lower and upper 40472 bounds, respectively, then the location and scale 40473 parameters are: 40474 40475 location = a 40476 scale = b - a 40477 40478 The general form of the distribution can then be found 40479 by using the relation 40480 40481 H(x;c,a,b) = H((x-a)/(b-a);c,0,1) 40482 40483 The reflected power distribution is a special case of the 40484 beta distribution where the first shape parameter = 1 40485 (the power distribution is a special case of beta 40486 distribution where the second shape parameter = 1). 40487 40488Syntax: 40489 LET <y> = RPOCHAZ(<x>,<c>,<a>,<b>) 40490 <SUBSET/EXCEPT/FOR qualification> 40491 where <x> is a number, parameter, or variable containing 40492 values in the interval (a,b); 40493 <y> is a variable or a parameter (depending on what 40494 <x> is) where the computed reflected power cumulative 40495 hazard value is stored; 40496 <c> is a positive number, parameter, or variable that 40497 specifies the shape parameter; 40498 <a> is a number, parameter, or variable that 40499 specifies the lower limit; 40500 <b> is a number, parameter, or variable that 40501 specifies the upper limit; 40502 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 40503 40504 If <a> and <b> are omitted, they default to 0 and 1, 40505 respectively. 40506 40507Examples: 40508 LET A = RPOCHAZ(0.3,0.2) 40509 LET Y = RPOCHAZ(X,0.5,0,5) 40510 PLOT RPOCHAZ(X,2.3) FOR X = 0 0.01 0.99 40511 40512Note: 40513 Library functions are distinguished from let subcommands 40514 in the following ways. 40515 1) Functions enclose the input value in parenthesis. Let 40516 subcommands use spaces. 40517 2) Functions can accept (and return) either parameters 40518 (i.e., single values) or variables (i.e., an array of 40519 values) while let subcommands are specific in which they 40520 accept as input and what they return as output. 40521 3) Functions can accept expressions while let subcommands 40522 do not. For example, the following is legal: 40523 LET Y2 = ABS(Y1-INT(Y1)) 40524 For let subcommands, you typically have to do something 40525 like the following: 40526 LET YTEMP = Y**2 + 8 40527 LET A = SUM YTEMP 40528 40529Default: 40530 None 40531 40532Synonyms: 40533 None 40534 40535Related Commands: 40536 RPOPDF = Compute the reflected power probability density 40537 function. 40538 RPOCDF = Compute the reflected power cumulative distribution 40539 function. 40540 RPOPPF = Compute the reflected power percent point function. 40541 RPOHAZ = Compute the reflected power hazard function. 40542 POWPDF = Compute the power probability density function. 40543 BETPDF = Compute the beta probability density function. 40544 TOPPDF = Compute the Topp and Leone probability density 40545 function. 40546 RGTPDF = Compute the generalized reflected Topp and Leone 40547 probability density function. 40548 GTLPDF = Compute the generalized Topp and Leone probability 40549 density function. 40550 TSPPDF = Compute the two-sided power probability density 40551 function. 40552 TRIPDF = Compute the triangular probability density function. 40553 TRAPDF = Compute the trapezoid probability density function. 40554 UNIPDF = Compute the uniform probability density function. 40555 JSBPDF = Compute the Johnson SB probability density function. 40556 40557Reference: 40558 Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Beta: 40559 Other Continuous Families of Distributions with Bounded 40560 Support and Applications", World Scientific, pp. 199-201. 40561 40562Applications: 40563 Distributional Modeling 40564 40565Implementation Date: 40566 2007/12 40567 40568Program: 40569 LABEL CASE ASIS 40570 TITLE CASE ASIS 40571 TITLE OFFSET 2 40572 . 40573 MULTIPLOT 2 2 40574 MULTIPLOT CORNER COORDINATES 0 0 100 95 40575 MULTIPLOT SCALE FACTOR 40576 . 40577 LET C = 0.5 40578 TITLE C = ^c 40579 PLOT RPOCHAZ(X,C) FOR X = 0 0.01 0.99 40580 . 40581 LET C = 1 40582 TITLE C = ^c 40583 PLOT RPOCHAZ(X,C) FOR X = 0 0.01 0.99 40584 . 40585 LET C = 1.5 40586 TITLE C = ^c 40587 PLOT RPOCHAZ(X,C) FOR X = 0 0.01 0.99 40588 . 40589 LET C = 2 40590 TITLE C = ^c 40591 PLOT RPOCHAZ(X,C) FOR X = 0 0.01 0.99 40592 . 40593 END OF MULTIPLOT 40594 . 40595 JUSTIFICATION CENTER 40596 MOVE 50 97 40597 TEXT Reflected Power Cumulative Hazard Functions 40598 40599-----RPOHAZ (LET)-------------------------------- 40600 40601RPOHAZ 40602 40603Name: 40604 RPOHAZ (LET) 40605 40606Type: 40607 Library Function 40608 40609Purpose: 40610 Compute the reflected power hazard function with 40611 shape parameter c. 40612 40613Description: 40614 The standard reflected power distribution has the 40615 following hazard function: 40616 40617 h(x;c) = c/(1-x) 40618 0 <= x <= 1, c > 0 40619 40620 with c denoting the shape parameter. 40621 40622 This distribution can be extended with lower and upper 40623 bound parameters. If a and b denote the lower and upper 40624 bounds, respectively, then the location and scale 40625 parameters are: 40626 40627 location = a 40628 scale = b - a 40629 40630 The general form of the distribution can then be found 40631 by using the relation 40632 40633 h(x;c,a,b) = (1/(b-a))*h((x-a)/(b-a);c,0,1) 40634 40635 The reflected power distribution is a special case of the 40636 beta distribution where the first shape parameter = 1 40637 (the power distribution is a special case of beta 40638 distribution where the second shape parameter = 1). 40639 40640Syntax: 40641 LET <y> = RPOHAZ(<x>,<c>,<a>,<b>) 40642 <SUBSET/EXCEPT/FOR qualification> 40643 where <x> is a number, parameter, or variable containing 40644 values in the interval (a,b); 40645 <y> is a variable or a parameter (depending on what 40646 <x> is) where the computed reflected power hazard 40647 value is stored; 40648 <c> is a positive number, parameter, or variable that 40649 specifies the shape parameter; 40650 <a> is a number, parameter, or variable that 40651 specifies the lower limit; 40652 <b> is a number, parameter, or variable that 40653 specifies the upper limit; 40654 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 40655 40656 If <a> and <b> are omitted, they default to 0 and 1, 40657 respectively. 40658 40659Examples: 40660 LET A = RPOHAZ(0.3,0.2) 40661 LET Y = RPOHAZ(X,0.5,0,5) 40662 PLOT RPOHAZ(X,2.3) FOR X = 0 0.01 1 40663 40664Note: 40665 Library functions are distinguished from let subcommands 40666 in the following ways. 40667 1) Functions enclose the input value in parenthesis. Let 40668 subcommands use spaces. 40669 2) Functions can accept (and return) either parameters 40670 (i.e., single values) or variables (i.e., an array of 40671 values) while let subcommands are specific in which they 40672 accept as input and what they return as output. 40673 3) Functions can accept expressions while let subcommands 40674 do not. For example, the following is legal: 40675 LET Y2 = ABS(Y1-INT(Y1)) 40676 For let subcommands, you typically have to do something 40677 like the following: 40678 LET YTEMP = Y**2 + 8 40679 LET A = SUM YTEMP 40680 40681Default: 40682 None 40683 40684Synonyms: 40685 None 40686 40687Related Commands: 40688 RPOPDF = Compute the reflected power probability density 40689 function. 40690 RPOCDF = Compute the reflected power cumulative distribution 40691 function. 40692 RPOPPF = Compute the reflected power percent point function. 40693 RPOCHAZ = Compute the reflected power cumulative hazard 40694 function. 40695 POWPDF = Compute the power probability density function. 40696 BETPDF = Compute the beta probability density function. 40697 TOPPDF = Compute the Topp and Leone probability density 40698 function. 40699 RGTPDF = Compute the generalized reflected Topp and Leone 40700 probability density function. 40701 GTLPDF = Compute the generalized Topp and Leone probability 40702 density function. 40703 TSPPDF = Compute the two-sided power probability density 40704 function. 40705 TRIPDF = Compute the triangular probability density function. 40706 TRAPDF = Compute the trapezoid probability density function. 40707 UNIPDF = Compute the uniform probability density function. 40708 JSBPDF = Compute the Johnson SB probability density function. 40709 40710Reference: 40711 Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Beta: 40712 Other Continuous Families of Distributions with Bounded 40713 Support and Applications", World Scientific, pp. 199-201. 40714 40715Applications: 40716 Distributional Modeling 40717 40718Implementation Date: 40719 2007/12 40720 40721Program: 40722 LABEL CASE ASIS 40723 TITLE CASE ASIS 40724 TITLE OFFSET 2 40725 . 40726 MULTIPLOT 2 2 40727 MULTIPLOT CORNER COORDINATES 0 0 100 95 40728 MULTIPLOT SCALE FACTOR 40729 . 40730 LET C = 0.5 40731 TITLE C = ^c 40732 PLOT RPOHAZ(X,C) FOR X = 0.01 0.01 0.99 40733 . 40734 LET C = 1 40735 TITLE C = ^c 40736 PLOT RPOHAZ(X,C) FOR X = 0.01 0.01 0.99 40737 . 40738 LET C = 1.5 40739 TITLE C = ^c 40740 PLOT RPOHAZ(X,C) FOR X = 0.01 0.01 0.99 40741 . 40742 LET C = 2 40743 TITLE C = ^c 40744 PLOT RPOHAZ(X,C) FOR X = 0.01 0.01 0.99 40745 . 40746 END OF MULTIPLOT 40747 . 40748 JUSTIFICATION CENTER 40749 MOVE 50 97 40750 TEXT Reflected Power Hazard Functions 40751 40752-----RPOPDF (LET)-------------------------------- 40753 40754RPOPDF 40755 40756Name: 40757 RPOPDF (LET) 40758 40759Type: 40760 Library Function 40761 40762Purpose: 40763 Compute the reflected power probability density function 40764 with shape parameter c. 40765 40766Description: 40767 The standard reflected power distribution has the 40768 following probability density function: 40769 40770 f(x;c) = c*(1-x)**(c-1) 40771 0 <= x <= 1, c > 0 40772 40773 with c denoting the shape parameter. 40774 40775 This distribution can be extended with lower and upper 40776 bound parameters. If a and b denote the lower and upper 40777 bounds, respectively, then the location and scale 40778 parameters are: 40779 40780 location = a 40781 scale = b - a 40782 40783 The general form of the distribution can then be found 40784 by using the relation 40785 40786 f(x;c,a,b) = f((x-a)/(b-a);c,0,1)/(b-a) 40787 40788 The reflected power distribution is a special case of the 40789 beta distribution where the first shape parameter = 1 40790 (the power distribution is a special case of the beta 40791 distribution where the second shape parameter = 1). 40792 40793Syntax: 40794 LET <y> = RPOPDF(<x>,<c>,<a>,<b>) 40795 <SUBSET/EXCEPT/FOR qualification> 40796 where <x> is a number, parameter, or variable containing 40797 values in the interval (a,b); 40798 <y> is a variable or a parameter (depending on what 40799 <x> is) where the computed reflected power pdf value 40800 is stored; 40801 <c> is a positive number, parameter, or variable that 40802 specifies the shape parameter; 40803 <a> is a number, parameter, or variable that 40804 specifies the lower limit; 40805 <b> is a number, parameter, or variable that 40806 specifies the upper limit; 40807 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 40808 40809 If <a> and <b> are omitted, they default to 0 and 1, 40810 respectively. 40811 40812Examples: 40813 LET A = RPOPDF(0.3,0.2) 40814 LET Y = RPOPDF(X,0.5,0,5) 40815 PLOT RPOPDF(X,2.3) FOR X = 0 0.01 1 40816 40817Note: 40818 Reflected power random numbers, probability plots, and 40819 goodness of fit tests can be generated with the commands: 40820 40821 LET C = <value> 40822 LET A = <value> 40823 LET B = <value> 40824 LET Y = REFLECTED POWER RANDOM NUMBERS FOR I = 1 1 N 40825 REFLECTED POWER PROBABILITY PLOT Y 40826 REFLECTED POWER PROBABILITY PLOT Y2 X2 40827 REFLECTED POWER PROBABILITY PLOT Y3 XLOW XHIGH 40828 REFLECTED POWER KOLMOGOROV SMIRNOV GOODNESS OF FIT Y 40829 REFLECTED POWER CHI-SQUARE GOODNESS OF FIT Y2 X2 40830 REFLECTED POWER CHI-SQUARE GOODNESS OF FIT Y3 XLOW XHIGH 40831 40832 The following commands can be used to estimate the c 40833 shape parameter for the reflected power distribution: 40834 40835 LET C1 = <value> 40836 LET C2 = <value> 40837 REFLECTED POWER PPCC PLOT Y 40838 REFLECTED POWER PPCC PLOT Y2 X2 40839 REFLECTED POWER PPCC PLOT Y3 XLOW XHIGH 40840 REFLECTED POWER KS PLOT Y 40841 REFLECTED POWER KS PLOT Y2 X2 40842 REFLECTED POWER KS PLOT Y3 XLOW XHIGH 40843 40844 The default values for C1 and C2 are 0.5 and 25. 40845 40846 The probability plot can then be used to estimate the 40847 lower and upper limits (lower limit = PPA0, 40848 upper limit = PPA0 + PPA1). 40849 40850 The following options may be useful for these commands. 40851 40852 1) Instead of generating the ppcc plot or ks plot on 40853 the original data, we can generate them on 40854 selected percentiles of the data. For example, 40855 if we have 1,000 points, we can choose to generate 40856 the plots on 100 evenly spaced percentiles with 40857 the command 40858 40859 SET PPCC PLOT DATA POINTS 100 40860 40861 This can be used to speed up the generation of 40862 the plot for larger data sets. 40863 40864 The percent point function for the reflected power 40865 distribution is available in closed form, so 40866 this option is typically not needed. 40867 40868 2) For the ks plot, we can fix the location and scale. 40869 This is equivalent to assuming that the lower and 40870 upper limits are known (e.g., we could use the 40871 data minimum and maximum as the lower and upper 40872 limit values). Given that the lower and upper 40873 limits are LOWLIM and UPPLIM, enter the commands 40874 40875 LET KSLOC = LOWLIM 40876 LET KSSCALE = UPPLIM 40877 40878 The ppcc plot is invariant to location and scale, 40879 so we cannot fix the lower and upper limits. 40880 40881 The BOOTSTRAP DISTRIBUTION command can be used to find 40882 uncertainty intervals for the ppcc plot, ks plot, and 40883 maximum likelihood estimates. 40884 40885Note: 40886 Library functions are distinguished from let subcommands 40887 in the following ways. 40888 1) Functions enclose the input value in parenthesis. Let 40889 subcommands use spaces. 40890 2) Functions can accept (and return) either parameters 40891 (i.e., single values) or variables (i.e., an array of 40892 values) while let subcommands are specific in which they 40893 accept as input and what they return as output. 40894 3) Functions can accept expressions while let subcommands 40895 do not. For example, the following is legal: 40896 LET Y2 = ABS(Y1-INT(Y1)) 40897 For let subcommands, you typically have to do something 40898 like the following: 40899 LET YTEMP = Y**2 + 8 40900 LET A = SUM YTEMP 40901 40902Default: 40903 None 40904 40905Synonyms: 40906 None 40907 40908Related Commands: 40909 RPOCDF = Compute the reflected power cumulative distribution 40910 function. 40911 RPOPPF = Compute the reflected power percent point function. 40912 RPOHAZ = Compute the reflected power hazard function. 40913 RPOCHAZ = Compute the reflected power cumulative hazard 40914 POWPDF = Compute the power probability density function. 40915 BETPDF = Compute the beta probability density function. 40916 TOPPDF = Compute the Topp and Leone probability density 40917 function. 40918 RGTPDF = Compute the generalized reflected Topp and Leone 40919 probability density function. 40920 GTLPDF = Compute the generalized Topp and Leone probability 40921 density function. 40922 TSPPDF = Compute the two-sided power probability density 40923 function. 40924 TRIPDF = Compute the triangular probability density function. 40925 TRAPDF = Compute the trapezoid probability density function. 40926 UNIPDF = Compute the uniform probability density function. 40927 JSBPDF = Compute the Johnson SB probability density function. 40928 40929Reference: 40930 Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Beta: 40931 Other Continuous Families of Distributions with Bounded 40932 Support and Applications", World Scientific, pp. 199-201. 40933 40934Applications: 40935 Distributional Modeling 40936 40937Implementation Date: 40938 2007/12 40939 40940Program 1: 40941 LABEL CASE ASIS 40942 TITLE CASE ASIS 40943 TITLE OFFSET 2 40944 . 40945 MULTIPLOT 2 2 40946 MULTIPLOT CORNER COORDINATES 0 0 100 95 40947 MULTIPLOT SCALE FACTOR 40948 . 40949 LET C = 0.5 40950 TITLE C = ^c 40951 PLOT RPOPDF(X,C) FOR X = 0 0.01 0.99 40952 . 40953 LET C = 1 40954 TITLE C = ^c 40955 PLOT RPOPDF(X,C) FOR X = 0 0.01 1 40956 . 40957 LET C = 1.5 40958 TITLE C = ^c 40959 PLOT RPOPDF(X,C) FOR X = 0 0.01 1 40960 . 40961 LET C = 2 40962 TITLE C = ^c 40963 PLOT RPOPDF(X,C) FOR X = 0 0.01 1 40964 . 40965 END OF MULTIPLOT 40966 . 40967 JUSTIFICATION CENTER 40968 MOVE 50 97 40969 TEXT Reflected Power Probability Density Functions 40970 40971Program 2: 40972 let c = 2.2 40973 let y = reflected power rand numb for i = 1 1 200 40974 let csav = c 40975 . 40976 let c1 = 0.5 40977 let c2 = 4 40978 reflected power ppcc plot y 40979 just center 40980 move 50 5 40981 let c = shape 40982 text maxppcc = ^maxppcc, C = ^c 40983 move 50 2 40984 text Csav = ^csav 40985 . 40986 char x 40987 line blank 40988 reflected power prob plot y 40989 move 50 5 40990 text PPA0 = ^ppa0, PPA1 = ^ppa1 40991 move 50 2 40992 let upplim = ppa0 + ppa1 40993 text Lower Limit = ^ppa0, Upper Limit = ^upplim 40994 char blank 40995 line solid 40996 . 40997 class lower 0 40998 class upper 1 40999 class width 0.05 41000 relative hist y 41001 line color blue 41002 limits freeze 41003 pre-erase off 41004 let a = ppa0 41005 let b = a + (ppa1 - ppa0) 41006 plot rpopdf(x,c,a,b) for x = a 0.01 b 41007 limits 41008 pre-erase on 41009 line color black all 41010 . 41011 let ksloc = ppa0 41012 let ksscale = upplim 41013 reflected power kolm smir goodness of fit y 41014 41015-----RPOPPF (LET)-------------------------------- 41016 41017RPOPPF 41018 41019Name: 41020 RPOPPF (LET) 41021 41022Type: 41023 Library Function 41024 41025Purpose: 41026 Compute the reflected power percent point function 41027 with shape parameter c. 41028 41029Description: 41030 The standard reflected power distribution has the 41031 following percent point function: 41032 41033 G(p;c) = 1 - (1-p)**(1/c) 41034 0 <= p <= 1, c > 0 41035 41036 with c denoting the shape parameter. 41037 41038 This distribution can be extended with lower and upper 41039 bound parameters. If a and b denote the lower and upper 41040 bounds, respectively, then the location and scale 41041 parameters are: 41042 41043 location = a 41044 scale = b - a 41045 41046 The general form of the distribution can then be found 41047 by using the relation 41048 41049 G(p;c,a,b) = a + (b-a)*G(p;c,0,1) 41050 41051 The reflected power distribution is a special case of the 41052 beta distribution where the first shape parameter = 1 41053 (the power distribution is a special case of beta 41054 distribution where the second shape parameter = 1). 41055 41056Syntax: 41057 LET <y> = RPOPPF(<p>,<c>,<a>,<b>) 41058 <SUBSET/EXCEPT/FOR qualification> 41059 where <p> is a number, parameter, or variable containing 41060 values in the interval (0,1); 41061 <y> is a variable or a parameter (depending on what 41062 <p> is) where the computed reflected power ppf value 41063 is stored; 41064 <c> is a positive number, parameter, or variable that 41065 specifies the shape parameter; 41066 <a> is a number, parameter, or variable that 41067 specifies the lower limit; 41068 <b> is a number, parameter, or variable that 41069 specifies the upper limit; 41070 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 41071 41072 If <a> and <b> are omitted, they default to 0 and 1, 41073 respectively. 41074 41075Examples: 41076 LET A = RPOPPF(0.95,0.2) 41077 LET Y = RPOPPF(X,0.5,0,5) 41078 PLOT RPOPPF(X,2.3) FOR X = 0 0.01 1 41079 41080Note: 41081 Library functions are distinguished from let subcommands 41082 in the following ways. 41083 1) Functions enclose the input value in parenthesis. Let 41084 subcommands use spaces. 41085 2) Functions can accept (and return) either parameters 41086 (i.e., single values) or variables (i.e., an array of 41087 values) while let subcommands are specific in which they 41088 accept as input and what they return as output. 41089 3) Functions can accept expressions while let subcommands 41090 do not. For example, the following is legal: 41091 LET Y2 = ABS(Y1-INT(Y1)) 41092 For let subcommands, you typically have to do something 41093 like the following: 41094 LET YTEMP = Y**2 + 8 41095 LET A = SUM YTEMP 41096 41097Default: 41098 None 41099 41100Synonyms: 41101 None 41102 41103Related Commands: 41104 RPOPDF = Compute the reflected power probability density 41105 function. 41106 RPOCDF = Compute the reflected power cumulative distribution 41107 function. 41108 RPOHAZ = Compute the reflected power hazard function. 41109 RPOCHAZ = Compute the reflected power cumulative hazard 41110 function. 41111 POWPDF = Compute the power probability density function. 41112 BETPDF = Compute the beta probability density function. 41113 TOPPDF = Compute the Topp and Leone probability density 41114 function. 41115 RGTPDF = Compute the generalized reflected Topp and Leone 41116 probability density function. 41117 GTLPDF = Compute the generalized Topp and Leone probability 41118 density function. 41119 TSPPDF = Compute the two-sided power probability density 41120 function. 41121 TRIPDF = Compute the triangular probability density function. 41122 TRAPDF = Compute the trapezoid probability density function. 41123 UNIPDF = Compute the uniform probability density function. 41124 JSBPDF = Compute the Johnson SB probability density function. 41125 41126Reference: 41127 Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Beta: 41128 Other Continuous Families of Distributions with Bounded 41129 Support and Applications", World Scientific, pp. 199-201. 41130 41131Applications: 41132 Distributional Modeling 41133 41134Implementation Date: 41135 2007/12 41136 41137Program: 41138 LABEL CASE ASIS 41139 TITLE CASE ASIS 41140 TITLE OFFSET 2 41141 . 41142 MULTIPLOT 2 2 41143 MULTIPLOT CORNER COORDINATES 0 0 100 95 41144 MULTIPLOT SCALE FACTOR 41145 . 41146 LET C = 0.5 41147 TITLE C = ^c 41148 PLOT RPOPPF(P,C) FOR P = 0.01 0.01 1 41149 . 41150 LET C = 1 41151 TITLE C = ^c 41152 PLOT RPOPPF(P,C) FOR P = 0 0.01 1 41153 . 41154 LET C = 1.5 41155 TITLE C = ^c 41156 PLOT RPOPPF(P,C) FOR P = 0 0.01 1 41157 . 41158 LET C = 2 41159 TITLE C = ^c 41160 PLOT RPOPPF(P,C) FOR P = 0 0.01 1 41161 . 41162 END OF MULTIPLOT 41163 . 41164 JUSTIFICATION CENTER 41165 MOVE 50 97 41166 TEXT Reflected Power Percent Point Functions 41167 41168-----RSCRIPT------------------------------------------------------- 41169 41170RSCRIPT 41171 41172Name: 41173 RSCRIPT 41174 41175Type: 41176 Support Command 41177 41178Purpose: 41179 Run an R script within a Dataplot session. 41180 41181Description: 41182 It may on occassion be useful to run an R script within a Dataplot 41183 session. Note that Dataplot assumes that R is already installed on 41184 your local system. Also, any R packages that your script needs should 41185 already be installed. Dataplot does not initiate an install of R if 41186 it not already installed. 41187 41188 If R is not installed on your default path, you can specify it 41189 using the SET R PATH command. For example, the following can 41190 be used for version 3.6.1 under Windows 41191 41192 set r path "c:\program files\r\r-3.6.1\bin\" 41193 41194 On Linux systems, R is typically installed in "/usr/bin" which is in 41195 the default path on most systems. So for Linux systems, the 41196 SET R PATH command is typically not required. However, if R is not 41197 in the default path, you can use the SET R PATH command. 41198 41199 On Windows platforms, the RSCRIPT command is equivalent to entering 41200 41201 set system persist off 41202 set system hidden on 41203 system <r-path>\rscript.exe <r-script-file> <arg-list> 41204 41205 Note that if either the R path or the <r-script-file> contains 41206 spaces (and so will be quoted), then "set system hidden" will be 41207 set to "off". 41208 41209 On Linux platforms, the RSCRIPT command is equivalent to entering 41210 41211 system <r-path>/Rscript <r-script-file> <arg-list> 41212 41213 Rscript is a binary front end to R for scripting with R. 41214 41215Syntax: 41216 RSCRIPT <script-file> <arg-list> 41217 where <script-file> contains the name of a file containing an 41218 R script; 41219 and where <arg-list> is an optional list of arguments to the script. 41220 41221Examples: 41222 RSCRIPT plot.R 41223 41224Note: 41225 This command is host dependent. It has been tested on Windows 41226 and Linux systems. Note that the SYSTEM command must be activated 41227 for this command to work. 41228 41229Note: 41230 Dataplot does no error checking on the specified script file. It 41231 is passed as is to the Rscript (RSCRIPT.EXE) command. 41232 41233Note: 41234 The CAPTURE SCRIPT command can be used to generate the R script 41235 within a Dataplot macro. This is demonstrated in the Program 41236 example below. 41237 41238Note: 41239 The name of the script file is case sensitive on Linux and MacOS 41240 systems. It is not case sensitive on Windows systems. 41241 41242 If Dataplot does not find the R script file, it will search for 41243 it in the "scripts" sub-directory in the Dataplot auxiliary 41244 directory. Currently (2019/12), there are no R scripts in that 41245 directory, although this may change in future releases of Dataplot. 41246 41247Note: 41248 Dataplot does not support R as a synonym for RSCRIPT. This is 41249 due to the fact that R has long been used as a synonym for the 41250 REPEAT command. 41251 41252Default: 41253 None 41254 41255Synonyms: 41256 None 41257 41258Related Commands: 41259 SYSTEM = Issue an operating system command within Dataplot. 41260 PYTHON = Run a Python script within Dataplot. 41261 CAPTURE SCRIPT = Create a script file within Dataplot. 41262 PSVIEW = View Postscript, PDF and image files. 41263 LIST = View the contents of a file. 41264 41265Applications: 41266 Run R scripts 41267 41268Implementation Date: 41269 2019/12 41270 41271Program: 41272 . Step 1: Create the R script using "capture script" 41273 . 41274 rm rout.txt rout.pdf r_test.r 41275 . 41276 capture script r_test.r 41277 # This is R program file r_test.r 11/4/19 41278 # Purpose: Generate a sequence, square it, and plot it 41279 # Date: 11/4/19 41280 # 41281 # -----start point----- 41282 # 41283 x=seq(1,20,length.out=20) 41284 y=x^2 41285 both=c(x,y) 41286 41287 sink("rout.txt") 41288 both 41289 sink() 41290 41291 pdf("rout.pdf") 41292 plot(x,y) 41293 dev.off() 41294 end of capture 41295 . 41296 list r_test.r 41297 . 41298 . Step 2: Determine if running on Windows or Linux and set R path 41299 . 41300 let computer = 1 41301 probe iopsy1 41302 if probeval = 1 41303 let computer = 2 41304 end of if 41305 . 41306 . May need to tweak path for R based on version and 41307 . optionally set desired Postscript viewer 41308 . 41309 if computer = 1 41310 set r path "c:\program files\r\r-3.6.1\bin\" 41311 end of if 41312 . 41313 . Step 3: Run the R script 41314 . 41315 rscript r_test.r 41316 . 41317 . Step 4: Display the outputs in Dataplot 41318 . 41319 list rout.txt 41320 . 41321 psview rout.pdf 41322 41323-----RUKHIN 1 TEST (LET)-------------------------- 41324 41325RUKHIN 1 TEST 41326 41327Name: 41328 RUKHIN 1 TEST (LET) 41329 41330Type: 41331 Let Subcommand 41332 41333Purpose: 41334 For three binomial proportions, compute the p-value and lower and 41335 upper confidence limits for 41336 41337 H0: p1 = p2*p3 41338 41339 where p1, p2, and p3 are the four binomial proportions. 41340 41341Description: 41342 For each of the binomial proportions, we actually use the 41343 correction terms 41344 41345 p(i) = (x(i) + 0.5)/(n(i) + 1) 41346 41347 with p(i), x(i), and n(i) denoting the binomial proportion, 41348 the number of successes and the number of trials for the i-th 41349 binomial proportion. 41350 41351 The computed test statistic is 41352 41353 p1 - p2*p3 41354 41355 and the associated standard error is 41356 41357 SE = SQRT(term1 + term2 + term3) 41358 41359 where 41360 41361 term1 = p1*(1 - p1)/n1 41362 term2 = (p3**2)*p2*(1 - p2)/n2 41363 term3 = (p2**2)*p3*(1 - p3)/n3 41364 41365 The p-value for a lower tailed test is 41366 41367 1 - NORCDF((p2*p3 - p1)/SE) 41368 41369 The p-value for an upper tailed test is 41370 41371 1 - NORCDF((p1 - p2*p3)/SE) 41372 41373 The p-value for a two tailed test is 41374 41375 2*(1 - NORCDF((p1 - p2*p3)/SE) 41376 41377 The confidence interval is 41378 41379 (p1 - p2*p3) +/- NORPPF(ALPHA/2)*SE 41380 41381 Although this is a fairly specialized test, it does have 41382 applicability in the following test scenario. Suppose we are 41383 testing scanning devices to see if they can detect certain 41384 radionuclides. Further suppose that in one case we have a "primary" 41385 screening device and then a "secondary" screening device. For 41386 example, the "primary" device may be an alarm which then sends the 41387 object to a more accurate (but more costly or more time consuming) 41388 device to perform an id. In this case, the binomial success for the 41389 primary device is that it alarms when the radionuclide is present and 41390 the binomial success for the secondary device is that it returns the 41391 correct id. The RUKHIN 1 test could then be used to compare the 41392 performance of the primary/secondary device relative to using the 41393 secondary device only. In this testing scenario, it is common for 41394 the primary device to be "moving" while the secondary device is 41395 typically "stationary". So the more accurate device may not 41396 perform as well when it is used as a primary device relative to 41397 its use as a secondary device. 41398 41399Syntax 1: 41400 LET <pval> <lowlim> <upplim> = RUKHIN 1 TEST 41401 <p1> <n1> <p2> <n2> <p3> <n3> <alpha> 41402 <SUBSET/EXCEPT/FOR qualification> 41403 where <p1> is constant, parameter, or variable that contains the 41404 proportion of successes for the first sample; 41405 <n1> is constant, parameter, or variable that contains the 41406 number of trials for the first sample; 41407 <p2> is constant, parameter, or variable that contains the 41408 proportion of successes for the second sample; 41409 <n2> is constant, parameter, or variable that contains the 41410 number of trials for the second sample; 41411 <p3> is constant, parameter, or variable that contains the 41412 proportion of successes for the third sample; 41413 <n3> is constant, parameter, or variable that contains the 41414 number of trials for the third sample; 41415 <alpha> is constant or parameter that contains the significance 41416 level; 41417 <pval> contains the returned p-value; 41418 <lowlim> contains the computed lower confidence limit; 41419 <upplim> contains the computed upper confidence limit; 41420 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 41421 41422 This syntax performs a two-tailed hypothesis test. 41423 41424 The <p1>, <n1>, <p2>, <n2>, <p3>, and <n3> arguments can be either 41425 parameters or variables. If they are variables, then the variables 41426 must have the same number of elements. The <alpha> argument is 41427 always assumed to be either a constant or a parameter. 41428 41429 If the arguments are all parameters, then <pval>, <lowlim> and 41430 <upplim> will be parameters. Otherwise, they will be variables. 41431 41432Syntax 2: 41433 LET <pval> <lowlim> <upplim> = RUKHIN 1 LOWER TAIL TEST 41434 <p1> <n1> <p2> <n2> <p3> <n3> <alpha> 41435 <SUBSET/EXCEPT/FOR qualification> 41436 where <p1> is constant, parameter, or variable that contains the 41437 proportion of successes for the first sample; 41438 <n1> is constant, parameter, or variable that contains the 41439 number of trials for the first sample; 41440 <p2> is constant, parameter, or variable that contains the 41441 proportion of successes for the second sample; 41442 <n2> is constant, parameter, or variable that contains the 41443 number of trials for the second sample; 41444 <p3> is constant, parameter, or variable that contains the 41445 proportion of successes for the third sample; 41446 <n3> is constant, parameter, or variable that contains the 41447 number of trials for the third sample; 41448 <alpha> is constant or parameter that contains the significance 41449 level; 41450 <pval> contains the returned p-value; 41451 <lowlim> contains the computed lower confidence limit; 41452 <upplim> contains the computed upper confidence limit; 41453 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 41454 41455 This syntax performs a lower-tailed hypothesis test. However, 41456 the confidence limits correspond to the two-tailed test. 41457 41458 The <p1>, <n1>, <p2>, <n2>, <p3>, and <n3> arguments can be either 41459 parameters or variables. If they are variables, then the variables 41460 must have the same number of elements. The <alpha> argument is 41461 always assumed to be either a constant or a parameter. 41462 41463 If the arguments are all parameters, then <pval>, <lowlim> and 41464 <upplim> will be parameters. Otherwise, they will be variables. 41465 41466Syntax 3: 41467 LET <pval> <lowlim> <upplim> = RUKHIN 1 UPPER TAIL TEST 41468 <p1> <n1> <p2> <n2> <p3> <n3> <alpha> 41469 <SUBSET/EXCEPT/FOR qualification> 41470 where <p1> is constant, parameter, or variable that contains the 41471 proportion of successes for the first sample; 41472 <n1> is constant, parameter, or variable that contains the 41473 number of trials for the first sample; 41474 <p2> is constant, parameter, or variable that contains the 41475 proportion of successes for the second sample; 41476 <n2> is constant, parameter, or variable that contains the 41477 number of trials for the second sample; 41478 <p3> is constant, parameter, or variable that contains the 41479 proportion of successes for the third sample; 41480 <n3> is constant, parameter, or variable that contains the 41481 number of trials for the third sample; 41482 <alpha> is constant or parameter that contains the significance 41483 level; 41484 <pval> contains the returned p-value; 41485 <lowlim> contains the computed lower confidence limit; 41486 <upplim> contains the computed upper confidence limit; 41487 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 41488 41489 This syntax performs an upper-tailed hypothesis test. However, 41490 the confidence limits correspond to the two-tailed test. 41491 41492 The <p1>, <n1>, <p2>, <n2>, <p3>, and <n3> arguments can be either 41493 parameters or variables. If they are variables, then the variables 41494 must have the same number of elements. The <alpha> argument is 41495 always assumed to be either a constant or a parameter. 41496 41497 If the arguments are all parameters, then <pval>, <lowlim> and 41498 <upplim> will be parameters. Otherwise, they will be variables. 41499 41500Examples: 41501 LET PVAL AL AU = RUKHIN 1 TEST P1 N1 P2 N2 P3 N3 ALPHA 41502 LET PVAL AL AU = RUKHIN 1 LOWER TAILED TEST P1 N1 P2 N2 P3 N3 ALPHA 41503 LET PVAL AL AU = RUKHIN 1 UPPER TAILED TEST P1 N1 P2 N2 P3 N3 ALPHA 41504 41505Default: 41506 None 41507 41508Synonyms: 41509 None 41510 41511Related Commands: 41512 RUKHIN 3 TEST = Test binomial proportions 41513 p1*p2 = p3*p4. 41514 RUKHIN 2 TEST = Test binomial proportions 41515 p1 = 0.5*p2. 41516 BINOMIAL RATIO CONF LIMITS = Compute confidence limits for 41517 the ratio of two binomial 41518 proportions. 41519 BINOMIAL PRODUCT CONF LIMITS = Compute confidence limits for 41520 the product of two binomial 41521 proportions. 41522 AGRESTI-COULL CONF LIMITS = Compute the Agresti-Coull confidence 41523 limits for binomial proportions. 41524 EXACT BINOMIAL CONF LIMITS = Compute the exact binomial confidence 41525 limits for binomial proportions. 41526 DIFFERENCE OF PROP CONF LIMITS = Compute the confidence limtis for 41527 the difference of two binomial 41528 proportions. 41529 BINOMIAL PROPORTION = Compute the binomial proportion 41530 statistic. 41531 AGRESTI-COULL = Compute Agresti-Coull confidence 41532 limits statistic for binomial 41533 proportions. 41534 BINOMIAL PROPORTION TEST = Perform a binomial proportions test. 41535 CROSS TABULATE (LET) = Perform a cross tabulation for a 41536 specified statistic. 41537 41538Reference: 41539 Private communication with Andrew Rukhin and Bill Strawderman. 41540 41541Applications: 41542 Statistics 41543 41544Implementation Date: 41545 2008/09 41546 41547Program: 41548 LET P1 = 0.8 41549 LET N2 = 40 41550 LET P2 = 0.95 41551 LET N2 = 40 41552 LET P3 = 0.6 41553 LET N3 = 40 41554 LET ALPHA = 0.90 41555 . 41556 LET PVAL AL AU = RUKHIN 1 TEST P1 N1 P2 N2 P3 N3 ALPHA 41557 41558-----RUKHIN 2 TEST (LET)-------------------------- 41559 41560RUKHIN 2 TEST 41561 41562Name: 41563 RUKHIN 2 TEST (LET) 41564 41565Type: 41566 Let Subcommand 41567 41568Purpose: 41569 For two binomial proportions, compute the p-value and lower and 41570 upper confidence limits for 41571 41572 H0: p1 = 0.5*p2 41573 41574 where p1 and p2 are the two binomial proportions. 41575 41576Description: 41577 For each of the binomial proportions, we actually use the 41578 correction terms 41579 41580 p(i) = (x(i) + 0.5)/(n(i) + 1) 41581 41582 with p(i), x(i), and n(i) denoting the binomial proportion, 41583 the number of successes and the number of trials for the i-th 41584 binomial proportion. 41585 41586 The computed test statistic is 41587 41588 p1 - 0.5*p2 41589 41590 and the associated standard error is 41591 41592 SE = SQRT(term1 + term2) 41593 41594 where 41595 41596 term1 = p1*(1 - p1)/n1 41597 term2 = p2*(1 - p2)/(4*n2) 41598 41599 The p-value for a lower tailed test is 41600 41601 1 - NORCDF((0.5*p2 - p1)/SE) 41602 41603 The p-value for an upper tailed test is 41604 41605 1 - NORCDF((p1 - 0.5*p2)/SE) 41606 41607 The p-value for a two tailed test is 41608 41609 2*(1 - NORCDF((p1 - 0.5*p2)/SE) 41610 41611 The confidence interval is 41612 41613 (p1 - 0.5*p2) +/- NORPPF(ALPHA/2)*SE 41614 41615Syntax 1: 41616 LET <pval> <lowlim> <upplim> = RUKHIN 2 TEST 41617 <p1> <n1> <p2> <n2> <alpha> 41618 <SUBSET/EXCEPT/FOR qualification> 41619 where <p1> is constant, parameter, or variable that contains the 41620 proportion of successes for the first sample; 41621 <n1> is constant, parameter, or variable that contains the 41622 number of trials for the first sample; 41623 <p2> is constant, parameter, or variable that contains the 41624 proportion of successes for the second sample; 41625 <n2> is constant, parameter, or variable that contains the 41626 number of trials for the second sample; 41627 <alpha> is constant or parameter that contains the significance 41628 level; 41629 <pval> contains the returned p-value; 41630 <lowlim> contains the computed lower confidence limit; 41631 <upplim> contains the computed upper confidence limit; 41632 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 41633 41634 This syntax performs a two-tailed hypothesis test. 41635 41636 The <p1>, <n1>, <p2>, and <n2> arguments can be either parameters 41637 or variables. If they are variables, then the variables must have 41638 the same number of elements. The <alpha> argument is always assumed 41639 to be either a constant or a parameter. 41640 41641 If the arguments are all parameters, then <pval>, <lowlim> and 41642 <upplim> will be parameters. Otherwise, they will be variables. 41643 41644Syntax 2: 41645 LET <pval> <lowlim> <upplim> = RUKHIN 2 LOWER TAIL TEST 41646 <p1> <n1> <p2> <n2> <alpha> 41647 <SUBSET/EXCEPT/FOR qualification> 41648 where <p1> is constant, parameter, or variable that contains the 41649 proportion of successes for the first sample; 41650 <n1> is constant, parameter, or variable that contains the 41651 number of trials for the first sample; 41652 <p2> is constant, parameter, or variable that contains the 41653 proportion of successes for the second sample; 41654 <n2> is constant, parameter, or variable that contains the 41655 number of trials for the second sample; 41656 <alpha> is constant or parameter that contains the significance 41657 level; 41658 <pval> contains the returned p-value; 41659 <lowlim> contains the computed lower confidence limit; 41660 <upplim> contains the computed upper confidence limit; 41661 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 41662 41663 This syntax performs a lower-tailed hypothesis test. However, 41664 the confidence limits correspond to the two-tailed test. 41665 41666 The <p1>, <n1>, <p2>, and <n2> arguments can be either parameters 41667 or variables. If they are variables, then the variables must have 41668 the same number of elements. The <alpha> argument is always assumed 41669 to be either a constant or a parameter. 41670 41671 If the arguments are all parameters, then <pval>, <lowlim> and 41672 <upplim> will be parameters. Otherwise, they will be variables. 41673 41674Syntax 3: 41675 LET <pval> <lowlim> <upplim> = RUKHIN 2 UPPER TAIL TEST 41676 <p1> <n1> <p2> <n2> <alpha> 41677 <SUBSET/EXCEPT/FOR qualification> 41678 where <p1> is constant, parameter, or variable that contains the 41679 proportion of successes for the first sample; 41680 <n1> is constant, parameter, or variable that contains the 41681 number of trials for the first sample; 41682 <p2> is constant, parameter, or variable that contains the 41683 proportion of successes for the second sample; 41684 <n2> is constant, parameter, or variable that contains the 41685 number of trials for the second sample; 41686 <alpha> is constant or parameter that contains the significance 41687 level; 41688 <pval> contains the returned p-value; 41689 <lowlim> contains the computed lower confidence limit; 41690 <upplim> contains the computed upper confidence limit; 41691 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 41692 41693 This syntax performs an upper-tailed hypothesis test. However, 41694 the confidence limits correspond to the two-tailed test. 41695 41696 The <p1>, <n1>, <p2>, and <n2> arguments can be either parameters 41697 or variables. If they are variables, then the variables must have 41698 the same number of elements. The <alpha> argument is always assumed 41699 to be either a constant or a parameter. 41700 41701 If the arguments are all parameters, then <pval>, <lowlim> and 41702 <upplim> will be parameters. Otherwise, they will be variables. 41703 41704Examples: 41705 LET PVAL AL AU = RUKHIN 2 TEST P1 N1 P2 N2 ALPHA 41706 LET PVAL AL AU = RUKHIN 2 LOWER TAILED TEST P1 N1 P2 N2 ALPHA 41707 LET PVAL AL AU = RUKHIN 2 UPPER TAILED TEST P1 N1 P2 N2 ALPHA 41708 41709Default: 41710 None 41711 41712Synonyms: 41713 None 41714 41715Related Commands: 41716 RUKHIN 1 TEST = Test binomial proportions 41717 p1 = p2*p3. 41718 RUKHIN 3 TEST = Test binomial proportions 41719 p1*p2 = p3*p4. 41720 BINOMIAL RATIO CONF LIMITS = Compute confidence limits for 41721 the ratio of two binomial 41722 proportions. 41723 BINOMIAL PRODUCT CONF LIMITS = Compute confidence limits for 41724 the product of two binomial 41725 proportions. 41726 AGRESTI-COULL CONF LIMITS = Compute the Agresti-Coull confidence 41727 limits for binomial proportions. 41728 EXACT BINOMIAL CONF LIMITS = Compute the exact binomial confidence 41729 limits for binomial proportions. 41730 DIFFERENCE OF PROP CONF LIMITS = Compute the confidence limtis for 41731 the difference of two binomial 41732 proportions. 41733 BINOMIAL PROPORTION = Compute the binomial proportion 41734 statistic. 41735 AGRESTI-COULL = Compute Agresti-Coull confidence 41736 limits statistic for binomial 41737 proportions. 41738 BINOMIAL PROPORTION TEST = Perform a binomial proportions test. 41739 CROSS TABULATE (LET) = Perform a cross tabulation for a 41740 specified statistic. 41741 41742Reference: 41743 Private communication with Andrew Rukhin and Bill Strawderman. 41744 41745Applications: 41746 Statistics 41747 41748Implementation Date: 41749 2008/09 41750 41751Program: 41752 LET P1 = 0.9 41753 LET N2 = 40 41754 LET P2 = 0.6 41755 LET N2 = 40 41756 LET ALPHA = 0.90 41757 . 41758 LET PVAL AL AU = RUKHIN 2 TEST P1 N1 P2 N2 ALPHA 41759 41760-----RUKHIN 3 TEST (LET)-------------------------- 41761 41762RUKHIN 3 TEST 41763 41764Name: 41765 RUKHIN 3 TEST (LET) 41766 41767Type: 41768 Let Subcommand 41769 41770Purpose: 41771 For four binomial proportions, compute the p-value and lower and 41772 upper confidence limits for 41773 41774 H0: p1*p2 = p3*p4 41775 41776 where p1, p2, p3, and p4 are the four binomial proportions. 41777 41778Description: 41779 For each of the binomial proportions, we actually use the 41780 correction terms 41781 41782 p(i) = (x(i) + 0.5)/(n(i) + 1) 41783 41784 with p(i), x(i), and n(i) denoting the binomial proportion, 41785 the number of successes and the number of trials for the i-th 41786 binomial proportion. 41787 41788 The computed test statistic is 41789 41790 p1*p2 - p3*p4 41791 41792 and the associated standard error is 41793 41794 SE = SQRT(term1 + term2 + term3 + term4) 41795 41796 where 41797 41798 term1 = (p2**2)*p1*(1 - p1)/n1 41799 term2 = (p1**2)*p2*(1 - p2)/n2 41800 term3 = (p4**2)*p3*(1 - p3)/n3 41801 term4 = (p3**2)*p4*(1 - p4)/n4 41802 41803 The p-value for a lower tailed test is 41804 41805 1 - NORCDF((p3*p4 - p1*p2)/SE) 41806 41807 The p-value for an upper tailed test is 41808 41809 1 - NORCDF((p1*p2 - p3*p4)/SE) 41810 41811 The p-value for a two tailed test is 41812 41813 2*(1 - NORCDF((p3*p4 - p1*p2)/SE) 41814 41815 The confidence interval is 41816 41817 (p1*p2 - p3*p4) +/- NORPPF(ALPHA/2)*SE 41818 41819 Although this is a fairly specialized test, it does have 41820 applicability in the following test scenario. Suppose we are 41821 testing scanning devices to see if they can detect certain 41822 radionuclides. Further suppose we have a "primary" screening 41823 device and then a "secondary" screening device. For example, the 41824 "primary" device may be an alarm which then sends the object to a 41825 more accurate (but more costly or more time consuming) device to 41826 perform an id. In this case, the binomial success for the primary 41827 device is that it alarms when the radionuclide is present and the 41828 binomial success for the secondary device is that it returns the 41829 correct id. The RUKHIN 3 test could then be used to compare the 41830 performance of two different sets of primary/secondary devices. 41831 41832Syntax 1: 41833 LET <pval> <lowlim> <upplim> = RUKHIN 3 TEST 41834 <p1> <n1> <p2> <n2> <p3> <n3> <p4> <n4> <alpha> 41835 <SUBSET/EXCEPT/FOR qualification> 41836 where <p1> is constant, parameter, or variable that contains the 41837 proportion of successes for the first sample; 41838 <n1> is constant, parameter, or variable that contains the 41839 number of trials for the first sample; 41840 <p2> is constant, parameter, or variable that contains the 41841 proportion of successes for the second sample; 41842 <n2> is constant, parameter, or variable that contains the 41843 number of trials for the second sample; 41844 <p3> is constant, parameter, or variable that contains the 41845 proportion of successes for the third sample; 41846 <n3> is constant, parameter, or variable that contains the 41847 number of trials for the third sample; 41848 <p4> is constant, parameter, or variable that contains the 41849 proportion of successes for the fourth sample; 41850 <n4> is constant, parameter, or variable that contains the 41851 number of trials for the fourth sample; 41852 <alpha> is constant or parameter that contains the significance 41853 level; 41854 <pval> contains the returned p-value; 41855 <lowlim> contains the computed lower confidence limit; 41856 <upplim> contains the computed upper confidence limit; 41857 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 41858 41859 This syntax performs a two-tailed hypothesis test. 41860 41861 The <p1>, <n1>, <p2>, <n2>, <p3>, <n3>, <p4> and <n4> arguments 41862 can be either parameters or variables. If they are variables, then 41863 the variables must have the same number of elements. The <alpha> 41864 argument is always assumed to be either a constant or a parameter. 41865 41866 If the arguments are all parameters, then <pval>, <lowlim> and 41867 <upplim> will be parameters. Otherwise, they will be variables. 41868 41869Syntax 2: 41870 LET <pval> <lowlim> <upplim> = RUKHIN 3 LOWER TAIL TEST 41871 <p1> <n1> <p2> <n2> <p3> <n3> <p4> <n4> <alpha> 41872 <SUBSET/EXCEPT/FOR qualification> 41873 where <p1> is constant, parameter, or variable that contains the 41874 proportion of successes for the first sample; 41875 <n1> is constant, parameter, or variable that contains the 41876 number of trials for the first sample; 41877 <p2> is constant, parameter, or variable that contains the 41878 proportion of successes for the second sample; 41879 <n2> is constant, parameter, or variable that contains the 41880 number of trials for the second sample; 41881 <p3> is constant, parameter, or variable that contains the 41882 proportion of successes for the third sample; 41883 <n3> is constant, parameter, or variable that contains the 41884 number of trials for the third sample; 41885 <p4> is constant, parameter, or variable that contains the 41886 proportion of successes for the fourth sample; 41887 <n4> is constant, parameter, or variable that contains the 41888 number of trials for the fourth sample; 41889 <alpha> is constant or parameter that contains the significance 41890 level; 41891 <pval> contains the returned p-value; 41892 <lowlim> contains the computed lower confidence limit; 41893 <upplim> contains the computed upper confidence limit; 41894 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 41895 41896 This syntax performs a lower-tailed hypothesis test. However, 41897 the confidence limits correspond to the two-tailed test. 41898 41899 The <p1>, <n1>, <p2>, <n2>, <p3>, <n3>, <p4> and <n4> arguments 41900 can be either parameters or variables. If they are variables, then 41901 the variables must have the same number of elements. The <alpha> 41902 argument is always assumed to be either a constant or a parameter. 41903 41904 If the arguments are all parameters, then <pval>, <lowlim> and 41905 <upplim> will be parameters. Otherwise, they will be variables. 41906 41907Syntax 3: 41908 LET <pval> <lowlim> <upplim> = RUKHIN 3 UPPER TAIL TEST 41909 <p1> <n1> <p2> <n2> <p3> <n3> <p4> <n4> <alpha> 41910 <SUBSET/EXCEPT/FOR qualification> 41911 where <p1> is constant, parameter, or variable that contains the 41912 proportion of successes for the first sample; 41913 <n1> is constant, parameter, or variable that contains the 41914 number of trials for the first sample; 41915 <p2> is constant, parameter, or variable that contains the 41916 proportion of successes for the second sample; 41917 <n2> is constant, parameter, or variable that contains the 41918 number of trials for the second sample; 41919 <p3> is constant, parameter, or variable that contains the 41920 proportion of successes for the third sample; 41921 <n3> is constant, parameter, or variable that contains the 41922 number of trials for the third sample; 41923 <p4> is constant, parameter, or variable that contains the 41924 proportion of successes for the fourth sample; 41925 <n4> is constant, parameter, or variable that contains the 41926 number of trials for the fourth sample; 41927 <alpha> is constant or parameter that contains the significance 41928 level; 41929 <pval> contains the returned p-value; 41930 <lowlim> contains the computed lower confidence limit; 41931 <upplim> contains the computed upper confidence limit; 41932 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 41933 41934 This syntax performs an upper-tailed hypothesis test. However, 41935 the confidence limits correspond to the two-tailed test. 41936 41937 The <p1>, <n1>, <p2>, <n2>, <p3>, <n3>, <p4> and <n4> arguments 41938 can be either parameters or variables. If they are variables, then 41939 the variables must have the same number of elements. The <alpha> 41940 argument is always assumed to be either a constant or a parameter. 41941 41942 If the arguments are all parameters, then <pval>, <lowlim> and 41943 <upplim> will be parameters. Otherwise, they will be variables. 41944 41945Examples: 41946 LET PVAL AL AU = RUKHIN 3 TEST P1 N1 P2 N2 P3 N3 P4 N4 ALPHA 41947 LET PVAL AL AU = RUKHIN 3 LOWER TAILED TEST ... 41948 P1 N1 P2 N2 P3 N3 P4 N4 ALPHA 41949 LET PVAL AL AU = RUKHIN 3 UPPER TAILED TEST ... 41950 P1 N1 P2 N2 P3 N3 P4 N4 ALPHA 41951 41952Default: 41953 None 41954 41955Synonyms: 41956 None 41957 41958Related Commands: 41959 RUKHIN 1 TEST = Test binomial proportions 41960 p1 = p2*p3. 41961 RUKHIN 2 TEST = Test binomial proportions 41962 p1 = 0.5*p2. 41963 BINOMIAL RATIO CONF LIMITS = Compute confidence limits for 41964 the ratio of two binomial 41965 proportions. 41966 BINOMIAL PRODUCT CONF LIMITS = Compute confidence limits for 41967 the product of two binomial 41968 proportions. 41969 AGRESTI-COULL CONF LIMITS = Compute the Agresti-Coull confidence 41970 limits for binomial proportions. 41971 EXACT BINOMIAL CONF LIMITS = Compute the exact binomial confidence 41972 limits for binomial proportions. 41973 DIFFERENCE OF PROP CONF LIMITS = Compute the confidence limtis for 41974 the difference of two binomial 41975 proportions. 41976 BINOMIAL PROPORTION = Compute the binomial proportion 41977 statistic. 41978 AGRESTI-COULL = Compute Agresti-Coull confidence 41979 limits statistic for binomial 41980 proportions. 41981 BINOMIAL PROPORTION TEST = Perform a binomial proportions test. 41982 CROSS TABULATE (LET) = Perform a cross tabulation for a 41983 specified statistic. 41984 41985Reference: 41986 Private communication with Andrew Rukhin and Bill Strawderman. 41987 41988Applications: 41989 Statistics 41990 41991Implementation Date: 41992 2010/06 41993 41994Program: 41995 LET P1 = 0.95 41996 LET N1 = 40 41997 LET P2 = 0.8 41998 LET N2 = 40 41999 LET P3 = 0.95 42000 LET N3 = 40 42001 LET P4 = 0.6 42002 LET N4 = 40 42003 LET ALPHA = 0.90 42004 . 42005 LET PVAL AL AU = RUKHIN 3 TEST P1 N1 P2 N2 P3 N3 P4 N4 ALPHA 42006 42007-----RUNGE KUTTA (LET)------------------------------------------------- 42008 42009RUNGE KUTTA 42010 42011Name: 42012 RUNGE KUTTA (LET) 42013 42014Type: 42015 Let Subcommand 42016 42017Purpose: 42018 Solve first and second order initial value ordinary differential 42019 equations via Runge Kutta methods. 42020 42021Description: 42022 Differential equations are those which involve a relation between 42023 derivatives. For example, the equation 42024 y = x**2 42025 can be expressed as the differential equation 42026 dy/dx = 2x 42027 In this case, instead of giving a value of y for each value of x, 42028 the differential equation gives the slope at each value of x. 42029 42030 The following should be noted: 42031 1) The term ordinary refers to the fact that only ordinary 42032 derivatives are involved (that is, no partial derivatives). 42033 DATAPLOT does not currently support any methods for solving 42034 partial differential equations. 42035 2) The dependent variable is the variable being differentiated and 42036 the independent variable is the variable with respect to which 42037 the differentiations are taken. In the example dy/dx = 2x, x is 42038 the independent variable and y is the dependent variable. 42039 3) The order is the order of the highest derivative. Currently, 42040 the RUNGE KUTTA command is limited to first and second order 42041 differential equations. First order differential equations are 42042 often expressed as: 42043 dy/dx = F(x,y) 42044 while second order differential equations are often expressed as: 42045 d**2y/dx = G(x, y, dy/dx) 42046 Higher order differential equations can be expressed in a similar 42047 manner. 42048 4) The degree is the power to which the highest order derivative is 42049 raised. The RUNGE KUTTA command only deals with first degree 42050 differential equations. 42051 5) An analytic solution is an equation of the form 42052 y = F(x) 42053 which results in the original differential equation when it is 42054 differentiated. Although the RUNGE KUTTA command does not 42055 provide an analytic solution (that is, the function F), it can 42056 generate the y value for any corresponding x value. The RUNGE 42057 KUTTA command returns y values (and dy/dx values for the second 42058 order case) for a given set of X values. 42059 6) Differential equations are complicated by the fact that there is 42060 an infinite number of solutions (this is due to the fact that the 42061 derivative of any constant is zero). However, if the solution is 42062 required to pass through a specific point (x0,y0), then the 42063 solution is unique. This point is referred to as an initial 42064 value. Boundary value problems are those in which more than 42065 one initial point is specified. The RUNGE KUTTA command can 42066 solve initial value problems, but it does not solve boundary 42067 value problems. DATAPLOT does not currently provide any methods 42068 for solving boundary value problems. 42069 42070Syntax 1: (for first order differential equations) 42071 LET <y> = RUNGE KUTTA <f> <x1> <SUBSET/EXCEPT/FOR qualification> 42072 where <f> is a function or functional expression that defines the 42073 differential equation (this function often contains <y>); 42074 <x1> is a variable that defines the desired grid of X values; 42075 <y> is a variable where the computed solution to the 42076 differential equation is saved (the first element of this 42077 variable must be previously defined); 42078 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 42079 rarely used in this context. 42080 42081 The initial value (x0, y0) is specified by the first elements of 42082 <x1> and <y> respectively. These points must be specified before 42083 entering the RUNGE KUTTA command. The solution is the set of 42084 points <y> and <x1>. 42085 42086Syntax 2: (for second order differential equations) 42087 LET <y> <yd> = RUNGE KUTTA <f> <x1> 42088 <SUBSET/EXCEPT/FOR qualification> 42089 where <f> is a function or functional expression that defines the 42090 differential equation (this function often contains <y> 42091 and <yd>); 42092 <x1> is a variable that defines the desired grid of X values; 42093 <y> is the variable where the computed values for the 42094 dependent variable are saved (the first element of this 42095 variable must be previously defined); 42096 <yd> is the variable where the computed values for the dy/dx 42097 term are saved (the first element of this variable must 42098 be previously defined); 42099 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 42100 rarely used in this context. 42101 42102 The initial value (x0, y0, yd0) is specified by the first elements 42103 of <x1>, <y>, and <yd> respectively. These points must be 42104 specified before entering the RUNGE KUTTA command. The solution is 42105 the set of points <y>, <yd>, and <x1>. 42106 42107Examples: 42108 LET Y = RUNGE KUTTA 2*X X1 42109 LET Y = RUNGE KUTTA F X1 42110 LET Y YD = RUNGE KUTTA F X1 42111 42112Note: 42113 DATAPLOT uses a fourth order Runge-Kutta algorithm. This algorithm 42114 is documented in the Numerical Recipes book. It is also covered in 42115 most numerical analysis textbooks. Runge-Kutta methods have the 42116 advantage of almost always succeeding, but they do not always 42117 have as high an accuracy or the computational efficiency as more 42118 sophisticated methods such as Bulirsch-Stoer or predictor-corrector 42119 methods. 42120 42121 Runge-Kutta methods are not appropriate for stiff differential 42122 equations. 42123 42124Default: 42125 None 42126 42127Synonyms: 42128 None 42129 42130Related Commands: 42131 DERIVATIVE = Compute the derivative of a function. 42132 INTEGRAL = Compute the integral of a function. 42133 ROOTS = Compute the roots of a function. 42134 INTERPOLATE = Interpolate a function. 42135 42136Reference: 42137 "Numerical Recipes: The Art of Scientific Computing (FORTRAN 42138 Version)", Press, Flannery, Teukolsky, and Vetterling. Cambridge 42139 University Press, 1989 (chapter 14). 42140 42141Applications: 42142 Differential Equations 42143 42144Implementation Date: 42145 87/10 42146 42147Program 1: (first order example) 42148 . THIS IS THE DATAPLOT PROGRAM FILE RAIN.DP 42149 . PURPOSE--DETERMINE THE EQUATION OF MOTION OF A RAINDROP 42150 . WITH SEVERAL DIFFERENT AIR RESISTANCE VALUES. 42151 . ANALYSIS TECHNIQUE--RUNGE-KUTTA SOLUTION TO DIFFERENTIAL EQUATION. 42152 . NOTE--Y = SPEED AFTER TIME X 42153 . X = TIME (IN SECONDS) 42154 . M = MASS 42155 . C = AIR RESISTANCE 42156 . START POINT----------------------------------- 42157 . STEP 1--DEFINE THE RIGHT-HAND SIDE FUNCTION OF Y' = F 42158 . DEFINE THE DESIRED GRID OF X VALUES 42159 . DEFINE INITIAL CONDITION 42160 . DEFINE A TABLE OF VALUES FOR C 42161 LET FUNCTION F = 32-(C/M)*Y**2 42162 LET X = 0 .1 5 42163 LET Y(1)=0 42164 LET M = 1 42165 LET CTAB = DATA 2 1 .5 .1 .01 0 42166 . STEP 2--SOLVE THE DIFFERENTIAL EQUATION FOR EACH VALUE OF C 42167 LOOP FOR K = 1 1 6 42168 LET C = CTAB(K) 42169 LET Y = RUNGE-KUTTA F X 42170 LET Y^K = Y 42171 END OF LOOP 42172 . STEP 3--PLOT OUT THE 6 TRACES 42173 Y1LABEL SPEED 42174 XLABEL TIME (IN SECONDS) 42175 X2LABEL STARTING SPEED = 0 42176 X3LABEL AIR RESISTANCE = 2, 1, .5, .1, .01, 0 42177 PLOT Y1 Y2 Y3 Y4 Y5 Y6 VS X 42178 42179Program 2: (second order example) 42180 . THIS IS THE DATAPLOT PROGRAM FILE BEAM.DP 42181 . PURPOSE--DETERMINE DEFLECTION VS DISTANCE TRACE OF ELASTIC BEAM 42182 . ANCHORED AT ONE END AND WITH A LOAD AT THE OTHER END 42183 . (CANTILEVER). 42184 . TECHNIQUE--RUNGE-KUTTA SOLUTION OF 2ND ORDER DIFFERENTIAL EQUATION 42185 . APPLICATION--STRUCTURAL ENGINEERING 42186 . SOURCE--DORN, WILLIAM S. AND MCCRACKEN, DANIEL D., NUMERICAL 42187 . METHODS WITH FORTRAN IV CASE STUDIES, JOHN WILEY AND SONS 42188 . NEW YORK, 1972, PAGES 391-401. 42189 . TO FIND--DEFLECTION VALUE FOR VARIOUS DISTANCES OUT ONTO THE BEAM 42190 . NOTE--THE ELASTIC DEFLECTION SATISFIES THE DIFFERENTIAL EQUATION-- 42191 . Y'' / (1 + (Y')**2 )**(3/2) = P*(L-X) / (E*I) 42192 . Y'' = P*(L-X) / (E*I) * (1 + (Y')**2 )**(3/2) 42193 . WITH Y(0) = 0 AND Y'(0) = 0 42194 . WHERE 42195 . Y = DEFLECTION FROM HORIZONTAL (IN INCHES) 42196 . X = DISTANCE OUT ONTO BEAM (X = 0, 2, 4, 6, ..., 100 42197 . INCHES) 42198 . P = LOAD (IN POUNDS) AT FREE END (HERE = 64) 42199 . L = LENGTH (IN INCHES) OF BEAM (HERE = 100) 42200 . E = YOUNG'S MODULUS (= 6 * 10**6) 42201 . I = MOMENT OF INERTIA OF CROSS SECTION (HERE = 0.128 42202 . INCHES**4) 42203 . 42204 . STEP 1--DEFINE THE PHYSICAL PARAMETERS OF THE BEAM 42205 LET P = 64 42206 LET L = 100 42207 LET E = 6*10**6 42208 LET I = 0.128 42209 . STEP 2--DEFINE THE RIGHT-SIDE FUNCTION OF Y''(X) = F 42210 LET FUNCTION F1 = P*(L-X)/(E*I) 42211 LET FUNCTION F2 = (1+YP**2)**(3/2) 42212 LET FUNCTION F = F1*F2 42213 . STEP 3--DEFINE INITIAL CONDITIONS AND THE DESIRED SEQUENCE 42214 . OF POINTS AT WHICH TO COMPUTE THE SOLUTION CURVE. 42215 LET Y(1) = 0 42216 LET YP(1) = 0 42217 LET X = SEQUENCE 0 2 100 42218 . STEP 4--SOLVE THE DIFFERENTIAL EQUATION 42219 LET Y YP = RUNGE-KUTTA F X 42220 MULTIPLOT 2 1; MULTIPLOT CORNER COORDINATES 0 0 100 100 42221 PLOT Y X 42222 PRINT X Y YP 42223 . STEP 5--PLOT OUT THE SOLUTION CURVE 42224 LET YBE = (P/(6*E*I))*(X**2)*(3*L-X) 42225 TITLE PLOT THE SOLUTION CURVE 42226 LINES SOLID DOTTED 42227 PLOT Y YBE VS X 42228 END OF MULTIPLOT 42229 42230-----RUNS--------------------------------------------------- 42231 42232RUNS 42233 42234Name: 42235 RUNS 42236 42237Type: 42238 Analysis Command 42239 42240Purpose: 42241 Perform a runs test. 42242 42243Description: 42244 This test is designed to test the hypothesis that a sample has been 42245 drawn at random. The data is split into 2 mutually exclusive 42246 groups. A run is a series of values that fall into the same group. 42247 The number of runs of a given length are computed and compared to 42248 the expected number from a random sample. 42249 42250Syntax: 42251 RUNS <x1> <SUBSET/EXCEPT/FOR qualification> 42252 where <x1> is the variable for which the runs test is to be 42253 performed; 42254 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 42255 42256Examples: 42257 RUNS Y1 42258 RUNS Y1 SUBSET TAG > 0 42259 42260Note: 42261 A runs test divides the data into 2 mutually exclusive sets. For 42262 quantitative data, this usually means data are split into groups 42263 above the mean and below the mean. 42264 42265Default: 42266 None 42267 42268Synonyms: 42269 None 42270 42271Related Commands: 42272 PROBABILITY PLOT = Generates a probability plot. 42273 LET = Computes data transformations. 42274 RUN SEQUENCE PLOT = Generates a run sequence plot. 42275 42276Applications: 42277 XX 42278 42279Implementation Date: 42280 XX 42281 42282Program: 42283 LET = Y1 NORMAL RANDOM NUMBERS FOR I = 1 1 100 42284 RUNS Y1 42285 42286-----RUN SEQUENCE PLOT----------------------------------------------- 42287 42288RUN SEQUENCE PLOT 42289 42290Name: 42291 RUN SEQUENCE PLOT 42292 42293Type: 42294 Graphics Command 42295 42296Purpose: 42297 Generates a run sequence plot. 42298 42299Description: 42300 A run sequence plot is a graphical data analysis technique for 42301 preliminary scanning of the data. It consists of: 42302 Vertical axis = i-th observation; 42303 Horizontal axis = dummy index i. 42304 The runs sequence plot is thus a plot of the raw data plotted in 42305 the same order that it resides in the variable. This is a useful 42306 first step in the analysis of any data (not just time series data) 42307 in that it provides information about trends, patterns in 42308 variation, and outliers. It also gives the analyst an excellent 42309 "feel" for the data. 42310 42311Syntax: 42312 RUN SEQUENCE PLOT <x> <SUBSET/EXCEPT/FOR qualification> 42313 where <x> is the variable of raw data values under analysis; 42314 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 42315 42316Examples: 42317 RUN SEQUENCE PLOT Y 42318 RUN SEQUENCE PLOT Y2 42319 42320Note: 42321 Plot points can be plotted as characters, connected lines, spikes, 42322 or bars. These are set independently of each other. The default 42323 is to plot each trace as a connected line with no symbol, no bar, 42324 and no spike. The LINE, CHARACTER, SPIKE, and BAR commands are 42325 used to set the switches for plotting a given trace as a connected 42326 line, a character, a spike, or a bar respectively. 42327 42328 There are attribute setting commands for lines, characters, spikes, 42329 and bars. See the documentation for LINE, CHARACTER, SPIKE, and 42330 BAR for a complete list of these commands. Attributes are set 42331 giving a list of values. The first trace uses the first setting, 42332 the second trace uses the second setting, and so on. For example, 42333 CHARACTER SIZE 2.0 3.0 1.5 sets the character size for trace 1 to 42334 2.0, the character size for trace 2 to 3.0, and the character size 42335 for trace 3 to 1.5. Attributes can be set for up to 100 traces. 42336 42337Default: 42338 None 42339 42340Synonyms: 42341 PLOT Y is equivalent to RUN SEQUENCE PLOT Y. 42342 42343Related Commands: 42344 CHARACTERS = Sets the types for plot characters. 42345 LINES = Sets the types for plot lines. 42346 SPIKES = Sets the on/off switches for plot spikes. 42347 BARS = Sets the on/off switches for plot bars. 42348 TITLE = Sets the plot title. 42349 LABEL = Sets the plot axis labels. 42350 LEGEND = Sets the plot legends. 42351 MULTIPLOT = Generate multiple plots per page. 42352 PLOT = Generates a data or function plot. 42353 42354Applications: 42355 XX 42356 42357Implementation Date: 42358 XX 42359 42360Program: 42361 SKIP 25 42362 READ BOXJE142.DAT YIELD 42363 . 42364 TITLE AUTOMATIC 42365 Y1LABEL YIELD 42366 X1LABEL SEQUENCE NUMBER 42367 XLIMITS 0 70 42368 XTIC OFFSET 2 2 42369 PLOT YIELD 42370 42371------------------------------------------------------------- 42372 42373 42374 42375 42376 42377 42378 42379 42380 42381 42382 42383 42384 42385 42386 42387 42388 42389 42390 42391 42392 42393 42394 42395 42396 42397 42398 42399 42400 42401 42402 42403 42404 42405 42406 42407 42408 42409 42410 42411 42412 42413 42414 42415 42416 42417 42418 42419 42420 42421 42422 42423 42424 42425 42426 42427 42428 42429 42430 42431 42432 42433 42434 42435 42436 42437 42438 42439 42440 42441 42442 42443 42444 42445 42446 42447 42448 42449 42450 42451 42452 42453 42454 42455 42456 42457 42458 42459 42460 42461 42462 42463 42464 42465 42466 42467 42468 42469 42470 42471 42472 42473 42474 42475 42476 42477 42478 42479 42480 42481 42482 42483 42484 42485 42486 42487 42488 42489 42490 42491 42492 42493 42494 42495 42496 42497 42498 42499 42500------------------------- *S* ZZZZZ-------------------- 42501 42502-----S CHART----------------------------------------------------- 42503 42504S CHART 42505 42506Name: 42507 S CHART 42508 42509Type: 42510 Graphics Command 42511 42512Purpose: 42513 Generates a standard deviation control chart. 42514 42515Description: 42516 A standard deviation control chart is a data analysis analysis 42517 technique for determining if a measurement process has gone out of 42518 statistical control. The S chart is sensitive to changes in 42519 variation in the measurement process. It consists of: 42520 Vertical axis = the standard deviation for each sub-group. 42521 Horizontal axis = sub-group designation. 42522 In addition, horizontal lines are drawn at the mean standard 42523 deviation value and at the upper and lower control limits. 42524 42525Syntax: 42526 S CHART <y> <x> <SUBSET/EXCEPT/FOR/qualification> 42527 where <y> is the response (= dependent) variable (containing the 42528 raw data values); 42529 <x> is an independent variable (containing the 42530 sub-group identifications); 42531 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 42532 42533Examples: 42534 S CHART Y X 42535 42536Note: 42537 The distribution of the response variable is assumed to be normal. 42538 This assumption is the basis for calculating the upper and lower 42539 control limits. 42540 42541Note: 42542 The attributes of the 4 traces can be controlled by the standard 42543 LINES, CHARACTERS, BARS, and SPIKES commands. Trace 1 is the 42544 response variable, trace2 is the mean line, and traces 3 and 4 are 42545 the control limits. Some analysts prefer to draw the response 42546 variable as a spike or character rather than a connected line. 42547 42548Note: 42549 Versions prior to December 1993 have a bug in that the S CHART 42550 command conflicts with the SAVE command. Use the SD CHART or the 42551 SD CONTROL CHART syntax (see SYNONYMS section below) for these 42552 versions. 42553 42554Default: 42555 None 42556 42557Synonyms: 42558 SD CHART for S CHART 42559 S CONTROL CHART for S CHART 42560 SD CONTROL CHART for S CHART 42561 42562Related Commands: 42563 R CHART = Generates a range control chart. 42564 X CHART = Generates a mean control chart. 42565 P CHART = Generates a p control chart. 42566 NP CHART = Generates a Np control chart. 42567 U CHART = Generates a U control chart. 42568 C CHART = Generates a C control chart. 42569 CHARACTERS = Sets the types for plot characters. 42570 LINES = Sets the types for plot lines. 42571 SPIKES = Sets the on/off switches for plot spikes. 42572 BARS = Sets the on/off switches for plot bars. 42573 PLOT = Generates a data or function plot. 42574 LAG PLOT = Generates a lag plot. 42575 4-PLOT = Generates 4-plot univariate analysis. 42576 STANDARD DEVI PLOT = Generates a standard deviation (vs subset) 42577 plot. 42578 42579Applications: 42580 Quality Control 42581 42582Implementation Date: 42583 88/2 42584 42585Program: 42586 SKIP 25 42587 READ GEAR.DAT DIAMETER BATCH 42588 . 42589 LINE SOLID SOLID DOT DOT 42590 TITLE AUTOMATIC 42591 X1LABEL GROUP-ID 42592 Y1LABEL STANDARD DEVIATION 42593 SD CHART DIAMETER BATCH 42594 42595-----SAMPLE RANDOM PERMUTATION (LET)----------------------------------- 42596 42597SAMPLE RANDOM PERMUTATION 42598 42599Name: 42600 SAMPLE RANDOM PERMUTATION (LET) 42601 42602Type: 42603 Let Subcommand 42604 42605Purpose: 42606 Generate a series of random permutations where possibly 42607 only a subset of the random permutations will be retained 42608 and where a specified proportion of the permutation values 42609 are allowed. 42610 42611Description: 42612 For a given size N, to generate a random permutation the integers 42613 from 1 to N are randomly sampled (without replacement) until all 42614 elements have been selected. This is implemented with the command 42615 42616 LET Y = RANDOM PERMUTATION FOR I = 1 1 N 42617 42618 This SAMPLE RANDOM PERMUTATION command was motivated by the desire to 42619 simulate the following problem. 42620 42621 Given a worm that has infected a single computer, simulate 42622 the following: 42623 42624 1. The infected machine will propogate to NKEEP IP addresses 42625 from a master list of NPOP IP addresses. 42626 42627 2. Of the NPOP addresses, only a proportion, p, denote 42628 addresses corresponding to an actual machine. That is, 42629 there will be p*NPOP valid addresses. 42630 42631 3. Each newly infected machine will likewise attempt 42632 to propogate to NKEEP addresses. 42633 42634 This process will be repated until all IP addresses corresponding 42635 to valid machines are infected. 42636 42637 The Program 1 example demonstrates how this simulation can be 42638 implemented using the SAMPLE RANDOM PERMUTATION command. 42639 42640Syntax: 42641 LET <y> <tag> = SAMPLE RANDOM PERMUTATION <npop> <nkeep> <p> <niter> 42642 where <npop> is a number or parameter that specifies the size of 42643 the random permutation; 42644 <nkeep> is a number of parameter that specifies how many 42645 permutated values are kept at each step; 42646 <p> is a parameter or number (greater than 0 and less than 42647 or equal to 1) that specifies the proportion of 42648 valid permutation values; 42649 <niter> is a number of parameter (less than or equal to 42650 <npop>) that specifies how many sets of randon 42651 permutations are generated; 42652 <y> is a variable where the permutated values are saved; 42653 <tag> is a variable that identifies which iteration generated 42654 the permuted values. 42655 42656Examples: 42657 LET Y TAG = SAMPLE RANDOM PERMUTATION NPOP NKEEP P NITER 42658 42659Note: 42660 The SEED command can be used to specify a seed for the random 42661 number generation. The SET RANDOM NUMBER GENERATOR command can be 42662 used to specify which random number generator to use. 42663 42664Note: 42665 By default, only the unique permutation values in the output variable 42666 are saved. If you want all permutation values to be saved, then 42667 enter the command 42668 42669 SET SAMPLE RANDOM PERMUTATION DISTINCT OFF 42670 42671 This is demonstrated in the Program 2 and Program 3 examples below. 42672 42673Note: 42674 Although this command was implemented with a specific simulation 42675 scenario in mind, it does have wider applicability. 42676 42677 Specifically, it can be used to efficiently implement two sample 42678 permutation tests. The Program 2 and Program 3 examples below 42679 demonstrate a two sample permutation test for the difference between 42680 the means of two samples. These examples can be easily adapted to 42681 test for the difference between other location statistics such as 42682 the median or the trimmed mean. 42683 42684 Based on extensive simulation studies, Higgins recommends that 42685 1,600 random permutations should be sufficient for most purposes. 42686 42687Note: 42688 This routine uses a random permutation algorithm suggested by Knuth. 42689 Specifically, it adapts the RANDPERM routine of Knoble. 42690 42691Default: 42692 None 42693 42694Synonyms: 42695 None 42696 42697Related Commands: 42698 LET = Generate data transformations. 42699 RANDOM PERMUTATION = Generate a random permutation. 42700 SEED = Specify the seed for random number 42701 generation. 42702 RANDOM NUMBER GENERATOR = Specify the random number generator to 42703 use. 42704 RANDOM NUMBER = Generate random numbers from a specified 42705 distribution. 42706 BOOTSTRAP SAMPLE = Generate a bootstrap sample. 42707 42708References: 42709 Knuth (1998), "The Art of Computer Programming: Volume 2 Seminumerical 42710 Algorithms, Third Edition", Section 3.4.2, Addison-Wesley. 42711 42712 Knoble RANDPERM algorithm downloaded from: 42713 "http://coding.derkeiler.com/Archive/Fortran/comp.lang.fortran/ 42714 2006-03/msg00748.html" 42715 42716 Higgins (2004), "Introduction to Modern Nonparametric Statistics", 42717 Duxbury Press, Chapter 2. 42718 42719Applications: 42720 Simulation, Permutation Tests 42721 42722Implementation Date: 42723 2017/08 42724 42725Program 1: 42726 set random number generator fibbonacci congruential 42727 seed 56791 42728 . 42729 let npop = 64000 42730 let nkeep = 10 42731 let p = 0.25 42732 let maxiter = 20 42733 let maxit2 = 19 42734 let nmax = p*npop 42735 . 42736 let y(1) = 1 42737 let nyv(1) = 1 42738 let y = 0 for i = 2 1 maxiter 42739 let iterv = sequence 0 1 maxit2 42740 . 42741 loop for k = 1 1 maxiter 42742 let niter = size y 42743 let ynew tag = sample random permutation npop nkeep p niter 42744 let ny = size y 42745 let nyv(k) = ny 42746 let y = combine y ynew 42747 let y = distinct y 42748 if ny >= nmax 42749 break loop 42750 end of if 42751 end of loop 42752 . 42753 set write decimals 0 42754 print iterv nyv 42755 42756Program 2: 42757 set random number generator fibbonacci congruential 42758 seed 32119 42759 . 42760 . Read the data 42761 . 42762 dimension 15 columns 42763 . 42764 skip 25 42765 read auto83b.dat y1 y2 42766 retain y2 subset y2 >= 0 42767 let y = comb y1 y2 42768 let n1 = size y1 42769 let n2 = size y2 42770 skip 0 42771 . 42772 . Compute the statistic for the original sample 42773 . 42774 let mean1 = mean y1 42775 let mean2 = mean y2 42776 let statval = mean1 - mean2 42777 . 42778 . Generate the random permutations 42779 . 42780 let npop = n1 + n2 42781 let nkeep = npop 42782 let p = 1 42783 let niter = 1600 42784 let ntot = npop*niter 42785 let repeat = data n1 n2 42786 let val = data 1 2 42787 let tag2 = sequence val repeat for i = 1 1 ntot 42788 set sample random permutation distinct off 42789 . 42790 let yindx tag1 = sample random permutation npop nkeep p niter 42791 let ynew = gather y yindx 42792 . 42793 . Now compute the statistic for the permutations 42794 . 42795 set let cross tabulate collapse 42796 let ynew2 = ynew 42797 let tag12 = tag1 42798 retain ynew2 tag12 subset tag2 = 1 42799 let ym1 = cross tabulate mean ynew2 tag12 42800 let ynew2 = ynew 42801 let tag12 = tag1 42802 retain ynew2 tag12 subset tag2 = 2 42803 let ym2 = cross tabulate mean ynew2 tag12 42804 let ydiff = ym1 - ym2 42805 . 42806 . Now plot the results of the permutation test 42807 . 42808 let xq = 0.025 42809 let low025 = quantile ydiff 42810 let low025 = round(low025,2) 42811 let xq = 0.975 42812 let upp975 = quantile ydiff 42813 let upp975 = round(upp975,2) 42814 . 42815 let xq = 0.025 42816 let low025 = quantile ydiff 42817 let low025 = round(low025,2) 42818 let xq = 0.975 42819 let upp975 = quantile ydiff 42820 let upp975 = round(upp975,2) 42821 . 42822 title offset 2 42823 title case asis 42824 label case asis 42825 y1label Count 42826 x1label Difference of Means for Permutations 42827 let statval = round(statval,2) 42828 x2label color red 42829 x2label Difference of Means for Original Sample: ^statval 42830 x3label color blue 42831 x3label 2.5 Percentile: ^low025, 97.5 Percentile: ^upp975 42832 xlimits -15 15 42833 title Histogram of Difference of Means for ^niter Permutations (AUTO83B.DAT) 42834 . 42835 histogram ydiff 42836 . 42837 line color red 42838 line dash 42839 drawdsds statval 20 statval 90 42840 line color blue 42841 line dash 42842 drawdsds low025 20 low025 90 42843 drawdsds upp975 20 upp975 90 42844 42845Program 3: 42846 set random number generator fibbonacci congruential 42847 seed 32119 42848 . 42849 . Read the data 42850 . 42851 dimension 15 columns 42852 . 42853 let y1 = norm rand numb for i = 1 1 200 42854 let y2 = norm rand numb for i = 1 1 80 42855 let y2 = y2 + 0.1 42856 let y = comb y1 y2 42857 let n1 = size y1 42858 let n2 = size y2 42859 skip 0 42860 . 42861 . Generate the random permutations 42862 . 42863 let mean1 = mean y1 42864 let mean2 = mean y2 42865 let statval = mean1 - mean2 42866 . 42867 let npop = n1 + n2 42868 let nkeep = npop 42869 let p = 1 42870 let niter = 1600 42871 let ntot = npop*niter 42872 let repeat = data n1 n2 42873 let val = data 1 2 42874 let tag2 = sequence val repeat for i = 1 1 ntot 42875 set sample random permutation distinct off 42876 . 42877 let yindx tag1 = sample random permutation npop nkeep p niter 42878 let ynew = gather y yindx 42879 . 42880 . Now compute the statistic for the permutations 42881 . 42882 set let cross tabulate collapse 42883 let ynew2 = ynew 42884 let tag12 = tag1 42885 retain ynew2 tag12 subset tag2 = 1 42886 let ym1 = cross tabulate mean ynew2 tag12 42887 let ynew2 = ynew 42888 let tag12 = tag1 42889 retain ynew2 tag12 subset tag2 = 2 42890 let ym2 = cross tabulate mean ynew2 tag12 42891 let ydiff = ym1 - ym2 42892 . 42893 . Now plot the results of the permutation test 42894 . 42895 let xq = 0.025 42896 let low025 = quantile ydiff 42897 let low025 = round(low025,2) 42898 let xq = 0.975 42899 let upp975 = quantile ydiff 42900 let upp975 = round(upp975,2) 42901 . 42902 title offset 2 42903 title case asis 42904 label case asis 42905 y1label Count 42906 x1label Difference of Means for Permutations 42907 let statval = round(statval,2) 42908 x2label color red 42909 x2label Difference of Means for Original Sample: ^statval 42910 x3label color blue 42911 x3label 2.5 Percentile: ^low025, 97.5 Percentile: ^upp975 42912 xlimits -0.5 0.5 42913 title Histogram of Difference of Means for ^niter Permutations 42914 . 42915 histogram ydiff 42916 . 42917 line color red 42918 line dash 42919 drawdsds statval 20 statval 90 42920 line color blue 42921 line dash 42922 drawdsds low025 20 low025 90 42923 drawdsds upp975 20 upp975 90 42924 42925-----SAVE------------------------------------------------------- 42926 42927SAVE 42928 42929Name: 42930 SAVE 42931 42932Type: 42933 Support Command 42934 42935Purpose: 42936 Selectively save one of, or a set of, the last 20 DATAPLOT 42937 commands that had been entered. 42938 42939Description: 42940 The saved commands can be re-executed by entering the command / 42941 (i.e., the slash character) at any later time in the current 42942 DATAPLOT session. 42943 42944Syntax 1: 42945 SAVE <id1> <id2> 42946 where <id1> is the line number of the first command to re-execute; 42947 and <id2> is the line number of the last command to re-execute. 42948 42949 The line numbers are obtained by preceding the SAVE command by a 42950 list command with no arguments. All the commands between the 42951 first and last line are re-executed as well. 42952 42953Syntax 2: 42954 SAVE <list> 42955 where <list> is a list of 3 or more commands to save. 42956 42957 The line numbers are obtained by preceding the SAVE command by a 42958 list command with no arguments. Only the commands listed are 42959 saved. 42960 42961Syntax 3: 42962 SAVE <file> <id1> <id2> 42963 where <file> is the name of a file where the saved commands are 42964 written; 42965 <id1> is the line number of the first command to re-execute; 42966 and <id2> is the line number of the last command to re-execute. 42967 42968 The line numbers are obtained by preceding the SAVE command by a 42969 list command with no arguments. All the commands between the 42970 first and last line are re-executed as well. This syntax is useful 42971 for saving more than one command sequence. The / command 42972 re-executes the most recently entered SAVE sequence. However, 42973 the CALL <file> command can be used to execute any SAVE sequence 42974 that was written to a file. 42975 42976Syntax 4: 42977 SAVE <file> <list> 42978 where <file> is the name of a file where the saved commands are 42979 written; 42980 and <list> is a list of 3 or more commands to save. 42981 42982 The line numbers are obtained by preceding the SAVE command by a 42983 list command with no arguments. Only the commands listed are 42984 saved. This syntax is useful for saving more than one command 42985 sequence. The / command re-executes the most recently entered SAVE 42986 sequence. However, the CALL <file> command can be used to execute 42987 any SAVE sequence that was written to a file. 42988 42989Examples: 42990 SAVE 6 3 --to save commands 6, 5, 4, and 3 ago 42991 SAVE 3 6 --to save commands 6, 5, 4, and 3 ago 42992 SAVE 6 6 --to save command 6 ago 42993 SAVE 6 --to save command 6 ago 42994 SAVE 1 --to save the last command ago 42995 SAVE --to save the last command ago 42996 SAVE 2 5 8 --to save commands 2, 5, and 8 ago 42997 SAVE COMM.DP 2 5 8 --to save commands 2, 5, and 8 ago to a file 42998 SAVE COMM.DP 6 3 --to save commands 2, 5, and 8 ago to a file 42999 43000Default: 43001 If only one argument is entered, then only that command is 43002 saved. 43003 If no arguments are entered, then the last command is saved. 43004 43005Synonyms: 43006 S 43007 43008Note: 43009 The SAVE command is almost always preceded by the LIST command 43010 (with no arguments). LIST will print the last 20 commands that 43011 were entered. Based on that list, the analyst can then enter the 43012 SAVE command to selectively save one or more of those commands. 43013 For example, 43014 43015 LIST 43016 SAVE 6 3 43017 43018 would list the last 20 commands and then save the sixth, fifth, 43019 fourth, and third commands ago. See the LIST command for details. 43020 43021Note: 43022 DATAPLOT actually saves the last 200 (50 in earlier versions) 43023 commands. Enter the command SET LIST LINES <n> where <n> is 43024 between 1 and 200 to control the number of commands that LIST 43025 prints. 43026 43027Note: 43028 The SAVE command is commonly used for the re-execution of long 43029 complicated commands (e.g., PLOT with a complicated mathematical 43030 expression). The saved commands can be re-executed at any time by 43031 entering the command /. 43032 43033Note: 43034 The S synonym for the SAVE command is heavily used. 43035 43036Note: 43037 DATAPLOT has no restrictions on the file name other than it be a 43038 valid file name on the local operating system and that it contain 43039 a period "." in the file name itself or as a trailing character. 43040 DATAPLOT strips off trailing periods on those systems where it is 43041 appropriate to do so. On systems where trailing periods can be a 43042 valid file name (e.g., Unix), DATAPLOT opens the file with the 43043 trailing period. 43044 43045 Some users prefer to give all macro files a ".DP" or ".dp" 43046 extension. Although this is a useful method for keeping track of 43047 macro files, it is strictly a user convention and is not enforced 43048 by DATAPLOT in any way. 43049 43050Note: 43051 File names are case sensitive on Unix file systems. For Unix, 43052 DATAPLOT opens the file as given. All other currently supported 43053 systems are not case sensitive regarding file names. 43054 43055 As a further caution for Unix hosts, certain expansion characters 43056 (specifically ~ to refer to your home directory) are interpreted 43057 by the shell and are not recognized by the Fortran compiler. These 43058 expansion characters are interpreted as literal characters and do 43059 not yield the intended file name. 43060 43061Default: 43062 If only one argument is entered, then only that command is 43063 saved. 43064 If no arguments are entered, then the last command is saved. 43065 43066Synonyms: 43067 S 43068 43069Related Commands: 43070 / = Re-execute previously saved commands. 43071 LIST = List the previously entered commands. 43072 REPEAT = Selectively re-execute previously entered commands. 43073 CALL = Execute commands stored in a file. 43074 CREATE = Echo entered commands to a file. 43075 43076Applications: 43077 Interactive Usage 43078 43079Implementation Date: 43080 Pre-1987 43081 43082Program: 43083 XX 43084 43085-----SAVE MEMORY-------------------------------------------------- 43086 43087SAVE MEMORY 43088 43089Name: 43090 SAVE MEMORY 43091 43092Type: 43093 Support Command 43094 43095Purpose: 43096 Writes out all internal DATAPLOT parameters, variables, functions, 43097 and switches to a file. 43098 43099Description: 43100 The SAVE MEMORY command allows the analyst to interrupt a DATAPLOT 43101 run (due to a meeting, lunch, etc.) without loss. The RESTORE 43102 MEMORY command allows the analyst to reload the settings and resume 43103 at the point of interruption. 43104 43105Syntax: 43106 SAVE MEMORY <file name> 43107 where <file name> is the name of a file where the internal settings 43108 are saved. 43109 43110 If the file name does not contain a period, place a period (no 43111 spaces) at the end of the file name. 43112 43113Examples: 43114 SAVE MEMORY OUT. 43115 SAVE MEMORY SCRATCH. 43116 SAVE MEMORY TEMP. 43117 43118Note: 43119 DATAPLOT has no restrictions on the file name other than it be a 43120 valid file name on the local operating system and that it contain 43121 a period "." in the file name itself or as a trailing character. 43122 DATAPLOT strips off trailing periods on those systems where it is 43123 appropriate to do so. On systems where trailing periods can be a 43124 valid file name (e.g., Unix), DATAPLOT opens the file with the 43125 trailing period. 43126 43127Note: 43128 File names are case sensitive on Unix file systems. For Unix, 43129 DATAPLOT opens the file as given. All other currently supported 43130 systems are not case sensitive regarding file names. 43131 43132 As a further caution for Unix hosts, certain expansion characters 43133 (specifically ~ to refer to your home directory) are interpreted 43134 by the shell and are not recognized by the Fortran compiler. These 43135 expansion characters are interpreted as literal characters and do 43136 not yield the intended file name. 43137 43138Default: 43139 None 43140 43141Synonyms: 43142 None 43143 43144Related Commands: 43145 RESTORE MEMORY = Restore all internal DATAPLOT settings from a 43146 previously saved file. 43147 RESET = Reset internal DATAPLOT settings to their default 43148 values. 43149 43150Applications: 43151 Interactive Usage 43152 43153Implementation Date: 43154 Pre-1987 43155 43156Program: 43157 XX 43158 43159-----SAVE PLOT-------------------------------------------------- 43160 43161SAVE PLOT 43162 43163Name: 43164 SAVE PLOT 43165 43166Type: 43167 Support Command 43168 43169Purpose: 43170 Save the current plot for later recall via the REPEAT PLOT 43171 command. 43172 43173Description: 43174 The SAVE PLOT and REPEAT PLOT commands allow you to save and 43175 recall graphs. The primary use of this is to compare the current 43176 graph to previously created graphs. 43177 43178 This command is host dependent. It is currently supported for 43179 the following platforms: 43180 43181 1) Unix platforms via the X11 device driver; 43182 2) Windows 95/98/NT command line version built with the 43183 Microsoft Fortran compiler (saved in Windows bitmap format); 43184 3) Dataplot GUI (both Unix and Windows 95/98/NT). 43185 43186Syntax 1: 43187 SAVE PLOT <file> 43188 where <file> is the name of a file in which the current graph 43189 will be saved. 43190 43191 This syntax saves the current plot in the specified file. 43192 If the file name is omitted, the plot is saved in the 43193 file "pixmap.<n>" where <n> is a counter. The counter 43194 starts at 1 for each new Dataplot session. 43195 43196Syntax 2: 43197 SAVE PLOT <file> AUTOMATIC 43198 where <file> is the name of a file in which the current graph 43199 will be saved. 43200 43201 This syntax saves all subsequent plots in the specified file. 43202 The current plot is not saved, only plots subsequent to 43203 when the SAVE PLOT command is entered. 43204 43205 A counter is added to the file name, that is, if the file 43206 name specified was SCATPLOT, then the saved graphs are in 43207 SCATPLOT.1, SCATPLOT.2, etc. If the file name is omitted, 43208 the plot is saved in the file "pixmap.<n>" where <n> is 43209 the counter. 43210 43211 The counter starts at 1 for each new Dataplot session. 43212 43213Examples: 43214 READ FILE.DAT Y1 Y2 Y3 43215 HISTOGRAM Y1 43216 SAVE PLOT HIST.1 43217 HISTOGRAM Y2 43218 SAVE PLOT HIST.2 43219 HISTOGRAM Y3 43220 SAVE PLOT HIST.3 43221 43222Default: 43223 The default file name is "pixmap.<n>" where <n> is a 43224 counter (reset to 1 for each new Dataplot session). 43225 43226Synonyms: 43227 SAVE GRAPH, SP, and SG are all synonyms for SAVE PLOT. 43228 43229Note: 43230 The saved plots are essentially screen dumps. There is 43231 currently no "linking" in the sense that if a given variable 43232 is changed the saved plots are automatically updated. 43233 43234Note: 43235 As a technical note for the X11 implementation, the plots 43236 are saved in X11 "bitmap" format. This is distinct from 43237 the X11 image format that is used by xwd to save a screen 43238 image. This choice was made for performance reasons (xlib 43239 provides direct routines for reading and writing bitmaps, 43240 but not for reading and writing images). The primary 43241 limitations are: 43242 43243 i) Color is not supported for X11 bitmaps. Elements drawn 43244 in color will not be saved in the bitmap. 43245 43246 ii) You cannot use the X11 tools xwd and xwud to view the 43247 saved plots independently of Dataplot. However, they 43248 can be viewed by any software the reads X11 bitmaps. 43249 43250Note: 43251 Be aware that for SAVE GRAPH AUTOMATIC the saving for a given 43252 plot is not executed until the next screen erase (typically the 43253 next plot) is encountered to allow for multi-plotting and the 43254 addition of diagrammatic graphics to a plot. 43255 43256Note: 43257 The REPEAT PLOT command is used to display a plot saved 43258 with SAVE PLOT. The LIST PLOT command lists the currently 43259 saved plots (by sequence number, file name, and title). 43260 The CYCLE PLOT command allows you to cycle through the 43261 pixmaps in the current list by clicking mouse buttons. 43262 The PIXMAP TITLE command allows you to specify the title 43263 for a saved plot. This title is simply for ease of 43264 identification in listing the saved plots and is not 43265 saved as part of the plot. 43266 43267Related Commands: 43268 LIST PLOT = List saved plots. 43269 REPEAT PLOT = Draw a previously saved graph. 43270 CYCLE PLOT = Cycle through previously saved graphs using 43271 mouse buttons. 43272 PIXMAP TITLE = Provide a temporary name for a saved graph. 43273 43274Applications: 43275 Interactive Usage 43276 43277Implementation Date: 43278 7/1997 43279 43280Program: 43281 READ BERGER1.DAT Y X 43282 FIT Y X 43283 4-PLOT RES 43284 SAVE PLOT RES.1 43285 QUADRATIC FIT Y X 43286 4-PLOT RES 43287 SAVE PLOT RES.2 43288 REPEAT PLOT RES.1 43289 REPEAT PLOT RES.2 43290 43291-----SCATTER PLOT MATRIX-------------------------------------- 43292 43293SCATTER PLOT MATRIX 43294 43295Name: 43296 SCATTER PLOT MATRIX 43297 43298Type: 43299 Graphics Command 43300 43301Purpose: 43302 Generates a scatter plot matrix. 43303 43304Description: 43305 A scatter plot matrix of Y1, Y2, ... , Yk is a matrix of 43306 all the pairwise scatter plots between Y1, Y2, ...., Yk. 43307 This is a simple, but powerful, technique for viewing all the 43308 pairwise relationships between the variables. 43309 43310 The pairwise plots need not be limited to scatter plots. 43311 Dataplot allows you to generate the pairwise plots for 43312 approximately 10 different plot types (and additional plot 43313 types will be added in future implementations). 43314 43315 There are a number of alternatives for the appearance of this 43316 plot. Dataplot tries to balance simplicity with flexibility 43317 by using default settings, but providing numerous SET commands 43318 to control the appearance of the plot. These are described in 43319 detail in the NOTES section below. 43320 43321Syntax 1: 43322 SCATTER PLOT MATRIX <y1> <y2> ... <yk> <SUBSET/EXCEPT/FOR qualification> 43323 where <y1> through <yk> are the response variables; 43324 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 43325 43326 Up to 25 response variables can be specified. 43327 43328Syntax 2: 43329 YOUDEN MATRIX PLOT <y1> <y2> ... <yk> <tag> <SUBSET/EXCEPT/FOR qualification> 43330 where <y1> through <yk> are the response variables; 43331 <tag> is a group id variable (and is always given last); 43332 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 43333 43334 This is a special form of the command that plots 43335 43336 PLOT Yi Yj TAG 43337 43338 for the individual plots. 43339 43340Syntax 3: 43341 DEX <stat> INTERACTION PLOT <y1> <y2> ... <yk> <SUBSET/EXCEPT/FOR qualification> 43342 where <y1> through <yk> are the response variables; 43343 <stat> defines a statistic, such as MEAN or MEDIAN, for 43344 the plot; 43345 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 43346 43347 This is a special form of the command that plots 43348 43349 DEX <stat> INTERACTION PLOT Yi Yj TAG 43350 43351 for the individual plots. <stat> is optional. 43352 43353Examples: 43354 SCATTER PLOT MATRIX Y1 Y2 Y3 Y4 Y5 43355 SCATTER PLOT MATRIX Y1 Y2 Y3 Y4 Y5 SUBSET TAG > 2 43356 43357Note: 43358 The concept of the scatter plot matrix generalizes quite 43359 nicely to any plot type for two variables. Dataplot 43360 supports the scatter plot matrix for a number of different plot 43361 types. The type of plot generated is controlled by the following 43362 command: 43363 43364 SET SCATTER PLOT MATRIX TYPE <value> 43365 43366 where <value> is one of the following. 43367 43368 The folllowing plot two variables (e.g., BIHISTOGRAM Y1 Y2). 43369 43370 PLOT - generate scatter plots (this is the default). 43371 The x and y axis labels are automatically set 43372 to the appropriate variable name. 43373 43374 QUANTILE-QUANTILE - generate quantile-quantile plots. This 43375 degenerates to percent point plots on the diagonal. 43376 The x and y axis labels are automatically set 43377 to the appropriate variable name. 43378 43379 BIHISTOGRAM - generate relative bihistograms. This 43380 degenerates to relative histograms on the diagonal. 43381 We recommend that you enter 43382 SET RELATIVE HISTOGRAM PERCENT to generate more 43383 consistent y-axis scales. The X1LABEL is set 43384 to the first variable name and the X2LABEL is set to 43385 the second variable name. If no YLABEL is 43386 already defined, the YLABEL is set to "Frequency". 43387 43388 CORRELATION - generate a cross-correlation plot. This 43389 degenerates to an autocorrelation plot on the 43390 diagonal. If X1LABEL and Y1LABEL are not 43391 previously defined, they are automatically set 43392 to "Lag" and "Correlation" respectively. The 43393 X2LABEL is set to "X1*X2" where X1 and X2 43394 represent the variable names. 43395 43396 LAG - generate a cross-lag plot. This degenerates to a 43397 lag plot on the diagonal. If X1LABEL and Y1LABEL 43398 are not previously defined, they are automatically 43399 set to "I+1" and "I" respectively. The 43400 X2LABEL is set to "X1*X2" where X1 and X2 43401 represent the variable names. 43402 43403 SPECTRAL - generate a cross-spectral plot. This degenerates 43404 to a spectral plot on the diagonal. If X1LABEL and 43405 Y1LABEL are not previously defined, they are 43406 automatically set to "Power" and "Frequency" 43407 respectively. The X2LABEL is set to "X1*X2" where 43408 X1 and X2 represent the variable names. 43409 43410 YOUDEN - this generates a Youden plot. That is, 43411 PLOT Y1 Y2 TAG where TAG is a group id variable. 43412 The TAG variable is the last variable listed on the 43413 SCATTER PLOT MATRIX command and is the same for all 43414 the plots. 43415 43416 The folllowing plot Y X1 X2 (e.g., DEX CONTOUR PLOT Y X1 X2). 43417 That is, the response variable is the first variable in the 43418 list, and it remains constant for all the pairwise plots. 43419 43420 DEX CONTOUR - this generates a dex contour plot. The 43421 diagonal plot is empty. The X2LABEL is set to 43422 "X1*X2" where X1 and X2 represent the variable names. 43423 No automatic labels are generated for X1LABEL and 43424 Y1LABEL. 43425 43426 DEX INTERACTION - generate a DEX INTERACTION PLOT. 43427 The X1LABEL is set to "X1*X2" where X1 and X2 43428 represent the variable names. No automatic labels 43429 are generated for X2LABEL and Y1LABEL. 43430 43431 DEX <statistic> INTERACTION - generate a DEX <statistic> 43432 INTERACTION PLOT. The X1LABEL is set to 43433 "X1*X2" where X1 and X2 represent the variable names. 43434 No automatic labels are generated for X2LABEL and 43435 Y1LABEL. 43436 43437 CROSS TABULATE <statistic> - generate a CROSS TABULATE 43438 <statistic> plot. This generates to a 43439 <statistic> STATISTIC plot on the diagonal. 43440 The X1LABEL is set to "X1*X2" where X1 and X2 43441 represent the variable names. No automatic labels 43442 are generated for X2LABEL and Y1LABEL. 43443 43444 If no <statistic> is given, then a special form 43445 of the CROSS TABULATE PLOT is generated. For this 43446 case, there is no response variable 43447 (i.e., CROSS TABULATE PLOT X1 X2 as oppossed to 43448 CROSS TABULATE MEAN PLOT Y X1 X2). The X1LABEL 43449 and Y1LABEL are set to the appropriate variable 43450 name. 43451 43452 A few of the above plots support a <statistic> option. This 43453 can be one of 30+ supported statistics (the supported statistics 43454 are identical to those for the STATISTIC PLOT and the BOOTSTRAP 43455 PLOT). It is typically a location statistic (e.g., MEAN, 43456 MEDIAN) or a scale statistic (e.g., STANDARD DEVIATION, VARIANCE, 43457 MAD). 43458 43459 Dataplot automatically defines X1LABEL, X2LABEL, and YLABEL 43460 commands for these plots. You can control the attributes 43461 of these labels with the standard label setting commands. 43462 If you have defined variable labels (with the VARIABLE LABEL 43463 command), these will automatically be substituted for variable 43464 names in the labels. 43465 43466 If you have defined variable labels with the VARIABLE LABEL 43467 command and you want to suppress the automatic expansion 43468 of the variable name to the variable label, enter 43469 43470 SET VARIABLE LABEL EXPAND OFF 43471 43472 To restore the default that variable names will be expanded to 43473 the corresponding variable label, enter 43474 43475 SET VARIABLE LABEL EXPAND ON 43476 43477Note: 43478 The following option controls which axis tic marks, tic mark 43479 labels, and axis labels are plotted. 43480 43481 SET SCATTER PLOT MATRIX LABELS <ON/OFF/XON/YON/BOX> 43482 43483 OFF means that all axis labels are suppressed (this can be 43484 useful if a large number of variables are being plotted). ON 43485 means that both X and Y axis labels are printed. XON only 43486 plots the x axis labels and YON only plots the y axis labels. 43487 43488 BOX is a special option that creates an extra column on the 43489 left and an extra row on the bottom. The axis label is 43490 printed in this box. 43491 43492 The default is ON (both x and y axis labels are printed). 43493 43494Note: 43495 The following option controls where the x axis tic marks, 43496 tic mark labels, and axis label are printed. 43497 43498 SET SCATTER PLOT MATRIX X AXIS <BOTTOM/TOP/ALTERNATE> 43499 43500 BOTTOM specifies that the x axis labels are printed on the 43501 bottom axis (on the last row only). TOP specifies that 43502 the x axis labels are printed on the top axis (first row 43503 only). ALTERNATE specifies that the x axis labels alternate 43504 between the top (first row) and bottom axis (last row). 43505 We recommend using the TIC OFFSET command to avoid overlap 43506 of axis labels and tic marks. 43507 43508 The default is ALTERNATE. 43509 43510Note: 43511 The following option controls where the y axis tic marks, 43512 tic mark labels, and axis label are printed. 43513 43514 SET SCATTER PLOT MATRIX Y AXIS <LEFT/RIGHT/ALTERNATE> 43515 43516 LEFT specifies that the y axis labels are printed on the 43517 left axis (on the first column only). RIGHT specifies that 43518 the y axis labels are printed on the right axis (last column 43519 only). ALTERNATE specifies that the y axis labels alternate 43520 between the left (first column) and right axis (last column). 43521 We recommend using the TIC OFFSET command to avoid overlap 43522 of axis labels and tic marks. 43523 43524 The default is ALTERNATE. 43525 43526Note: 43527 Users have different preferences in terms of whether the 43528 plot frames for neighboring plots are connected or not. 43529 This is controlled with the following option. 43530 43531 SET SCATTER PLOT MATRIX FRAME <DEFAULT/CONNECTED/USER> 43532 43533 DEFAULT connects neighboring frames (i.e., the FRAME CORNER 43534 COORDINATES are set to 0 0 100 100). USER uses whatever 43535 frame coordinates are currently set (15 20 85 90 by default) 43536 and makes no special provisions for axis labels and tic marks 43537 (i.e., you set them as you normally would, each plot uses 43538 whatever you have set). CONNECTED uses whatever frame 43539 coordinates have been set by the user, but it draws the axis 43540 labels and tic marks as if DEFAULT were being used (that is, as 43541 determined by the SET SCATTER PLOT MATRIX <LABELS/X AXIS/Y AXIS> 43542 commands described above). Typically, CONNECTED is used to 43543 put a small bit of space between plots. For example, you 43544 might use FRAME CORNER COORDINATES 3 3 97 97 before the 43545 SCATTER PLOT MATRIX command. 43546 43547 The default is DEFAULT. 43548 43549Note: 43550 When the tic marks and tic mark labels are all plotted on the 43551 same side (i.e., SET SCATTER PLOT MATRIX Y AXIS is 43552 set to LEFT or RIGHT or SET SCATTER PLOT MATRIX X AXIS is 43553 set to BOTTOM or TOP), then overlap between plots is possible. 43554 The TIC OFFSET command can be used to avoid this. In addition, 43555 you can stagger the tic labels with the following command: 43556 43557 SET SCATTER PLOT MATRIX LABEL DISPLACEMENT 43558 <NORMAL/STAGGERED/VALUE> 43559 43560 NORMAL means that all tic labels are plotted at a distance 43561 determined by the TIC LABEL DISPLACEMENT command. STAGGERED 43562 means that alternating plots will be staggered. That is, one 43563 will use the standard displacement while the next uses a 43564 staggered value. Entering this command with a numeric value 43565 specifies the amount of the displacement for the staggered 43566 tic labels. For example, 43567 43568 TIC MARK LABEL DISPLACEMENT 10 43569 SET SCATTER PLOT MATRIX LABEL DISPLACEMENT STAGGERED 43570 SET SCATTER PLOT MATRIX LABEL DISPLACEMENT 25 43571 43572 These commands specify that the default tic label displacement 43573 is 10 and the staggered tic mark label displacement is 25. 43574 43575Note: 43576 It is often helpful on scatter plot matrices to overlay a 43577 fitted line on the plots. The following command is used 43578 to specify the type of fit. 43579 43580 SET SCATTER PLOT MATRIX FIT <NONE/LOWESS/LINE/QUAD/SMOOTH> 43581 43582 NONE means that no fitted line is plotted. LOWESS means 43583 that a locally weighted least squares line will be overlaid. 43584 LINE means that a linear fit (Y = A0 + A1*X) will be overlaid. 43585 QUAD means that a quadratic fit (Y = A0 + A1*X + A2*X**2) will 43586 be overlaid. SMOOTH means that a least squares smoothing will 43587 be overlaid. 43588 43589 For LOWESS, it is recommended that the lowess fraction be set 43590 fairly high (e.g., LOWESS FRACTION 0.6). 43591 43592 The fitted line is currently only generated if the scatter plot 43593 matrix plot type is PLOT. 43594 43595 The default is for no fitted line to be overlaid on the plot. 43596 If a overlaid fit is desired, the most common choice is to use 43597 LOWESS. 43598 43599Note: 43600 Dataplot supports a special plot type 43601 43602 PLOT Y X TAG 43603 43604 In this form of the plot command, TAG is a group identifier 43605 variable. Points belonging to the same group are plotted with 43606 the same attributes (controlled by the CHARACTER and LINE commands 43607 and their various attribute setting commands). 43608 43609 Using a tag variable has two common purposes: 43610 43611 1) If your data has natural groups (e.g., batch 1 and batch 2). 43612 2) To identify certain points. The most common application 43613 would be to flag outliers. 43614 43615 You can specify that the scatter plot matrix use the form 43616 of the PLOT command by using the command 43617 43618 SET SCATTER PLOT MATRIX TAG <ON/OFF> 43619 43620 OFF specifies that the standard plot command (PLOT Y1 Y2) will 43621 be used. ON specifies that the last variable on the 43622 SCATTER PLOT MATRIX command is a tag variable. That is, it is 43623 not plotted directly, but is instead the third variable on 43624 all the plot commands generated by the scatter plot matrix. 43625 43626 Currently, this command only applies if the scatter plot matrix 43627 plot type is set to PLOT. 43628 43629 This form is common enough that the command 43630 43631 YOUDEN MATRIX PLOT Y1 Y2 ... YK TAG 43632 43633 implements this automatically. That is, YOUDEN MATRIX PLOT 43634 is equivalent to 43635 43636 SET SCATTER PLOT MATRIX TAG ON 43637 SCATTER PLOT MATRIX Y1 Y2 ... YK TAG 43638 43639 In some cases, you may want to use a tag variable for both 43640 purposes. That is, you may have natural groups in your data, 43641 but you also want to flag certain outlying points. You can 43642 do this by using a SUBSET clauuse. For example, 43643 43644 LIMITS 0 120 43645 SET SCATTER PLOT MATRIX TAG ON 43646 CHARACTER CIRCLE SQUARE TRIANGLE 43647 CHARACTER FILL OFF OFF OFF 43648 SCATTER PLOT MATRIX Y1 Y2 Y3 Y4 TAG SUBSET Y2 <= 100 43649 PRE-ERASE OFF 43650 CHARACTER FILL ON ON ON 43651 SCATTER PLOT MATRIX Y1 Y2 Y3 Y4 TAG SUBSET Y2 > 100 43652 43653 The SET SCATTER PLOT MATRIX LIMITS command, discussed below, 43654 can be used to control the axis limits for the individual plots. 43655 43656 The default is OFF. 43657 43658Note: 43659 Dataplot allows you to set axis limits with the LIMITS command. 43660 For the scatter plot matrix, it is often desirable to set 43661 the axis limits for each plot. This can be done with the 43662 command 43663 43664 SET SCATTER PLOT MATRIX LIMITS <LOW1> <UPP1> <LOW2> <UPP2> ... 43665 43666 Note that the pairs of limits correspond to the variable list 43667 in the SCATTER PLOT MATRIX command. That is, if Y3 is the 43668 third variable in the command, Dataplot will set the YLIMITS 43669 when Y3 is plotted on the y axis and the XLIMITS when Y3 is 43670 plotted on the x axis. 43671 43672 This command is particularly useful if you want to overlay 43673 scatter plot matrices (the example discussed for the 43674 SET SCATTER PLOT MATRIX TAG command gives an example of where 43675 you might want to do this). 43676 43677 The default is to allow the axis limits to float with the data. 43678 43679Note: 43680 Dataplot supports a subregion capability. This is used to 43681 draw "engineering limits" on a plot. For a scatter plot matrix, 43682 if you specify engineering limits, you typically want these 43683 limits to vary with each plot. They can be specified with the 43684 command 43685 43686 SET SCATTER PLOT MATRIX SUBREGION LIMITS <LOW1> <UPP1> 43687 <LOW2> <UPP2> ... 43688 43689 This command is similar to the SET SCATTER PLOT MATRIX LIMITS 43690 command in that the list corresponds to the variables entered 43691 on the SCATTER PLOT MATRIX command. 43692 43693 Only one set of subregion limits can be set for each variable. 43694 43695 The default is that no subregion limits are set. 43696 43697Note: 43698 For a scatter plot matrix, there are numerous choices for what 43699 to plot on the diagonal. This is controlled with the command 43700 43701 SET SCATTER PLOT MATRIX DIAGONAL <BLANK/LINE/HISTOGRAM/BOXPLOT> 43702 43703 If BLANK, an empty plot is generated and the variable label 43704 is plotted in the center of the empty plot. If LINE, a 43705 PLOT Y1 Y1 is generated (this will simply be a 45 degree line, 43706 but it does give some indication of the univariate distribution 43707 of the variable). If HISTOGRAM, a relative histogram of the 43708 variable is generated. For the HISTOGRAM, the axis labels do 43709 not apply to the histogram plot. A relative histogram is drawn 43710 to make comparisons more meaningful. If BOXPLOT, a box plot of 43711 the variable is generated. The BOXPLOT only applies if the 43712 SET SCATTER PLOT MATRIX TAG ON command is entered. That is, the 43713 box plot is only used if there are groups in the data. For the 43714 box plot, the y axis limtis are valid, but the x axis limits 43715 are not. 43716 43717 This command only applies if the scatter plot matrix plot 43718 type is PLOT, CROSS TABULATE, or DEX CONTOUR. 43719 43720 The default is BLANK. 43721 43722Note: 43723 The scatter plot matrix is redundant in the sense that 43724 PLOT Y1 Y2 is equivalent to PLOT Y2 Y1 (with the axes reversed). 43725 For this reason, some analysts prefer to omit plots below the 43726 diagonal. This can be controlled with the command 43727 43728 SET SCATTER PLOT MATRIX LOWER DIAGONAL <ON/OFF> 43729 43730 If OFF, the plots below the diagonal are omitted. If ON, the 43731 plots below the diagonal are drawn. 43732 43733 The default is ON. 43734 43735Note: 43736 You can specify a special X2LABEL for the plots with the 43737 following command 43738 43739 SET SCATTER PLOT MATRIX X2LABEL <OFF/ 43740 CORRELATION/PERCENT CORRELATION/EFFECT/ 43741 PERCENT ACCEPT/NUMBER ACCEPT/ACCEPT TOTAL> 43742 43743 where 43744 OFF - no special X2LABEL is drawn. 43745 CORRELATION - the correlation of the points on the plot 43746 is printed with the X2LABEL. This option 43747 is typically used with the plot type PLOT. 43748 PERCENT CORRELATION - this is the same as CORRELATION, except 43749 that the correlation is printed as a percent. 43750 EFFECT - the difference between the low and high value 43751 is printed. This option is typically used with 43752 the plot type DEX <stat> INTERACTION (and doesn't 43753 really make any sense with the other plot types). 43754 PERCENT ACCEPT - this option prints the percentage of points 43755 inside the first subregion. If no subregions are 43756 defined, this option makes no sense. It is 43757 typically used to specify the percentage of points 43758 within engineering limits. 43759 NUMBER ACCEPT - this option is similar to PERCENT ACCEPT. 43760 However, the number of points rather than the 43761 percentage is printed. 43762 ACCEPT TOTAL - this option is similar to NUMBER ACCEPT. 43763 However, it prints the number accepted first, 43764 then the total number of points. 43765 ACCEPT TOTAL PERCENT - this option is similar to ACCEPT TOTAL. 43766 However, after printing the number accepted and 43767 the total number, it prints the percentage 43768 accepted. 43769 43770 43771 The following commands can be used to add a prefix and suffix 43772 to the X2LABEL. For example, you might want the PERCENT 43773 CORRELATION to append a "%" after the percent correlation 43774 and to start with "CORR = ". 43775 43776 SET X2LABEL PREFIX <prefix> 43777 SET X2LABEL SUFFIX <suffix> 43778 43779 The appearance and location of the X2LABEL are controlled 43780 with the standard X2LABEL attribute setting commands. 43781 43782 There are occassions where you may want to use the values 43783 computed in the X2LABEL for additional numeric computations. 43784 These values are automatically written to the file 43785 "dpst5f.dat". The values are printed in the order the plots 43786 are generated. 43787 43788Note: 43789 You can use standard plot control commands to control the 43790 appearance of the scatter plot matrix. 43791 43792 For example, 43793 43794 MULTIPLOT CORNER COORDINATES 5 5 95 95 43795 MULTIPLOT SCALE FACTOR 3 43796 TIC OFFSET UNITS SCREEN 43797 TIC OFFSET 5 5 43798 43799 is a fairly typical set of commands commonly used with 43800 scatter plot matrices. 43801 43802Default: 43803 None 43804 43805Synonyms: 43806 MATRIX PLOT is a synonym for SCATTER PLOT MATRIX. 43807 SET MATRIX PLOT is a synonym for SET SCATTER PLOT MATRIX. 43808 43809Related Commands: 43810 PLOT = Generates a data or function plot. 43811 FACTOR PLOT = Generate a factor plot. 43812 CONDITIONAL PLOT = Generate a conditional (subset) plot. 43813 43814Reference: 43815 "Visualizing Data", Cleveland, William S., Hobart Press, 1993. 43816 43817 "Graphical Exploratory Data Analysis", du Toit, Steyn, and Stumpf, 43818 Springer-Verlang, 1986. 43819 43820Applications: 43821 Exploratory Data Analysis, Multivariate Data Analysis 43822 43823Implementation Date: 43824 2000/1 43825 43826Program: 43827 read iris.dat y1 y2 y3 y4 tag 43828 multiplot corner coordinates 10 10 90 90 43829 multiplot scale factor 4 43830 tic offset units screen 43831 tic offset 5 5 43832 line blank blank blank 43833 character 1 2 3 43834 set matrix plot tag on 43835 matrix plot y1 y2 y3 y4 tag 43836 43837-----SCATTER (LET)------------------------------------- 43838 43839SCATTER 43840 43841Name: 43842 SCATTER (LET) 43843 43844Type: 43845 Let Subcommand 43846 43847Purpose: 43848 Save rows of a variable based on index values 43849 contained in another variable. 43850 43851Description: 43852 The GATHER command (HELP GATHER for details) can be used 43853 to extract specific rows of a variable based on an index 43854 variable. 43855 43856 The SCATTER command is most often used after a GATHER 43857 command. That is, we use GATHER to extract specific rows 43858 of a variable, perform operations that modify these extracted 43859 values, and then use SCATTER to save these modfied values 43860 back in the original variable. 43861 43862Syntax: 43863 LET <y> = SCATTER <x> <index> 43864 where <x> is a response variable; 43865 <index> is a variable containing row numbers; 43866 and <y> is a variable where the values of <x> will be saved. 43867 43868Examples: 43869 LET Y = SCATTER X INDEX 43870 43871Default: 43872 None 43873 43874Synonyms: 43875 None 43876 43877Related Commands: 43878 GATHER = Extract specified rows of data from a variable 43879 based on an index variable. 43880 SEQUENCE = Generate a patterned sequence of values. 43881 SORT = Sort a column of numbers. 43882 RANK = Rank a column of numbers. 43883 CODE = Code a column of numbers. 43884 SUBSET = Specifies a subset to be included in a plot, 43885 analysis, or LET command. 43886 RETAIN = Retain specified rows or a subset of a 43887 variable. 43888 43889Applications: 43890 Data Transformation 43891 43892Implementation Date: 43893 2008/11 43894 43895Program: 43896 let n = 30 43897 let xseq = sequence 1 1 n 43898 let x = normal rand numb for i = 1 1 n 43899 let iindex = data 10 14 8 23 19 43900 . 43901 let y = -10 for i = 1 1 n 43902 let y = scatter x iindex 43903 set write decimals 3 43904 print xseq x y iindex 43905 43906-----SEARCH------------------------------------------------------- 43907 43908SEARCH 43909 43910Name: 43911 SEARCH 43912 43913Type: 43914 Support Command 43915 43916Purpose: 43917 Search a file for a string. 43918 43919Syntax 1: 43920 SEARCH <file name> <string> 43921 where <file name> is the file to be searched; 43922 and <string> is the string to search for. 43923 43924 This syntax prints all lines where a match is found. 43925 43926Syntax 2: 43927 SEARCH1 <file name> <string> 43928 where <file name> is the file to be searched; 43929 and where <string> is the string to search for. 43930 43931 This syntax prints the first line where a match is found. 43932 43933Syntax 3: 43934 SEARCHB <file name> <string> 43935 where <file name> is the file to be searched; 43936 and <string> is the string to search for. 43937 43938 This syntax prints from the first line where a match is found to 43939 the next blank line. 43940 43941Syntax 4: 43942 SEARCHDA <file name> <string> 43943 where <file name> is the file to be searched; 43944 and <string> is the string to search for. 43945 43946 This syntax prints from the first line where a match is found to 43947 the next dashed line. 43948 43949Syntax 5: 43950 SEARCH REFERENCE <string> 43951 where <string> is the string to search for. 43952 43953 This syntax searches the file refman.tex located in the Dataplot 43954 HELP directory. This file is used by the WEB HELP command to access 43955 the Dataplot reference manual on the Dataplot web pages. 43956 43957Syntax 6: 43958 SEARCH HANDBOOK <string> 43959 where <string> is the string to search for. 43960 43961 This syntax searches the file handbk.tex located in the Dataplot 43962 HELP directory. This file is used by the WEB HANDBOOK command to 43963 access the NIST/SEMATECH e-Handbook of Statistics web pages. 43964 43965Syntax 7: 43966 SEARCH DIRECTORY <string> 43967 where <string> is the string to search for. 43968 43969 This syntax searches the file dpdirf.tex located in the Dataplot 43970 HELP directory. This file contains a one line description of 43971 Dataplot commands sorted by category. 43972 43973Syntax 8: 43974 SEARCH DICTIONARY <string> 43975 where <string> is the string to search for. 43976 43977 This syntax searches the file dpdicf.tex located in the Dataplot 43978 HELP directory. This file contains a one line description of 43979 Dataplot commands sorted alphabetically. 43980 43981Examples: 43982 SEARCH PLOTCALIB. PLOT 43983 SEARCH PROG.PLOTLAB READ 43984 SEARCH REFERENCE MEAN PLOT 43985 SEARCH HANDBOOK RELIABILITY 43986 43987Note: 43988 In versions prior to 2018/04, only the first word of 43989 <string> was matched. For example, 43990 SEARCH REFERENCE MEAN PLOT would find all lines in 43991 refman.tex that contain the word MEAN. 43992 43993 Starting with the 2018/04 version, 43994 SEARCH REFERENCE MEAN PLOT will now only match the lines 43995 containing the phrase MEAN PLOT. Note that words MEAN PLOT must 43996 appear contiguously (i.e., as a single phrase) on the line. 43997 It does not do a separate search for MEAN and then for 43998 PLOT and it does not match lines where MEAN and PLOT do not 43999 appear together. For example, "MEAN OF THE PLOT" would not be 44000 a match for "MEAN PLOT". 44001Note: 44002 Dataplot will save the line number of the first match in the 44003 parameter LINENUMB. 44004 44005Note: 44006 Only the first 80 characters of the line will be printed. 44007 44008Note: 44009 The search is not case sensitive. 44010 44011Note: 44012 The FOR clause can be used to search a restricted part of the 44013 file. For example, 44014 44015 SEARCH PROG.PLOTLAB PLOT FOR I = 1 1 200 44016 44017 searches only the first 200 lines of the file. 44018 44019Note: 44020 DATAPLOT has no restrictions on the file name other than it be a 44021 valid file name on the local operating system and that it contain 44022 a period "." in the file name itself or as a trailing character. 44023 DATAPLOT strips off trailing periods on those systems where it is 44024 appropriate to do so. On systems where trailing periods can be a 44025 valid file name (e.g., Unix), DATAPLOT tries to open the file with 44026 the trailing period. If this fails, it then tries to open the file 44027 with the trailing period stripped off. 44028 44029Note: 44030 File names are case sensitive on Unix file systems. For Unix, 44031 DATAPLOT attempts to open the file as given. If this fails, it 44032 attempts to open the file as all upper case characters. If this 44033 fails, it attempts to open the file as all lower case characters. 44034 All other currently supported systems are not case sensitive 44035 regarding file names. 44036 44037 As a further caution for Unix hosts, certain expansion characters 44038 (specifically ~ to refer to your home directory) are interpreted 44039 by the shell and are not recognized by the Fortran compiler. These 44040 expansion characters are interpreted as literal characters and do 44041 not yield the intended file name. 44042 44043Default: 44044 None 44045 44046Synonyms: 44047 SEARCHALL is a synonym for SEARCH. 44048 44049 ? is a synonym for SEARCH REFERENCE 44050 SEARCH is a synonym for SEARCH REFERENCE 44051 SEARCH RM is a synonym for SEARCH REFERENCE 44052 44053 ??? is a synonym for SEARCH HANDBOOK 44054 SEARCH HB is a synonym for SEARCH HANDBOOK 44055 SEARCH HANDBK is a synonym for SEARCH HANDBOOK 44056 44057 SEARCH DIR is a synonym for SEARCH DIRECTORY 44058 SEARCH DIRE is a synonym for SEARCH DIRECTORY 44059 SEARCH DIC is a synonym for SEARCH DICTIONARY 44060 SEARCH DICT is a synonym for SEARCH DICTIONARY 44061 44062Related Commands: 44063 LIST = Print the contents of the file. 44064 WEB HELP = Access Dataplot's web-based documentation. 44065 WEB HANDBOOK = Access the NIST/SEMATECH Handbook of Statistical 44066 Methods web pages. 44067 44068Applications: 44069 Documentation 44070 44071Implementation Date: 44072 1988/01 44073 1988/08: Support for DICTIONARY and DIRECTORY searches 44074 1994/01: Support for SEARCH1 option 44075 2003/02: Support for saving LINENUMB 44076 2018/04: Support for REFERENCE and HANDBOOK searches 44077 2018/04: Support for multi-word searches 44078 2018/04: Add various synonyms 44079 44080Program: 44081 SEARCH REFERENCE MEAN PLOT 44082 WEB HELP MEAN PLOT 44083 44084-----SEARCH DIRECTORY (SET)-------------------------------------------- 44085 44086SEARCH DIRECTORY 44087 44088Name: 44089 SEARCH DIRECTORY (SET) 44090 44091Type: 44092 Set Subcommand 44093 44094Purpose: 44095 Specify the name of the directory where Dataplot will look for files. 44096 44097Description: 44098 When Dataplot encounters a file name (on the LIST, READ, WRITE, or CALL 44099 commands), it will do the following: 44100 44101 1. It will first look for the file in the current directory (you 44102 can enter the PWD command if you are not sure what that is). 44103 44104 2. If the command 44105 44106 SET HOME PATH ON 44107 44108 has been given, then your home directory will be searched next. 44109 44110 3. If it does not find the file, it will look for the file in 44111 the Dataplot auxillary directory. By default, this will be 44112 "C:\Program Files (x86)\NIST\DATAPLOT" under Windows systems 44113 and "/usr/local/lib/dataplot" under Unix/Linux/Mac OS X 44114 systems. However, this may be different on your platform. 44115 44116 Dataplot first searches this directory and then the following 44117 sub-directories "help", "data", "dex", "10step", "macros", 44118 "programs", "text", "menu", "ps", and "scripts" are searched 44119 (in the order given). 44120 44121 Note that under Unix/Linux/Mac OS X systems, which are case sensitive, 44122 Datatplot will first try to open the file name as given. If the file 44123 is not found, then Dataplot will convert the file name to all upper 44124 case and try to open the file. If the file is not found, then Dataplot 44125 will convert the file name to all lower case and try to open the 44126 file. Note that this file name conversion is performed in each 44127 directory before moving to the next directory. 44128 44129 Some users may find it convenient to keep macros and datasets that will 44130 be used in subsequent Dataplot sessions in a common directory. The 44131 SEARCH DIRECTORY command allows you to specify a directory to be 44132 searched for file names. This directory will be searched after the 44133 current directory but before the Dataplot auxillary directories. 44134 44135 Currently, this command is limited to a single directory. 44136 44137 Note: The 2020/05 version of Dataplot added the SET SEARCH2 DIRECTORY, 44138 SET SEARCH3 DIRECTORY, SET SEARCH4 DIRECTORY, 44139 SET SEARCH5 DIRECTORY and SET SEARCH6 DIRECTORY commands to 44140 allow up to six user specified directories to be searched. 44141 44142 The 2 to 6 suffix specifies the order in which the directories 44143 are searched. However, you do not have to define them in any 44144 particular order. For example, you can enter a SET SEARCH4 44145 DIRECTORY command without entering a SET SEARCH3 DIRECTORY or 44146 a SET SEARCH2 DIRECTORY command. 44147 44148Syntax 1: 44149 SET SEARCH DIRECTORY <string> 44150 where <string> specifies the desired directory name. 44151 44152Syntax 2: 44153 SET SEARCH2 DIRECTORY <string> 44154 where <string> specifies the desired directory name. 44155 44156 This specifies a second user specified directory. 44157 44158Syntax 3: 44159 SET SEARCH3 DIRECTORY <string> 44160 where <string> specifies the desired directory name. 44161 44162 This specifies a third user specified directory. 44163 44164Syntax 4: 44165 SET SEARCH4 DIRECTORY <string> 44166 where <string> specifies the desired directory name. 44167 44168 This specifies a fourth user specified directory. 44169 44170Syntax 5: 44171 SET SEARCH5 DIRECTORY <string> 44172 where <string> specifies the desired directory name. 44173 44174 This specifies a fifth user specified directory. 44175 44176Syntax 6: 44177 SET SEARCH6 DIRECTORY <string> 44178 where <string> specifies the desired directory name. 44179 44180 This specifies a sixth user specified directory. 44181 44182Examples: 44183 SET SEARCH DIRECTORY C:\DATAPLOT_MACROS 44184 SET SEARCH DIRECTORY C:\DATAPLOT_DATASETS 44185 SET SEARCH DIRECTORY /home/heckert/dataplot_macros 44186 SET SEARCH2 DIRECTORY C:\MY_DATAPLOT_FILES 44187 44188Default: 44189 None 44190 44191Synonyms: 44192 SET SEARCH PATH 44193 44194Related Commands: 44195 SET PATH = Define the location for Dataplot's auxillary files. 44196 LIST = List the contents of a file. 44197 READ = Read data from a file. 44198 WRITE = Write data to a file. 44199 CALL = Execute commands stored in a file. 44200 44201Applications: 44202 File Usage 44203 44204Implementation Date: 44205 2014/10 44206 2020/05: Added SEARCH2, SEARCH3, SEARCH4, SEARCH5 and SEARCH6 options 44207 44208Program: 44209 . Assume "sample.dp" is in the /home/heckert/dataplot/macros directory 44210 . 44211 SET SEARCH DIRECTORY /home/heckert/dataplot/macros 44212 CALL sample.dp 44213 44214-----SEASONAL LOWESS----------------------------------------------- 44215 44216SEASONAL LOWESS 44217 44218Name: 44219 SEASONAL LOWESS 44220 44221Type: 44222 Analysis Command 44223 44224Purpose: 44225 The SEASONAL LOWESS command decomposes a time series into 44226 trend, seasonal, and residual components using techniques 44227 based on locally weighted least squares. That is, 44228 44229 X(t) = TREND(t) + SEAS(t) + RES(t) 44230 44231Description: 44232 There are a number of time series techniques that are 44233 based on decomposing time series into a trend, seasonal, 44234 and residual component. The most popular of these is 44235 based on exponential smoothing. Seasonal lowess is a 44236 decomposition method based on locally weighted least 44237 squares. 44238 44239 In general, these methods are an alternative to 44240 autoregressive/moving average (ARMA) models. Decomposition 44241 methods are a preferrable approach when the trend and seasonal 44242 components dominate the series. 44243 44244 The seasonal and trend components are written to the file 44245 DPST1F.DAT (dpst1f.dat on Unix systems) and can be read 44246 back into Dataplot for further plotting and analysis. The 44247 internal variable RES contains the residual component and 44248 the internal variable PRED contains the trend plus the 44249 seasonality component. The sample program below demonstrates 44250 a common plot for displaying these components. 44251 44252 The SEASONAL LOWESS command accepts a number of options 44253 which can be defined by LET commands. The most important is 44254 the PERIOD parameter which identifies the number of seasons 44255 (e.g., 12 for monthly data). PERIOD defaults to 12. The 44256 STLWIDTH parameter identifies the number of data points to use 44257 in the LOWESS steps and defaults to N/10. It is similar to 44258 specifying the LOWESS FRACTION for standard LOWESS smoothing. 44259 The more points used, the more smoothing that occurs. The 44260 STLSDEG and STLTDEG parameters identify the polynomial degree 44261 used in the lowess for the seasonal and trend components 44262 respectively. By default, the 44263 seasonal lowess performs some robustness iterations. Enter 44264 44265 LET STLROBST = 1 to suppress this. 44266 44267 The mathematical details of this technique is described in 44268 44269 Cleveland, Cleveland, McRae, and Terpenning, "STL: A 44270 Seasonal-Trend Decomposition Procedure Based on Loess", 44271 Statistics Research Report, AT&T Bell Laboratories. 44272 44273 Dataplot uses the source code provided by these authors to 44274 implement the SEASONAL LOWESS command. 44275 44276Syntax: 44277 LET PERIOD = <value> 44278 LET STLWIDTH = <value> 44279 LET STLSDEG = <0/1/2> 44280 LET STLTDEG = <0/1/2> 44281 LET STLROBST = <0/1> 44282 SEASONAL LOWESS <y> <SUBSET/EXCEPT/FOR qualification> 44283 READ DPST1F.DAT SEAS TREND 44284 where <y> is the variable containing the raw data for which 44285 a seasonal lowess is to be performed; 44286 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 44287 44288 The LET commands are described in the Description section 44289 above. The READ DPST1F.DAT command is used to read the 44290 seasonal and trend components back into Dataplot. 44291 44292Examples: 44293 LET PERIOD = 12 44294 LET STLWIDTH = 24 44295 LET STLSDEG = 1 44296 LET STLTDEG = 1 44297 LET STLROBST = 0 44298 SEASONAL LOWESS Y 44299 44300Default: 44301 There is no default for the SEASONAL LOWESS command itself. 44302 The defaults for the various LET commands are given in the 44303 Description section. 44304 44305Synonyms: 44306 SEASONAL LOESS is a synonym for SEASONAL LOWESS. 44307 44308Related Commands: 44309 LOWESS SMOOTH = Perform a lowess smooth. 44310 ARMA = Perform an ARMA fit. 44311 FIT = Carries out a least squares fit. 44312 44313Reference: 44314 "STL: A Seasonal-Trend Decomposition Procedure Based on Loess", 44315 Cleveland, Cleveland, McRae, and Terpenning, Statistics 44316 Research Report, AT&T Bell Laboratories. 44317 44318 "Visualizing Data", Cleveland, William S., Hobart Press, 1993. 44319 44320Applications: 44321 Robust Time Series Analysis 44322 44323Implementation Date: 44324 2000/1 44325 44326Program: 44327 skip 25 44328 read mlco2mon.dat co2 date year month 44329 . 44330 . Perform Seasonal Lowess 44331 . 44332 let period = 12 44333 let stlsdeg = 1 44334 let stltdeg = 1 44335 seasonal lowess co2 44336 skip 0 44337 read dpst1f.dat seas trend 44338 . 44339 . Generate plot 44340 . 44341 multiplot 4 1 44342 multiplot scale factor 3 44343 multiplot corner coordinates 0 10 100 95 44344 frame corner coordinates 15 0 85 100 44345 xlimits 0 150 44346 tic offset units data 44347 xtic offset 0 15 44348 major xtic mark number 4 44349 xtic marks off 44350 xtic mark labels off 44351 . 44352 ylimits 320 360 44353 major ytic mark number 5 44354 ytic offser 10 10 44355 y1label raw data 44356 plot co2 44357 y1label trend 44358 plot trend 44359 major ytic mark number 5 44360 ylimits -4 4 44361 ytic offser 0.5 0.5 44362 y1label seasonal 44363 plot seas 44364 y1label residuals 44365 x1tic marks on 44366 x1tic mark labels on 44367 plot res 44368 end of multiplot 44369 . 44370 justification center 44371 move 50 97 44372 text SEASONAL LOWESS DECOMPOSITION FOR CO2 CONCENTRATIONS 44373 44374-----SEASONAL SUBSERIES PLOT-------------------------------------- 44375 44376SEASONAL SUBSERIES PLOT 44377 44378Name: 44379 SEASONAL SUBSERIES PLOT 44380 44381Type: 44382 Graphics Command 44383 44384Purpose: 44385 Generates a seasonal subseries plot. 44386 44387Description: 44388 A seasonal subseries plot is used to determine if there is 44389 significant seasonality in a time series. Instead of a straight 44390 time order plot, it splits the plot into the corresponding 44391 seasons (or periods). For example, for monthly data, all the 44392 January values are plotted, then all the February values, and 44393 so on. Reference lines are drawn at the seasonal means. 44394 44395Syntax: 44396 LET PERIOD = <value> 44397 LET START = <value> 44398 SEASONAL SUBSERIES PLOT <y> <SUBSET/EXCEPT/FOR qualification> 44399 where <y> is the variable of raw data values for which the 44400 the seasonal subseries will be plotted; 44401 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 44402 44403 The LET command is uses to define the period (e.g., the period 44404 for monthly data is typically 12) and the start value. The 44405 start value is used when the data do not start in the first 44406 unit of the period (e.g., if you have monthly data that starts 44407 in March instead of January, you would use LET START = 3). 44408 44409 44410Examples: 44411 LET PERIOD = 12 44412 LET START = 3 44413 SEASONAL SUBSERIES PLOT Y 44414 44415 LET PERIOD = 4 44416 LET START = 1 44417 SEASONAL SUBSERIES PLOT Y 44418 44419Note: 44420 The sample program below shows how to use various plot control 44421 commands to label the plot. 44422 44423Default: 44424 None 44425 44426Synonyms: 44427 None 44428 44429Related Commands: 44430 RUN SEQUENCE PLOT = Generates a run sequence plot. 44431 SPECTRAL PLOT = Generate a spectral plot. 44432 AUTOCORRELATION PLOT = Generate an autocorrelation plot. 44433 ARMA = Fit an ARMA model. 44434 SEASONAL LOWESS = Generate a lowess based trend/seasonality/ 44435 residual decomposition of a time series. 44436 44437Reference: 44438 "Visualizing Data", Cleveland, William S., Hobart Press, 1993. 44439 44440Applications: 44441 Time Series Analysis 44442 44443Implementation Date: 44444 2000/1 44445 44446Program: 44447 skip 25 44448 read mlco2mon.dat co2 date year month 44449 . 44450 . Linear Fit to Detrend Data 44451 . 44452 fit co2 date 44453 let co2res = res 44454 . 44455 . Seasonal Subseries Plot 44456 . 44457 xlimits 7 167 44458 xtic offset 7 7 44459 major xtic mark number 12 44460 minor xtic mark number 0 44461 x1tic mark label format alpha 44462 x1tic mark label content Jan Feb Mar Apr May June July Aug Sep ... 44463 Oct Nov Dec 44464 x1label Month 44465 y1label CO2 Concentrations 44466 let period = 12 44467 let start = 5 44468 title Seasonal Subseries Plot of CO2 Concentrations 44469 seasonal subseries plot co2res 44470 44471-----SEC (LET)--------------------------------------------------- 44472 44473SEC 44474 44475Name: 44476 SEC (LET) 44477 44478Type: 44479 Library Function 44480 44481Purpose: 44482 Compute the secant (the reciprocal of the cosine) for a variable or 44483 parameter. 44484 44485Description: 44486 The secant is defined for all real numbers except PI/2 +/- K*PI 44487 where K is an integer. The range is 1 to plus infinity and -1 to 44488 negative infinity. By default, the angle is specified in radian 44489 units. To use degree values, enter the command ANGLE UNITS DEGREES 44490 (ANGLE UNITS RADIANS resets it). 44491 44492Syntax: 44493 LET <y2> = SEC(<y1>) <SUBSET/EXCEPT/FOR qualification> 44494 where <y1> is a variable or a parameter; 44495 <y2> is a variable or a parameter (depending on what <y1> is) 44496 where the computed secant value is stored; 44497 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 44498 44499Examples: 44500 LET A = SEC(-2) 44501 LET A = SEC(A1) 44502 LET X2 = SEC(X1) 44503 LET X2 = SEC(PI/2) 44504 44505Note: 44506 Library functions are distinguished from let subcommands 44507 in the following ways. 44508 1) Functions enclose the input value in parenthesis. Let 44509 subcommands use spaces. 44510 2) Functions can accept (and return) either parameters 44511 (i.e., single values) or variables (i.e., an array of 44512 values) while let subcommands are specific in which they 44513 accept as input and what they return as output. 44514 3) Functions can accept expressions while let subcommands 44515 do not. For example, the following is legal: 44516 LET Y2 = ABS(Y1-INT(Y1)) 44517 For let subcommands, you typically have to do something 44518 like the following: 44519 LET YTEMP = Y**2 + 8 44520 LET A = SUM YTEMP 44521 44522Default: 44523 None 44524 44525Synonyms: 44526 None 44527 44528Related Commands: 44529 SIN = Compute the sine. 44530 COS = Compute the cosine. 44531 TAN = Compute the tangent. 44532 COT = Compute the cotangent. 44533 CSC = Compute the cosecant. 44534 ARCCOS = Compute the arccosine. 44535 ARCSIN = Compute the arcsine. 44536 ARCTAN = Compute the arctangent. 44537 ARCCOT = Compute the arccotangent. 44538 ARCSEC = Compute the arcsecant. 44539 ARCCSC = Compute the arcsecant. 44540 44541Reference: 44542 Consult any standard trigonometry or pre-calculus textbook. 44543 44544Applications: 44545 XX 44546 44547Implementation Date: 44548 XX 44549 44550Program: 44551 TITLE PLOT SECANT FROM -3.1 TO 3.1 44552 X1LABEL ANGLE (IN RADIANS) 44553 Y1LABEL SECANT VALUE 44554 READ X Y TAG 44555 -3.1 1 1 44556 3.1 1 1 44557 -3.1 -1 2 44558 3.1 -1 2 44559 1.57 20 3 44560 1.57 -20 3 44561 -1.57 20 4 44562 -1.57 -20 4 44563 END OF DATA 44564 YLIMITS -20 20 44565 XLIMITS -3 3 44566 XTIC OFFSET .4 .4 44567 LINES SOLID SOLID SOLID SOLID DOT DOT DOT DOT DOT 44568 PLOT SEC(X) FOR X = .01 .01 1.56 AND 44569 PLOT SEC(X) FOR X = 1.58 .01 3.10 AND 44570 PLOT SEC(X) FOR X =- .01 -.01 -1.56 AND 44571 PLOT SEC(X) FOR X = -1.58 -.01 -3.10 AND 44572 PLOT Y X TAG 44573 44574-----SECH (LET)--------------------------------------------------- 44575 44576SECH 44577 44578Name: 44579 SECH (LET) 44580 44581Type: 44582 Library Function 44583 44584Purpose: 44585 Compute the hyperbolic secant for a variable or parameter. 44586 44587Description: 44588 The equation for the hyperbolic secant is: 44589 sech(x) = 1/(e**x + e**-x) 44590 The hyperbolic secant is defined for all real numbers. The range is 44591 zero to one. 44592 44593Syntax: 44594 LET <y2> = SECH(<y1>) <SUBSET/EXCEPT/FOR qualification> 44595 where <y1> is a variable or a parameter; 44596 <y2> is a variable or a parameter (depending on what <y1> is) 44597 where the computed hyperbolic secant value is stored; 44598 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 44599 44600Examples: 44601 LET A = SECH(-2) 44602 LET A = SECH(A1) 44603 LET X2 = SECH(X1) 44604 LET X2 = SECH(PI/2) 44605 44606Note: 44607 Library functions are distinguished from let subcommands 44608 in the following ways. 44609 1) Functions enclose the input value in parenthesis. Let 44610 subcommands use spaces. 44611 2) Functions can accept (and return) either parameters 44612 (i.e., single values) or variables (i.e., an array of 44613 values) while let subcommands are specific in which they 44614 accept as input and what they return as output. 44615 3) Functions can accept expressions while let subcommands 44616 do not. For example, the following is legal: 44617 LET Y2 = ABS(Y1-INT(Y1)) 44618 For let subcommands, you typically have to do something 44619 like the following: 44620 LET YTEMP = Y**2 + 8 44621 LET A = SUM YTEMP 44622 44623Default: 44624 None 44625 44626Synonyms: 44627 None 44628 44629Related Commands: 44630 SIN = Compute the sine. 44631 COS = Compute the cosine. 44632 TAN = Compute the tangent. 44633 COT = Compute the cotangent. 44634 SEC = Compute the secant. 44635 CSC = Compute the cosecant. 44636 ARCCOS = Compute the arccosine. 44637 ARCSIN = Compute the arcsine. 44638 ARCTAN = Compute the arctangent. 44639 ARCCOT = Compute the arccotangent. 44640 ARCSEC = Compute the arcsecant. 44641 ARCCSC = Compute the arcsecant. 44642 SINH = Compute the hyperbolic sine. 44643 COSH = Compute the hyperbolic cosine. 44644 TANH = Compute the hyperbolic tangent. 44645 COTH = Compute the hyperbolic cotangent. 44646 SECH = Compute the hyperbolic secant. 44647 CSCH = Compute the hyperbolic cosecant. 44648 ARCCOSH = Compute hyperbolic arccosine. 44649 ARCCOTH = Compute hyperbolic arccotangent. 44650 ARCCSCH = Compute hyperbolic arccosecant. 44651 ARCSECH = Compute hyperbolic arcsecant. 44652 ARCSINH = Compute hyperbolic arcsine. 44653 ARCTANH = Compute hyperbolic arctangent. 44654 44655Applications: 44656 Trigonometry 44657 44658Implementation Date: 44659 Pre-1987 44660 44661Program: 44662 TITLE AUTOMATIC 44663 PLOT SECH(X) FOR X = -3.1 .05 3.1 44664 44665-----SDECDF (LET)-------------------------------- 44666 44667SDECDF 44668 44669Name: 44670 SDECDF (LET) 44671 44672Type: 44673 Library Function 44674 44675Purpose: 44676 Compute the skew double exponential cumulative distribution 44677 function. 44678 44679Description: 44680 The skew double exponential distribution has the following 44681 cumulative distribution function: 44682 44683 F(x,lambda)=0.5*EXP((1+lambda)*x)/(1+LAMBDA) 44684 - infinity < x <= 0 44685 =1 + EXP(-x) - 0.5/(EXP((1+lambda)*x)*(-1-lambda)) 44686 0 < x < infinity 44687 lambda >= 0 44688 44689 For lambda = 0, the skew double exponential reduces to the 44690 double exponential distribution. As lambda goes to infinity, 44691 the skew double exponential tends to the exponential 44692 distribution. 44693 44694 The standard skew double exponential distribution can be 44695 generalized with location and scale parameters. 44696 44697 The skew double exponential distribution is also known as 44698 the skew Laplace distribution. 44699 44700Syntax: 44701 LET <y> = SDECDF(<x>,<lambda>,<loc>,<scale>) 44702 <SUBSET/EXCEPT/FOR qualification> 44703 where <x> is a variable or a parameter; 44704 <lambda> is a number of parameter that specifies the 44705 value of the shape parameter; 44706 <loc> is an optional number or parameter that specifies the 44707 value of the location parameter; 44708 <scale> is an optional positive number or parameter that 44709 specifies the value of the scale parameter; 44710 <y> is a variable or a parameter (depending on what <x> is) 44711 where the computed skew double exponential cdf value 44712 is stored; 44713 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 44714 44715Examples: 44716 LET Y = SDECDF(3,1) 44717 LET Y = SDECDF(X1,LAMBDA) 44718 PLOT SDECDF(X,LAMBDA) FOR X = -5 0.1 5 44719 44720Note: 44721 Library functions are distinguished from let subcommands 44722 in the following ways. 44723 1) Functions enclose the input value in parenthesis. Let 44724 subcommands use spaces. 44725 2) Functions can accept (and return) either parameters 44726 (i.e., single values) or variables (i.e., an array of 44727 values) while let subcommands are specific in which they 44728 accept as input and what they return as output. 44729 3) Functions can accept expressions while let subcommands 44730 do not. For example, the following is legal: 44731 LET Y2 = ABS(Y1-INT(Y1)) 44732 For let subcommands, you typically have to do something 44733 like the following: 44734 LET YTEMP = Y**2 + 8 44735 LET A = SUM YTEMP 44736 44737Default: 44738 None 44739 44740Synonyms: 44741 None 44742 44743Related Commands: 44744 SDEPDF = Compute the skew double exponential probability density 44745 function. 44746 SDEPPF = Compute the skew double exponential percent point 44747 function. 44748 ADEPDF = Compute the asymmetric double exponential probability density 44749 function. 44750 DEXCDF = Compute the double exponential probability density 44751 function. 44752 EXPCDF = Compute the exponential probability density function. 44753 SNCDF = Compute the skew normal probability density function. 44754 STCDF = Compute the skew t probability density function. 44755 44756Reference: 44757 "The Laplace Distribution and Generalizations: A Revisit with 44758 Applications to Communications, Economics, Engineering, and 44759 Finance", Birkhauser, 2001, p. 136. 44760 44761 "A Class of Distributions Which Includes the Normal Ones", 44762 Azzalini, Scandinavian Journal of Statistics, 12, 171-178. 44763 44764Applications: 44765 Distributional Modeling 44766 44767Implementation Date: 44768 6/2004 44769 44770Program: 44771 Y1LABEL Probability 44772 X1LABEL X 44773 LABEL CASE ASIS 44774 TITLE CASE ASIS 44775 CASE ASIS 44776 MULTIPLOT 2 2 44777 MULTIPLOT CORNER COORDINATES 0 0 100 95 44778 MULTIPLOT SCALE FACTOR 2 44779 TITLE Lambda = 0 44780 PLOT SDECDF(X,0) FOR X = -5 0.1 5 44781 TITLE Lambda = 1 44782 PLOT SDECDF(X,1) FOR X = -5 0.1 5 44783 TITLE Lambda = 5 44784 PLOT SDECDF(X,5) FOR X = -5 0.1 5 44785 TITLE Lambda = 10 44786 PLOT SDECDF(X,10) FOR X = -5 0.1 5 44787 END OF MULTIPLOT 44788 MOVE 50 97 44789 JUSTIFICATIONC CENTER 44790 TEXT Skew Double Exponential Distribution 44791 44792-----SDEPDF (LET)-------------------------------- 44793 44794SDEPDF 44795 44796Name: 44797 SDEPDF (LET) 44798 44799Type: 44800 Library Function 44801 44802Purpose: 44803 Compute the skew double exponential probability density 44804 function. 44805 44806Description: 44807 The skew double exponential distribution has the following 44808 probability density function: 44809 44810 f(x,lambda)=0.5*EXP((1+lambda)*x) - infinity < x <= 0 44811 =EXP(-x) - 0.5*EXP(-(1+lambda)*x) 0 < x < infinity 44812 lambda >= 0 44813 44814 For lambda = 0, the skew double exponential reduces to the 44815 double exponential distribution. As lambda goes to infinity, 44816 the skew double exponential tends to the exponential 44817 distribution. 44818 44819 The standard skew double exponential distribution can be 44820 generalized with location and scale parameters. 44821 44822 The skew double exponential distribution is also known as 44823 the skew Laplace distribution. 44824 44825Syntax: 44826 LET <y> = SDEPDF(<x>,<lambda>,<loc>,<scale>) 44827 <SUBSET/EXCEPT/FOR qualification> 44828 where <x> is a variable or a parameter; 44829 <lambda> is a number of parameter that specifies the 44830 value of the shape parameter; 44831 <loc> is an optional number or parameter that specifies the 44832 value of the location parameter; 44833 <scale> is an optional positive number or parameter that 44834 specifies the value of the scale parameter; 44835 <y> is a variable or a parameter (depending on what <x> is) 44836 where the computed skew double exponential pdf value 44837 is stored; 44838 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 44839 44840Examples: 44841 LET Y = SDEPDF(3,1) 44842 LET Y = SDEPDF(X1,LAMBDA) 44843 PLOT SDEPDF(X,LAMBDA) FOR X = -5 0.01 5 44844 44845Note: 44846 To generate skew double exponential random numbers, enter 44847 the commands 44848 44849 LET LAMBDA = <value> 44850 LET Y = SKEW DOUBLE EXPONENTIAL RANDOM NUMBERS FOR I = 1 1 N 44851 44852 To generate a skew double exponential probability plot or a 44853 skew double exponential Kolmogorov-Smirnov or chi-square 44854 goodness of fit test, enter the following commands 44855 44856 LET LAMBDA = <value> 44857 SKEW DOUBLE EXPONENTIAL PROBABILITY PLOT Y 44858 SKEW DOUBLE EXPONENTIAL KOLMOGOROV SMIRNOV GOODNESS OF FIT Y 44859 SKEW DOUBLE EXPONENTIAL CHI-SQUARE GOODNESS OF FIT Y 44860 44861 To generate a PPCC or Kolmogorov-Smirnov plot, enter the 44862 following commands 44863 44864 LET LAMBDA1 = <value> 44865 LET LAMBDA2 = <value> 44866 SKEW DOUBLE EXPONENTIAL PPCC PLOT Y 44867 SKEW DOUBLE EXPONENTIAL KS PLOT Y 44868 44869 The default values for LAMBDA1 and LAMBDA2 are 0 and 10. 44870 44871Note: 44872 Library functions are distinguished from let subcommands 44873 in the following ways. 44874 1) Functions enclose the input value in parenthesis. Let 44875 subcommands use spaces. 44876 2) Functions can accept (and return) either parameters 44877 (i.e., single values) or variables (i.e., an array of 44878 values) while let subcommands are specific in which they 44879 accept as input and what they return as output. 44880 3) Functions can accept expressions while let subcommands 44881 do not. For example, the following is legal: 44882 LET Y2 = ABS(Y1-INT(Y1)) 44883 For let subcommands, you typically have to do something 44884 like the following: 44885 LET YTEMP = Y**2 + 8 44886 LET A = SUM YTEMP 44887 44888Default: 44889 None 44890 44891Synonyms: 44892 SKEW LAPLACE is a synonym for SKEW DOUBLE EXPONENTIAL 44893 44894Related Commands: 44895 SDECDF = Compute the skew double exponential cumulative 44896 distribution function. 44897 SDEPPF = Compute the skew double exponential percent point 44898 function. 44899 ADEPDF = Compute the asymmetric double exponential probability density 44900 function. 44901 DEXPDF = Compute the double exponential probability density 44902 function. 44903 EXPPDF = Compute the exponential probability density function. 44904 SNPDF = Compute the skew normal probability density function. 44905 STPDF = Compute the skew t probability density function. 44906 44907Reference: 44908 "The Laplace Distribution and Generalizations: A Revisit with 44909 Applications to Communications, Economics, Engineering, and 44910 Finance", Birkhauser, 2001, p. 136. 44911 44912 "A Class of Distributions Which Includes the Normal Ones", 44913 Azzalini, Scandinavian Journal of Statistics, 12, 171-178. 44914 44915Applications: 44916 Distributional Modeling 44917 44918Implementation Date: 44919 6/2004 44920 44921Program: 44922 Y1LABEL Probability 44923 X1LABEL X 44924 LABEL CASE ASIS 44925 TITLE CASE ASIS 44926 CASE ASIS 44927 MULTIPLOT 2 2 44928 MULTIPLOT CORNER COORDINATES 0 0 100 95 44929 MULTIPLOT SCALE FACTOR 2 44930 TITLE Lambda = 0 44931 PLOT SDEPDF(X,0) FOR X = -5 0.1 5 44932 TITLE Lambda = 1 44933 PLOT SDEPDF(X,1) FOR X = -5 0.1 5 44934 TITLE Lambda = 5 44935 PLOT SDEPDF(X,5) FOR X = -5 0.1 5 44936 TITLE Lambda = 10 44937 PLOT SDEPDF(X,10) FOR X = -5 0.1 5 44938 END OF MULTIPLOT 44939 MOVE 50 97 44940 JUSTIFICATIONC CENTER 44941 TEXT Skew Double Exponential Distribution 44942 44943-----SDEPPF (LET)-------------------------------- 44944 44945SDEPPF 44946 44947Name: 44948 SDEPPF (LET) 44949 44950Type: 44951 Library Function 44952 44953Purpose: 44954 Compute the skew double exponential percent point function. 44955 44956Description: 44957 The skew double exponential distribution has the following 44958 probability density function: 44959 44960 f(x,lambda)=0.5*EXP((1+lambda)*x) - infinity < x <= 0 44961 =EXP(-x) - 0.5*EXP(-(1+lambda)*x) 0 < x < infinity 44962 lambda >= 0 44963 44964 44965 To compute the percent point function, Dataplot computes 44966 the cumulative distribution function for X = 0. If this 44967 value is PCUT and P is the input probability value, then 44968 44969 G(p,lambda) = LOG[2*p*(1-lambda)]/(1+lambda)] p <= PCUT 44970 44971 If P is greater than PCUT, then Dataplot computes the percent 44972 point function by numerically inverting the cumulative 44973 distribution function. 44974 44975 For lambda = 0, the skew double exponential reduces to the 44976 double exponential distribution. As lambda goes to infinity, 44977 the skew double exponential tends to the exponential 44978 distribution. 44979 44980 The standard skew double exponential distribution can be 44981 generalized with location and scale parameters. 44982 44983 The skew double exponential distribution is also known as 44984 the skew Laplace distribution. 44985 44986Syntax: 44987 LET <y> = SDEPPF(<p>,<lambda>,<loc>,<scale>) 44988 <SUBSET/EXCEPT/FOR qualification> 44989 where <p> is a variable, a number or a parameter in the 44990 interval (0,1); 44991 <lambda> is a number of parameter that specifies the 44992 value of the shape parameter; 44993 <loc> is an optional number or parameter that specifies the 44994 value of the location parameter; 44995 <scale> is an optional positive number or parameter that 44996 specifies the value of the scale parameter; 44997 <y> is a variable or a parameter (depending on what <x> is) 44998 where the computed skew double exponential ppf value 44999 is stored; 45000 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 45001 45002Examples: 45003 LET A = SDEPPF(0.95,1) 45004 LET X = SDEPPF(P1,LAMBDA) 45005 PLOT SDEPPF(P,LAMBDA) FOR P = 0.01 0.01 0.99 45006 45007Note: 45008 Library functions are distinguished from let subcommands 45009 in the following ways. 45010 1) Functions enclose the input value in parenthesis. Let 45011 subcommands use spaces. 45012 2) Functions can accept (and return) either parameters 45013 (i.e., single values) or variables (i.e., an array of 45014 values) while let subcommands are specific in which they 45015 accept as input and what they return as output. 45016 3) Functions can accept expressions while let subcommands 45017 do not. For example, the following is legal: 45018 LET Y2 = ABS(Y1-INT(Y1)) 45019 For let subcommands, you typically have to do something 45020 like the following: 45021 LET YTEMP = Y**2 + 8 45022 LET A = SUM YTEMP 45023 45024Default: 45025 None 45026 45027Synonyms: 45028 None 45029 45030Related Commands: 45031 SDECDF = Compute the skew double exponential cumulative 45032 distribution function. 45033 SDEPDF = Compute the skew double exponential probability density 45034 function. 45035 ADEPDF = Compute the asymmetric double exponential probability density 45036 function. 45037 DEXPDF = Compute the double exponential probability density 45038 function. 45039 EXPPDF = Compute the exponential probability density function. 45040 SNPDF = Compute the skew normal probability density function. 45041 STPDF = Compute the skew t probability density function. 45042 45043Reference: 45044 "The Laplace Distribution and Generalizations: A Revisit with 45045 Applications to Communications, Economics, Engineering, and 45046 Finance", Birkhauser, 2001, p. 136. 45047 45048 "A Class of Distributions Which Includes the Normal Ones", 45049 Azzalini, Scandinavian Journal of Statistics, 12, 171-178. 45050 45051Applications: 45052 Distributional Modeling 45053 45054Implementation Date: 45055 6/2004 45056 45057Program: 45058 X1LABEL Probability 45059 Y1LABEL X 45060 LABEL CASE ASIS 45061 TITLE CASE ASIS 45062 X1LABEL DISPLACEMENT 12 45063 CASE ASIS 45064 MULTIPLOT 2 2 45065 MULTIPLOT CORNER COORDINATES 0 0 100 95 45066 MULTIPLOT SCALE FACTOR 2 45067 TITLE Lambda = 0 45068 PLOT SDEPPF(P,0) FOR P = 0.01 0.01 0.99 45069 TITLE Lambda = 1 45070 PLOT SDEPPF(P,1) FOR P = 0.01 0.01 0.99 45071 TITLE Lambda = 5 45072 PLOT SDEPPF(P,5) FOR P = 0.01 0.01 0.99 45073 TITLE Lambda = 10 45074 PLOT SDEPPF(P,10) FOR P = 0.01 0.01 0.99 45075 END OF MULTIPLOT 45076 MOVE 50 97 45077 JUSTIFICATIONC CENTER 45078 TEXT Skew Double Exponential Distribution 45079 45080-----SEED------------------------------------------------------- 45081 45082SEED 45083 45084Name: 45085 SEED 45086 45087Type: 45088 Support Command 45089 45090Purpose: 45091 Specify the seed for random number generation. 45092 45093Description: 45094 Each distinct seed generates a different sequence of random numbers 45095 (the seed allows the random number generator to duplicate the same 45096 sequence of random numbers). 45097 45098 Dataplot supports several different random number generators. 45099 The desired generator can be set with the command 45100 45101 SET RANDOM NUMBER GENERATOR <generator> 45102 45103 where <generator> is one of the following: 45104 45105 FIBONACCI 45106 LINEAR CONGRUENTIAL 45107 MULTIPLICATIVE CONGRUENTIAL 45108 GFSR 45109 FUSHIMI 45110 AS183 45111 GENZ 45112 LUXURY 45113 FIBONACCI CONGRUENTIAL 45114 45115 The deault generator is the FIBONACCI CONGRUENTIAL generator 45116 (the default prior to 2018/05 was the FIBONACCI generator). 45117 45118 The seed value applies to the following generators 45119 45120 FIBONACCI 45121 FIBONACCI CONGRUENTIAL 45122 MULTIPLICATIVE CONGRUENTIAL 45123 AS183 45124 45125 For the FIBONACCI and FIBONACCI CONGRUENTIAL generators, the 45126 minimum seed value should be 305 and the seed should be an 45127 odd number. Values of the seed less than 305 are equivalent 45128 to 305 and even values of the seed are equivalent to the 45129 nearest odd number. 45130 45131 For the other generators, if you want to obtain a different 45132 sequence of random numbers you can do something like the 45133 following 45134 45135 LET ISKIP = 50000 45136 LET NRAND = 10000 45137 LET YJUNK = UNIFORM RANDOM NUMBERS FOR I = 1 1 ISKIP 45138 LET Y = UNIFORM RANDOM NUMBERS FOR I = 1 1 NRAND 45139 45140 This example will first generate 50,000 random numbers that 45141 will not be used. It then generates 10,000 random numbers 45142 that will be used. To obtain a different sequence of random 45143 numbers, modify the value of ISKIP. 45144 45145Syntax: 45146 SEED <iseed> 45147 where <iseed> is an integer number or parameter that defines the 45148 seed. 45149 45150Examples: 45151 SEED 55671 45152 SEED DEFAULT 45153 45154Note: 45155 To return the current value of the seed, enter 45156 45157 PROBE SEED 45158 45159Default: 45160 305 (Pre-2019/03) 45161 3005 (2019/03) 45162 45163Synonyms: 45164 None 45165 45166Related Commands: 45167 RANDOM NUMBERS (LET) = Generate random numbers for various 45168 distributions.. 45169 45170Applications: 45171 Random Number Generation 45172 45173Implementation Date: 45174 Pre-1987 45175 45176Program: 45177 SEED 4021 45178 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 45179 SEED 34201 45180 LET Y2 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 45181 SEED 19793 45182 LET Y3 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 45183 SEED 46987 45184 LET Y4 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 45185 LINE COLOR BLACK BLUE RED GREEN 45186 MULTIPLE KERNEL DENSITY PLOT Y1 Y2 Y3 Y4 45187 45188-----SEGMENT COLOR---------------------------------------------------- 45189 45190SEGMENT COLOR 45191 45192Name: 45193 SEGMENT ... COLOR 45194 45195Type: 45196 Plot Control Command 45197 45198Purpose: 45199 Specifies the color for the line segments to appear on subsequent 45200 plots. 45201 45202Description: 45203 Segments are straight lines that the analyst can position anywhere 45204 on the plot. The segments appear on all subsequent plots until 45205 blanked out or overridden with new segment coordinates. The 45206 segment colors hold for all subsequent plots until defaulted or 45207 overridden with new colors. Up to 100 such line segments can be 45208 specified. 45209 45210 Segments are most typically used in legend boxes to identify 45211 curves. 45212 45213Syntax: 45214 SEGMENT <id> COLOR <color> 45215 where <id> is an integer number or parameter in the range 1 to 100 45216 that specifies the segment identifier; 45217 and <color> is a character string or index number that specifies 45218 the desired color. 45219 45220Examples: 45221 SEGMENT 2 COLOR GREEN 45222 SEGMENT 2 COLOR BLUE 45223 45224Note: 45225 A SEGMENT ... COLOR command with no arguments reverts the line 45226 segment color to default; thus SEGMENT 1 COLOR with no arguments 45227 reverts the color for line segment 1 to default. A SEGMENT ... 45228 COLOR command with no <id> refers to all 100 line segments; thus 45229 SEGMENT COLOR GREEN assigns the color green to all 100 line 45230 segments. SEGMENT COLOR with no <id> and no arguments reverts the 45231 color to default for all 100 line segments. 45232 45233Default: 45234 All line segments are drawn in black. 45235 45236Synonyms: 45237 None 45238 45239Related Commands: 45240 SEGMENT COORDINATES = Specify a segment location. 45241 SEGMENT PATTERN = Specify the line type for a segment. 45242 SEGMENT THICKNESS = Specify the line thickness for a segment. 45243 LEGEND = Specify a legend for a subsequent plot. 45244 ARROW COORDINATES = Specify the location of an arrow. 45245 BOX COORDINATES = Specify the location of a box. 45246 45247Applications: 45248 Presentation Graphics 45249 45250Implementation Date: 45251 XX 45252 45253Program: 45254 . POLLUTION SOURCE ANALYSIS, LLOYD CURRIE, DATE--1990 45255 . SUBSET OF CURRIE.DAT REFERENCE FILE 45256 . 45257 SERIAL READ LEAD 45258 164 426 59 98 312 263 607 497 213 54 160 262 547 325 419 94 70 45259 END OF DATA 45260 SERIAL READ POT 45261 106 175 61 79 94 121 424 328 107 218 140 179 246 231 245 339 99 45262 END OF DATA 45263 LET N = SIZE LEAD; LET X = SEQUENCE 1 1 N 45264 . 45265 LINE COLOR G20 G80 45266 LINE THICKNESS 0.3 ALL 45267 SEGMENT 1 COORDINATES 17 87 22 87 45268 SEGMENT 2 COORDINATES 17 83 22 83 45269 SEGMENT 1 COLOR G20 45270 SEGMENT 2 COLOR G80 45271 SEGMENT THICKNESS 0.3 45272 LEGEND 1 COORDINATES 23 86; LEGEND 1 POTASSIUM 45273 LEGEND 2 COORDINATES 23 82; LEGEND 2 LEAD 45274 TITLE DEMONSTRATE SEGMENT COLOR 45275 PLOT POT LEAD VS X 45276 45277-----SEGMENT COORDINATES---------------------------------------------- 45278 45279SEGMENT COORDINATES 45280 45281Name: 45282 SEGMENT ... COORDINATES 45283 45284Type: 45285 Plot Control Command 45286 45287Purpose: 45288 Specifies the location of a line segment to appear on subsequent 45289 plots. 45290 45291Description: 45292 Segments are straight lines that the analyst can position anywhere 45293 on the plot. The segments appear on all subsequent plots until 45294 blanked out or overridden with new segment coordinates. The 45295 segment colors hold for all subsequent plots until defaulted or 45296 overridden with new colors. Up to 100 such line segments can be 45297 specified. 45298 45299 The SEGMENT COORDINATES command defines the (x,y) values for the 45300 start and the end points respectively of the line segment. 45301 45302 Segments are most typically used in legend boxes to identify 45303 curves. 45304 45305Syntax: 45306 SEGMENT <id> COORDINATES <x1> <y1> <x2> <y2> 45307 where <id> is an integer number or parameter in the range 1 to 100 45308 that specifies the segment identifier; 45309 <x1> is a number or parameter in the decimal range 0 to 100 45310 that specifies the x coordinate of the start point; 45311 <y1> is a number or parameter in the decimal range 0 to 100 45312 that specifies the y coordinate of the start point; 45313 <x2> is a number or parameter in the decimal range 0 to 100 45314 that specifies the x coordinate of the stop point; 45315 and <y2> is a number or parameter in the decimal range 0 to 100 45316 that specifies the y coordinate of the stop point. 45317 45318Examples: 45319 SEGMENT 2 COORDINATES 20 80 60 60 45320 SEGMENT 2 COORDINATES 20 60 40 80 45321 45322Note: 45323 A SEGMENT ... COORDINATES command with no arguments omits the line 45324 segment from subsequent plots; thus SEGMENT 1 COORDINATES with no 45325 arguments omits line segment 1 from subsequent plots. A SEGMENT 45326 ... COORDINATES command with no <id> refers to all 100 line 45327 segments; thus SEGMENT COORDINATES 30 80 40 60 assigns the 45328 coordinates (30,80) and (40,60) to all 100 line segments (but 45329 this has no practical use). SEGMENT COORDINATES with no <id> and 45330 no arguments omits all 100 line segments from subsequent plots. 45331 45332Default: 45333 No line segments are drawn. 45334 45335Synonyms: 45336 None 45337 45338Related Commands: 45339 SEGMENT COLOR = Specify the color for a segment. 45340 SEGMENT PATTERN = Specify the line type for a segment. 45341 SEGMENT THICKNESS = Specify the line thickness for a segment. 45342 LEGEND = Specify a legend for a subsequent plot. 45343 LEGEND COORDINATES = Specify the location of a legend for a 45344 subsequent plot. 45345 ARROW COORDINATES = Specify the location of an arrow. 45346 BOX COORDINATES = Specify the location of a box. 45347 45348Applications: 45349 Presentation Graphics 45350 45351Implementation Date: 45352 XX 45353 45354Program: 45355 . POLLUTION SOURCE ANALYSIS, LLOYD CURRIE, DATE--1990 45356 . SUBSET OF CURRIE.DAT REFERENCE FILE 45357 . 45358 SERIAL READ LEAD 45359 164 426 59 98 312 263 607 497 213 54 160 262 547 325 419 94 70 45360 END OF DATA 45361 SERIAL READ POT 45362 106 175 61 79 94 121 424 328 107 218 140 179 246 231 245 339 99 45363 END OF DATA 45364 LET N = SIZE LEAD; LET X = SEQUENCE 1 1 N 45365 . 45366 LINE SOLID DASH 45367 SEGMENT 1 COORDINATES 17 87 22 87 45368 SEGMENT 2 COORDINATES 17 83 22 83 45369 SEGMENT 2 PATTERN DASH 45370 LEGEND 1 COORDINATES 23 86; LEGEND 1 POTASSIUM 45371 LEGEND 2 COORDINATES 23 82; LEGEND 2 LEAD 45372 TITLE SEGMENT COORDINATES COMMAND 45373 PLOT POT LEAD VS X 45374 45375-----SEGMENT PATTERN------------------------------------------------- 45376 45377SEGMENT PATTERN 45378 45379Name: 45380 SEGMENT ... PATTERN 45381 45382Type: 45383 Plot Control Command 45384 45385Purpose: 45386 Specifies the line pattern for the line segments to appear on 45387 subsequent plots. 45388 45389Description: 45390 Segments are straight lines that the analyst can position anywhere 45391 on the plot. The segments appear on all subsequent plots until 45392 blanked out or overridden with new segment coordinates. The 45393 segment colors hold for all subsequent plots until defaulted or 45394 overridden with new colors. Up to 100 such line segments can be 45395 specified. 45396 45397 Segments are most typically used in legend boxes to identify 45398 curves. 45399 45400Syntax: 45401 SEGMENT <id> PATTERN <pattern> 45402 where <id> is an integer number or parameter in the range 1 to 100 45403 that specifies the segment identifier; 45404 and <pattern> is a character string that specifies the desired 45405 line pattern. 45406 45407Examples: 45408 SEGMENT 2 PATTERN SOLID 45409 SEGMENT 2 PATTERN DASH 45410 45411Note: 45412 A SEGMENT ... PATTERN command with no arguments reverts the line 45413 segment pattern to default; thus SEGMENT 1 PATTERN with no 45414 arguments reverts the pattern for line segment 1 to default. A 45415 SEGMENT ... PATTERN command with no <id> refers to all 100 line 45416 segments; thus SEGMENT PATTERN SOLID assigns the pattern solid to 45417 all 100 line segments. SEGMENT PATTERN with no <id> and no 45418 arguments reverts the pattern to default for all 100 line segments. 45419 45420Default: 45421 All segments are drawn with solid lines. 45422 45423Synonyms: 45424 None 45425 45426Related Commands: 45427 SEGMENT COLOR = Specify the color for a segment. 45428 SEGMENT COORDINATES = Specify a segment location. 45429 SEGMENT THICKNESS = Specify the line thickness for a segment. 45430 LEGEND = Specify a legend for a subsequent plot. 45431 ARROW COORDINATES = Specify the location of an arrow. 45432 BOX COORDINATES = Specify the location of a box. 45433 45434Applications: 45435 Presentation Graphics 45436 45437Implementation Date: 45438 XX 45439 45440Program: 45441 . POLLUTION SOURCE ANALYSIS, LLOYD CURRIE, DATE--1990 45442 . SUBSET OF CURRIE.DAT REFERENCE FILE 45443 . 45444 SERIAL READ LEAD 45445 164 426 59 98 312 263 607 497 213 54 160 262 547 325 419 94 70 45446 END OF DATA 45447 SERIAL READ POT 45448 106 175 61 79 94 121 424 328 107 218 140 179 246 231 245 339 99 45449 END OF DATA 45450 LET N = SIZE LEAD; LET X = SEQUENCE 1 1 N 45451 . 45452 LINE DASH DOT 45453 SEGMENT 1 COORDINATES 17 87 22 87 45454 SEGMENT 2 COORDINATES 17 83 22 83 45455 SEGMENT 1 PATTERN DASH 45456 SEGMENT 2 PATTERN DOT 45457 LEGEND 1 COORDINATES 23 86; LEGEND 1 POTASSIUM 45458 LEGEND 2 COORDINATES 23 82; LEGEND 2 LEAD 45459 TITLE SEGMENT COORDINATES COMMAND 45460 PLOT POT LEAD VS X 45461 45462-----SEGMENT THICKNESS------------------------------------------------- 45463 45464SEGMENT THICKNESS 45465 45466Name: 45467 SEGMENT ... THICKNESS 45468 45469Type: 45470 Plot Control Command 45471 45472Purpose: 45473 Specifies the thickness for the line segments to appear on 45474 subsequent plots. 45475 45476Description: 45477 Segments are straight lines that the analyst can position anywhere 45478 on the plot. The segments appear on all subsequent plots until 45479 blanked out or overridden with new segment coordinates. The 45480 segment colors hold for all subsequent plots until defaulted or 45481 overridden with new colors. Up to 100 such line segments can be 45482 specified. 45483 45484 The thickness is specified in DATAPLOT 0 to 100 coordinates (i.e., 45485 as a percentage of the vertical device size). A value of 0.1 45486 yields a single line width on most devices. Typical values are 45487 between 0.05 and 0.3. 45488 45489 Segments are most typically used in legend boxes to identify 45490 curves. 45491 45492Syntax: 45493 SEGMENT <id> THICKNESS <thickness> 45494 where <id> is an integer number or parameter in the range 1 to 100 45495 that specifies the segment identifier; 45496 and <thickness> is a decimal number or parameter in the range 0 45497 to 100 that specifies the desired line thickness. 45498 45499Examples: 45500 SEGMENT 2 THICKNESS 0.2 45501 SEGMENT 2 THICKNESS 0.3 45502 45503Note: 45504 A SEGMENT ... THICKNESS command with no arguments reverts the line 45505 segment thickness to default; thus SEGMENT 1 THICKNESS with no 45506 arguments reverts the thickness for line segment 1 to default. A 45507 SEGMENT ... THICKNESS command with no <id> refers to all 100 line 45508 segments; thus SEGMENT THICKNESS 0.2 assigns the thickness 0.2 to 45509 all 100 line segments. SEGMENT THICKNESS with no <id> and no 45510 arguments reverts the thickness to default for all 100 line 45511 segments. 45512 45513Default: 45514 All segment line thicknesses are 0.1. 45515 45516Synonyms: 45517 None 45518 45519Related Commands: 45520 SEGMENT COLOR = Specify the color for a segment. 45521 SEGMENT COORDINATES = Specify a segment location. 45522 SEGMENT PATTERN = Specify the line type for a segment. 45523 LEGEND = Specify a legend for a subsequent plot. 45524 ARROW COORDINATES = Specify the location of an arrow. 45525 BOX COORDINATES = Specify the location of a box. 45526 45527Applications: 45528 Presentation Graphics 45529 45530Implementation Date: 45531 XX 45532 45533Program: 45534 . POLLUTION SOURCE ANALYSIS, LLOYD CURRIE, DATE--1990 45535 . SUBSET OF CURRIE.DAT REFERENCE FILE 45536 . 45537 SERIAL READ LEAD 45538 164 426 59 98 312 263 607 497 213 54 160 262 547 325 419 94 70 45539 END OF DATA 45540 SERIAL READ POT 45541 106 175 61 79 94 121 424 328 107 218 140 179 246 231 245 339 99 45542 END OF DATA 45543 LET N = SIZE LEAD; LET X = SEQUENCE 1 1 N 45544 . 45545 LINE THICKNESS 0.1 0.3 45546 SEGMENT 1 COORDINATES 17 87 22 87 45547 SEGMENT 2 COORDINATES 17 83 22 83 45548 SEGMENT 1 THICKNESS 0.1 45549 SEGMENT 2 THICKNESS 0.3 45550 LEGEND 1 COORDINATES 23 86; LEGEND 1 POTASSIUM 45551 LEGEND 2 COORDINATES 23 82; LEGEND 2 LEAD 45552 TITLE DEMONSTRATE SEGMENT THICKNESS 45553 PLOT POT LEAD VS X 45554 45555-----SEMCDF (LET)-------------------------------- 45556 45557SEMCDF 45558 45559Name: 45560 SEMCDF (LET) 45561 45562Type: 45563 Library Function 45564 45565Purpose: 45566 Compute the semi-circular cumulative distribution function. 45567 45568Description: 45569 The semi-circular distribution is the distribution onto one axis 45570 of the points uniformly distributed within the unit circle. As 45571 such, it is useful for testing 2-dimensional uniformity. 45572 45573 The formula for the cumulative distribution function is: 45574 45575 F(x;mu,r) = 0.5 + x*SQRT(r**2 - (x-mu)**2)/(PI*r**2) + 45576 ARCSIN((x-mu)/r)/PI 45577 -r <= x <= r 45578 45579 with mu and r denoting the location and scale parameters, 45580 respectively. 45581 45582 The case where mu = 0 and r = 1 is referred to as the 45583 standard semi-circular distribution. 45584 45585Syntax: 45586 LET <y> = SEMCDF(<x>,<mu>,<r>) <SUBSET/EXCEPT/FOR qualification> 45587 where <x> is a variable, number, or parameter; 45588 <mu> is a variable, number, or parameter that specifies 45589 the location parameter; 45590 <r> is a variable, number, or parameter that specifies 45591 the scale parameter; 45592 <y> is a variable or a parameter (depending on what <x> is) 45593 where the computed semi-circular cdf value is stored; 45594 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 45595 45596 If <mu> and <r> are omitted, they default to 0 and 1, 45597 respectively. 45598 45599Examples: 45600 LET A = SEMCDF(0.5) 45601 LET A = SEMCDF(0.5,0,5) 45602 LET X2 = SEMCDF(X1) 45603 45604Note: 45605 Library functions are distinguished from let subcommands 45606 in the following ways. 45607 1) Functions enclose the input value in parenthesis. Let 45608 subcommands use spaces. 45609 2) Functions can accept (and return) either parameters 45610 (i.e., single values) or variables (i.e., an array of 45611 values) while let subcommands are specific in which they 45612 accept as input and what they return as output. 45613 3) Functions can accept expressions while let subcommands 45614 do not. For example, the following is legal: 45615 LET Y2 = ABS(Y1-INT(Y1)) 45616 For let subcommands, you typically have to do something 45617 like the following: 45618 LET YTEMP = Y**2 + 8 45619 LET A = SUM YTEMP 45620 45621Default: 45622 None 45623 45624Synonyms: 45625 None 45626 45627Related Commands: 45628 SEMPDF = Compute the semi-circular probability density function. 45629 SEMPPF = Compute the semi-circular percent point function. 45630 UNIPDF = Compute the uniform probability density function. 45631 UNICDF = Compute the uniform cumulative distribution function. 45632 UNIPPF = Compute the uniform percent point function. 45633 NORCDF = Compute the normal cumulative distribution function. 45634 NORPDF = Compute the normal probability density function. 45635 NORPPF = Compute the normal percent point function. 45636 45637Reference: 45638 "Continuous Univariate Distributions - 2", Johnson and Kotz, 45639 Houghton Mifflin, 1970 (chapter 25). 45640 45641 "Simple and Robust Linear Estimation of the Location Parameter of 45642 a Symmetric Distribution", Filliben, unpublished Ph.d dissertation, 45643 Princeton University, 1969 (pp. 21-44, 229-231). 45644 45645Applications: 45646 Distributional Modeling 45647 45648Implementation Date: 45649 1994/4: Implemented for the standard case 45650 2006/10: Implemented for the general case 45651 45652Program: 45653 YLIMITS 0 1 45654 MAJOR YTIC NUMBER 6 45655 MINOR YTIC NUMBER 1 45656 YTIC DECIMAL 1 45657 XLIMITS -1 1 45658 XTIC OFFSET 0.1 0.1 45659 TITLE AUTOMATIC 45660 PLOT SEMCDF(X) FOR X = -1 0.01 1 45661 45662-----SEMI CIRCLE------------------------------------------------------- 45663 45664SEMI CIRCLE 45665 45666Name: 45667 SEMI-CIRCLE 45668 45669Type: 45670 Diagrammatic Graphics Command 45671 45672Purpose: 45673 Draws a semi-circle. 45674 45675Description: 45676 The 2 pairs of coordinates define the (x,y) values for one end and 45677 the other end (respectively) of the diameter of the semi-circle. 45678 45679Syntax: 45680 SEMI-CIRCLE <x1> <y1> <x2> <y2> 45681 where <x1> is a decimal number or parameter in the range 0 to 100 45682 that specifies the horizontal coordinate of one end; 45683 <y1> is a decimal number or parameter in the range 0 to 100 45684 that specifies the vertical coordinate of one end; 45685 <x2> is a decimal number or parameter in the range 0 to 100 45686 that specifies the horizontal coordinate of the other 45687 end; 45688 and <y2> is a decimal number or parameter in the range 0 to 100 45689 that specifies the vertical coordinate of the other end. 45690 45691Examples: 45692 SEMI-CIRCLE 50 50 60 60 45693 SEMI-CIRCLE 50 50 60 50 45694 SEMI-CIRCLE 20 20 30 30 45695 SEMI-CIRCLE 50 20 60 20 45696 45697Note: 45698 The line style (i.e., solid, dash), color, and thickness are 45699 controlled by the LINE, LINE COLOR, and LINE THICKNESS commands. 45700 The REGION FILL command can be used to generate solid filled 45701 circles while the REGION PATTERN command can be used to generate 45702 hatch filled patterns. 45703 45704Default: 45705 None 45706 45707Synonyms: 45708 None 45709 45710Related Commands: 45711 CIRCLE = Draws a circle. 45712 POINT = Draws a point. 45713 ARROW = Draws an arrow. 45714 TRIANGLE = Draws a triangle. 45715 BOX = Draws a box. 45716 HEXAGON = Draws a hexagon. 45717 SEMI-CIRCLE = Draws a semi-circle. 45718 ARC = Draws an arc. 45719 ELLIPSE = Draws an ellipse. 45720 OVAL = Draws an oval. 45721 DIAMOND = Draws a diamond. 45722 DRAW = Draws a line. 45723 MOVE = Moves to a point. 45724 LINES = Sets the line type for figures and plot lines. 45725 LINE THICKNESSES = Sets the line thickness for figures and plot 45726 lines. 45727 LINE COLOR = Sets the line colors for figures and plot lines. 45728 CROSS-HAIR = Activates and reads the cross-hair. 45729 TEXT = Writes a text string. 45730 45731Applications: 45732 XX 45733 45734Implementation Date: 45735 XX 45736 45737Program: 45738 SEMI-CIRCLE 10 10 20 20 45739 SEMI-CIRCLE 60 10 80 30 45740 . 45741 THICKNESS 0.7 45742 SEMI-CIRCLE 10 30 20 40 45743 THICKNESS 0.2 45744 . 45745 LINE DASH 45746 SEMI-CIRCLE 10 50 20 60 45747 LINE SOLID 45748 . 45749 LINE COLOR G50 45750 SEMI-CIRCLE 10 80 20 90 45751 LINE COLOR BLACK 45752 . 45753 REGION FILL ON 45754 SEMI-CIRCLE 30 30 35 35 45755 REGION FILL COLOR G50 45756 SEMI-CIRCLE 40 40 60 60 45757 . 45758 REGION FILL COLOR BLACK 45759 REGION PATTERN D1D2 45760 REGION PATTERN SPACING 3 45761 SEMI-CIRCLE 75 60 90 72 45762 45763-----SEMI INTERQUARTILE RANGE (LET)------------------------------- 45764 45765SEMI INTERQUARTILE RANGE 45766LOWER SEMI INTERQUARTILE RANGE 45767UPPER SEMI INTERQUARTILE RANGE 45768 45769Name: 45770 SEMI INTERQUARTILE RANGE (LET) 45771 45772Type: 45773 Let Subcommand 45774 45775Purpose: 45776 Compute either the lower semi-interquartile range or the upper 45777 semi-interquartile range for a variable. 45778 45779Description: 45780 The interquartile range is: 45781 45782 IQ = UPPER QUARTILE - LOWER QUARTILE 45783 45784 That is, it is the difference betweeen the 75th and 25th 45785 percentiles of a variable. 45786 45787 The lower semi-interquartile range is: 45788 45789 SIQR(L) = q2 - q1 45790 45791 and the upper semi-interquartile range is: 45792 45793 SIQR(U) = q3 - q2 45794 45795 with q1, q2, and q3 denoting the lower quartile, median, and 45796 upper quartile respectively. 45797 45798 The semi-interquartile range is sometimes used in place of the 45799 interquartile range when there is significant skewness in the 45800 data. For example, it can be used to provide an alternate 45801 definition of the fences in a box plot. 45802 45803Syntax 1: 45804 LET <par> = LOWER SEMI INTERQUARTILE RANGE <y> 45805 <SUBSET/EXCEPT/FOR qualification> 45806 where <y> is the response variable; 45807 <par> is a parameter where the computed lower semi-interquartile 45808 range is stored; 45809 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 45810 45811Syntax 2: 45812 LET <par> = UPPER SEMI INTERQUARTILE RANGE <y> 45813 <SUBSET/EXCEPT/FOR qualification> 45814 where <y> is the response variable; 45815 <par> is a parameter where the computed upper semi-interquartile 45816 range is stored; 45817 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 45818 45819Examples: 45820 LET A = LOWER SEMI INTERQUARTILE RANGE Y1 45821 LET A = UPPER SEMI INTERQUARTILE RANGE Y1 45822 LET A = UPPER SEMI INTERQUARTILE RANGE Y1 SUBSER TAG > 2 45823 LET A = INTERQUARTILE RANGE Y1 SUBSET TAG > 2 45824 45825Note: 45826 Dataplot statistics can be used in a number of commands. For 45827 details, enter 45828 45829 HELP STATISTICS 45830 45831Default: 45832 None 45833 45834Synonyms: 45835 None 45836 45837Related Commands: 45838 INTERQUARTILE RANGE = Compute the interquartile range of a variable. 45839 BOX PLOT = Generate a box plot. 45840 45841References: 45842 Walker, Dovedo, Chakraborti and Hilton (2019), "An Improved Boxplot 45843 for Univariate Data". American Statistician, Vol. 72, No. 4, 45844 pp. 348-353. 45845 45846Applications: 45847 Robust Data Analysis 45848 45849Implementation Date: 45850 2019/08 45851 45852Program: 45853 LET NU = 1 45854 LET Y = CHISQUARE RANDOM NUMBERS FOR I = 1 1 100 45855 LET SIQRL = LOWER SEMI INTERQUARTILE RANGE Y 45856 LET SIQRU = UPPER SEMI INTERQUARTILE RANGE Y 45857 PRINT SIQRL SIQRU 45858 45859-----SEMPDF (LET)-------------------------------- 45860 45861SEMPDF 45862 45863Name: 45864 SEMPDF (LET) 45865 45866Type: 45867 Library Function 45868 45869Purpose: 45870 Compute the semi-circular probability density function. 45871 45872Description: 45873 The semi-circular distribution is the distribution onto one axis 45874 of the points uniformly distributed within the unit circle. As 45875 such, it is useful for testing 2-dimensional uniformity. 45876 45877 The probability density function for the semi-circular 45878 distribution is: 45879 45880 f(x;mu,r) = 2*sqrt(r**2 - (x-mu)**2)/(PI*r**2) -r <= x <= r 45881 45882 with mu and r denoting the location and scale parameters, 45883 respectively. The scale parameter, r, is the radius of 45884 the semi-circle (or ellipse if r not equal to 1). 45885 45886 The case where mu = 0 and r = 1 is referred to as the 45887 standard semi-circular distribution and has the following 45888 probability density function: 45889 45890 f(x) = 2*sqrt(1-x**2)/PI -1 <= x <= 1 45891 45892 This distribution has mean 0 and standard deviation r/2. 45893 45894Syntax: 45895 LET <y> = SEMPDF(<x>,<mu>,<r>) <SUBSET/EXCEPT/FOR qualification> 45896 where <x> is a variable, number, or parameter; 45897 <mu> is a variable, number, or parameter that specifies 45898 the location parameter; 45899 <r> is a variable, number, or parameter that specifies 45900 the scale parameter; 45901 <y> is a variable or a parameter (depending on what <x> is) 45902 where the computed semi-circular pdf value is stored; 45903 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 45904 45905 If <mu> and <r> are omitted, they default to 0 and 1, 45906 respectively. 45907 45908Examples: 45909 LET A = SEMPDF(0.5) 45910 LET A = SEMPDF(1.2,0,5) 45911 LET X2 = SEMPDF(X1) 45912 45913Note: 45914 Semi-circular random numbers, probability plots, and 45915 goodness of fit tests can be generated with the commands: 45916 45917 LET Y = SEMI-CIRCULAR RANDOM NUMBERS FOR I = 1 1 N 45918 SEMI-CIRCULAR PROBABILITY PLOT Y 45919 SEMI-CIRCULAR PROBABILITY PLOT Y2 X2 45920 SEMI-CIRCULAR PROBABILITY PLOT Y3 XLOW XHIGH 45921 SEMI-CIRCULAR KOLMOGOROV SMIRNOV GOODNESS OF FIT Y 45922 SEMI-CIRCULAR CHI-SQUARE GOODNESS OF FIT Y2 X2 45923 SEMI-CIRCULAR CHI-SQUARE GOODNESS OF FIT Y3 XLOW XHIGH 45924 45925 The location and scale estimates can be obtained from the 45926 probability plot (location = PPA0 and scale = PPA1). 45927 45928 The BOOTSTRAP DISTRIBUTION command can be used to find 45929 uncertainty intervals for the location and scale parameters 45930 based on the probability plot. 45931 45932Note: 45933 Library functions are distinguished from let subcommands 45934 in the following ways. 45935 1) Functions enclose the input value in parenthesis. Let 45936 subcommands use spaces. 45937 2) Functions can accept (and return) either parameters 45938 (i.e., single values) or variables (i.e., an array of 45939 values) while let subcommands are specific in which they 45940 accept as input and what they return as output. 45941 3) Functions can accept expressions while let subcommands 45942 do not. For example, the following is legal: 45943 LET Y2 = ABS(Y1-INT(Y1)) 45944 For let subcommands, you typically have to do something 45945 like the following: 45946 LET YTEMP = Y**2 + 8 45947 LET A = SUM YTEMP 45948 45949Default: 45950 None 45951 45952Synonyms: 45953 None 45954 45955Related Commands: 45956 SEMCDF = Compute the semi-circular cumulative distribution 45957 function. 45958 SEMPPF = Compute the semi-circular percent point function. 45959 UNIPDF = Compute the uniform probability density function. 45960 UNICDF = Compute the uniform cumulative distribution function. 45961 UNIPPF = Compute the uniform percent point function. 45962 NORCDF = Compute the normal cumulative distributoin function. 45963 NORPDF = Compute the normal probability density function. 45964 NORPPF = Compute the normal percent point function. 45965 45966Reference: 45967 "Continuous Univariate Distributions - 2", Johnson and Kotz, 45968 Houghton Mifflin, 1970 (chapter 25). 45969 45970 "Simple and Robust Linear Estimation of the Location Parameter of 45971 a Symmetric Distribution", Filliben, unpublished Ph.d dissertation, 45972 Princeton University, 1969 (pp. 21-44, 229-231). 45973 45974Applications: 45975 Distributional Modeling 45976 45977Implementation Date: 45978 94/4: Implemented for the standard case 45979 2006/10: Updated to support the general case 45980 45981Program: 45982 XLIMITS -1 1 45983 XTIC OFFSET 0.1 0.1 45984 TITLE AUTOMATIC 45985 PLOT SEMPDF(X) FOR X = -1 0.01 1 45986 45987-----SEMPPF (LET)-------------------------------- 45988 45989SEMPPF 45990 45991Name: 45992 SEMPPF (LET) 45993 45994Type: 45995 Library Function 45996 45997Purpose: 45998 Compute the semi-circular percent point function. 45999 46000Description: 46001 The semi-circular distribution has the following cumulative 46002 distribution function: 46003 46004 F(x;mu,r) = 0.5 + x*SQRT(r**2 - (x-mu)**2)/(PI*r**2) + 46005 ARCSIN((x-mu)/r)/PI 46006 -r <= x <= r 46007 46008 with mu and r denoting the location and scale parameters, 46009 respectively. 46010 46011 The percent point function is computed by numerically 46012 inverting the cumulative distribution function. 46013 46014Syntax: 46015 LET <y> = SEMPPF(<p>,<mu>,<r>) <SUBSET/EXCEPT/FOR qualification> 46016 where <p> is a variable, number, or parameter in the interval 46017 (0,1); 46018 <mu> is a variable, number, or parameter that specifies 46019 the location parameter; 46020 <r> is a variable, number, or parameter that specifies 46021 the scale parameter; 46022 <y> is a variable or a parameter (depending on what <p> is) 46023 where the computed semi-circular ppf value is stored; 46024 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 46025 46026 If <mu> and <r> are omitted, they default to 0 and 1, 46027 respectively. 46028 46029Examples: 46030 LET A = SEMPPF(0.99) 46031 LET A = SEMPPF(0.99,0,5) 46032 LET X2 = SEMPPF(X1) 46033 46034Note: 46035 Library functions are distinguished from let subcommands 46036 in the following ways. 46037 1) Functions enclose the input value in parenthesis. Let 46038 subcommands use spaces. 46039 2) Functions can accept (and return) either parameters 46040 (i.e., single values) or variables (i.e., an array of 46041 values) while let subcommands are specific in which they 46042 accept as input and what they return as output. 46043 3) Functions can accept expressions while let subcommands 46044 do not. For example, the following is legal: 46045 LET Y2 = ABS(Y1-INT(Y1)) 46046 For let subcommands, you typically have to do something 46047 like the following: 46048 LET YTEMP = Y**2 + 8 46049 LET A = SUM YTEMP 46050 46051Default: 46052 None 46053 46054Synonyms: 46055 None 46056 46057Related Commands: 46058 SEMCDF = Compute the semi-circular cumulative distribution 46059 function. 46060 SEMPDF = Compute the semi-circular probability density function. 46061 UNIPDF = Compute the uniform probability density function. 46062 UNICDF = Compute the uniform cumulative distribution function. 46063 UNIPPF = Compute the uniform percent point function. 46064 NORCDF = Compute the normal cumulative distributoin function. 46065 NORPDF = Compute the normal probability density function. 46066 NORPPF = Compute the normal percent point function. 46067 46068Reference: 46069 "Continuous Univariate Distributions - 2", Johnson and Kotz, 46070 Houghton Mifflin, 1970 (chapter 25). 46071 46072 "Simple and Robust Linear Estimation of the Location Parameter of 46073 a Symmetric Distribution", Filliben, unpublished Ph.d dissertation, 46074 Princeton University, 1969 (pp. 21-44, 229-231). 46075 46076Applications: 46077 Distributional Modeling 46078 46079Implementation Date: 46080 1994/4: Implemented for the standard case 46081 2006/10: Implemented for the general case 46082 46083Program: 46084 XLIMITS 0 1 46085 MAJOR XTIC NUMBER 6 46086 MINOR XTIC NUMBER 1 46087 XTIC DECIMAL 1 46088 YLIMITS -1 1 46089 YTIC OFFSET 0.1 0.1 46090 TITLE AUTOMATIC 46091 PLOT SEMPPF(P) FOR P = 0 0.01 1 46092 46093-----SEQUENCE------------------------------------------------------- 46094 46095SEQUENCE 46096 46097Name: 46098 SEQUENCE (LET) 46099 46100Type: 46101 Let Subcommand 46102 46103Purpose: 46104 Generate a sequence of values. 46105 46106Description: 46107 This command is useful for generating variables that have constant 46108 increments. Increments can be either positive or negative. 46109 Increments can also be real numbers (i.e., they are not restricted 46110 to integers). 46111 46112 Specifically, you specify a start value, an increment, and 46113 a stop value. You can also optionally specify a repeat factor 46114 (this defaults to 1 if not specified). 46115 46116 The 2010/11 version of Dataplot updated this command to support 46117 variable arguments for the start, increment, stop, and repeat 46118 factors. If more than one of these is a variable (as oppossed 46119 to a constant/parameter), then these variable must have the 46120 same length. If a variable is used for one or more of the 46121 arguments, then we essentially create k separate sequences 46122 (where k is the number of elements in the variable) and 46123 append the results together. Arguments that are entered as 46124 constants or parameters will use the same value for each sequence. 46125 46126 In addition, a new syntax was added where the first argument 46127 is a list of values and the second argument is the number of 46128 times that each value is repeated. This syntax is useful when 46129 you want to generate a simple sequence with repeat values 46130 where the number of repeats is variable. 46131 46132 See the Note section below for some examples of using this new 46133 syntax. 46134 46135Syntax 1: 46136 LET <resp> = SEQUENCE <start> <inc> <stop> 46137 where <start> is a constant, parameter, or variable that specifies 46138 the beginning value for the sequence; 46139 <inc> is a constant, parameter, or variable that specifies 46140 the increment value of the sequence; 46141 <stop> is a constant, parameter, or variable that specifies 46142 the ending value of the sequence; 46143 and <resp> is a variable where the generated sequence is saved. 46144 46145 This is the most common syntax for this command. 46146 46147Syntax 2: 46148 LET <resp> = SEQUENCE <start> <inc> <stop> 46149 FOR I = <start2> <inc2> <stop2> 46150 where <start> is a constant, parameter, or variable that specifies 46151 the beginning value for the sequence; 46152 <inc> is a constant, parameter, or variable that specifies 46153 the increment value of the sequence; 46154 <stop> is a constant, parameter, or variable that specifies 46155 the ending value of the sequence; 46156 <start2> is a number or parameter that identifies the 46157 first row of <resp> in which the sequence is saved 46158 (typically it has a value of 1); 46159 <inc2> is a number or parameter that identifies the row 46160 increment of <resp> in which the sequence is saved 46161 (typically it has a value of 1); 46162 <stop2> is a number or parameter that identifies the last row 46163 of <resp> in which the sequence is saved; 46164 and <resp> is a variable where the generated sequence is saved. 46165 46166 This syntax is similar to syntax 1 except that the generated 46167 sequence is repeated until the rows of <resp> are filled as 46168 specified by the FOR clause. 46169 46170Syntax 3: 46171 LET <resp> = SEQUENCE <start> <repeat> <inc> <stop> 46172 where <start> is a constant, parameter, or variable that specifies 46173 the beginning value for the sequence; 46174 <repeat> is a constant, parameter, or variable that specifies 46175 the number of times each value in the sequence is 46176 repeated; 46177 <inc> is a constant, parameter, or variable that specifies 46178 the increment value of the sequence; 46179 <stop> is a constant, parameter, or variable that specifies 46180 the ending value of the sequence; 46181 and <resp> is a variable where the generated sequence is saved. 46182 46183 This syntax is useful for generating sequence like 1 1 1 2 2 2 46184 3 3 3 4 4 4. 46185 46186Syntax 4: 46187 LET <resp> = SEQUENCE <start> <repeat> <inc> <stop> 46188 FOR I = <start2> <inc2> <stop2> 46189 where <start> is a constant, parameter, or variable that specifies 46190 the beginning value for the sequence; 46191 <repeat> is a constant, parameter, or variable that specifies 46192 the number of times each value in the sequence is 46193 repeated; 46194 <inc> is a constant, parameter, or variable that specifies 46195 the increment value of the sequence; 46196 <stop> is a constant, parameter, or variable that specifies 46197 the ending value of the sequence; 46198 <start2> is a number or parameter that identifies the first 46199 row of <resp> in which the sequence is saved (typically it 46200 has a value of 1); 46201 <inc2> is a number or parameter that identifies the row 46202 increment of <resp> in which the sequence is saved 46203 (typically it has a value of 1); 46204 <stop2> is a number or parameter that identifies the last row 46205 of <resp> in which the sequence is saved; 46206 and <resp> is a variable where the generated sequence is saved. 46207 46208 This syntax is similar to syntax 3 except that the generated 46209 sequence is repeated until the rows of <resp> are filled as 46210 specified by the FOR clause. 46211 46212Syntax 5: 46213 LET <resp> = SEQUENCE <values> <repeat> 46214 where <values> is a constant, parameter, or variable that specifies 46215 the values for the sequence; 46216 <repeat> is a constant, parameter, or variable that specifies 46217 the number of times each value in <values> is 46218 repeated; 46219 and <resp> is a variable where the generated sequence is saved. 46220 46221 This syntax is useful when the number of repeated values varies. 46222 For example, you can do something like 46223 46224 LET VAL = SEQUENCE 1 1 5 46225 LET REP = DATA 3 3 2 4 4 46226 46227 to generate the sequence 46228 46229 1 1 1 2 2 2 3 3 4 4 4 4 5 5 5 5 46230 46231Examples: 46232 LET X = SEQUENCE 1 1 100 46233 LET X = SEQUENCE 1 1 10 FOR I = 1 1 100 46234 LET X = SEQUENCE -4 9 1 4 46235 LET X = SEQUENCE 1 50 1 2 FOR I = 1 1 100 46236 46237Note: 46238 To generate the sequence 46239 46240 1, 2, 3, 4, 5, 31, 32, 33, 61, 62, 63, 64, 65, 66, 67 46241 46242 you can enter the commands 46243 46244 LET START = DATA 1 31 61 46245 LET STOP = DATA 5 33 67 46246 LET Y = SEQUENCE START 1 STOP 46247 46248 To generate the sequence 46249 46250 1 1 1 2 2 3 3 3 3 4 4 4 4 4 46251 46252 you can enter the command 46253 46254 LET VAL = SEQUENCE 1 1 4 46255 LET REP = DATA 3 2 4 5 46256 LET Y = SEQUENCE VAL REP 46257 46258 Additional examples of using the variables with the SEQUENCE 46259 command are given in the Program section below. 46260 46261Default: 46262 None 46263 46264Synonyms: 46265 The word SEQUENCE can be omitted from the command. 46266 46267Related Commands: 46268 PATTERN = Generate numbers with a specific pattern. 46269 DATA = Place numbers in a variable. 46270 COMBINE = Combine constants, parameters, and variables 46271 into a single variable. 46272 FIBONNACCI NUMBERS = Generate Fibonnacci numbers. 46273 LOGISTIC NUMBERS = Generate numbers from a logistic sequence. 46274 46275Applications: 46276 Data Management 46277 46278Implementation Date: 46279 Pre-1987 46280 2010/11: Added support for variables as arguments 46281 2010/11: Added support for Syntax 5 46282 46283Program 1: 46284 LET X = SEQUENCE -4 1 4 FOR I = 1 1 81 46285 LET Y = SEQUENCE -4 9 1 4 46286 LET Z = X**2+Y**2-X*Y 46287 LET Z0 = SEQUENCE 5 5 40 46288 CONTOUR PLOT Z X Y Z0 46289 46290Program 2: 46291 set write decimals 1 46292 . 46293 . Step 1: First test basic current usage 46294 . 46295 let y = sequence 1 1 10 46296 print y 46297 pause 46298 delete y 46299 . 46300 let y = sequence 1 3 1 10 46301 print y 46302 pause 46303 delete y 46304 . 46305 . Step 2: Now test "variable" syntax 46306 . 46307 let rep = data 1 2 3 1 2 3 1 2 3 1 46308 let y = sequence 1 rep 1 10 46309 print y 46310 pause 46311 delete y rep 46312 . 46313 let stop = sequence 10 1 1 46314 let y = sequence 1 2 1 stop 46315 print y 46316 pause 46317 delete y stop 46318 . 46319 let start = data 1 100 1000 46320 let inc = data 1 10 100 46321 let stop = data 10 1000 10000 46322 let rep = data 3 2 1 46323 let y = sequence start rep inc stop 46324 print y 46325 pause 46326 delete y start rep inc stop 46327 . 46328 let start = data 1 2 3 4 5 46329 let rep = data 5 3 1 4 2 46330 let y = sequence start rep 46331 print y 46332 pause 46333 delete y start rep 46334 46335 46336SEQUENCE 46337 46338Name: 46339 SEQUENCE 46340 46341Type: 46342 Plot Control Command 46343 46344Purpose: 46345 Specifies that a sequence number be automatically inscribed in the 46346 upper right corner of subsequent plots. 46347 46348Description: 46349 This is useful for the ordering of the plot hardcopies after a 46350 session where many plots have been generated. 46351 46352Syntax: 46353 SEQUENCE <ON or OFF> <start> 46354 where ON specifies that sequence numbers are generated on 46355 subsequent plots and OFF specifies that they are not; 46356 and <start> specifies a starting number for the sequence (only 46357 used if ON specified). 46358 46359Examples: 46360 SEQUENCE ON 46361 SEQUENCE OFF 46362 SEQUENCE 46363 SEQUENCE ON 11 46364 46365Note: 46366 SEQUENCE ON with no <start> specified is equivalent to SEQUENCE ON 46367 1 . SEQUENCE with no arguments is equivalent to SEQUENCE ON 1 . 46368 46369Default: 46370 Sequence numbers are not generated. 46371 46372Synonyms: 46373 None 46374 46375Related Commands: 46376 PLOT = Generates a data or function plot. 46377 BELL = Sets the automatic bell switch for plots. 46378 PRE-ERASE = Sets the automatic pre-erase switch for plots. 46379 HARDCOPY = Sets the automatic copy switch for plots. 46380 RING = Rings the bell (immediately). 46381 ERASE = Erases the screen (immediately). 46382 COPY = Copies the screen (immediately). 46383 46384Applications: 46385 Presentation Graphics 46386 46387Implementation Date: 46388 Pre-1987 46389 46390Program: 46391 . POLLUTION SOURCE ANALYSIS, LLOYD CURRIE, DATE--1990 46392 . SUBSET OF CURRIE.DAT REFERENCE FILE 46393 . 46394 LET ID2 = DATA 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 46395 LET LEAD = DATA ... 46396 164 426 59 98 312 263 607 497 213 54 160 262 547 325 419 94 70 46397 LET POT = DATA ... 46398 106 175 61 79 94 121 424 328 107 218 140 179 246 231 245 339 99 46399 . 46400 SEQUENCE ON 46401 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 46402 TITLE SCATTER PLOT; X1LABEL LEAD; Y1LABEL POTASSIUM 46403 LINE BLANK ALL; CHARACTER CIRCLE; CHARACTER FILL ON 46404 PLOT POT LEAD 46405 . 46406 CHARACTER CIRCLE SQUARE; CHARACTER FILL OFF ALL 46407 TITLE SCATTER PLOT WITH GROUPS 46408 LEGEND 1 CIRC() - GROUP 1; LEGEND 2 SQUA() - GROUP 2 46409 LEGEND FILL ON; LEGEND FONT DUPLEX 46410 PLOT POT LEAD ID2 46411 . 46412 CHARACTER CIRCLE CIRCLE SQUARE SQUARE; CHARACTER FILL OFF ON OFF ON 46413 LET X = SEQUENCE 1 1 17 46414 LEGEND 1 CIRC() - POTASSIUM; LEGEND 2 SQUA() - LEAD 46415 X1LABEL SEQUENCE; Y1LABEL; TITLE CHARACTER FILL REPRESENTS GROUP ID 46416 PLOT POT X ID2 AND 46417 PLOT LEAD X ID2 46418 . 46419 CHARACTER BLANK ALL; LINE SOLID DASH 46420 SEGMENT 1 COORDINATES 16 85 19 85 46421 SEGMENT 2 COORDINATES 16 81 19 81 46422 SEGMENT 2 PATTERN DASH 46423 TITLE MULTIPLE TRACES AS LINES 46424 PLOT POT LEAD VS X 46425 END OF MULTIPLOT 46426 46427-----SEQUENTIAL DIFFERENCE (LET)------------------------------------- 46428 46429SEQUENTIAL DIFFERENCE 46430 46431Name: 46432 SEQUENTIAL DIFFERENCE (LET) 46433 46434Type: 46435 Let Subcommand 46436 46437Purpose: 46438 Compute the sequential differences (i.e., X(I) - X(I-1)) between 46439 the elements of a variable. 46440 46441Description: 46442 Given a data series with N points, the sequential difference 46443 will contain the points 46444 46445 Y(1) = X(2) - X(1) 46446 Y(2) = X(3) - X(2) 46447 ... 46448 Y(N-1) = X(N) - X(N-1) 46449 46450 If there are less than two points in the series, nothing will be 46451 done. 46452 46453 One use of sequential differencing is to remove trend from 46454 time series data. 46455 46456 The 2016/02 version of Dataplot generalized this command in 46457 the following two ways. 46458 46459 1. In additon to the difference, the following additional 46460 sequential values can also be computed: 46461 46462 SEQUENTIAL SUM - X(I) + X(I-1) 46463 SEQUENTIAL PRODUCT - X(I) * X(I-1) 46464 SEQUENTIAL MEAN - (X(I) + X(I-1))/2 46465 SEQUENTIAL MINIMUM - MIN(X(I), X(I-1)) 46466 SEQUENTIAL MAXIMUM - MAX(X(I), X(I-1)) 46467 SEQUENTIAL LOWER - X(I-1) 46468 SEQUENTIAL UPPER - X(I) 46469 46470 2. A group-id variable can be included. That is, the data 46471 values in each group will differenced. If there are K 46472 groups, then the differenced series will have N - K 46473 points. 46474 46475 The original data series does not have to be sorted 46476 by group. However, the output series will be sorted 46477 as follows: 46478 46479 a. The data will be sorted by group in the order that 46480 the groups are detected in the original series. 46481 46482 b. Within a group, the order in the output series 46483 will be based on the order of the input series. 46484 46485 For example, if X is the group-id variable and Y is the 46486 response variable 46487 46488 X(1) = 1 46489 X(2) = 2 46490 X(3) = 3 46491 X(4) = 1 46492 X(5) = 2 46493 X(6) = 3 46494 X(7) = 1 46495 X(8) = 2 46496 X(9) = 3 46497 46498 then the output group-id variable (X2) and differenced 46499 variable will be in the order 46500 46501 X2(1) = 1, Y2(1) = Y(4) - Y(1) 46502 X2(2) = 1, Y2(2) = Y(7) - Y(4) 46503 X2(3) = 2, Y2(3) = Y(5) - Y(2) 46504 X2(4) = 2, Y2(4) = Y(8) - Y(5) 46505 X2(5) = 3, Y2(5) = Y(6) - Y(3) 46506 X2(6) = 3, Y2(6) = Y(9) - Y(6) 46507 46508Syntax 1: 46509 LET <y> = SEQUENTIAL <stat> <x> <SUBSET/EXCEPT/FOR qualification> 46510 where <x> is the response variable; 46511 <stat> is one of DIFFERENCE, SUM, PRODUCT, MEAN, MINIMUM, 46512 MAXIMUM, LOWER, or UPPER; 46513 <y> is a variable containing the differenced series; 46514 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 46515 46516Syntax 2: 46517 LET <y2> <x2> = SEQUENTIAL <stat> <y> <x> 46518 <SUBSET/EXCEPT/FOR qualification> 46519 where <y> is the response variable; 46520 <x> is a the group-id variable; 46521 <stat> is one of DIFFERENCE, SUM, PRODUCT, MEAN, MINIMUM, 46522 MAXIMUM, LOWER, or UPPER; 46523 <y2> is a variable containing the differenced series; 46524 <x2> is a variable containing the group-id of the 46525 differenced series; 46526 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 46527 46528Examples: 46529 LET XD = SEQUENTIAL DIFFERENCE PRESSURE 46530 LET XD = SEQUENTIAL MEAN PRESSURE 46531 LET XD = SEQUENTIAL SUM PRESSURE 46532 LET XD = SEQUENTIAL DIFFERENCE PRESSURE SUBSET X > 4 46533 LET YDIFF X2 = SEQUENTIAL DIFFERENCE Y X 46534 46535Default: 46536 None 46537 46538Synonyms: 46539 DIFFERENCE is a synonym for SEQUENTIAL DIFFERENCE 46540 SEQUENTIAL AVERAGE is a synonym for SEQUENTIAL MEAN 46541 SEQUENTIAL MIN is a synonym for SEQUENTIAL MINIMUM 46542 SEQUENTIAL MAX is a synonym for SEQUENTIAL MAXIMUM 46543 46544Related Commands: 46545 CUMULATIVE SUM = Compute the cumulative sum of the elements of a 46546 variable. 46547 SORT = Sort the elements of a variable. 46548 COCODE = Generate a cocoded variable. 46549 CODE = Generate a coded variable. 46550 SEQUENCE = Generate a sequence of numbers. 46551 PATTERN = Generate numbers with a specific pattern. 46552 46553Applications: 46554 Data Transformations 46555 46556Implementation Date: 46557 Pre-1987 46558 2016/02: Support for SUM, PRODUCT, MEAN, MINIMUM, MAXIMUM, 46559 LOWER, and UPPER 46560 2016/02: Support for group-id variable 46561 46562Program 1: 46563 LET X1 = DATA 12 4 2 3 9 7 46564 LET XD = SEQUENTIAL DIFFERENCE X1 46565 46566 The variable XD will contain the following values: 46567 46568 8, 2, 1, 6, 2 46569 46570Program 2: 46571 . Step 1: Define the data 46572 . 46573 let y = sequence 1 1 10 46574 . 46575 . Step 2: Compute the sequential statistics 46576 . 46577 let ydiff = sequential difference y 46578 let ysum = sequential sum y 46579 let yprod = sequential product y 46580 let ymean = sequential mean y 46581 let ymin = sequential min y 46582 let ymax = sequential max y 46583 . 46584 . Step 3: Print the results 46585 . 46586 set write decimals 1 46587 print y ydiff ysum yprod ymean ymin ymax 46588 46589Program 3: 46590 . Step 1: Define the data 46591 . 46592 dimension 40 columns 46593 let y = sequence 1 1 10 46594 let x = sequence 1 5 1 2 46595 . 46596 . Step 2: Compute the sequential statistics 46597 . 46598 let ydiff ygroup = sequential difference y x 46599 let ysum ygroup = sequential sum y x 46600 let yprod ygroup = sequential product y x 46601 let ymean ygroup = sequential mean y x 46602 let ymin ygroup = sequential min y x 46603 let ymax ygroup = sequential max y x 46604 let ylow ygroup = sequential lower y x 46605 let yupp ygroup = sequential upper y x 46606 . 46607 . Step 3: Print the results 46608 . 46609 set write decimals 1 46610 print ygroup ydiff ysum yprod ymean ymin ymax ylow yupp 46611 46612----------SERIAL READ-------------------------------------- 46613 46614SERIAL READ 46615 46616Name: 46617 SERIAL READ 46618 46619Type: 46620 Support Command 46621 46622Purpose: 46623 Reads data into variables: 46624 1) from a mass storage file; 46625 2) from within a CALLed DATAPLOT sub-program; 46626 3) from the terminal 46627 46628Description: 46629 The rules regarding SERIAL READ are as follows: 46630 1) If there are k variables listed on the SERIAL READ 46631 statement, then all the data on each line image is read and 46632 sequentially fed into the next available elements of the k 46633 variables. There is no restriction on the number of data 46634 values on any given line image. A major difference between 46635 the SERIAL READ command and the READ command is that the 46636 SERIAL READ command reads in all data on a line, whereas the 46637 READ command only reads in the first k data values on a line. 46638 In practice, the READ command is more heavily used than the 46639 SERIAL READ command. An example of the use of the SERIAL 46640 READ command is 46641 SERIAL READ X Y 46642 1 1 2 4 3 9 4 16 5 46643 25 6 36 7 49 46644 8 64 46645 9 46646 81 10 100 46647 END OF DATA 46648 which results in X containing the 10 elements 1, 2, ... 10; 46649 and Y containing the 10 elements 1, 4, 9, ... 100. 46650 2) The number of variables being read at one time must be 46651 between 1 and 10, inclusive. 46652 3) The full line image is scanned (for reading from a mass 46653 storage file, the full line image is 132 columns; for reading 46654 from within a sub-program and for reading from the terminal, 46655 the full line image is 80 columns). For variations on this, 46656 see the COLUMN LIMITS command. 46657 4) Data values on a line image must be separated by at least one 46658 blank. 46659 5) Data values can be free-format. They need not be aligned in 46660 specific columns. 46661 6) The format of individual data values is general. It can be 46662 integer, floating point, or exponential. It is stored 46663 internally as a single precision real number. 46664 7) All reads start from the beginning of the file (for 46665 variations of this, see the SKIP and ROW LIMITS commands). 46666 8) The analyst need not be concerned about the number of 46667 observations for each variable. DATAPLOT automatically 46668 determines and reports this value at the end of the read. 46669 9) The read terminates when a line image is encountered which 46670 consists of 46671 END OF DATA 46672 or 46673 END DATA 46674 or when the end of the file is reached. 46675 46676Syntax 1: 46677 SERIAL READ <x1> <x2> ... <xk> 46678 where <x1>, <x2>, ..., <xk> are the desired variable names. 46679 46680 This syntax is used to read the data from the terminal or from a 46681 DATAPLOT sub-program. 46682 46683Syntax 2: 46684 SERIAL READ <file> <x1> <x2> ... <xk> 46685 where <file> is the name of the mass storage file where the data 46686 resides; 46687 and <x1>, <x2>, ..., <xk> are the desired variable names. 46688 46689 This syntax is used to read the data from a file. 46690 46691Examples: 46692 SERIAL READ CALIB. PRES TEMP TIME 46693 SERIAL READ ASTM. Y1 Y2 Y3 X DAY LAB 46694 SERIAL READ Y1 Y2 Y3 X DAY LAB 46695 SERIAL READ Y 46696 46697Note: 46698 The most common use of SERIAL READ is to read a large number of 46699 values into a single variable. 46700 46701Note: 46702 By default, DATAPLOT does free format reads. However, it has the 46703 capability for supporting FORTRAN style formats. Formatted reads 46704 can be about 10 times faster on many systems which can be helpful 46705 for large data files. Enter HELP READ FORMAT for more details. 46706 46707Note: 46708 Blank lines in data files are ignored. 46709 46710Note: 46711 DATAPLOT supports the ability to embed comment lines within the 46712 data file. Enter HELP COMMENT CHECK for details. 46713 46714Note: 46715 In order to determine whether the first argument is a file name or 46716 a variable name, it looks for a period in the name. If it finds 46717 one, it assumes a file name. If it does not, it assumes a variable 46718 name. If your file name does not contain a period, attach a 46719 trailing period (no spaces) to the file name on the READ command. 46720 46721Note: 46722 DATAPLOT has no restrictions on the file name other than it be a 46723 valid file name on the local operating system and that it contain 46724 a period "." in the file name itself or as a trailing character. 46725 DATAPLOT strips off trailing periods on those systems where it is 46726 appropriate to do so. On systems where trailing periods can be a 46727 valid file name (e.g., Unix), DATAPLOT tries to open the file with 46728 the trailing period. If this fails, it then tries to open the file 46729 with the trailing period stripped off. 46730 46731 Some users prefer to give all data files a ".DAT" or ".dat" 46732 extension. Although this is a useful method for keeping track of 46733 data files, it is strictly a user convention and is not enforced 46734 by DATAPLOT in any way. 46735 46736Note: 46737 File names are case sensitive on Unix file systems. For Unix, 46738 DATAPLOT attempts to open the file as given. If this fails, it 46739 attempts to open the file as all upper case characters. If this 46740 fails, it attempts to open the file as all lower case characters. 46741 All other currently supported systems are not case sensitive 46742 regarding file names. 46743 46744 As a further caution for Unix hosts, certain expansion characters 46745 (specifically ~ to refer to your home directory) are interpreted 46746 by the shell and are not recognized by the Fortran compiler. These 46747 expansion characters are interpreted as literal characters and do 46748 not yield the intended file name. 46749 46750Default: 46751 1) If no file name is specified, and if a CALL is being 46752 executed, then the data values should be listed directly 46753 in the DATAPLOT sub-program immediately after the SERIAL 46754 READ command (do not forget the END OF DATA statement). 46755 2) If no file name is specified, and if commands are being 46756 manually entered/executed one at a time from the terminal, 46757 then the data should be entered directly from the terminal 46758 immediately after the SERIAL READ command (also terminated 46759 by an END OF DATA statement). 46760 46761Synonyms: 46762 None 46763 46764Related Commands: 46765 READ FUNCTION = Read a function. 46766 READ MATRIX = Read a matrix. 46767 READ PARAMETER = Read a parameter. 46768 READ STRING = Read a string. 46769 READ = Perform a read. 46770 SET READ FORMAT = Define a FORTRAN style format for reads. 46771 DATA (LET) = Enter data values into a variable. 46772 46773Applications: 46774 Data I/O 46775 46776Implementation Date: 46777 Pre-1987 46778 46779Program: 46780 XX 46781 46782-----SET------------------------------------------------------- 46783 46784SET 46785 46786Name: 46787 SET 46788 46789Type: 46790 Support Command 46791 46792Purpose: 46793 Defines the values of certain internal underlying Fortran 46794 variables. 46795 46796Description: 46797 This command allows access to information which can assist in 46798 implementation, tracing and debugging. Most options are used by 46799 the service group which implements DATAPLOT on your computer. 46800 However some SET options are used by the general DATAPLOT user. 46801 These are documented separately in the HELP file. The PROBE 46802 command returns the current value of the variables available with 46803 the SET command. 46804 46805Syntax: 46806 SET <Fortran variable name> <setting> 46807 where <Fortran variable name> is the name of the underlying Fortran 46808 variable; 46809 and <settings> is a number, parameter, or character string that 46810 specifies the value to assign to the variable. 46811 46812Examples: 46813 SET IBUGAN ON 46814 SET IBUGA2 ON 46815 SET IBUGSU ON 46816 SET IBUGMA ON 46817 SET IPR 7 46818 46819Note: 46820 The following SET commands are currently available. 46821 46822 SET commands for general users (these are documented 46823 separately, for more details enter HELP <command>): 46824 46825 SET READ FORMAT <string> - specify a FORTRAN format statement 46826 for the READ command. 46827 46828 SET WRITE FORMAT <string> - specify a FORTRAN format 46829 statement for the WRITE command. 46830 46831 SET WRITE DECIMAL <numb> - specify the number of decimal 46832 places for the WRITE and PRINT commands. 46833 46834 SET IPR <file unit number> - specify the unit for DATAPLOT 46835 alphanumeric output. 46836 46837 SET FOURIER WRITE - 46838 46839 SET FOURIER EXPONENT <- or +> - 46840 46841 SET HELP LINES - specify the number of lines printed for a 46842 help screen (a carriage return prints the next screen). 46843 46844 SET LIST LINES - specify the number of lines printed by the 46845 LIST command (a carriage return prints the next screen). 46846 46847 SET READ REWIND <ON/OFF> - specifies whether files are 46848 rewound before being read. 46849 46850 SET WRITE REWIND <ON/OFF> - specifies whether files are 46851 rewound before being written to. 46852 46853 SET PREPLOT <device> - specifies the device that preplot and 46854 postplot definitions apply to. Equivalent to the PREPOST 46855 command. 46856 46857 SET POSTPLOT <device> - same as SET PREPLOT. 46858 46859 SET IO TERMINAL - used in writing menu macros. Allows I/O to 46860 take place from the terminal while executing a macro. 46861 46862 SET IO - turns off the SET IO TERMINAL command. 46863 46864 Device specific SET commands. These are documented in more 46865 detail in the HELP for that device (HELP POSTSCRIPT, HELP 46866 QUIC, HELP CALCOMP, HELP ZETA and HELP GENERAL). 46867 46868 SET GENERAL JUSTIFICATION <ON/OFF> 46869 SET GENERAL REGION FILL <ON/OFF> 46870 SET GENERAL FONT <ON/OFF> 46871 SET GENERAL PEN WIDTH <ON/OFF> 46872 SET GENERAL PEN THICKNESS <number> 46873 46874 SET QUIC FONT <number> 46875 SET QUIC PPI <number> 46876 SET QUIC [LANDSCAPE/PORTRAIT] MARGIN LEFT <number> 46877 SET QUIC [LANDSCAPE/PORTRAIT] MARGIN RIGHT <number> 46878 SET QUIC [LANDSCAPE/PORTRAIT] MARGIN TOP <number> 46879 SET QUIC [LANDSCAPE/PORTRAIT] MARGIN BOTTOM <number> 46880 46881 SET QMS FONT <number> 46882 SET QMS PPI <number> 46883 SET QMS [LANDSCAPE/PORTRAIT] MARGIN LEFT <number> 46884 SET QMS [LANDSCAPE/PORTRAIT] MARGIN RIGHT <number> 46885 SET QMS [LANDSCAPE/PORTRAIT] MARGIN TOP <number> 46886 SET QMS [LANDSCAPE/PORTRAIT] MARGIN BOTTOM <number> 46887 46888 SET POSTSCRIPT FONT <number> 46889 SET POSTSCRIPT PPI <number> 46890 SET POSTSCRIPT [LANDSCAPE/PORTRAIT] MARGIN LEFT <number> 46891 SET POSTSCRIPT [LANDSCAPE/PORTRAIT] MARGIN RIGHT <number> 46892 SET POSTSCRIPT [LANDSCAPE/PORTRAIT] MARGIN TOP <number> 46893 SET POSTSCRIPT [LANDSCAPE/PORTRAIT] MARGIN BOTTOM <number> 46894 46895 SET ZETA COLORS <number> 46896 SET ZETA WIDTH <number> 46897 46898 SET CALCOMP COLORS <number> 46899 SET CALCOMP WIDTH <number> 46900 46901 SET commands for DATAPLOT implementation and debugging. 46902 These are not needed by the general user. The most common 46903 usage is to turn on the "debugging" variables. These 46904 print the values of DATAPLOT variables while DATAPLOT is 46905 executing and can be a valuable debugging tool. Looking at 46906 the bug variables in a given routine can guide which specific 46907 ones to turn on. 46908 46909 SET ISUBRO <string> - turns on debugging for a specific 46910 subroutine. Enter the last 4 characters of the subroutine 46911 name. 46912 SET IBUGMA <ON/OFF> - machine constants 46913 SET IBUGIN <ON/OFF> - initialization 46914 SET IBUGLS <ON/OFF> - 46915 SET IBUGMS <ON/OFF> - 46916 SET IBUGGC <ON/OFF> - 46917 SET IBUGTY <ON/OFF> - 46918 SET IBUGTE <ON/OFF> - 46919 SET IBUGPC <ON/OFF> - plot control commands 46920 SET IBUGP2 <ON/OFF> - plot control commands 46921 SET IBUGOD <ON/OFF> - output devices 46922 SET IBUGO2 <ON/OFF> - output devices 46923 SET IBUGSU <ON/OFF> - support commands 46924 SET IBUGS2 <ON/OFF> - support commands 46925 SET IBUGGR <ON/OFF> - graphics commands 46926 SET IBUGG2 <ON/OFF> - graphics commands 46927 SET IBUGG3 <ON/OFF> - graphics commands 46928 SET IBUGAN <ON/OFF> - analysis commands 46929 SET IBUGA2 <ON/OFF> - analysis commands 46930 SET IBUGA3 <ON/OFF> - analysis commands 46931 SET IBUGPL <ON/OFF> - 46932 SET IBUGGP <ON/OFF> - 46933 SET IBUGP1 <ON/OFF> - 46934 SET IBUGP3 <ON/OFF> - 46935 SET IBUGDG <ON/OFF> - diagrammatic graphics commands 46936 SET IBUGD2 <ON/OFF> - diagrammatic graphics commands 46937 SET IBUGCO <ON/OFF> - 46938 SET IBUGEV <ON/OFF> - 46939 SET IBUGQ <ON/OFF> - 46940 SET IBUGRE <ON/OFF> - 46941 SET IBUGWR <ON/OFF> - 46942 SET IBUGSO <ON/OFF> - 46943 SET IBUGTO <ON/OFF> - 46944 SET IBUGUG <ON/OFF> - underlying graphics 46945 SET IBUGU2 <ON/OFF> - underlying graphics 46946 SET IBUGU3 <ON/OFF> - underlying graphics 46947 SET IBUGU4 <ON/OFF> - underlying graphics 46948 SET IBUGEX <ON/OFF> - expert subsystem 46949 SET IBUGE2 <ON/OFF> - expert subsystem 46950 SET IBUGHE <ON/OFF> - help 46951 SET IBUGH2 <ON/OFF> - help 46952 46953 Data variables: 46954 46955 SET MAXNK 46956 SET NK 46957 SET MAXCOL 46958 SET NUMCOL 46959 SET MAXN 46960 SET N 46961 SET MAXCHF 46962 SET NUMCHF 46963 SET MAXFUN 46964 SET NUMFUN 46965 SET MAXCHM 46966 SET NPLOTP 46967 SET ITRANS 46968 SET ICHAPA 46969 46970 Machine constants (use PROBE to retrieve their current value): 46971 46972 SET IRD - unit for alphanumeric input 46973 SET IPR - unit for alphanumeric output 46974 SET CPUMIN - smallest real number 46975 SET CPUMAX - largest real number 46976 SET NUMBPC - number of bits per character 46977 SET NUMCPW - number of characters per word 46978 SET NUMBPW - number bits per word 46979 SET IFEEDB - feedback switch 46980 SET IPRINT - print switch 46981 SET IECHO - echo switch 46982 46983 Housekeeping variables (use PROBE to retrieve their current value): 46984 46985 SET MAXWID 46986 SET IWIDTH 46987 SET MAXWSV 46988 SET IWIDSV 46989 SET ICOM - the current command (characters 1-4) 46990 SET ICOM2 - the current command (characters 5-8) 46991 SET MAXARG - maximum number of arguments 46992 SET NUMARG - number of arguments in current command 46993 SET IARG - command arguments in integer format 46994 SET ARG - command arguments in real format 46995 SET IHARG - command arguments in character format 46996 SET MAXNAM - maximum number of names 46997 SET NUMNAM - current number of names 46998 SET IHNAME - names (characters 1-4) 46999 SET IHNAM2 - names (characters 5-8) 47000 SET IUSE - 47001 SET IVALUE - 47002 SET VALUE - 47003 SET IN - 47004 SET IVSTAR - 47005 SET IVSTOP - 47006 SET IMESNU - unit for message file 47007 SET INEWNU - unit for news file 47008 SET IMAINU - unit for mail file 47009 SET IHELNU - unit for help file 47010 SET IBUGNU - unit for bugs file 47011 SET IQUENU - unit for query file 47012 SET ILOGNU - unit for log file 47013 SET IREANU - unit for user file to be read 47014 SET IWRINU - unit for user file to be written to 47015 SET ICRENU - unit for create macro file 47016 SET ISAVNU - unit for save memory file 47017 SET ISCRNU - unit for scratch file 47018 SET IDATNU - unit for file 47019 SET IPL1NU - unit for DEVICE 2 graphics output file 47020 SET IPL2NU - unit for DEVICE 3 graphics output file 47021 SET IMESNA - name for message file 47022 SET INEWNA - name for news file 47023 SET IMAINA - name for mail file 47024 SET IHELNA - name for help file 47025 SET IBUGNA - name for bugs file 47026 SET IQUENA - name for query file 47027 SET ILOGNA - name for log file 47028 SET IREANA - name for user file to be read 47029 SET IWRINA - name for user file to be written to 47030 SET ICRENA - name for create macro file 47031 SET ISAVNA - name for save memory file 47032 SET ISCRNA - name for scratch file 47033 SET IDATNA - name for file 47034 SET IPL1NA - name for DEVICE 2 graphics output file 47035 SET IPL2NA - name for DEVICE 3 graphics output file 47036 SET IMESST - status of message file 47037 SET INEWST - status of news file 47038 SET IMAIST - status of mail file 47039 SET IHELST - status of help file 47040 SET IBUGST - status of bugs file 47041 SET IQUEST - status of query file 47042 SET ILOGST - status of log file 47043 SET IREAST - status of user file to be read 47044 SET IWRIST - status of user file to be written to 47045 SET ICREST - status of create macro file 47046 SET ISAVST - status of save memory file 47047 SET ISCRST - status of scratch file 47048 SET IDATST - status of file 47049 SET IPL1ST - status of DEVICE 2 graphics output file 47050 SET IPL2ST - status of DEVICE 3 graphics output file 47051 47052Default: 47053 None 47054 47055Synonyms: 47056 None 47057 47058Related Commands: 47059 PROBE = Print the value of an underlying Fortran variable. 47060 47061Applications: 47062 Utility Commands 47063 47064Implementation Date: 47065 Pre-1987 47066 New SET commands have been continuously added 47067 47068Program: 47069 XX 47070 47071-----SET COMMANDS (LET)----------------------------------------------------- 47072 47073SET COMMANDS 47074The following are DATAPLOT set commands: 47075 SET CARDINALITY = Computes a set cardinality. 47076 SET UNION = Carries out a set union. 47077 SET INTERSECTION = Carries out a set intersection. 47078 SET COMPLEMENT = Carries out a set complement. 47079 SET CART PRODUCT = Carries out a set Cartesian product. 47080 SET ELEMENTS = Extracts the distinct elements of set. 47081 47082-----SET CARDINALITY (LET)--------------------------------------- 47083 47084SET CARDINALITY (LET) 47085 47086Name: 47087 SET CARDINALITY (LET) 47088 47089Type: 47090 Subcommand under LET 47091 47092Purpose: 47093 Compute the total number of elements in a set (with numeric 47094 elements). 47095 47096Description: 47097 This cardinality counts repeats if repeats exist. The cardinality 47098 of the following set: 47099 1 3 5 7 9 1 4 9 16 1 8 27 47100 is 12. 47101 47102Syntax: 47103 LET <p> = SET CARDINALITY <v> <SUBSET/EXCEPT/FOR qualification> 47104 where <v> is the variable whose elements are the elements of the 47105 input set; 47106 <p> is a parameter where the computed cardinality is saved; 47107 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 47108 rarely used in this context. 47109 47110Examples: 47111 LET N = SET CARDINALITY Y 47112 LET N = SET CARDINALITY Y SUBSET Y1 > 10 47113 LET N = SET CARDINALITY Y FOR I = 1 1 3 47114 47115Note: 47116 If the elements of a mathematical "set" are numbers (or can be 47117 translated into numbers-- always possible), then a DATAPLOT variable 47118 can be used to store the items of the mathematical "set". Thus if 47119 the analyst wanted to "store the set" with the 12 elements-- 47120 1 3 5 7 11 1 4 9 16 1 8 27 47121 he/she can do so by forming the variable Y via: 47122 SERIAL READ Y 47123 1 3 5 7 11 1 4 9 16 1 8 27 47124 END OF DATA 47125 or 47126 LET Y = DATA 1 3 5 7 11 1 4 9 16 1 8 27 47127 47128Default: 47129 None 47130 47131Synonyms: 47132 SIZE (LET) for SET CARDINALITY (LET) 47133 47134Related Commands: 47135 SET UNION = Carries out a set union. 47136 SET INTERSECTION = Carries out a set intersection. 47137 SET COMPLEMENT = Carries out a set complement. 47138 SET CART PRODUCT = Carries out a set Cartesian product. 47139 SET ELEMENTS = Extracts the distinct elements of set. 47140 PLOT = Plots data or functions. 47141 47142Applications: 47143 Mathematics 47144 47145Implementation Date: 47146 88/7 47147 47148Program: 47149 LET Y = DATA 1 3 5 7 11 1 4 9 16 1 8 27 47150 LET N = SET CARDINALITY Y 47151 SET WRITE DECIMALS 0 47152 WRITE Y N 47153 47154-----SET CARTESIAN PRODUCT (LET)----------------------------------- 47155 47156SET CARTESIAN PRODUCT (LET) 47157 47158Name: 47159 SET CARTESIAN PRODUCT (LET) 47160 47161Type: 47162 Subcommand under LET 47163 47164Purpose: 47165 Carry out the cartesian product of 2 sets (with numeric elements). 47166 47167Description: 47168 The Cartesian product of two sets is the set containing all the 47169 possible element pairs of the 2 original sets. For example, the 47170 Cartesian product of the 3-element set: 47171 1 3 5 47172 and the 4-element set: 47173 1 4 9 16 47174 is the 12-element pair of sets: 47175 1 1 47176 1 4 47177 1 9 47178 1 16 47179 3 1 47180 3 4 47181 3 9 47182 3 16 47183 5 1 47184 5 4 47185 5 9 47186 5 16 47187 47188Syntax: 47189 LET <v3> <v4> = SET CARTESIAN PRODUCT <v1> <v2> 47190 <SUBSET/EXCEPT/FOR qualification> 47191 where <v1> is the variable whose elements are the elements of the 47192 first set; 47193 <v2> is the variable whose elements are the elements of the 47194 second set; 47195 <v3> is the variable whose elements are the elements of the 47196 resultant set corresponding to <v1>; 47197 <v4> is the variable whose elements are the elements of the 47198 resultant set corresponding to <v2>; 47199 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 47200 rarely used in this context. 47201 47202Examples: 47203 LET Y3 Y4 = SET CARTESIAN PRODUCT Y1 Y2 47204 LET Y3 Y4 = SET CARTESIAN PRODUCT Y1 Y2 SUBSET Y1 > 10 47205 LET Y3 Y4 = SET CARTESIAN PRODUCT Y1 Y2 FOR I = 1 1 3 47206 47207Note: 47208 If the elements of a mathematical "set" are numbers (or can be 47209 translated into numbers-- always possible), then a DATAPLOT variable 47210 can be used to store the items of the mathematical "set". Thus if 47211 the analyst wanted to "store the set" with the 12 elements-- 47212 1 3 5 7 11 1 4 9 16 1 8 27 47213 he/she can do so by forming the variable Y via: 47214 SERIAL READ Y 47215 1 3 5 7 11 1 4 9 16 1 8 27 47216 END OF DATA 47217 or 47218 LET Y = DATA 1 3 5 7 11 1 4 9 16 1 8 27 47219 47220Default: 47221 None 47222 47223Synonyms: 47224 None 47225 47226Related Commands: 47227 SET CARDINALITY = Computes the number of elements in a set. 47228 SET UNION = Carries out a set union. 47229 SET INTERSECTION = Carries out a set intersection. 47230 SET COMPLEMENT = Carries out a set complement. 47231 SET DISTINCT = Extracts the distinct elements of set. 47232 PLOT = Plots data or functions. 47233 VECTOR DOT PRODUCT = Carries out a vector cross product. 47234 MATRIX MULT = Carries out a matrix multiplication. 47235 47236Applications: 47237 Mathematics 47238 47239Implementation Date: 47240 87/10 47241 47242Program: 47243 LET Y1 = DATA 1 3 5 7 9 47244 LET Y2 = DATA 1 4 9 16 47245 LET Y3 Y4 = SET CARTESIAN PRODUCT Y1 Y2 47246 SET WRITE DECIMALS 0 47247 WRITE Y3 Y4 47248 47249-----SET COMPLEMENT (LET)---------------------------------------- 47250 47251SET COMPLEMENT (LET) 47252 47253Name: 47254 SET COMPLEMENT (LET) 47255 47256Type: 47257 Subcommand under LET 47258 47259Purpose: 47260 Carry out the complement of 2 sets (with numeric elements). 47261 47262Description: 47263 The complement is of set 1 with respect to set 2 (the assumed 47264 superset). The resultant set is those elements in set 2 which are 47265 not in set 1. For example, the complement of the 3-element set: 47266 1 5 7 47267 with respect to the 5-element set: 47268 1 3 5 7 9 47269 is the 2-element set: 47270 3 9 47271 47272Syntax: 47273 LET <v3> = SET COMPLEMENT <v1> <v2> 47274 <SUBSET/EXCEPT/FOR qualification> 47275 where <v1> is the variable whose elements are the elements of the 47276 first set; 47277 <v2> is the variable whose elements are the elements of the 47278 second set; 47279 <v3> is the variable whose elements are the elements of the 47280 resultant set; 47281 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 47282 rarely used in this context. 47283 47284Examples: 47285 LET Y3 = SET COMPLEMENT Y1 Y2 47286 LET Y3 = SET COMPLEMENT Y1 Y2 SUBSET Y1 > 10 47287 LET Y3 = SET COMPLEMENT Y1 Y2 FOR I = 1 1 3 47288 47289Note: 47290 If the elements of a mathematical "set" are numbers (or can be 47291 translated into numbers-- always possible), then a DATAPLOT variable 47292 can be used to store the items of the mathematical "set". Thus if 47293 the analyst wanted to "store the set" with the 12 elements-- 47294 1 3 5 7 11 1 4 9 16 1 8 27 47295 he/she can do so by forming the variable Y via: 47296 SERIAL READ Y 47297 1 3 5 7 11 1 4 9 16 1 8 27 47298 END OF DATA 47299 or 47300 LET Y = DATA 1 3 5 7 11 1 4 9 16 1 8 27 47301 47302Default: 47303 None 47304 47305Synonyms: 47306 None 47307 47308Related Commands: 47309 SET CARDINALITY = Computes the number of elements in a set. 47310 SET UNION = Carries out a set union. 47311 SET INTERSECTION = Carries out a set intersection. 47312 SET CART PRODUCT = Carries out a set Cartesian product. 47313 SET ELEMENTS = Extracts the distinct elements of set. 47314 PLOT = Plots data or functions. 47315 COMPLEX SUBTRACTION = Carries out complex subtraction. 47316 POLY SUBTRACTION = Carries out polynomial subtraction. 47317 VECTOR SUBTRACTION = Carries out vector subtraction. 47318 LOGICAL OR = Carries out logical or. 47319 MATRIX SUBTRACTION = Carries out matrix subtraction. 47320 47321Applications: 47322 Mathematics 47323 47324Implementation Date: 47325 87/10 47326 47327Program: 47328 LET Y1 = DATA 1 5 7 47329 LET Y2 = DATA 1 3 5 7 9 47330 LET Y3 = SET COMPLEMENT Y1 Y2 47331 SET WRITE DECIMALS 0 47332 WRITE Y1 Y2 Y3 47333 47334-----SET DISTINCT (LET)------------------------------------------ 47335 47336SET DISTINCT (LET) 47337 47338Name: 47339 SET DISTINCT (LET) 47340 47341Type: 47342 Subcommand under LET 47343 47344Purpose: 47345 Extract the distinct elements of a set (with numeric elements). 47346 47347Description: 47348 The distinct elements of a set are those elements of the original 47349 set but with multiple occurrences ignored. The set of distinct 47350 elements of the 12-element set: 47351 1 3 5 7 9 1 4 9 16 1 8 27 47352 is the 9-element resultant set: 47353 1 3 5 7 9 4 16 8 27 47354 47355Syntax: 47356 LET <v2> = SET DISTINCT <v1> <SUBSET/EXCEPT/FOR qualification> 47357 where <v1> is the variable whose elements are the elements of the 47358 input set; 47359 <v2> is the variable where the resultant set is saved; 47360 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 47361 rarely used in this context. 47362 47363Examples: 47364 LET Y3 = SET DISTINCT Y1 47365 LET Y3 = SET DISTINCT Y1 SUBSET Y1 > 10 47366 LET Y3 = SET DISTINCT Y1 FOR I = 1 1 20 47367 47368Note: 47369 If the elements of a mathematical "set" are numbers (or can be 47370 translated into numbers-- always possible), then a DATAPLOT variable 47371 can be used to store the items of the mathematical "set". Thus if 47372 the analyst wanted to "store the set" with the 12 elements-- 47373 1 3 5 7 11 1 4 9 16 1 8 27 47374 he/she can do so by forming the variable Y via: 47375 SERIAL READ Y 47376 1 3 5 7 11 1 4 9 16 1 8 27 47377 END OF DATA 47378 or 47379 LET Y = DATA 1 3 5 7 11 1 4 9 16 1 8 27 47380 47381Default: 47382 None 47383 47384Synonyms: 47385 DISTINCT for SET DISTINCT (LET) 47386 SET ELEMENTS (LET) for SET DISTINCT (LET) 47387 47388Related Commands: 47389 SET CARDINALITY = Computes the number of elements in a set. 47390 SET UNION = Carries out a set union. 47391 SET INTERSECTION = Carries out a set intersection. 47392 SET COMPLEMENT = Carries out a set complement. 47393 SET CART PRODUCT = Carries out a set Cartesian product. 47394 PLOT = Plots data or functions. 47395 47396Applications: 47397 Mathematics 47398 47399Implementation Date: 47400 88/7 47401 47402Program: 47403 LET Y1 = DATA 1 3 5 7 11 1 4 9 16 1 8 27 47404 LET Y2 = SET DISTINCT Y1 47405 SET WRITE DECIMALS 0 47406 WRITE Y1 Y2 47407 47408-----SET INTERSECTION (LET)-------------------------------------- 47409 47410SET INTERSECTION (LET) 47411 47412Name: 47413 SET INTERSECTION (LET) 47414 47415Type: 47416 Subcommand under LET 47417 47418Purpose: 47419 Carry out the intersection of 2 sets (with numeric elements). 47420 47421Description: 47422 The intersection of 2 sets is the set containing the elements 47423 common to both sets. For example, the intersection of the 47424 5-element set: 47425 1 3 5 7 9 47426 and the 4-element set: 47427 1 4 9 16 47428 is the 2-element set: 47429 1 9 47430 47431Syntax: 47432 LET <v3> = SET INTERSECTION <v1> <v2> 47433 <SUBSET/EXCEPT/FOR qualification> 47434 where <v1> is the variable whose elements are the elements of the 47435 first set; 47436 <v2> is the variable whose elements are the elements of the 47437 second set; 47438 <v3> is the variable whose elements are the elements of the 47439 resultant set; 47440 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 47441 rarely used in this context. 47442 47443Examples: 47444 LET Y3 = SET INTERSECTION Y1 Y2 47445 LET Y3 = SET INTERSECTION Y1 Y2 SUBSET Y1 > 10 47446 LET Y3 = SET INTERSECTION Y1 Y2 FOR I = 1 1 3 47447 47448Note: 47449 If the elements of a mathematical "set" are numbers (or can be 47450 translated into numbers-- always possible), then a DATAPLOT variable 47451 can be used to store the items of the mathematical "set". Thus if 47452 the analyst wanted to "store the set" with the 12 elements-- 47453 1 3 5 7 11 1 4 9 16 1 8 27 47454 he/she can do so by forming the variable Y via: 47455 SERIAL READ Y 47456 1 3 5 7 11 1 4 9 16 1 8 27 47457 END OF DATA 47458 or 47459 LET Y = DATA 1 3 5 7 11 1 4 9 16 1 8 27 47460 47461Default: 47462 None 47463 47464Synonyms: 47465 None 47466 47467Related Commands: 47468 SET CARDINALITY = Computes the number of elements in a set. 47469 SET UNION = Carries out a set union. 47470 SET COMPLEMENT = Carries out a set complement. 47471 SET CART PRODUCT = Carries out a set Cartesian product. 47472 SET DISTINCT = Extracts the distinct elements of set. 47473 PLOT = Plots data or functions. 47474 COMPLEX SUBTRACTION = Carries out a complex subtraction. 47475 POLY SUBTRACTION = Carries out a polynomial subtraction. 47476 VECTOR SUBTRACTION = Carries out a vector subtraction. 47477 LOGICAL OR = Carries out a logical or. 47478 MATRIX SUBTRACTION = Carries out a matrix subtraction. 47479 47480Applications: 47481 Mathematics 47482 47483Implementation Date: 47484 93/9 47485 47486Program: 47487 . PURPOSE--DETERMINE THE SOLUTIONS OF A DIOPHANTINE EQUATION-- 47488 . FIND THE INTEGER SOLUTIONS (X AND Y) OF X**2 + 1 = 2*Y**4 47489 . 47490 . STEP 1--DEFINE THE FUNCTION OF INTEREST IN Y = F(X) FORM. 47491 . DEFINE A SEQUENCE OF X VALUES AND COMPUTE CORRESPONDING Y. 47492 LET FUNCTION F = ((X**2+1)/2)**0.25 47493 LET X = SEQUENCE 0 1 500 47494 LET Y = F 47495 . STEP 2--DETERMINE THE INTERSECTION OF THE Y VALUES 47496 . WITH THE (INTEGER) X VALUES. 47497 LET Y2 = SET INTERSECTION X Y 47498 PRINT Y2 47499 . STEP 3--IN ANOTHER FASHION, DETERMINE THE Y VALUES WHICH ARE 47500 . INTEGER AND THE (NECESSARILY INTEGER) X VALUES 47501 LET Y3 = FRACT(Y) 47502 LINE SOLID BLANK 47503 CHARACTER BLANK X 47504 PLOT Y X AND 47505 PLOT Y X SUBSET Y3 0 47506 47507-----SET UNION (LET)--------------------------------------------- 47508 47509SET UNION (LET) 47510 47511Name: 47512 SET UNION (LET) 47513 47514Type: 47515 Subcommand under LET 47516 47517Purpose: 47518 Carry out the union of 2 sets (with numeric elements). 47519 47520Description: 47521 The union of two sets is the set containing elements that are in 47522 either of the 2 original sets (but not necessarily both sets). 47523 Repeats are only counted once. For example, the union of the 47524 5-element set: 47525 1 3 5 7 9 47526 and the 4-element set: 47527 1 4 9 16 47528 is the 9-element set: 47529 1 3 5 7 9 1 4 9 16 47530 47531Syntax: 47532 LET <v3> = SET UNION <v1> <v2> <SUBSET/EXCEPT/FOR qualification> 47533 where <v1> is the variable whose elements are the elements of the 47534 first set; 47535 <v2> is the variable whose elements are the elements of the 47536 second set; 47537 <v3> is the variable whose elements are the elements of the 47538 resultant set; 47539 and where the <SUBSET/EXCEPT/FOR qualification> is optional and 47540 rarely used in this context. 47541 47542Examples: 47543 LET Y3 = SET UNION Y1 Y2 47544 LET Y3 = SET UNION Y1 Y2 SUBSET Y1 > 10 47545 LET Y3 = SET UNION Y1 Y2 FOR I = 1 1 3 47546 47547Note: 47548 If the elements of a mathematical "set" are numbers (or can be 47549 translated into numbers-- always possible), then a DATAPLOT variable 47550 can be used to store the items of the mathematical "set". Thus if 47551 the analyst wanted to "store the set" with the 12 elements-- 47552 1 3 5 7 11 1 4 9 16 1 8 27 47553 he/she can do so by forming the variable Y via: 47554 SERIAL READ Y 47555 1 3 5 7 11 1 4 9 16 1 8 27 47556 END OF DATA 47557 or 47558 LET Y = DATA 1 3 5 7 11 1 4 9 16 1 8 27 47559 47560Default: 47561 None 47562 47563Synonyms: 47564 None 47565 47566Related Commands: 47567 SET CARDINALITY = Computes the number of elements in a set. 47568 SET INTERSECTION = Carries out a set intersection. 47569 SET COMPLEMENT = Carries out a set complement. 47570 SET CART PRODUCT = Carries out a set Cartesian product. 47571 SET DISTINCT = Extracts the distinct elements of set. 47572 PLOT = Plots data or functions. 47573 COMPLEX ADDITION = Carries out a complex addition. 47574 POLY ADDITION = Carries out a polynomial addition. 47575 VECTOR ADDITION = Carries out a vector addition. 47576 LOGICAL AND = Carries out a logical and. 47577 MATRIX ADDITION = Carries out a matrix addition. 47578 47579Applications: 47580 Mathematics 47581 47582Implementation Date: 47583 87/10 47584 47585Program: 47586 LET Y1 = DATA 1 3 5 7 9 47587 LET Y2 = DATA 1 4 9 16 47588 LET Y3 = SET UNION Y1 Y2 47589 SET WRITE DECIMALS 0 47590 WRITE Y1 Y2 Y3 47591 47592-----SHANNON DIVERSITY INDEX (LET)------------------------------------- 47593 47594SHANNON DIVERSITY INDEX 47595 47596Name: 47597 SHANNON DIVERSITY INDEX (LET) 47598 47599Type: 47600 Let Subcommand 47601 47602Purpose: 47603 Compute the Shannon diversity index. 47604 47605Description: 47606 Diversity indices are statistics used to summarize the diversity of a 47607 population in which each member belongs to a unique group. For 47608 example, in ecology the groups are typically species. In ecology, 47609 species richness refers to number of species and species eveness 47610 refers to homogeneity of the species. That is, the more equal the 47611 proportions for each of the groups, the more homogeneous, or even, 47612 they are. Different fields of application may use different 47613 terminology for these concepts. 47614 47615 Given a vector of frequencies (counts), f(i), the Shannon diversity 47616 index is computed as 47617 47618 H = {n*LOG(n) - SUM[i=1 to k][f(i)*LOG(f(i))]}/n 47619 47620 with k and n denoting the number of groups and the total count, 47621 respectively. If f(i) = 0, then the f(i)*LOG(f(i)) term is set 47622 to 0. 47623 47624 The maximum value of the index is LOG(k). This value occurs when 47625 each group has the same frequency (i.e., maximum eveness). 47626 47627 The Shannon equitability index is simply the Shannon diversity 47628 index divided by the maximum diversity 47629 47630 E(H) = H/LOG(k) 47631 47632 This normalizes the Shannon diversity index to a value between 0 and 47633 1. Note that lower values indicate more diversity while higher 47634 values indicate less diversity. Specifically, an index value of 1 47635 means that all groups have the same frequency. Some analysts 47636 use 1 - E(H) so that higher values indicate higher diversity. 47637 Some analysts also use 1/E(H). 47638 47639 In some cases, you may have proportions rather than counts. In 47640 this case, the formula for the Shannon diversity index is 47641 47642 H = -SUM[i=1 to k][p(i)*LOG(p(i))] 47643 47644 with p(i) denoting the proportion in group k. As above, the Shannon 47645 equitability index is computed as 47646 47647 E(H) = H/LOG(k) 47648 47649 You may also have raw data. That is, each row of the response 47650 variable identifies which group that row belongs to. In this case, 47651 Dataplot will generate the frequency table and use the formulas 47652 above to compute the index. 47653 47654Syntax 1: 47655 LET <par> = SHANNON <DIVERSITY/EQUITABILITY> INDEX <y> 47656 <SUBSET/EXCEPT/FOR qualification> 47657 where <y> is the response variable; 47658 <DIVERSITY/EQUITABILITY> specifies whether the diversity or 47659 equitability index is computed; 47660 <par> is a parameter where the Shannon diversity index is saved; 47661 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 47662 47663 This syntax is used when the response variable is either a set 47664 of proportions or a set of counts. Dataplot sums the values in 47665 the response variable. If the sum equals 1, then it assumes the 47666 response variable contains proportions. Otherwise, it assumes 47667 the response variable contains frequencies. In either case, 47668 if negative values are encountered an error is reported. 47669 47670Syntax 2: 47671 LET <par> = RAW SHANNON <DIVERSITY/EQUITABILITY> INDEX <y> 47672 <SUBSET/EXCEPT/FOR qualification> 47673 where <y> is the response variable; 47674 <DIVERSITY/EQUITABILITY> specifies whether the diversity or 47675 equitability index is computed; 47676 <par> is a parameter where the Shannon diversity index is saved; 47677 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 47678 47679 This syntax is used when the response variable is a group-id 47680 variable. The group frequencies will be computed automatically. 47681 47682Examples: 47683 LET SDI = SHANNON DIVERSITY P 47684 LET SEI = SHANNON EQUITABILITY P 47685 47686Note: 47687 The Shannon diversity/equitability is used in a wide variety of 47688 fields. It may be referred to by a different name or have a 47689 slightly different formulation in various fields. 47690 47691Note: 47692 Dataplot statistics can be used in a number of commands. For 47693 details, enter 47694 47695 HELP STATISTICS 47696 47697 The SHANNON DIVERSITY INDEX command is not typically used in the context 47698 of these other commands. 47699 47700Default: 47701 None 47702 47703Synonyms: 47704 SHANNON EVENESS INDEX is a synonym for SHANNON EQUIABILIY INDEX 47705 47706Related Commands: 47707 SIMPSON DIVERSITY INDEX = Compute the Simpson diversity index. 47708 47709References: 47710 Weaver, W.; C.E. Shannon (1949), "The Mathematical Theory of 47711 Communication," Urbana, Illinois: University of Illinois. 47712 47713 Shannon, C.E. (July and October 1948), "A mathematical theory of 47714 communication," Bell System Technical Journal 27: 379–423 and 623–656. 47715 47716 Brani Vidakovic (2011), "Statistics for Bioengineering 47717 Sciences: With MATLAB and WinBUGS Support," Springer, p. 23. 47718 47719Applications: 47720 Data Management 47721 47722Implementation Date: 47723 2011/12 47724 47725Program: 47726 let p = data 0.25 0.15 0.40 0.20 47727 let nk = size p 47728 . 47729 let a = shannon diversity index p 47730 let b = shannon equitability index p 47731 . 47732 . Following example from page 23 of: 47733 . 47734 . Brani Vidakovic (2011), "Statistics for Bioengineering 47735 . Sciences: With MATLAB and WinBUGS Support", Springer. 47736 . 47737 read y x 47738 115 1 47739 108 1 47740 25 1 47741 6 1 47742 28 1 47743 25 1 47744 6 1 47745 1 1 47746 220 2 47747 134 2 47748 183 2 47749 39 2 47750 12 2 47751 6 2 47752 6 2 47753 12 2 47754 83 3 47755 104 3 47756 16 3 47757 8 3 47758 14 3 47759 18 3 47760 2 3 47761 1 3 47762 99 4 47763 94 4 47764 21 4 47765 8 4 47766 18 4 47767 18 4 47768 5 4 47769 2 4 47770 end of data 47771 . 47772 set write decimals 4 47773 tabulate shannon diversity index y x 47774 tabulate shannon equitability index y x 47775 . 47776 let yn = cross tabulate sum y x 47777 let pn = y/yn 47778 tabulate shannon diversity index pn x 47779 tabulate shannon equitability index pn x 47780 47781-----SHUFFLE GROUPS (LET)--------------------------------------- 47782 47783SHUFFLE GROUPS 47784 47785Name: 47786 SHUFFLE GROUPS (LET) 47787 47788Type: 47789 Let Subcommand 47790 47791Purpose: 47792 Given a response variable and a group-id variable, re-arrange the 47793 groups based on an index variable (the response variable is not 47794 randomized within the group). 47795 47796Description: 47797 The motivation for this command is to allow the rows (or columns) 47798 of a matrix or image to be randomly re-arranged. The randomization 47799 can be either with replacement or without replacement (this is 47800 determined by the index variable). 47801 47802 The size of the index variable should be equal to the number of groups 47803 in the group-id variable. Although this command was motivated by 47804 cases where the group sizes are equal, this is not required. If the 47805 group sizes are note equal, the output variable may not be the same 47806 length as the input variable. 47807 47808Syntax: 47809 LET <y2> = SHUFFLE GROUPS <y> <x> <index> 47810 <SUBSET/EXCEPT/FOR qualification> 47811 where <y> is a response variable; 47812 <x> is a group-id variable; 47813 <index> is a variable defining the order for the groups in the 47814 output variable; 47815 <y2> is a response variable containing the re-arranged groups; 47816 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 47817 47818 The response variable and group-id variable should have the same 47819 number of elements. The index variable must be the same size as the 47820 number of groups in the group-id variable. 47821 47822 If there are k groups in the group-id variable, then the values in 47823 the index variable should be between 1 and k. An error will be 47824 reported if they are not. 47825 47826Examples: 47827 LET Y2 = SHUFFLE GROUPS Y X XINDEX 47828 47829Default: 47830 None 47831 47832Synonyms: 47833 None 47834 47835Related Commands: 47836 RANDOM PERMUTATION = Generate a set of random permutations. 47837 MATRIX RENUMBER = Permute the rows and columns of a matrix. 47838 47839Applications: 47840 Data Manipulation 47841 47842Implementation Date: 47843 2014/07 47844 47845Program: 47846 . Step 1: Read the data 47847 . 47848 read x y 47849 1 1 47850 1 2 47851 1 3 47852 1 4 47853 1 5 47854 2 11 47855 2 12 47856 2 13 47857 2 14 47858 2 15 47859 3 21 47860 3 22 47861 3 23 47862 3 24 47863 3 25 47864 4 31 47865 4 32 47866 4 33 47867 4 34 47868 4 35 47869 end of data 47870 . 47871 . Step 2: Now reshuffle the groups 47872 . 47873 let iindex = data 3 1 4 2 47874 let yout = shuffle groups y x iindex 47875 . 47876 . Step 3: Print the results 47877 . 47878 set write decimals 0 47879 print x y yout 47880 47881-----SIMPSON DIVERSITY INDEX (LET)-------------------------------------- 47882 47883SIMPSON DIVERSITY INDEX 47884 47885Name: 47886 SIMPSON DIVERSITY INDEX (LET) 47887 47888Type: 47889 Let Subcommand 47890 47891Purpose: 47892 Compute the Simpson diversity index. 47893 47894Description: 47895 Diversity indices are statistics used to summarize the diversity of a 47896 population in which each member belongs to a unique group. For 47897 example, in ecology the groups are typically species. In ecology, 47898 species richness refers to number of species and species eveness 47899 refers to homogeneity of the species. That is, the more equal the 47900 proportions for each of the groups, the more homogeneous, or even, 47901 they are. Different fields of application may use different 47902 terminology for these concepts. 47903 47904 Given a vector of frequencies (counts), f(i), the Simpson diversity 47905 index is computed as 47906 47907 D = SUM[i=1 to k][(f(i)/n)**2] 47908 47909 with k and n denoting the number of groups and the total count, 47910 respectively. 47911 47912 This index has a value between 0 and 1. Lower values indicate more 47913 diversity while higher values indicate less diversity. 47914 47915 In some cases, you may have proportions rather than counts. In 47916 this case, the formula for the Simpson diversity index is 47917 47918 D = SUM[i=1 to k][p(i)**2] 47919 47920 You may also have raw data. That is, each row of the response 47921 variable identifies which group that row belongs to. In this case, 47922 Dataplot will generate the frequency table and use the formulas 47923 above to compute the index. 47924 47925Syntax 1: 47926 LET <par> = SIMPSON DIVERSITY INDEX <y> 47927 <SUBSET/EXCEPT/FOR qualification> 47928 where <y> is the response variable; 47929 <par> is a parameter where the Simpson diversity index is saved; 47930 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 47931 47932 This syntax is used when the response variable is either a set 47933 of proportions or a set of counts. Dataplot sums the values in 47934 the response variable. If the sum equals 1, then it assumes the 47935 response variable contains proportions. Otherwise, it assumes 47936 the response variable contains frequencies. In either case, 47937 if negative values are encountered an error is reported. 47938 47939Syntax 2: 47940 LET <par> = RAW SIMPSON DIVERSITY INDEX <y> 47941 <SUBSET/EXCEPT/FOR qualification> 47942 where <y> is the response variable; 47943 <par> is a parameter where the Simpson diversity index is saved; 47944 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 47945 47946 This syntax is used when the response variable is a group-id 47947 variable. The group frequencies will be computed automatically. 47948 47949Examples: 47950 LET SDI = SIMPSON DIVERSITY P 47951 47952Note: 47953 The Simpson diversity is used in a wide variety of fields. It may be 47954 referred to by a different name or have a slightly different 47955 formulation in various fields. 47956 47957Note: 47958 Dataplot statistics can be used in a number of commands. For 47959 details, enter 47960 47961 HELP STATISTICS 47962 47963 The SIMPSON DIVERSITY INDEX command is not typically used in the context of these 47964 other commands. 47965 47966Default: 47967 None 47968 47969Synonyms: 47970 None 47971 47972Related Commands: 47973 SHANNON DIVERSITY INDEX = Compute the Shannon diversity index. 47974 47975References: 47976 Edward H. Simpson (1949), "Measurement of diversity," Nature 163:688. 47977 47978Applications: 47979 Data Management 47980 47981Implementation Date: 47982 2011/12 47983 47984Program: 47985 let p = data 0.25 0.15 0.40 0.20 47986 let nk = size p 47987 . 47988 let a = simpson diversity index p 47989 . 47990 . Following example from page 23 of: 47991 . 47992 . Brani Vidakovic (2011), "Statistics for Bioengineering 47993 . Sciences: With MATLAB and WinBUGS Support", Springer. 47994 . 47995 read y x 47996 115 1 47997 108 1 47998 25 1 47999 6 1 48000 28 1 48001 25 1 48002 6 1 48003 1 1 48004 220 2 48005 134 2 48006 183 2 48007 39 2 48008 12 2 48009 6 2 48010 6 2 48011 12 2 48012 83 3 48013 104 3 48014 16 3 48015 8 3 48016 14 3 48017 18 3 48018 2 3 48019 1 3 48020 99 4 48021 94 4 48022 21 4 48023 8 4 48024 18 4 48025 18 4 48026 5 4 48027 2 4 48028 end of data 48029 . 48030 set write decimals 4 48031 tabulate simpson diversity index y x 48032 . 48033 let yn = cross tabulate sum y x 48034 let pn = y/yn 48035 tabulate simpson diversity index pn x 48036 48037-----SHORTEST HALF MIDMEAN (LET)----------------------------------------- 48038 48039SHORTEST HALF MIDMEAN 48040 48041Name: 48042 SHORTEST HALF MIDMEAN (LET) 48043 48044Type: 48045 Let Subcommand 48046 48047Purpose: 48048 Compute the shortest half midmean for a variable. 48049 48050Description: 48051 The midmean of a variable is the mean of the observations between 48052 the 25th and 75th percentiles. The shortest half midmean uses the 48053 most compact half of the data rather than the middle half. This is 48054 essentially an asymetric version of the midmean. Although it has 48055 rather low efficiency (lower than the median), it is less sensitive 48056 to asymmetrically distributed outliers. The formula for the shortest 48057 half midmean is 48058 48059 M = SUM[i=k to k+m][X(i)]/m for the minimum 48060 (X(k+m) - X(k)) 48061 48062 m = n/2 n odd 48063 m = INT(n/2) + 1 n even 48064 48065 48066Syntax 1: 48067 LET <par> = SHORTEST HALF MIDMEAN <y> 48068 <SUBSET/EXCEPT/FOR qualification> 48069 where <y> is the response variable; 48070 <par> is a parameter where the computed shortest half midmean 48071 is stored; 48072 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 48073 48074Syntax 2: 48075 LET <par> = DIFFERENCE OF SHORTEST HALF MIDMEAN <y1> <y2> 48076 <SUBSET/EXCEPT/FOR qualification> 48077 where <y1> is the first response variable; 48078 <y2> is the second response variable; 48079 <par> is a parameter where the computed difference of shortest 48080 half midmeans is stored; 48081 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 48082 48083Examples: 48084 LET A = SHORTEST HALF MIDMEAN Y1 48085 LET A = SHORTEST HALF MIDMEAN Y1 SUBSET TAG > 2 48086 48087 LET A = DIFFERENCE OF SHORTEST HALFMIDMEAN Y1 Y2 48088 48089Note: 48090 Dataplot statistics can be used in a number of commands. For 48091 details, enter 48092 48093 HELP STATISTICS 48094 48095Default: 48096 None 48097 48098Synonyms: 48099 SHORTEST HALF MID MEAN is a synonym for SHORTEST HALF MIDMEAN 48100 48101Related Commands: 48102 MIDMEAN = Compute the midmean. 48103 SHORTEST HALF MIDRANGE = Compute the shortest half midrange. 48104 MEAN = Compute the mean. 48105 MEDIAN = Compute the median. 48106 STANDARD DEVIATION = Compute the standard deviation. 48107 48108References: 48109 David Duewer (2008), "A Comparison of Location Estimators for 48110 Interlaboratory Data Contaminated with Value and Uncertainty 48111 Outliers", Accredited Quality Assurance, Vol. 13, pp. 193-216. 48112 48113 Andrews, Bickel, Hampel, Huber, Rogers, and Tukey (1972), "Robust 48114 Estimates of Location", Princeton University Press, Princeton. 48115 48116 Rousseeuw (1985), "Multivariate Estimation with High Breakdown 48117 Point", in Grossman, Pflug, Nincze, Wetrz (eds), "Mathematical 48118 Statistics and Applications", Reidel, Dordrecht, The Netherlands, 48119 pp. 283-297. 48120 48121Applications: 48122 Robust Data Analysis 48123 48124Implementation Date: 48125 2017/02 48126 2017/06: Added DIFFERENCE OF SHORTEST HALF MIDMEAN 48127 48128Program 1: 48129 SKIP 25 48130 READ LGN.DAT Y 48131 LET SHMM = SHORTEST HALF MIDMEAN Y 48132 48133Program 2: 48134 . Step 1: Create the data 48135 . 48136 skip 25 48137 read gear.dat y x 48138 skip 0 48139 . 48140 char X 48141 line blank 48142 y1label Shortest Half Midmean 48143 x1label Group 48144 x1tic mark offset 0.5 0.5 48145 label case asis 48146 title case asis 48147 title Shortest Half Midmean of GEAR.DAT 48148 title offset 2 48149 . 48150 set statistic plot reference line average 48151 shortest half midmean plot y x 48152 . 48153 set write decimals 5 48154 tabulate shortest half midmean y x 48155 48156Program 3: 48157 SKIP 25 48158 READ IRIS.DAT Y1 TO Y4 X 48159 . 48160 LET A = DIFFERENCE OF SHORTEST HALF MIDMEAN Y1 Y2 48161 SET WRITE DECIMALS 4 48162 TABULATE DIFFERENCE OF SHORTEST HALF MIDMEAN Y1 Y2 X 48163 . 48164 XTIC OFFSET 0.2 0.2 48165 X1LABEL GROUP ID 48166 Y1LABEL DIFFERENCE OF SHORTEST HALF MIDMEAN 48167 CHAR X 48168 LINE BLANK 48169 DIFFERENCE OF SHORTEST HALF MIDMEAN PLOT Y1 Y2 X 48170 CHAR X ALL 48171 LINE BLANK ALL 48172 BOOTSTRAP DIFFERENCE OF SHORTEST HALF MIDMEAN PLOT Y1 Y2 X 48173 48174-----SHORTEST HALF MIDRANGE (LET)----------------------------------------- 48175 48176SHORTEST HALF MIDRANGE 48177 48178Name: 48179 SHORTEST HALF MIDRANGE (LET) 48180 48181Type: 48182 Let Subcommand 48183 48184Purpose: 48185 Compute the shortest half midrange for a variable. 48186 48187Description: 48188 The midrange of a variable is the mean of the minimum and 48189 maximum values. The shortest half midrange is based on the 48190 most compact half of the data. This is essentially an asymetric 48191 version of the mean of the lower quartile and the upper quartile. 48192 Although it has rather low efficiency (lower than the median), it 48193 is less sensitive to asymmetrically distributed outliers. The 48194 formula for the shortest half midrange is 48195 48196 M = (X(k) + X(k+m))/2 for the minimum (X(k+m) - X(k)) 48197 48198 m = n/2 n odd 48199 m = INT(n/2) + 1 n even 48200 48201Syntax 1: 48202 LET <par> = SHORTEST HALF MIDRANGE <y> 48203 <SUBSET/EXCEPT/FOR qualification> 48204 where <y> is the response variable; 48205 <par> is a parameter where the computed shortest half midrange 48206 is stored; 48207 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 48208 48209Syntax 2: 48210 LET <par> = DIFFERENCE OF SHORTEST HALF MIDRANGE <y1> <y2> 48211 <SUBSET/EXCEPT/FOR qualification> 48212 where <y1> is the first response variable; 48213 <y2> is the second response variable; 48214 <par> is a parameter where the computed difference of shortest 48215 half midranges is stored; 48216 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 48217 48218Examples: 48219 LET A = SHORTEST HALF MIDRANGE Y1 48220 LET A = SHORTEST HALF MIDRANGE Y1 SUBSET TAG > 2 48221 48222 LET A = DIFFERENCE OF SHORTEST HALF MIDRANGE Y1 Y2 48223 48224Note: 48225 Dataplot statistics can be used in a number of commands. For 48226 details, enter 48227 48228 HELP STATISTICS 48229 48230Default: 48231 None 48232 48233Synonyms: 48234 SHORTEST HALF MID RANGE is a synonym for SHORTEST HALF MIDRANGE 48235 48236Related Commands: 48237 MIDRANGE = Compute the midrange. 48238 SHORTEST HALF MIDMEAN = Compute the shortest half midmean. 48239 MEAN = Compute the mean. 48240 MEDIAN = Compute the median. 48241 STANDARD DEVIATION = Compute the standard deviation. 48242 48243References: 48244 David Duewer (2008), "A Comparison of Location Estimators for 48245 Interlaboratory Data Contaminated with Value and Uncertainty 48246 Outliers", Accredited Quality Assurance, Vol. 13, pp. 193-216. 48247 48248 Andrews, Bickel, Hampel, Huber, Rogers, and Tukey (1972), "Robust 48249 Estimates of Location", Princeton University Press, Princeton. 48250 48251 Rousseeuw (1985), "Multivariate Estimation with High Breakdown 48252 Point", in Grossman, Pflug, Nincze, Wetrz (eds), "Mathematical 48253 Statistics and Applications", Reidel, Dordrecht, The Netherlands, 48254 pp. 283-297. 48255Applications: 48256 Robust Data Analysis 48257 48258Implementation Date: 48259 2017/02 48260 2017/06: Added DIFFERENCE OF SHORTEST HALF MIDRANGE 48261 48262Program 1: 48263 SKIP 25 48264 READ LGN.DAT Y 48265 LET SHMM = SHORTEST HALF MIDRANGE Y 48266 48267Program 2: 48268 . Step 1: Create the data 48269 . 48270 skip 25 48271 read gear.dat y x 48272 skip 0 48273 . 48274 char X 48275 line blank 48276 y1label Shortest Half Midrange 48277 x1label Group 48278 x1tic mark offset 0.5 0.5 48279 label case asis 48280 title case asis 48281 title Shortest Half Midrange of GEAR.DAT 48282 title offset 2 48283 . 48284 set statistic plot reference line average 48285 shortest half midrange plot y x 48286 . 48287 set write decimals 5 48288 tabulate shortest half midrange y x 48289 48290Program 3: 48291 SKIP 25 48292 READ IRIS.DAT Y1 TO Y4 X 48293 . 48294 LET A = DIFFERENCE OF SHORTEST HALF MIDRANGE Y1 Y2 48295 SET WRITE DECIMALS 4 48296 TABULATE DIFFERENCE OF SHORTEST HALF MIDRANGE Y1 Y2 X 48297 . 48298 XTIC OFFSET 0.2 0.2 48299 X1LABEL GROUP ID 48300 Y1LABEL DIFFERENCE OF SHORTEST HALF MIDRANGE 48301 CHAR X 48302 LINE BLANK 48303 DIFFERENCE OF SHORTEST HALF MIDRANGE PLOT Y1 Y2 X 48304 CHAR X ALL 48305 LINE BLANK ALL 48306 BOOTSTRAP DIFFERENCE OF SHORTEST HALF MIDRANGE PLOT Y1 Y2 X 48307 48308-----SHOW COLORS------------------------------------------------------- 48309 48310SHOW COLORS 48311 48312Name: 48313 SHOW COLORS 48314 48315Type: 48316 Output Devices Command 48317 48318Purpose: 48319 List the colors (and corresponding index numbers) available in 48320 DATAPLOT. 48321 48322Description: 48323 DATAPLOT allows colors to be specified by name or by an index 48324 number. All devices recognize the same color names and index 48325 numbers and there is a consistent mapping from an index number to 48326 a color (e.g., index 1 always goes to black, index 2 always goes to 48327 red). Devices that do not support a given color map it to the 48328 closest available color (closest is an arbitrary choice). 48329 Specifying a device on this command shows the mapping from the 48330 DATAPLOT color to the color that is actually used on the device. 48331 48332Syntax 1: 48333 SHOW COLORS 48334 48335 This syntax lists the color names and their associated index 48336 numbers recognized by DATAPLOT. 48337 48338Syntax 2: 48339 SHOW COLORS <device> 48340 where <device> is one of the following: 48341 CALCOMP 48342 CGM 48343 HP 2622 48344 HPGL 48345 PC 48346 POSTSCRIPT 48347 REGIS 48348 SUN 48349 TEKTRONIX 4115 48350 TEKTRONIX 4662 48351 TEKTRONIX 4027 48352 X11 48353 ZETA. 48354 48355 This syntax shows the mapping from the DATAPLOT color to the 48356 actual color used on the given device. 48357 48358Examples: 48359 SHOW COLORS 48360 SHOW COLORS POSTSCRIPT 48361 SHOW COLORS TEKTRONIX 4115 48362 48363Note: 48364 In previous versions, specifying a color by index would select 48365 the slot number on penplotter devices. This is no longer the case. 48366 The index number now goes to a specific color, which then goes 48367 to the slot assigned to that color. While this is less intuitive 48368 for plotters, it allows color names and indices to be treated 48369 consistently across devices (e.g., index 1 means BLACK on all 48370 devices). The PEN MAP command can still be used to assign a color 48371 to a specific slot number for plotter devices (HPGL, CALCOMP, and 48372 ZETA). 48373 48374Default: 48375 None 48376 48377Synonyms: 48378 None 48379 48380Related Commands: 48381 ZETA = Direct graphical output to a Zeta device. 48382 POSTSCRIPT = Direct graphical output to a Postscript 48383 device. 48384 TEKTRONIX = Direct graphical output to a Tektronix 48385 device. 48386 DEVICE = Specify certain actions for the graphics 48387 output. 48388 PEN MAP = Specify the pen slot to color mapping for 48389 certain plotter devices. 48390 48391Applications: 48392 Presentation Graphics 48393 48394Implementation Date: 48395 Pre-1987 48396 48397Program: 48398 XX 48399 48400-----SHOW READ FORMAT------------------------------------------- 48401 48402SHOW READ FORMAT 48403 48404Name: 48405 READ FORMAT (SET) 48406 48407Type: 48408 Support Command 48409 48410Purpose: 48411 Show the current setting for the read format. 48412 48413Description: 48414 Formatted reads provide faster performance at the expense of 48415 requiring a structured data file. 48416 48417Syntax: 48418 SHOW READ FORMAT 48419 48420Examples: 48421 SHOW READ FORMAT 48422 48423Default: 48424 Free-format (i.e., no format). 48425 48426Synonyms: 48427 None 48428 48429Related Commands: 48430 READ = Carries out a column-wise input of data. 48431 SERIAL READ = Carries out a line-wise input of data. 48432 SET READ FORMAT = Specifies a Fortran-like format for subsequent 48433 reads. 48434 48435Applications: 48436 Input/Output 48437 48438Implementation Date: 48439 88/3 48440 48441Program: 48442 XX 48443 48444-----SHIFT PLOT-------------------------------------- 48445 48446SHIFT PLOT 48447 48448Name: 48449 SHIFT PLOT 48450 48451Type: 48452 Graphics Command 48453 48454Purpose: 48455 Generates a shift plot. 48456 48457Description: 48458 The shift plot is a plot of 48459 48460 y(q) - x(q) versus x(q) 48461 48462 with y(q) and x(q) denoting the qth quantiles of y and x, 48463 respectively. Although this plot can be generated for any 48464 pair of variables, the primary usage of this plot is for the 48465 case where x is a control group and y is an experimental 48466 method. Alternatively, x could represent an "old" method 48467 while y represents a "new" method. The plot measures how much 48468 the control group must be shifted so that it is comparable to 48469 the expermimental method (relative to the quantiles). 48470 48471 The quantiles of a distribution are the distribution's "percent 48472 points" (e.g., the 0.5 quantile = 50% point = median). 48473 48474 The plot consists of the following: 48475 Vertical axis = difference in the estimated quantiles 48476 between data set 1 and data set 2; 48477 Horizontal axis = estimated quantiles from data set 2. 48478 48479 The shift plot is a variation of the quantile-quantile plot 48480 and the Tukey mean-difference plot. 48481 48482Syntax 1: 48483 SHIFT PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 48484 where <y> is the response variable for the experimental group; 48485 <x> is the response variable for the control group; 48486 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 48487 48488 With this syntax, the quantiles correspond to the data points 48489 of the <x> variable. 48490 48491Syntax 2: 48492 SHIFT PLOT <y> <x> <q> <SUBSET/EXCEPT/FOR qualification> 48493 where <y> is the response variable for the experimental group; 48494 <x> is the response variable for the control group; 48495 <q> is a variable containing values between 0 and 1 that 48496 specifies the desired quantiles to plot; 48497 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 48498 48499 With this syntax, you explicitly give the desired quantiles. 48500 48501Examples: 48502 SHIFT PLOT Y X 48503 SHIFT PLOT Y X SUBSET X > 1 48504 SHIFT PLOT Y X XQ 48505 SHIFT PLOT Y X XQ SUBSET X > 1 48506 48507Default: 48508 None 48509 48510Synonyms: 48511 None 48512 48513Related Commands: 48514 CHARACTERS = Sets the type for plot characters. 48515 LINES = Sets the type for plot lines. 48516 QUANTILE-QUANTILE PLOT = Generates a q-q plot. 48517 TUKEY MEAN-DIFFERENCE PLOT = Generates a Tukey mean-difference 48518 plot. 48519 BIHISTOGRAM = Generates a bihistogram. 48520 T-TEST = Carries out a 2-sample t test. 48521 F-TEST = Carries out a 2-sample F test. 48522 48523Reference: 48524 "Introduction to Robust Estimation and Hypothesis Testing", 48525 Rand R. Wilcox, Academic Press, 1997. 48526 48527Applications: 48528 Exploratory Data Analysis 48529 48530Implementation Date: 48531 2003/2 48532 48533Program: 48534 SKIP 25 48535 READ AUTO83B.DAT Y1 Y2 48536 . 48537 DELETE Y2 SUBSET Y2 < 0 48538 LABEL CASE ASIS 48539 Y1LABEL Difference between Y1 and Y2 Quantiles 48540 X1LABEL Quantiles for Y1 48541 CHARACTER X 48542 LINE BLANK 48543 TIC OFFSET 0.3 0.3 48544 TIC OFFSET UNITS DATA 48545 SHIFT PLOT Y2 Y1 48546 48547-----SHIFT (LET)------------------------------------- 48548 48549SHIFT 48550 48551Name: 48552 SHIFT (LET) 48553 48554Type: 48555 Let Subcommand 48556 48557Purpose: 48558 Shift the contents of a variable either up or down. 48559 48560Description: 48561 It is sometimes convenient to move the elements of a 48562 variable either up or down. 48563 48564 For example, to shift the contents of the variable Y that 48565 contains 5 elements up (or right) by one element into the 48566 output vector Y2, we mean 48567 48568 Y(1) => Y2(2) 48569 Y(2) => Y2(3) 48570 Y(3) => Y2(4) 48571 Y(4) => Y2(5) 48572 Y(5) => Y2(6) 48573 48574 To shift the contents of Y down (or left) by one element, we mean 48575 48576 Y(2) => Y2(1) 48577 Y(3) => Y2(2) 48578 Y(4) => Y2(3) 48579 Y(5) => Y2(4) 48580 48581 One question is how do we define the end-point values for Y2 48582 (i.e., Y2(1) for the up shift and Y2(5) for the down shift)? 48583 48584 Dataplot handles this by first doing 48585 48586 Y2 = Y 48587 48588 for all elements. So for the up shift, Y2(1) = Y1(1) and 48589 for the down shift Y2(5) = Y(5). 48590 48591Syntax: 48592 LET <y> = SHIFT <x> <nshift> 48593 where <x> is a response variable; 48594 <nshift> is a number or parameter that specifies how 48595 how many elements to shift; 48596 and <y> is a variable that contains the shifted values. 48597 48598 The sign of NSHIFT specifies the direction. If NSHIFT is 48599 negative, the shift is down (or left) and if NSHIFT is positive 48600 the shift is up (or right). If NSHIFT is zero, then Y = X. 48601 48602Examples: 48603 LET Y = SHIFT X NSHIFT 48604 48605Note: 48606 If you want to handle the end points differently, then 48607 this can usually be accomplished with FOR clause. For 48608 example, the set the end points to zero, do something like 48609 48610 LET NSHIFT =5 48611 LET AVAL = 0 48612 LET Y2 = SHIFT Y NSHIFT 48613 LET Y2 = AVAL FOR I = 1 1 NSHIFT 48614 48615Default: 48616 None 48617 48618Synonyms: 48619 None 48620 48621Related Commands: 48622 CIRCULAR SHIFT = Perform a circular shift of a variable. 48623 SCATTER = Save data from a variable to specified 48624 rows of another variable based on an 48625 index variable. 48626 SEQUENCE = Generate a patterned sequence of values. 48627 SORT = Sort a column of numbers. 48628 RANK = Rank a column of numbers. 48629 CODE = Code a column of numbers. 48630 SUBSET = Specifies a subset to be included in a plot, 48631 analysis, or LET command. 48632 RETAIN = Retain specified rows or a subset of a 48633 variable. 48634 48635Applications: 48636 Data Transformation 48637 48638Implementation Date: 48639 2009/2 48640 48641Program: 48642 let y = normal random numbers for i = 1 1 10 48643 let nshift = 3 48644 let y2 = shift y nshift 48645 let nshift = -3 48646 let y3 = shift y nshift 48647 set write decimals 3 48648 print y y2 y3 48649 48650-----SIEVE PLOT (LET)-------------------------------- 48651 48652SIEVE PLOT 48653 48654Name: 48655 SIEVE PLOT (LET) 48656 48657Type: 48658 Graphics Command 48659 48660Purpose: 48661 Generate a sieve plot for a two-way contingency table. 48662 48663Description: 48664 Given two discrete variables where variable one has r 48665 possible values and variable two has c possible values, 48666 we can generate a cross-tabulation of these two variables. 48667 This results in a two-way, or RxC contingency table. 48668 48669 We can define the following values for the contingency 48670 table: 48671 48672 r = the number of rows in the contingency table 48673 c = the number of columns in the contingency table 48674 n(ij) = the observed frequency of the ith row and jth column 48675 m(ij) = the expected frequency of the ith row and jth column 48676 n(i+) = the observed frequency for the ith row 48677 n(+j) = the observed frequency for the jth row 48678 n(++) = the total sample size 48679 48680 When the two variables are independent, then the expected 48681 frequency is: 48682 48683 m(ij) = n(i+)*n(+j)/n(++) 48684 48685 In a sieve plot, each m(ij) is represented by a rectangle. 48686 The width of the rectangle is proportional to the total 48687 frequency in each column, n(+j), and the height is 48688 proportional to the total frequency in each row, n(i+). 48689 The area of the rectangle is then proportional to m(ij). 48690 48691 Each rectangle is then cross-ruled based on the observed 48692 frequency. The deviations from independence are reflected 48693 in the density of the shading. Denser shading indicates 48694 the observed frequency is greater than expected and 48695 sparse shading indicates the observed frequency is less 48696 than expected. As an additional cue, positive and negative 48697 departures from independence can be coded with different 48698 colors. 48699 48700Syntax 1: 48701 SIEVE PLOT <y1> <y2> <SUBSET/EXCEPT/FOR qualification> 48702 where <y1> is the first response variable; 48703 <y2> is the second response variable; 48704 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 48705 48706 This syntax is used for the case where you have raw data (i.e., 48707 the data has not yet been cross tabulated into a two-way table). 48708 48709Syntax 2: 48710 SIEVE PLOT <m> <SUBSET/EXCEPT/FOR qualification> 48711 where <m> is a matrix containing the two-way table; 48712 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 48713 48714 This syntax is used for the case where we the data have already 48715 been cross-tabulated into a two-way contingency table. 48716 48717Syntax 3: 48718 SIEVE PLOT <n11> <n12> <n21> <n22> 48719 where <n11> is a parameter containing the value for row 1, 48720 column 1 of a 2x2 table; 48721 <n12> is a parameter containing the value for row 1, 48722 column 2 of a 2x2 table; 48723 <n21> is a parameter containing the value for row 2, 48724 column 1 of a 2x2 table; 48725 <n22> is a parameter containing the value for row 2, 48726 column 2 of a 2x2 table. 48727 48728 This syntax is used for the special case where you have a 48729 2x2 table. In this case, you can enter the 4 values directly, 48730 although you do need to be careful that the parameters are 48731 entered in the order expected above. 48732 48733Examples: 48734 SIEVE PLOT Y1 Y2 48735 SIEVE PLOT M 48736 SIEVE PLOT N11 N12 N21 N22 48737 48738Note: 48739 The LINE and LINE COLOR commands can be used to set 48740 the attributes for the sieve plot. 48741 48742 Setting 1 = the line style and color for the frame 48743 of the rectangles 48744 Setting 2 = the line style and color for the cross-ruled 48745 lines when the observed frequency is greater 48746 than the expected frequency 48747 48748 Setting 3 = the line style and color for the cross-ruled 48749 lines when the observed frequency is less 48750 than the expected frequency 48751 48752 Although the program example below uses the TIC MARK LABEL 48753 commands to generate row and column labels, you may need 48754 to use the LEGEND or TEXT command to obtain more accurately 48755 centered labels. 48756 48757Default: 48758 None 48759 48760Synonyms: 48761 None 48762 48763Related Commands: 48764 ASSOCIATION PLOT = Generate an association plot. 48765 ROSE PLOT = Generate a Rose plot. 48766 BINARY TABULATION PLOT = Generate a binary tabulation plot. 48767 ROC CURVE = Generate a ROC curve. 48768 CHI-SQUARE INDEPENDENCE TEST = Perform a chi-square test for 48769 independence. 48770 ODDS RATIO INDEPENDENCE TEST = Perform a log(odds ratio) test for 48771 FISHER EXACT TEST = Perform Fisher's exact test. 48772 48773References: 48774 Friendly (2000), "Visualizing Categorical Data", SAS Institute 48775 Inc., pp. 85-89. 48776 48777 Riedwyl and Schupbach (1994), "Parquet Diagram to Plot 48778 Contingency Tables". In Faulbaum, editor, "Softstat '93: 48779 Advances In Statistical Software", pp. 293-299, 48780 Gustav Fischer, New York. 48781 48782Applications: 48783 Graphical Analysis of Categorical Data 48784 48785Implementation Date: 48786 2007/6 48787 48788Program: 48789 . Hair and Eye Color Data from page 61 of Friendly 48790 read matrix m 48791 5 29 14 16 48792 15 54 14 10 48793 20 84 17 94 48794 68 119 26 7 48795 end of data 48796 . 48797 label case asis 48798 tic mark label case asis 48799 title case asis 48800 title offset 2 48801 . 48802 x3label 48803 title Sieve Plot 48804 y1label displacement 12 48805 y1label Eye Color 48806 x1label Hair Color 48807 tic offset units data 48808 xlimits 1 4 48809 major xtic mark number 4 48810 minor xtic mark number 0 48811 xtic mark offset 0.5 0.5 48812 x1tic mark label format alpha 48813 x1tic mark label content Black Brown Red Blond 48814 ylimits 1 4 48815 major ytic mark number 4 48816 minor ytic mark number 0 48817 ytic mark offset 0.5 0.5 48818 y1tic mark label format alpha 48819 y1tic mark label content Green Hazel Blue Brown 48820 y1tic mark label justification right 48821 . 48822 line solid dash dash 48823 line color black blue green 48824 . 48825 sieve plot m 48826 48827-----SIGN (LET)-------------------------------- 48828 48829SIGN 48830 48831Name: 48832 SIGN (LET) 48833 48834Type: 48835 Library Function 48836 48837Purpose: 48838 Compute the sign of a number and assign a -1 to negative numbers 48839 and a +1 to positive numbers (zero is treated as a positive 48840 number). 48841 48842Syntax: 48843 LET <y2> = SIGN(<y1>,<n>) <SUBSET/EXCEPT/FOR qualification> 48844 where <y1> is a variable or a parameter containing decimal 48845 number(s); 48846 <y2> is a variable or a parameter (depending on what <y1> is) 48847 where the computed sign values are stored; 48848 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 48849 48850Examples: 48851 LET A = SIGN(14.2835) 48852 LET A = SIGN(A1) 48853 LET X2 = SIGN(X1) 48854 LET X2 = SIGN(X1-4) 48855 48856Note: 48857 Library functions are distinguished from let subcommands 48858 in the following ways. 48859 1) Functions enclose the input value in parenthesis. Let 48860 subcommands use spaces. 48861 2) Functions can accept (and return) either parameters 48862 (i.e., single values) or variables (i.e., an array of 48863 values) while let subcommands are specific in which they 48864 accept as input and what they return as output. 48865 3) Functions can accept expressions while let subcommands 48866 do not. For example, the following is legal: 48867 LET Y2 = ABS(Y1-INT(Y1)) 48868 For let subcommands, you typically have to do something 48869 like the following: 48870 LET YTEMP = Y**2 + 8 48871 LET A = SUM YTEMP 48872 48873Default: 48874 None 48875 48876Synonyms: 48877 None 48878 48879Related Commands: 48880 INT = Compute the integer portion of number. 48881 FRACT = Compute the fractional portion of number. 48882 ROUND = Round a number to a specified number of decimal places. 48883 MSD = Compute the most significant digit of a number. 48884 48885Applications: 48886 XX 48887 48888Implementation Date: 48889 Pre-1987 48890 48891Program: 48892 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 48893 LET Y2 = SIGN(Y1) 48894 PRINT Y1 Y2 48895 48896-----SIGNAL TO NOISE RATIO (LET)------------------------------ 48897 48898SIGNAL TO NOISE RATIO 48899 48900Name: 48901 SIGNAL TO NOISE RATIO (LET) 48902 48903Type: 48904 Let Subcommand 48905 48906Purpose: 48907 Compute the signal to noise ratio of a variable. 48908 48909Description: 48910 The sample signal to noise ratio (SNR) is defined as the ratio of 48911 the mean to the standard deviation: 48912 48913 SNR = xbar/s 48914 48915 where s is the sample standard deviation and xbar is the sample 48916 mean. 48917 48918 This is the reciprocal of the coefficient of variation: 48919 48920 cv = s/xbar 48921 48922 That is, it shows the variability, as defined by the standard 48923 deviation, relative to the mean. 48924 48925 This definition of signal to noise ratio should typically only be used 48926 for data measured on a ratio scale. That is, the data should be 48927 continuous and have a meaningful zero. Measurement data in the 48928 physical sciences and engineering are often on a ratio scale. 48929 As an example, temperatures measured on a Kelvin scale are on a 48930 ratio scale while temperaturs measured on a Celcius or Farenheit 48931 scale are interval scales rather than ratio scales. Given a set 48932 of temperature measurements, the signal to noise ratio on the 48933 Celcius scale will be different than the signal to noise ratio 48934 on the Farenheit scale. 48935 48936 Note that this is only one specific definition of the signal to noise 48937 ratio. There are numerous other definitions in common usage that are 48938 not described here. 48939 48940Syntax 1: 48941 LET <par> = SIGNAL TO NOISE RATIO <y> 48942 <SUBSET/EXCEPT/FOR qualification> 48943 where <y> is a response variable; 48944 <par> is a parameter where the signal to noise ratio value is 48945 saved; 48946 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 48947 48948Syntax 2: 48949 LET <par> = DIFFERENCE OF SIGNAL TO NOISE RATIO <y1> <y2> 48950 <SUBSET/EXCEPT/FOR qualification> 48951 where <y1> is the first response variable; 48952 <y2> is the second response variable; 48953 <par> is a parameter where the difference of the 48954 signal to noise ratios is saved; 48955 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 48956 48957Examples: 48958 LET SNR = SIGNAL TO NOISE RATIO Y1 48959 LET SNR = SIGNAL TO NOISE RATIO Y1 SUBSET TAG > 2 48960 48961 LET SNRDIFF = DIFFERENCE OF SIGNAL TO NOISE RATIO Y1 Y2 48962 48963Note: 48964 Dataplot statistics can be used in a number of commands. For 48965 details, enter 48966 48967 HELP STATISTICS 48968 48969Default: 48970 None 48971 48972Synonyms: 48973 SNR is a synonym for SIGNAL TO NOISE 48974 48975Related Commands: 48976 COEFFICIENT OF VARIATION = Compute the coefficient of variation of 48977 a variable. 48978 RELATIVE VARIANCE = Compute the relative variance of a 48979 variable. 48980 COEF OF VARI CONF LIMI = Compute confidence limits for the 48981 coefficient of variation. 48982 COEFFICIENT OF DISPERSION = Compute the coefficient of 48983 dispersion of a variable. 48984 MEAN = Compute the mean of a variable. 48985 STANDARD DEVIATION = Compute the standard deviation of a 48986 variable. 48987 48988Applications: 48989 Data Analysis 48990 48991Implementation Date: 48992 2017/01 48993 2017/03: Added DIFFERENCE OF SIGNAL TO NOISE 48994 48995Program 1: 48996 . Step 1: Create the data 48997 . 48998 skip 25 48999 read zarr13.dat y 49000 skip 0 49001 set write decimals 6 49002 . 49003 let snr = signal to noise ratio y 49004 let snr = round(snr,3) 49005 . 49006 . Step 2: Define plot control 49007 . 49008 title case asis 49009 title offset 2 49010 label case asis 49011 . 49012 y1label Signal to Noise Ratio 49013 x1label Bootstrap Sample 49014 title Bootstrap of Signal to Noise Ratio for ZARR13.DAT 49015 . 49016 bootstrap samples 2000 49017 bootstrap snr plot y 49018 . 49019 let bmean = round(bmean,3) 49020 let bsd = round(bsd,3) 49021 let b025 = round(b025,3) 49022 let b975 = round(b975,3) 49023 justification center 49024 move 50 6 49025 text Sample SNR: ^snr, Mean of Bootstrap Samples: ^bmean, SD of Bootstrap Samples: ^bsd 49026 move 50 3.5 49027 text 2.5 Percentile: ^B025, 97.5 Percentile: ^B975 49028 49029Program 2: 49030 . Step 1: Create the data 49031 . 49032 skip 25 49033 read gear.dat y x 49034 skip 0 49035 set write decimals 6 49036 . 49037 . Step 2: Define plot control 49038 . 49039 title case asis 49040 title offset 2 49041 label case asis 49042 . 49043 y1label Signal to Noise Ratio 49044 x1label Group 49045 title Signal to Noise Ratio for GEAR.DAT 49046 let ngroup = unique x 49047 xlimits 1 ngroup 49048 major x1tic mark number ngroup 49049 minor x1tic mark number 0 49050 tic mark offset units data 49051 x1tic mark offset 0.5 0.5 49052 y1tic mark offset 5 0 49053 . 49054 character X 49055 line blank 49056 . 49057 set statistic plot reference line average 49058 snr plot y x 49059 . 49060 tabulate snr y x 49061 49062Program 3: 49063 SKIP 25 49064 READ IRIS.DAT Y1 TO Y4 X 49065 . 49066 LET A = DIFFERENCE OF SNR Y1 Y2 49067 SET WRITE DECIMALS 4 49068 TABULATE DIFFERENCE OF SNR Y1 Y2 X 49069 . 49070 XTIC OFFSET 0.2 0.2 49071 X1LABEL GROUP ID 49072 Y1LABEL DIFFERENCE OF SNR 49073 CHAR X 49074 LINE BLANK 49075 DIFFERENCE OF SNR PLOT Y1 Y2 X 49076 CHAR X ALL 49077 LINE BLANK ALL 49078 BOOTSTRAP DIFFERENCE OF SNR PLOT Y1 Y2 X 49079 49080-----SIGN TEST-------------------------------------- 49081 49082SIGN TEST 49083 49084Name: 49085 SIGN TEST 49086 49087Type: 49088 Analysis Command 49089 49090Purpose: 49091 Perform a one sample or a paired two sample sign test. 49092 49093Description: 49094 The t-test is the standard test for testing that the 49095 difference between population means for two paired 49096 samples are equal. If the populations are non-normal, 49097 particularly for small samples, then the t-test may not 49098 be valid. The sign test is an alternative that can be 49099 applied when distributional assumptions are suspect. 49100 However, it is not as powerful as the t-test when the 49101 distributional assumptions are in fact valid. It can 49102 also be applied in the case where there is no quantitative 49103 scale, but it is possible to order the data (i.e., an 49104 49105 To form the sign test, compute d(i) = X(i) - Y(i) where 49106 X and Y are the two samples. Count the number of times 49107 d(i) is positive, R+, and the number of times it is 49108 negative, R-. If the samples have equal means and the 49109 populations are symmetric, then R+ and R- should be 49110 similar. If there are too many positives (R+) or 49111 negatives (R-), then we reject the hypothesis of 49112 equality. Ties are excluded from the analysis. Since 49113 there are only two choices (+ or -) for d(i), the test 49114 statistic for the sign test follows a binomial distribution 49115 with p=0.5. 49116 49117 Note that the binonial distribution is discrete, so the 49118 significane level will typically not be exact. 49119 49120 More formally, the hypothesis test is defined as follows. 49121 49122 H0: u1 = u2 49123 Ha: u1 <> u2 49124 Test Statistic: S- = BINCDF(R-,0.5,N) 49125 S+ = BINCDF(R+,0.5,N) 49126 where BINCDF is the cumulative distribution 49127 for the binomial distribution, R- is the 49128 number of minus signs (i.e., d(i) < 0), R+ 49129 is the number of plus signs (i.e., d(i) > 0), 49130 and N is the sample size excluding ties 49131 between the samples. 49132 Alpha: Typically set to .05. Due to the discreteness of the 49133 binomial distribution, the actual significance level 49134 will not in most cases be exact. 49135 Critical Region: 49136 S+ < alpha: one sided test: MU1 < MU2 49137 S- < alpha: one sided test: MU1 > MU2 49138 alpha/2 < S+ < 1 - alpha/2: two sided test: MU1 = MU2 49139 Conclusion: Reject null hypothesis if test statistic is 49140 in critical region 49141 49142 Although the above discussion was in terms of a paired two 49143 sample test, it can easily be adapted to the following 49144 additional cases: 49145 49146 1) For the one sample case that the population mean is 49147 equal to a value d0, simply compute d(i) = x(i) - d0 49148 and calculate R+ and R- based on d(i). 49149 49150 2) For the paired two sample case where we want to test 49151 that the difference between the two population means 49152 is equal to d0, compute d(i) = x(i) - y(i) - d0 and 49153 calculate R+ and R- based on d(i). 49154 49155Syntax 1: 49156 <LOWER TAILED/UPPER TAILED> SIGN TEST <y1> <mu> 49157 <SUBSET/EXCEPT/FOR qualification> 49158 where <LOWER TAILED/UPPER TAILED> is an optional keyword that 49159 specifies either a lower tailed or an upper tailed 49160 test; 49161 <y1> is a response variable; 49162 <mu> is an optional number or parameter that is the 49163 hypothesized mean value; 49164 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 49165 49166 This syntax implements the one sample sign test. If <mu> is 49167 omitted, it will be assumed to be zero. 49168 49169 If neither LOWER TAILED or UPPER TAILED is specified, the 49170 sign test will return the results for the two-tailed case, 49171 the lower tailed case, and the upper tailed case. If LOWER 49172 TAILED is specified, then only the results for the lower tailed 49173 case will be printed. If UPPER TAILED is specified, then only 49174 the results for the upper tailed case will be printed. 49175 49176Syntax 2: 49177 <LOWER TAILED/UPPER TAILED> SIGN TEST <y1> <y2> 49178 <SUBSET/EXCEPT/FOR qualification> 49179 where <LOWER TAILED/UPPER TAILED> is an optional keyword that 49180 specifies either a lower tailed or an upper tailed 49181 test; 49182 <y1> is the first response variable; 49183 <y2> is the second response variable; 49184 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 49185 49186 This syntax implements the two sample paired sign test where 49187 the hypothesized difference between the population means for 49188 the two samples is zero. 49189 49190Syntax 3: 49191 SIGN TEST <y1> <y2> <mu> <SUBSET/EXCEPT/FOR qualification> 49192 where <LOWER TAILED/UPPER TAILED> is an optional keyword that 49193 specifies either a lower tailed or an upper tailed 49194 test; 49195 <y1> is the first response variable; 49196 <y2> is the second response variable; 49197 <mu> is a number or parameter that is the hypothesized 49198 difference between the means of the two samples; 49199 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 49200 49201 This syntax implements the two sample paired sign test where 49202 the hypothesized difference between the population means for 49203 the two samples is not equal to zero. 49204 49205Syntax 4: 49206 <LOWER TAILED/UPPER TAILED> SIGN TEST <y1> ... <yk> 49207 <SUBSET/EXCEPT/FOR qualification> 49208 where <LOWER TAILED/UPPER TAILED> is an optional keyword that 49209 specifies either a lower tailed or an upper tailed 49210 test; 49211 <y1> ... <yk> is a list of 1 to 30 response variables; 49212 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 49213 49214 This syntax will implement all the pairwise sign tests for 49215 the listed response variables. For example, 49216 49217 SIGN TEST Y1 TO Y4 49218 49219 is equivalent to 49220 49221 SIGN TEST Y1 Y2 49222 SIGN TEST Y1 Y3 49223 SIGN TEST Y1 Y4 49224 SIGN TEST Y2 Y3 49225 SIGN TEST Y2 Y4 49226 SIGN TEST Y3 Y4 49227 49228 If either the first argument or the last argument is a parameter, 49229 this will be interpreted as the hypothesized mean value. 49230 49231Examples: 49232 SIGN TEST Y1 0 49233 SIGN TEST Y1 Y2 49234 SIGN TEST Y1 Y2 MU 49235 SIGN TEST Y1 Y2 SUBSET TAG > 2 49236 49237Note: 49238 The SIGN TEST will accept matrix arguments. Since this is a 49239 paired test, the total number of elements for each variable 49240 or matrix argument must be the same. Matrices are parsed in 49241 column order when generating the test. 49242 49243Note: 49244 Dataplot saves the following internal parameters after a 49245 sign test: 49246 49247 STATVAL = the value of the test statistic 49248 STATCDF = the CDF of the test statistic 49249 PVALUE = the p-value for the two-sided test 49250 PVALUELT = the p-value for the lower tailed test 49251 PVALUEUT = the p-value for the upper tailed test 49252 CUTLOW50 = the 50% lower tailed critical value 49253 CUTUPP50 = the 50% upper tailed critical value 49254 CUTLOW80 = the 80% lower tailed critical value 49255 CUTUPP80 = the 80% upper tailed critical value 49256 CUTLOW90 = the 90% lower tailed critical value 49257 CUTUPP90 = the 90% upper tailed critical value 49258 CUTLOW95 = the 95% lower tailed critical value 49259 CUTUPP95 = the 95% upper tailed critical value 49260 CUTLOW99 = the 99% lower tailed critical value 49261 CUTUPP99 = the 99% upper tailed critical value 49262 CUTLO999 = the 99.9% lower tailed critical value 49263 CUTUP999 = the 99,9% upper tailed critical value 49264 49265Note: 49266 The following statistics are also supported: 49267 49268 LET A = ONE SAMPLE SIGN TEST Y 49269 LET A = ONE SAMPLE SIGN TEST CDF Y 49270 LET A = ONE SAMPLE SIGN TEST PVALUE Y 49271 LET A = ONE SAMPLE SIGN TEST LOWER TAIL PVALUE Y 49272 LET A = ONE SAMPLE SIGN TEST UPPER TAIL PVALUE Y 49273 49274 LET A = TWO SAMPLE SIGN TEST Y1 Y2 49275 LET A = TWO SAMPLE SIGN TEST CDF Y1 Y2 49276 LET A = TWO SAMPLE SIGN TEST PVALUE Y1 Y2 49277 LET A = TWO SAMPLE SIGN TEST LOWER TAIL PVALUE Y1 Y2 49278 LET A = TWO SAMPLE SIGN TEST UPPER TAIL PVALUE Y1 Y2 49279 49280 In addition to the above LET command, built-in statistics are 49281 supported for about 20+ different commands (enter HELP STATISTICS 49282 for details). 49283 49284Default: 49285 None 49286 49287Synonyms: 49288 None 49289 49290Related Commands: 49291 T-TEST = Compute a t-test. 49292 SIGNED RANK TEST = Compute a signed rank test. 49293 CHI-SQUARED 2 SAMPLE TEST = Compute a two sample chi-square 49294 test. 49295 BIHISTOGRAM = Generates a bihistogram. 49296 QUANTILE-QUANTILE PLOT = Generate a quantile-quantile plot. 49297 BOX PLOT = Generates a box plot. 49298 49299Reference: 49300 Conover (1999), "Practical Non-Parametric Statistics", Third Edition, 49301 Wiley, pp. 157-165. 49302 49303 Snedecor and Cochran (1989), "Statistical Methods", Eigth Edition, 49304 Iowa State University Press, pp. 138-140. 49305 49306Applications: 49307 Confirmatory Data Analysis 49308 49309Implementation Date: 49310 1999/5 49311 2000/8: bug fix for 2-sided interval. Was actually calculating a 49312 90% interval rather than a 95% interval. 49313 2011/4: support for <LOWER TAILED/UPPER TAILED> option 49314 2011/4: support for Syntax 4 case, support for matrix arguments, 49315 support for TO syntax 49316 49317Program: 49318 SKIP 25 49319 READ NATR332.DAT Y1 Y2 49320 SIGN TEST Y1 Y2 49321 49322-----SIGNED RANK TEST-------------------------------------- 49323 49324SIGNED RANK TEST 49325 49326Name: 49327 SIGNED RANK TEST 49328 49329Type: 49330 Analysis Command 49331 49332Purpose: 49333 Perform a one sample or a paired two sample signed rank 49334 test. 49335 49336Description: 49337 The t-test is the standard test for testing that the 49338 difference between population means for two paired 49339 samples are equal. If the populations are non-normal, 49340 particularly for small samples, then the t-test may not 49341 be valid. The signed rank test is an alternative that can 49342 be applied when distributional assumptions are suspect. 49343 However, it is not as powerful as the t-test when the 49344 distributional assumptions are in fact valid. 49345 49346 The signed rank test is also commonly called the Wilcoxon 49347 signed rank test or simply the Wilcoxon test. 49348 49349 To form the signed rank test, compute d(i) = X(i) - Y(i) 49350 where X and Y are the two samples. Rank the d(i) without 49351 regard to sign. Tied values are not included in the Wilcoxon 49352 test. After ranking, restore the sign (plus or 49353 minus) to the ranks. Then compute W+ and W- as the 49354 sums of the positive and negative ranks respectively. 49355 If the two population means are in fact equal, then 49356 the sums of the ranks should also be nearly equal. If the 49357 difference between the sum of the ranks is too great, we 49358 reject the null hypothesis that the population means are 49359 equal. 49360 49361 Significance levels are based on the fact that if there 49362 is no difference in the population means, then there 49363 are 2**N equally likely ways for the N ranks to recieve 49364 signs. 49365 49366 More formally, the hypothesis test is defined as follows. 49367 49368 H0: u1 = u2 49369 Ha: u1 <> u2 49370 Test Statistic: W=MIN(W-,W+) where the computation of 49371 W- and W+ is discussed above. 49372 Alpha: Typically set to .05. Due to the discreteness of the 49373 ranks, the actual significance level will not in most 49374 cases be exact. 49375 Critical Region: For small samples (N <= 30), the critical 49376 regions have been tabulated. For N > 30, 49377 the test statistic W approaches a normal 49378 distribution with mean N(N+1)/4 and a 49379 standard deviation of SQRT[N(N+1)(2*N+1)/24]. 49380 The critical regions are thus based on the normal 49381 percent point function. That is, for a 2-sided 49382 test, 49383 49384 Uw - Sw*NORPPF(ALPHA/2) < W < Uw + Sw*NORPPF(1-ALPHA/2) 49385 49386 where Uw and Sw are the mean and standard deviation 49387 of W as described above and NORPPF is the normal 49388 percent point function. 49389 Conclusion: Reject null hypothesis if test statistic is 49390 in critical region 49391 49392 Although the above discussion was in terms of a paired two 49393 sample test, it can easily be adapted to the following 49394 additional cases: 49395 49396 1) For the one sample case that the population mean is 49397 equal to a value d0, simply compute d(i) = x(i) - d0 49398 and calculate W+ and W- based on d(i). 49399 49400 2) For the paired two sample case where we want to test 49401 that the difference between the two population means 49402 is equal to d0, compute d(i) = x(i) - y(i) - d0 and 49403 calculate W+ and W- based on d(i). 49404 49405Syntax 1: 49406 SIGNED RANK TEST <y1> <mu> <SUBSET/EXCEPT/FOR qualification> 49407 where <y1> is a response variable; 49408 <mu> is a number or parameter that is the hypothesized 49409 mean value; 49410 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 49411 49412 This syntax implements the one sample signed rank test. 49413 49414Syntax 2: 49415 SIGNED RANK TEST <y1> <y2> <SUBSET/EXCEPT/FOR qualification> 49416 where <y1> is the first response variable; 49417 <y2> is the second response variable; 49418 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 49419 49420 This syntax implements the two sample paired signed rank test 49421 where the hypothesized difference between the population means 49422 for the two samples is zero. 49423 49424Syntax 3: 49425 SIGNED RANK TEST <y1> <y2> <mu> 49426 <SUBSET/EXCEPT/FOR qualification> 49427 where <y1> is the first response variable; 49428 <y2> is the second response variable; 49429 <mu> is a number or parameter that is the hypothesized 49430 difference between the means of the two samples; 49431 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 49432 49433 This syntax implements the two sample paired signed rank test 49434 where the hypothesized difference between the population means 49435 for the two samples is equal to a non-zero value. 49436 49437Examples: 49438 SIGNED RANK TEST Y1 0 49439 SIGNED RANK TEST Y1 Y2 49440 SIGNED RANK TEST Y1 Y2 MU 49441 SIGNED RANK TEST Y1 Y2 SUBSET TAG > 2 49442 49443Note: 49444 DATAPLOT automatically prints the test statistic for both 49445 one sided and two sided tests. 49446 49447Note: 49448 Dataplot saves the following internal parameters after a 49449 sign test: 49450 49451 STATVAL = W, i.e., the minimum of the signed ranks 49452 STATCD2 = the normal cdf value of W 49453 CUTLOW90 = 0.05 critical value 49454 CUTUPP90 = 0.95 critical value 49455 CUTLOW95 = 0.025 critical value 49456 CUTUPP95 = 0.975 critical value 49457 CUTLOW99 = 0.005 critical value 49458 CUTUPP99 = 0.995 critical value 49459 49460 Note that the above critical values are the lower and upper 49461 tails for two sided tests (i.e., each tail is alpha/2. For 49462 example, CUTLOW90 is the lower 5% of the normal percent point 49463 function (adjusted for the mean and standard deviation). This 49464 is the critical regions for alpha = 0.10, so there is 0.05 in 49465 each tail. 49466 49467Note: 49468 The sign test is also an alternative to the t test for 49469 paired samples when the normality assumption is in doubt. 49470 The signed rank test is generally preferred over the sign 49471 test because it takes into account both the sign of the 49472 difference and the magnitude of the difference for paired 49473 samples while the sign test only takes the difference of 49474 the sign into account. 49475 49476Note: 49477 From Conover, the signed rank test is based on the following 49478 assumptions: 49479 49480 1. The distribution of each d(i) is symmetric. 49481 49482 2. The d(i) are mutually independent. 49483 49484 3. The d(i) all have the same mean. 49485 49486 4. The measurement scale of the d(i)'s is at least interval. 49487 49488 So the signed rank test weakens the assumption of normality of the 49489 paired t-test to an assumption of symmetry. The signed rank test is 49490 more powerful than a sign test (it takes the magnitude of the 49491 differences into account as well as the sign), but it has stronger 49492 assumptions than the sign test. So if your data is at approximately 49493 symmetric, then the signed rank test is preferred to the sign test. 49494 However, if the symmetry assumption is not reasonable, the sign test 49495 is preferred. 49496 49497 Also according to Conover, the null hypothesis can be stated either 49498 in terms of the mean or the median. This is due to the assumption 49499 of symmetry. 49500 49501Note: 49502 The following statistics are also supported: 49503 49504 LET A = ONE SAMPLE WILCOXON SIGNED RANK TEST Y 49505 LET A = ONE SAMPLE WILCOXON SIGNED RANK TEST CDF Y 49506 LET A = ONE SAMPLE WILCOXON SIGNED RANK TEST PVALUE Y 49507 LET A = ONE SAMPLE WILCOXON SIGNED RANK TEST LOWER ... 49508 TAIL PVALUE Y 49509 LET A = ONE SAMPLE WILCOXON SIGNED RANK TEST UPPER ... 49510 TAIL PVALUE Y 49511 49512 LET A = TWO SAMPLE WILCOXON SIGNED RANK TEST Y1 Y2 49513 LET A = TWO SAMPLE WILCOXON SIGNED RANK TEST CDF Y1 Y2 49514 LET A = TWO SAMPLE WILCOXON SIGNED RANK TEST PVALUE Y1 Y2 49515 LET A = TWO SAMPLE WILCOXON SIGNED RANK TEST LOWER ... 49516 TAIL PVALUE Y1 Y2<BR> 49517 LET A = TWO SAMPLE WILCOXON SIGNED RANK TEST UPPER ... 49518 TAIL PVALUE Y1 Y2 49519 49520 In addition to the above LET command, built-in statistics are 49521 supported for about 20+ different commands (enter HELP STATISTICS 49522 for details). 49523 49524Default: 49525 None 49526 49527Synonyms: 49528 The following are synonyms for SIGNED RANK TEST: 49529 49530 WILCOXON SIGNED RANK TEST 49531 WILCOXON SIGNED RANK 49532 WILCOXON SIGN TEST 49533 WILCOXON TEST 49534 SIGNED RANK 49535 49536Related Commands: 49537 T-TEST = Compute a t-test. 49538 SIGN TEST = Compute a sign test. 49539 CHI-SQUARED 2 SAMPLE TEST = Compute a two sample chi-square 49540 test. 49541 BIHISTOGRAM = Generates a bihistogram. 49542 QUANTILE-QUANTILE PLOT = Generate a quantile-quantile plot. 49543 BOX PLOT = Generates a box plot. 49544 49545Reference: 49546 Conover (1999), "Practical Non-Parametric Statistics," Third Edition, 49547 Wiley, pp. 352-364. 49548 49549 Snedecor and Cochran (1989), "Statistical Methods," Eigth Edition, 49550 Iowa State University Press, pp. 140-142. 49551 49552Applications: 49553 Confirmatory Data Analysis 49554 49555Implementation Date: 49556 1999/5 49557 2011/05: Switch algorithm to that given in Conover. 49558 49559Program: 49560 SKIP 25 49561 READ NATR332.DAT Y1 Y2 49562 SIGNED RANK TEST Y1 Y2 49563 49564-----SIN (LET)--------------------------------------------------- 49565 49566SIN 49567 49568Name: 49569 SIN (LET) 49570 49571Type: 49572 Library Function 49573 49574Purpose: 49575 Compute the sine for a variable or parameter. 49576 49577Description: 49578 The sine is defined for all real numbers and the returned value 49579 will be between -1 and 1. By default, the angle is specified in 49580 radian units. To use degree values, enter the command ANGLE UNITS 49581 DEGREES (ANGLE UNITS RADIANS resets it). 49582 49583Syntax: 49584 LET <y2> = SIN(<y1>) <SUBSET/EXCEPT/FOR qualification> 49585 where <y1> is a variable or a parameter; 49586 <y2> is a variable or a parameter (depending on what <y1> is) 49587 where the computed sine value is stored; 49588 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 49589 49590Examples: 49591 LET A = SIN(-2) 49592 LET A = SIN(A1) 49593 LET X2 = SIN(X1) 49594 LET X2 = SIN(PI/2) 49595 49596Note: 49597 Library functions are distinguished from let subcommands 49598 in the following ways. 49599 1) Functions enclose the input value in parenthesis. Let 49600 subcommands use spaces. 49601 2) Functions can accept (and return) either parameters 49602 (i.e., single values) or variables (i.e., an array of 49603 values) while let subcommands are specific in which they 49604 accept as input and what they return as output. 49605 3) Functions can accept expressions while let subcommands 49606 do not. For example, the following is legal: 49607 LET Y2 = ABS(Y1-INT(Y1)) 49608 For let subcommands, you typically have to do something 49609 like the following: 49610 LET YTEMP = Y**2 + 8 49611 LET A = SUM YTEMP 49612 49613Default: 49614 None 49615 49616Synonyms: 49617 None 49618 49619Related Commands: 49620 COS = Compute the cosine. 49621 TAN = Compute the tangent. 49622 COT = Compute the cotangent. 49623 SEC = Compute the secant. 49624 CSC = Compute the cosecant. 49625 ARCCOS = Compute the arccosine. 49626 ARCSIN = Compute the arcsine. 49627 ARCTAN = Compute the arctangent. 49628 ARCCOT = Compute the arccotangent. 49629 ARCSEC = Compute the arcsecant. 49630 ARCCSC = Compute the arcsecant. 49631 49632Reference: 49633 Consult any standard trigonometry or pre-calculus textbook. 49634 49635Applications: 49636 XX 49637 49638Implementation Date: 49639 XX 49640 49641Program: 49642 X1LABEL ANGLE VALUES (RADIANS) 49643 Y1LABEL SINE VALUE 49644 TITLE AUTOMATIC 49645 YLIMITS -1 1 49646 YTIC OFFSET 0.2 0.2 49647 PLOT SIN(X) FOR X = -3.1 .05 3.1 49648 49649-----SINE AMPLITUDE PLOT----------------------------------------- 49650 49651SINE AMPLITUDE PLOT 49652 49653Name: 49654 SINE AMPLITUDE PLOT 49655 49656Type: 49657 Graphics Command 49658 49659Purpose: 49660 Generates a sine amplitude plot. 49661 49662Description: 49663 A sine amplitude plot is a plot consisting of subsample sine 49664 amplitude versus subsample index. The subsample sine amplitude is 49665 the approximate least squares estimate of the amplitude in a 49666 single-frequency sinusoidal model based on data from that subsample 49667 only. The sine amplitude plot is used to answer the question-- 49668 "Does the subsample amplitude change over different subsamples?". 49669 It consists of: 49670 Vertical axis = subsample sine amplitude; 49671 Horizontal axis = subsample index. 49672 The sine amplitude plot yields 2 traces: 49673 1. a subsample sine amplitude trace; and 49674 2. a full-sample sine amplitude reference line. 49675 Like usual, the appearance of these 2 traces is 49676 controlled by the first 2 settings of the LINES, 49677 CHARACTERS, SPIKES, BARS, and similar attributes. 49678 49679Syntax: 49680 SINE AMPLITUDE PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 49681 where <y> is the response (= dependent) variable; 49682 <x> is the subsample identifier variable (this variable 49683 appears on the horizontal axis); 49684 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 49685 49686Examples: 49687 SINE AMPLITUDE PLOT Y X 49688 SINE AMPLITUDE PLOT Y X1 49689 49690Default: 49691 None 49692 49693Synonyms: 49694 SA PLOT 49695 49696Related Commands: 49697 CHARACTERS = Sets the type for plot char. 49698 LINES = Sets the type for plot lines. 49699 SINE FREQUENCY PLOT = Generates a sine frequency plot. 49700 COMPLEX DEMOD AMPL PLOT = Generate a complex demodulation 49701 amplitude plot. 49702 COMPLEX DEMOD FREQ PLOT = Generate a complex demodulation 49703 frequency plot. 49704 RANGE PLOT = Generates a range plot. 49705 MEAN PLOT = Generates a mean plot. 49706 AUTOCORRELATION PLOT = Generates a autocorrelation plot. 49707 SPECTRAL PLOT = Generates a spectral plot. 49708 BOX PLOT = Generates a box plot. 49709 PLOT = Generates a data or function plot. 49710 49711Applications: 49712 Time Series Analysis 49713 49714Implementation Date: 49715 88/2 49716 49717Program: 49718 TITLE AUTOMATIC 49719 LET X = SEQUENCE .1 .1 10.01 49720 LET AMP = SEQUENCE 0.1 25 0.1 0.405 49721 LET Y = AMP*SIN(X) 49722 LET TAG = SEQUENCE 1 25 1 4 49723 MULTIPLOT 2 1; MULTIPLOT CORNER COORDINATES 0 0 100 100 49724 PLOT Y X 49725 SINE AMPLITUDE PLOT Y TAG 49726 END OF MULTIPLOT 49727 49728-----SINE FREQUENCY PLOT----------------------------------------- 49729 49730SINE FREQUENCY PLOT 49731 49732Name: 49733 SINE FREQUENCY PLOT 49734 49735Type: 49736 Graphics Command 49737 49738Purpose: 49739 Generates a sine frequency plot. 49740 49741Description: 49742 A sine frequency plot is a plot consisting of subsample sine 49743 frequency versus subsample index. The subsample sine frequency is 49744 the approximate least squares estimate of the frequency in a 49745 single-frequency sinusoidal model based on data from that subsample 49746 only. The sine frequency plot is used to answer the question-- 49747 "Does the subsample frequency change over different subsamples?". 49748 It consists of: 49749 Vertical axis = subsample sine frequency; 49750 Horizontal axis = subsample index. 49751 The sine frequency plot yields 2 traces: 49752 1. a subsample sine frequency trace; and 49753 2. a full-sample sine frequency reference line. 49754 Like usual, the appearance of these 2 traces is 49755 controlled by the first 2 settings of the LINES, 49756 CHARACTERS, SPIKES, BARS, and similar attributes. 49757 49758Syntax: 49759 SINE FREQUENCY PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 49760 where <y> is the response (= dependent) variable; 49761 <x> is the subsample identifier variable (this variable 49762 appears on the horizontal axis); 49763 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 49764 49765Examples: 49766 SINE FREQUENCY PLOT Y X 49767 SINE FREQUENCY PLOT Y X1 49768 49769Default: 49770 None 49771 49772Synonyms: 49773 SF PLOT 49774 49775Related Commands: 49776 CHARACTERS = Sets the type for plot characters. 49777 LINES = Sets the type for plot lines. 49778 SINE AMPLITUDE PLOT = Generates a sine amplitude plot. 49779 COMPLEX DEMOD AMPL PLOT = Generates a complex demodulation 49780 amplitude plot. 49781 COMPLEX DEMOD FREQ PLOT = Generates a complex demodulation 49782 frequency plot. 49783 RANGE PLOT = Generates a range plot. 49784 MEAN PLOT = Generates a mean plot. 49785 AUTOCORRELATION PLOT = Generates an autocorrelation plot. 49786 BOX PLOT = Generates a box plot. 49787 RANGE PLOT = Generates a range plot. 49788 MEAN PLOT = Generates a mean plot. 49789 PLOT = Generates a data or function plot. 49790 49791Applications: 49792 Time Series Analysis 49793 49794Implementation Date: 49795 88/2 49796 49797Program: 49798 TITLE AUTOMATIC 49799 LET X = SEQUENCE .1 .1 10.01 49800 LET FREQ = SEQUENCE 1.0 25 .5 2.5 49801 LET Y = SIN(FREQ*X) 49802 LET TAG = SEQUENCE 1 25 1 4 49803 MULTIPLOT 2 1; MULTIPLOT CORNER COORDINATES 0 0 100 100 49804 PLOT Y X 49805 SINE FREQUENCY PLOT Y TAG 49806 END OF MULTIPLOT 49807 49808-----SINE TRANSFORM (LET)------------------------------------------ 49809 49810SINE TRANSFORM 49811 49812Name: 49813 SINE TRANSFORM (LET) 49814 49815Type: 49816 Let Subcommand 49817 49818Purpose: 49819 Compute the sine transform of a variable. 49820 49821Description: 49822 The sine transform converts a time domain function into a frequency 49823 domain function. In practice, functions are sampled at equally 49824 spaced discrete points. The discrete sine transform is: 49825 F(k) = SUM(j=0 to N-1) [f(j)sin(PI*j*k/N)] 49826 where f(j) is the data array for j = 0, 1, ... , N-1. 49827 49828 DATAPLOT calculates the discrete sine transform. If you wish to 49829 calculate these transforms for a function, then evaluate this 49830 function at a series of points. 49831 49832 See the REFERENCE section below for references which give a more 49833 detailed explanation of sine transforms. 49834 49835Syntax: 49836 LET <r1> = SINE TRANSFORM <y1> <SUBSET/EXCEPT/FOR qualification> 49837 where <y1> is a response variable for which the sine transform is to 49838 be computed; 49839 <r1> is a variable containing the computed sine transform; 49840 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 49841 49842Examples: 49843 LET RPART = SINE TRANSFORM Y1 49844 49845Default: 49846 None 49847 49848Synonyms: 49849 None 49850 49851Related Commands: 49852 FOURIER TRANSFORM = Compute the Fourier transform. 49853 INVERSE FOUR TRANS = Compute the inverse cosine transform. 49854 FFT = Compute the fast cosine transform. 49855 INVERSE FFT = Compute the inverse FFT. 49856 COSINE TRANSFORM = Compute the cosine transformation. 49857 SPECTRAL PLOT = Generate a spectral plot. 49858 49859Reference: 49860 "Numerical Recipes: The Art of Scientific Computing (FORTRAN 49861 Version)", Press, Flannery, Teukolsky, and Vetterling. Cambridge 49862 University Press, 1989 (chapter 12). 49863 49864 "Fourier Analysis of Time Series: An Introduction", Peter 49865 Bloomfield, John Wiley and Sons, 1976. 49866 49867Applications: 49868 Frequency analysis of time series, signal processing 49869 49870Implementation Date: 49871 87/5 49872 49873Program: 49874 TITLE SINE TRANSFORM 49875 LEGEND 1 TIME SERIES SMOOTHING 49876 . 49877 LET X = SEQUENCE 0 .1 25.55 49878 LET YS = SIN(X) 49879 LET YN = NORMAL RANDOM NUMBERS FOR I = 1 1 256 49880 LET YN = YN/10 49881 LET Y = YS+YN 49882 . 49883 LET U = SINE TRANSFORM Y 49884 LET NU = NUMBER U 49885 LET XU = SEQUENCE 1 1 NU 49886 LET XU = XU+50 49887 . 49888 LET U = 2.5*U 49889 PLOT U VS XU 49890 49891-----SINGLE SAMPLE ACCEPTANCE PLAN--------------------------------- 49892 49893SINGLE SAMPLE ACCEPTANCE PLAN 49894 49895Name: 49896 SINGLE SAMPLE ACCEPTANCE PLAN 49897 49898Type: 49899 Analysis Command 49900 49901Purpose: 49902 Generates a single sample acceptance plan. 49903 49904Description: 49905 A lot acceptance sampling plan is a sampling scheme and a 49906 set of rules for making decisions. The decision, based on 49907 counting the number of defectives in a sample, can be to 49908 accept the lot, reject the lot, or to take another sample. 49909 49910 For a single sampling plan, one sample of items is selected 49911 at random from a lot and the disposition of the lot is 49912 determined from the resulting information. These plans are 49913 also denoted as (n,c) plans since there are n observations 49914 and the lot is rejected if there are more than c defectives. 49915 49916 Single sample acceptance plans are the most common and 49917 easiest plans to use. However, they are not the most 49918 efficient in terms of the average number of samples needed. 49919 49920 The input to this command is the following four parameters: 49921 1) P1 = the acceptable quality level (AQL). The AQL is the 49922 a proportion defective that is the base line requirement 49923 for the quality of the producer's product. The producer 49924 would like to design a sampling plan such that there 49925 is a high probability of accepting a lot that has a 49926 defect level less than or equal to the AQL. In Dataplot, 49927 this value should be entered as a proportion (i.e., 49928 a value between 0 and 1.0). 49929 2) P2 = the lot tolerance percent defective (LTPD). The 49930 LTPD is a designated high defect level that would be 49931 unacceptable to the consumer. The consumer would like 49932 the sampling plan to have a low probability of accepting 49933 a lot with a defect level as high as the LTPD. In 49934 Dataplot, this value should be entered as a proportion 49935 (i.e., a value between 0 and 1.0). 49936 49937 Note that P2 should be greater than P1. 49938 49939 3) ALPHA = the Type I Error (Producers Risk). This is the 49940 probability, for a given (n,c) sampling plan, of 49941 rejecting a lot that has a defect level equal to the 49942 AQL. The producer suffers when this occurs because a 49943 lot with acceptable was rejected. Typical values for 49944 ALPHA range from 0.2 to 0.01. 49945 4) BETA = the Type II Error (Consumers Risk). This is the 49946 probability, for a given (n,c) sampling plan, of 49947 accepting a lot with a defect level equal to the 49948 LTPD. The consumer suffers when this occurs because 49949 a lot with unacceptable quality was accepted. Typical 49950 values for BETA range from 0.2 to 0.01. 49951 49952 The output is the following two numbers: 49953 1) N = the size sample to collect 49954 2) C = reject the lot if this number of defectives 49955 exceeded 49956 49957Syntax: 49958 SINGLE SAMPLE ACCEPTANCE PLAN <p1> <p2> <alpha> <beta> 49959 where <p1> is a number or parameter that specifies the AQL; 49960 <p2> is a number of parameter that specifies the LTPD; 49961 <alpha> is a number or parameter that is the producers 49962 risk; 49963 and where <beta> is a number or parameter that is the 49964 consumers risk. 49965 49966Examples: 49967 SINGLE SAMPLE ACCEPTANCE PLAN 0.05 0.10 0.01 0.10 49968 49969 LET P1 = 0.01 49970 LET P2 = 0.05 49971 LET ALPHA = 0.01 49972 LET BETA = 0.10 49973 SINGLE SAMPLE ACCEPTANCE PLAN P1 P2 ALPHA BETA 49974 49975Note: 49976 In addition to printing the values of N and C, Dataplot 49977 stores these values in the internal parameters SSN and 49978 SSNC. These parameters can be used in subsequent Dataplot 49979 analysis if needed. 49980 49981Note: 49982 Dataplot provides the following related macros: 49983 49984 OC_SSB.DP - generate an Operating Characteristic (OC) curve 49985 assuming binomial probabilities. The OC 49986 curve is a plot of probability of acceptance 49987 versus percent defective. 49988 OC_SSA.DP - generate an Operating Characteristic (OC) curve 49989 assuming hypergeometric probabilities. The OC 49990 curve is a plot of probability of acceptance 49991 versus percent defective. 49992 AOQSS.DP - generate an Average Outgoing Quality (AOQ) curve. 49993 For non-destructive samples, rejected lots are 49994 often 100% inspected and defective units are 49995 replaced with good units. This means that the 49996 only defective units are those in lots that 49997 were accepted. The AOQ is the long term defect 49998 level for these combined lots. The AOQ curve 49999 is a plot of this AOQ versus percent defective. 50000 ATISS.DP - generate an Average Total Inspection (ATI) curve. 50001 The ATI curve is a plot of probability of 50002 acceptance versus lot fraction defective. 50003 50004 You can enter LIST <macro> where <macro> is the name of one 50005 of the macros above for details on how to use them. 50006 50007Default: 50008 None 50009 50010Synonyms: 50011 None 50012 50013Related Commands: 50014 CONTROL CHART = Generate a control chart. 50015 CP = Compute a Cp capability index. 50016 CUSUM ARL = Generate a cusum average run length chart. 50017 50018Reference: 50019 Douglas Montgomery, "Introduction to Statistical Quality 50020 Control", John wiley, 1991. 50021 50022Applications: 50023 Quality Control 50024 50025Implementation Date: 50026 1999/3 50027 50028 2001/8: Updated code to print an error message if P2 <= P1 50029 50030Program: 50031 LET P1 = 0.01 50032 LET P2 = 0.05 50033 LET ALPHA = 0.05 50034 LET BETA = 0.10 50035 SINGLE SAMPLE ACCEPTANCE PLAN P1 P2 ALPHA BETA 50036 LET N = SSN 50037 LET C = SSC 50038 . Purpose--Generate an Operating Characteristic curve for a 50039 . single sample plan. 50040 . The OC is defined as: 50041 . BINCDF(c,p,n) versus p 50042 . where 50043 . n = sample size 50044 . c = acceptance number for defectives 50045 . p = desired binomial probabilities 50046 . 50047 LABEL CASE ASIS 50048 TITLE CASE ASIS 50049 Y1LABEL Probability of Acceptance, Pa 50050 X1LABEL Lot Fraction Defective, p 50051 TITLE OC Single Sample (^SSN, ^SSC) Curve 50052 . 50053 PLOT BINCDF(SSC,P,SSN) FOR P = 0.001 0.001 0.20 50054 50055-----SINH (LET)--------------------------------------------------- 50056 50057SINH 50058 50059Name: 50060 SINH (LET) 50061 50062Type: 50063 Library Function 50064 50065Purpose: 50066 Compute the hyperbolic sine for a variable or parameter. 50067 50068Description: 50069 The formula for the hyperbolic sine is: 50070 sinh(x) = (e**x - e**-x)/2 50071 This function is defined for all real x. The range is negative 50072 infinity to positive infinity. 50073 50074Syntax: 50075 LET <y2> = SINH(<y1>) <SUBSET/EXCEPT/FOR qualification> 50076 where <y1> is a variable or a parameter; 50077 <y2> is a variable or a parameter (depending on what <y1> is) 50078 where the computed hyperbolic sine value is stored; 50079 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 50080 50081Examples: 50082 LET A = SINH(-2) 50083 LET A = SINH(A1) 50084 LET X2 = SINH(X1) 50085 LET X2 = SINH(PI/2) 50086 50087Note: 50088 Library functions are distinguished from let subcommands 50089 in the following ways. 50090 1) Functions enclose the input value in parenthesis. Let 50091 subcommands use spaces. 50092 2) Functions can accept (and return) either parameters 50093 (i.e., single values) or variables (i.e., an array of 50094 values) while let subcommands are specific in which they 50095 accept as input and what they return as output. 50096 3) Functions can accept expressions while let subcommands 50097 do not. For example, the following is legal: 50098 LET Y2 = ABS(Y1-INT(Y1)) 50099 For let subcommands, you typically have to do something 50100 like the following: 50101 LET YTEMP = Y**2 + 8 50102 LET A = SUM YTEMP 50103 50104Default: 50105 None 50106 50107Synonyms: 50108 None 50109 50110Related Commands: 50111 SIN = Compute the sine. 50112 COS = Compute the cosine. 50113 TAN = Compute the tangent. 50114 COT = Compute the cotangent. 50115 SEC = Compute the secant. 50116 CSC = Compute the cosecant. 50117 ARCCOS = Compute the arccosine. 50118 ARCSIN = Compute the arcsine. 50119 ARCTAN = Compute the arctangent. 50120 ARCCOT = Compute the arccotangent. 50121 ARCSEC = Compute the arcsecant. 50122 ARCCSC = Compute the arcsecant. 50123 COSH = Compute the hyperbolic cosine. 50124 TANH = Compute the hyperbolic tangent. 50125 COTH = Compute the hyperbolic cotangent. 50126 SECH = Compute the hyperbolic secant. 50127 CSCH = Compute the hyperbolic cosecant. 50128 ARCCOSH = Compute hyperbolic arccosine. 50129 ARCCOTH = Compute hyperbolic arccotangent. 50130 ARCCSCH = Compute hyperbolic arccosecant. 50131 ARCSECH = Compute hyperbolic arcsecant. 50132 ARCSINH = Compute hyperbolic arcsine. 50133 ARCTANH = Compute hyperbolic arctangent. 50134 50135Applications: 50136 XX 50137 50138Implementation Date: 50139 XX 50140 50141Program: 50142 TITLE AUTOMATIC 50143 Y1LABEL HYPERBOLIC SINE VALUE 50144 PLOT SINH(X) FOR X = -5 .1 5 50145 50146-----SINHINT (LET)-------------------------------- 50147 50148SINHINT 50149 50150Name: 50151 SINHINT (LET) 50152 50153Type: 50154 Library Function 50155 50156Purpose: 50157 Compute the hyperbolic sine integral. 50158 50159Description: 50160 The hyperbolic sine integral is defined as: 50161 Shi(X) = INTEGRAL(SINH(t)/t)dt 50162 where the integral is taken from 0 to x and SINH is the hyperbolic 50163 sine function. 50164 50165Syntax: 50166 LET <y2> = SINHINT(<x>) <SUBSET/EXCEPT/FOR qualification> 50167 where <x> is a non-zero number, variable, or parameter; 50168 <y2> is a variable or a parameter (depending on what <x> is 50169 where the computed hyperbolic sine integral values 50170 are stored; 50171 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 50172 50173Examples: 50174 LET A = SINHINT(0.1) 50175 LET A = SINHINT(-0.1) 50176 LET X2 = SINHINT(X) 50177 50178Note: 50179 DATAPLOT uses the routine SICIEI written by Irene Stegum and 50180 Ruth Zucker of NIST (see the REFERENCE section below). 50181 50182Note: 50183 Library functions are distinguished from let subcommands 50184 in the following ways. 50185 1) Functions enclose the input value in parenthesis. Let 50186 subcommands use spaces. 50187 2) Functions can accept (and return) either parameters 50188 (i.e., single values) or variables (i.e., an array of 50189 values) while let subcommands are specific in which they 50190 accept as input and what they return as output. 50191 3) Functions can accept expressions while let subcommands 50192 do not. For example, the following is legal: 50193 LET Y2 = ABS(Y1-INT(Y1)) 50194 For let subcommands, you typically have to do something 50195 like the following: 50196 LET YTEMP = Y**2 + 8 50197 LET A = SUM YTEMP 50198 50199Default: 50200 None 50201 50202Synonyms: 50203 None 50204 50205Related Commands: 50206 SININT = Compute the hyperbolic sine integral. 50207 COSINT = Compute the hyperbolic cosine integral. 50208 COSHINT = Compute the hyperbolic cosine integral. 50209 EXPINTN = Compute the exponential integral of order N. 50210 LOGINT = Compute the logarithmic integral. 50211 DAWSON = Compute Dawson's integral. 50212 50213Reference: 50214 "SICIEI: Automatic Computing Methods for Special FUnctions. Part 50215 III. The Sine, Cosine, Exponential Integrals and Related 50216 Functions", Stegum and Zucker, Journal of Research of the National 50217 Bureau of Standards, 80B(2), 1976. 50218 50219 "Handbook of Mathematical Functions, Applied Mathematics Series, 50220 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 50221 1964 (chapter 5). 50222 50223Applications: 50224 Special Functions 50225 50226Implementation Date: 50227 94/9 50228 50229Program: 50230 TITLE AUTOMATIC 50231 PLOT SINHINT(X) FOR X = -10 0.1 10 50232 50233-----SINGULAR VALUES (LET)--------------------------------- 50234 50235SINGULAR VALUES 50236 50237Name: 50238 SINGULAR VALUES (LET) 50239 50240Type: 50241 Let Subcommand 50242 50243Purpose: 50244 Compute the singular values of a matrix. 50245 50246Description: 50247 DATAPLOT uses the singular value decomposition (SVD) to compute 50248 the singular values. 50249 50250 If X is a matrix with row and column dimensions n and p 50251 respectively, then an n by n orthogonal matrix U and a p by p 50252 orthogonal matrix V can be found such that: 50253 U'XV = [ SIGMA] - if n >= p 50254 [ 0 ] 50255 U'XV = [SIGMA 0] - if n < p 50256 where SIGMA is a m by m diagonal matrix (m is the minimum of 50257 n and p). The diagonal elements of SIGMA are the singular values 50258 of X and they are stored from largest to smallest. Singular values 50259 of zero (or near zero) indicate that the matrix is singular (i.e., 50260 not of full rank) or ill-conditioned. Chapters 2 and 14 of the 50261 Numerical Recipes book describe some applications of the SVD. 50262 50263 For large matrices, it can be impractical to compute U (which is 50264 n by n). However, U can be partitioned into 50265 U = (U1, U2) 50266 where U1 is n by p. Then 50267 X = U1xSIGMAxV' 50268 is called the singular value factorization of X. Several 50269 multivariate statistical techniques are based on this 50270 factorization. 50271 50272Syntax: 50273 LET <resp> = SINGULAR VALUES <mat1> 50274 <SUBSET/EXCEPT/FOR qualification> 50275 where <mat1> is a matrix for which the singular values are to be 50276 computed; 50277 <resp> is a variable where the resulting singular values are 50278 saved; 50279 and where the <SUBSET/EXCEPT/FOR qualification> is optional (and 50280 rarely used in this context). 50281 50282Examples: 50283 LET C = SINGULAR VALUES A 50284 50285Note: 50286 Matrices are created with either the READ MATRIX command or the 50287 MATRIX DEFINITION command. Enter HELP MATRIX DEFINITION and HELP 50288 READ MATRIX for details. 50289 50290Note: 50291 The columns of a matrix are accessible as variables by appending an 50292 index to the matrix name. For example, the 4x4 matrix C has 50293 columns C1, C2, C3, and C4. These columns can be operated on like 50294 any other DATAPLOT variable. 50295 50296Note: 50297 The maximum size matrix that DATAPLOT can handle is set when 50298 DATAPLOT is built on a particular site. The default maximums are 50299 100 columns and 500 rows. Earlier versions may be 20 rows and 20 50300 columns or 100 rows and 100 columns. 50301 50302Default: 50303 None 50304 50305Synonyms: 50306 None 50307 50308Related Commands: 50309 MATRIX ADDITION = Perform a matrix addition. 50310 MATRIX ADJOINT = Compute the adjoint matrix of a matrix. 50311 MATRIX COFACTOR = Compute a matrix cofactor. 50312 MATRIX DEFINITION = Set a matrix definition. 50313 MATRIX DETERMINANT = Compute a matrix determinant. 50314 MATRIX EIGENVALUES = Compute the matrix eigenvalues. 50315 MATRIX EIGENVECTORS = Compute the matrix eigenvectors. 50316 MATRIX EUCLID NORM = Compute the matrix Euclidean norm. 50317 MATRIX INVERSE = Compute a matrix inverse. 50318 MATRIX MINOR = Compute a matrix minor. 50319 MATRIX MULTIPLICAT = Perform a matrix multiplication. 50320 MATRIX NUMB OF COLU = Compute the number of columns in a matrix. 50321 MATRIX NUMB OF ROWS = Compute the number of rows in a matrix. 50322 MATRIX RANK = Compute the rank of a matrix. 50323 MATRIX SIMPLEX SOLU = Compute a matrix simplex solution. 50324 MATRIX SOLUTION = Solve a system of linear equations. 50325 MATRIX SPECTRAL NORM = Compute the matrix spectral norm. 50326 MATRIX SPECTRAL RADI = Compute the matrix spectral radius. 50327 MATRIX SUBMATRIX = Define a matrix submatrix. 50328 MATRIX SUBTRACTION = Perform a matrix subtraction. 50329 MATRIX TRACE = Compute a matrix trace. 50330 MATRIX TRANSPOSE = Compute a matrix transpose. 50331 CORRELATION MATRIX = Compute the correlation matrix of a matrix. 50332 VARIANCE-COVA MATRIX = Compute the variance-covariance matrix of a 50333 matrix. 50334 PRINCIPAL COMPONENTS = Compute the principal components of a 50335 matrix. 50336 SINGULAR VALUE DECOM = Compute the singular value decomposition of 50337 a matrix. 50338 SINGULAR VALUE FACT = Compute the singular value factorization of 50339 a matrix. 50340 50341Reference: 50342 "LINPACK User's Guide", Dongarra, Bunch, Moler, Stewart. Siam, 50343 1979. 50344 50345 "Numerical Recipes: The Art of Scientific Programming (FORTRAN 50346 Version)", Press, Flannery, Teukolsky, and Vetterling. Cambridge 50347 University Press, 1989 (chapter 2). 50348 50349Applications: 50350 Linear Algebra, Multivariate Analysis 50351 50352Implementation Date: 50353 93/8 50354 50355Program: 50356 . SOURCE: "GRAPHICAL EXPLORATORY DATA ANALYSIS", DU TOIT, ET AL 50357 . 28 STUDENTS FROM ABILITY TEST DATA SET (PAGE 6) 50358 . 50359 DIMENSION 100 COLUMNS 50360 READ MATRIX X 50361 11 19 21 21 18 20 21 15 14 15 13 15 16 19 19 19 20 17 17 39 21 9 50362 11 21 20 15 24 22 18 11 18 16 19 14 17 21 15 17 18 18 19 42 22 4 50363 0 18 19 16 18 18 23 11 13 13 15 11 11 15 18 13 15 18 13 38 18 6 50364 0 18 23 10 18 16 16 11 9 8 15 6 9 12 16 8 13 9 15 34 15 9 50365 0 24 24 19 20 23 24 22 18 16 19 16 19 19 21 21 20 18 20 46 21 2 50366 1 19 19 23 21 23 23 9 8 13 15 20 15 17 12 20 16 16 21 35 18 9 50367 0 21 20 19 21 21 23 11 16 11 18 18 14 21 17 14 19 18 16 42 19 4 50368 0 21 20 21 20 16 22 7 11 17 16 8 10 13 17 16 17 15 11 28 20 9 50369 1 19 20 19 22 18 21 11 12 7 15 9 11 13 12 13 17 12 12 38 19 8 50370 1 19 23 22 22 16 25 12 15 16 19 15 10 15 20 18 18 17 13 33 18 9 50371 0 17 13 8 18 13 18 12 8 9 12 12 11 9 14 15 12 13 9 23 16 9 50372 10 21 22 22 15 23 23 16 12 16 15 13 14 19 17 16 18 19 18 42 24 9 50373 11 18 18 17 16 15 22 8 11 10 16 8 14 10 13 10 14 9 14 27 14 8 50374 10 13 18 21 16 17 15 11 12 11 9 11 11 16 18 14 13 15 18 24 15 9 50375 11 17 13 17 20 22 19 15 11 11 12 11 13 15 15 15 13 16 12 33 10 9 50376 10 18 12 9 9 15 17 9 5 3 12 7 7 12 10 10 13 10 12 27 12 9 50377 10 22 15 24 17 15 20 10 12 12 11 9 12 19 16 16 8 11 17 30 22 6 50378 10 18 17 18 18 13 18 14 12 15 11 10 9 21 14 12 15 11 13 31 16 9 50379 10 17 15 14 14 12 13 9 10 11 9 7 11 13 15 11 13 10 13 31 11 9 50380 10 16 20 17 13 15 16 10 16 12 10 7 13 12 18 13 18 10 15 34 16 9 50381 1 24 21 22 21 21 25 11 17 17 21 11 15 15 18 16 16 17 17 37 21 3 50382 0 23 23 21 22 16 21 10 18 16 14 14 13 17 21 19 16 17 19 34 12 9 50383 1 22 22 21 24 18 24 6 16 14 20 16 18 12 12 13 18 18 21 31 19 4 50384 0 22 17 19 19 21 20 17 15 9 13 16 17 18 11 13 16 19 14 40 18 1 50385 0 20 23 23 22 22 24 11 18 16 16 16 20 13 16 18 18 20 20 41 21 3 50386 1 22 17 21 17 17 22 10 14 16 16 13 8 13 18 21 12 13 15 33 14 9 50387 1 21 18 20 23 21 22 8 15 9 17 11 13 13 20 20 21 15 20 38 21 6 50388 1 21 22 19 20 18 17 11 15 12 14 11 10 11 13 14 14 15 14 39 12 9 50389 END OF DATA 50390 LET S = SINGULAR VALUES X 50391 SET WRITE FORMAT F10.5 50392 PRINT S 50393 The computed singular values are: 50394 419.53979 32.21864 26.63654 22.93816 19.67355 18.49977 16.47950 50395 14.76893 14.27686 13.22598 12.82934 11.64946 10.87689 9.98086 50396 9.34820 7.87245 6.51996 6.08804 3.80118 3.12485 2.97399 0.78713 50397 50398-----SINGULAR VALUE DECOMPOSITION (LET)-------------------------- 50399 50400SINGULAR VALUE DECOMPOSITION 50401 50402Name: 50403 SINGULAR VALUE DECOMPOSITION (LET) 50404 50405Type: 50406 Let Subcommand 50407 50408Purpose: 50409 Compute the singular value decomposition of a matrix. 50410 50411Description: 50412 If X is a matrix with row and column dimensions n and p 50413 respectively, then an n by n orthogonal matrix U and a p by p 50414 orthogonal matrix V can be found such that: 50415 U'XV = [ SIGMA] - if n >= p 50416 [ 0 ] 50417 U'XV = [SIGMA 0] - if n < p 50418 where SIGMA is a m by m diagonal matrix (m is the minimum of 50419 n and p). The diagonal elements of SIGMA are the singular values 50420 of X and they are stored from largest to smallest. Singular values 50421 of zero (or near zero) indicate that the matrix is singular (i.e., 50422 not of full rank) or ill-conditioned. Chapters 2 and 14 of the 50423 Numerical Recipes book describe some applications of the SVD. 50424 50425 Since U and V are orthogonal (and so their inverses are equal to 50426 their transpose), the above equation can also be written as: 50427 X = U[SIGMA]V' 50428 [ 0 ] 50429 50430 For large matrices, it can be impractical to compute U (which is 50431 n by n). However, U can be partitioned into 50432 U = (U1, U2) 50433 where U1 is n by p. Then 50434 X = U1xSIGMAxV' 50435 is called the singular value factorization of X. Several 50436 multivariate statistical techniques are based on this 50437 factorization. 50438 50439Syntax: 50440 LET <u> <s> <v> = SINGULAR VALUE DECOMPOSITION <mat1> 50441 <SUBSET/EXCEPT/FOR qualification> 50442 where <mat1> is a matrix for which the singular values are to be 50443 computed; 50444 <u> is an n by n matrix where U is saved; 50445 <s> is a variable where the singular values are saved 50446 (length is minimum of n and p); 50447 <v> is an p by p matrix where V is saved; 50448 and where the <SUBSET/EXCEPT/FOR qualification> is optional (and 50449 rarely used in this context). 50450 50451Examples: 50452 LET U S V = SINGULAR VALUE DECOMPOSITION A 50453 50454Note: 50455 Matrices are created with either the READ MATRIX command or the 50456 MATRIX DEFINITION command. Enter HELP MATRIX DEFINITION and HELP 50457 READ MATRIX for details. 50458 50459Note: 50460 The columns of a matrix are accessible as variables by appending an 50461 index to the matrix name. For example, the 4x4 matrix C has 50462 columns C1, C2, C3, and C4. These columns can be operated on like 50463 any other DATAPLOT variable. 50464 50465Note: 50466 The maximum size matrix that DATAPLOT can handle is set when 50467 DATAPLOT is built on a particular site. The default maximums are 50468 100 columns and 500 rows. Earlier versions may be 20 rows and 20 50469 columns or 100 rows and 100 columns. 50470 50471Default: 50472 None 50473 50474Synonyms: 50475 None 50476 50477Related Commands: 50478 MATRIX ADDITION = Perform a matrix addition. 50479 MATRIX ADJOINT = Compute the adjoint matrix of a matrix. 50480 MATRIX COFACTOR = Compute a matrix cofactor. 50481 MATRIX DEFINITION = Set a matrix definition. 50482 MATRIX DETERMINANT = Compute a matrix determinant. 50483 MATRIX EIGENVALUES = Compute the matrix eigenvalues. 50484 MATRIX EIGENVECTORS = Compute the matrix eigenvectors. 50485 MATRIX EUCLID NORM = Compute the matrix Euclidean norm. 50486 MATRIX INVERSE = Compute a matrix inverse. 50487 MATRIX MINOR = Compute a matrix minor. 50488 MATRIX MULTIPLICAT = Perform a matrix multiplication. 50489 MATRIX NUMB OF COLU = Compute the number of columns in a matrix. 50490 MATRIX NUMB OF ROWS = Compute the number of rows in a matrix. 50491 MATRIX RANK = Compute the rank of a matrix. 50492 MATRIX SIMPLEX SOLU = Compute a matrix simplex solution. 50493 MATRIX SOLUTION = Solve a system of linear equations. 50494 MATRIX SPECTRAL NORM = Compute the matrix spectral norm. 50495 MATRIX SPECTRAL RADI = Compute the matrix spectral radius. 50496 MATRIX SUBMATRIX = Define a matrix submatrix. 50497 MATRIX SUBTRACTION = Perform a matrix subtraction. 50498 MATRIX TRACE = Compute a matrix trace. 50499 MATRIX TRANSPOSE = Compute a matrix transpose. 50500 CORRELATION MATRIX = Compute the correlation matrix of a matrix. 50501 VARIANCE-COVA MATRIX = Compute the variance-covariance matrix of a 50502 matrix. 50503 PRINCIPAL COMPONENTS = Compute the principal components of a 50504 matrix. 50505 SINGULAR VALUES = Compute the singular values of a matrix. 50506 SINGULAR VALUE FACT = Compute the singular value factorization of 50507 a matrix. 50508 50509Reference: 50510 "LINPACK User's Guide", Dongarra, Bunch, Moler, Stewart. Siam, 50511 1979. 50512 50513 "Numerical Recipes: The Art of Scientific Programming (FORTRAN 50514 Version)", Press, Flannery, Teukolsky, and Vetterling. Cambridge 50515 University Press, 1989 (chapter 2). 50516 50517Applications: 50518 Linear Algebra, Multivariate Analysis 50519 50520Implementation Date: 50521 93/8 50522 50523Program: 50524 . SOURCE: "GRAPHICAL EXPLORATORY DATA ANALYSIS", DU TOIT, ET AL 50525 . 28 STUDENTS FROM ABILITY TEST DATA SET (PAGE 6) 50526 . 50527 DIMENSION 100 COLUMNS 50528 READ MATRIX X 50529 11 19 21 21 18 20 21 15 14 15 13 15 16 19 19 19 20 17 17 39 21 9 50530 11 21 20 15 24 22 18 11 18 16 19 14 17 21 15 17 18 18 19 42 22 4 50531 0 18 19 16 18 18 23 11 13 13 15 11 11 15 18 13 15 18 13 38 18 6 50532 0 18 23 10 18 16 16 11 9 8 15 6 9 12 16 8 13 9 15 34 15 9 50533 0 24 24 19 20 23 24 22 18 16 19 16 19 19 21 21 20 18 20 46 21 2 50534 1 19 19 23 21 23 23 9 8 13 15 20 15 17 12 20 16 16 21 35 18 9 50535 0 21 20 19 21 21 23 11 16 11 18 18 14 21 17 14 19 18 16 42 19 4 50536 0 21 20 21 20 16 22 7 11 17 16 8 10 13 17 16 17 15 11 28 20 9 50537 1 19 20 19 22 18 21 11 12 7 15 9 11 13 12 13 17 12 12 38 19 8 50538 1 19 23 22 22 16 25 12 15 16 19 15 10 15 20 18 18 17 13 33 18 9 50539 0 17 13 8 18 13 18 12 8 9 12 12 11 9 14 15 12 13 9 23 16 9 50540 10 21 22 22 15 23 23 16 12 16 15 13 14 19 17 16 18 19 18 42 24 9 50541 11 18 18 17 16 15 22 8 11 10 16 8 14 10 13 10 14 9 14 27 14 8 50542 10 13 18 21 16 17 15 11 12 11 9 11 11 16 18 14 13 15 18 24 15 9 50543 11 17 13 17 20 22 19 15 11 11 12 11 13 15 15 15 13 16 12 33 10 9 50544 10 18 12 9 9 15 17 9 5 3 12 7 7 12 10 10 13 10 12 27 12 9 50545 10 22 15 24 17 15 20 10 12 12 11 9 12 19 16 16 8 11 17 30 22 6 50546 10 18 17 18 18 13 18 14 12 15 11 10 9 21 14 12 15 11 13 31 16 9 50547 10 17 15 14 14 12 13 9 10 11 9 7 11 13 15 11 13 10 13 31 11 9 50548 10 16 20 17 13 15 16 10 16 12 10 7 13 12 18 13 18 10 15 34 16 9 50549 1 24 21 22 21 21 25 11 17 17 21 11 15 15 18 16 16 17 17 37 21 3 50550 0 23 23 21 22 16 21 10 18 16 14 14 13 17 21 19 16 17 19 34 12 9 50551 1 22 22 21 24 18 24 6 16 14 20 16 18 12 12 13 18 18 21 31 19 4 50552 0 22 17 19 19 21 20 17 15 9 13 16 17 18 11 13 16 19 14 40 18 1 50553 0 20 23 23 22 22 24 11 18 16 16 16 20 13 16 18 18 20 20 41 21 3 50554 1 22 17 21 17 17 22 10 14 16 16 13 8 13 18 21 12 13 15 33 14 9 50555 1 21 18 20 23 21 22 8 15 9 17 11 13 13 20 20 21 15 20 38 21 6 50556 1 21 22 19 20 18 17 11 15 12 14 11 10 11 13 14 14 15 14 39 12 9 50557 END OF DATA 50558 LET U S V = SINGULAR VALUE DECOMPOSITION X 50559 50560-----SINGULAR VALUE FACTORIZATION (LET)-------------------------- 50561 50562SINGULAR VALUE FACTORIZATION 50563 50564Name: 50565 SINGULAR VALUE FACTORIZATION (LET) 50566 50567Type: 50568 Let Subcommand 50569 50570Purpose: 50571 Compute the singular value factorization of a matrix. 50572 50573Description: 50574 If X is a matrix with row and column dimensions n and p 50575 respectively, then an n by n orthogonal matrix U and a p by p 50576 orthogonal matrix V can be found such that: 50577 U'XV = [ SIGMA] - if n >= p 50578 [ 0 ] 50579 U'XV = [SIGMA 0] - if n < p 50580 where SIGMA is a m by m diagonal matrix (m is the minimum of 50581 n and p). The diagonal elements of SIGMA are the singular values 50582 of X and they are stored from largest to smallest. Singular values 50583 of zero (or near zero) indicate that the matrix is singular (i.e., 50584 not of full rank) or ill-conditioned. Chapters 2 and 14 of the 50585 Numerical Recipes book describe some applications of the SVD. 50586 50587 Since U and V are orthogonal (and so their inverses are equal to 50588 their transpose), the above equation can also be written as: 50589 X = U[SIGMA]V' 50590 [ 0 ] 50591 50592 For large matrices, it can be impractical to compute U (which is 50593 n by n). However, U can be partitioned into 50594 U = (U1, U2) 50595 where U1 is n by p. Then 50596 X = U1xSIGMAxV' 50597 is called the singular value factorization of X. Several 50598 multivariate statistical techniques are based on this factorization. 50599 The program example demonstrates the biplot proposed by Ruben 50600 Gabriel. 50601 50602Syntax: 50603 LET <u> <s> <v> = SINGULAR VALUE FACTORIZATION <mat1> 50604 where <mat1> is a matrix for which the singular values are to be 50605 computed; 50606 <u> is an n by p matrix where U is saved; 50607 <s> is a variable where the singular values are saved 50608 (length is minimum of n and p); 50609 <v> is an p by p matrix where V is saved. 50610 50611Examples: 50612 LET U S V = SINGULAR VALUE DECOMPOSITION A 50613 50614Note: 50615 DATAPLOT uses a LINPACK routine to compute the singular value 50616 factorization. 50617 50618Note: 50619 Matrices are created with either the READ MATRIX command or the 50620 MATRIX DEFINITION command. Enter HELP MATRIX DEFINITION and HELP 50621 READ MATRIX for details. 50622 50623Note: 50624 The columns of a matrix are accessible as variables by appending an 50625 index to the matrix name. For example, the 4x4 matrix C has 50626 columns C1, C2, C3, and C4. These columns can be operated on like 50627 any other DATAPLOT variable. 50628 50629Note: 50630 The maximum size matrix that DATAPLOT can handle is set when 50631 DATAPLOT is built on a particular site. The default maximums are 50632 100 columns and 500 rows. Earlier versions may be 20 rows and 20 50633 columns or 100 rows and 100 columns. 50634 50635Default: 50636 None 50637 50638Synonyms: 50639 None 50640 50641Related Commands: 50642 MATRIX ADDITION = Perform a matrix addition. 50643 MATRIX ADJOINT = Compute the adjoint matrix of a matrix. 50644 MATRIX COFACTOR = Compute a matrix cofactor. 50645 MATRIX DEFINITION = Set a matrix definition. 50646 MATRIX DETERMINANT = Compute a matrix determinant. 50647 MATRIX EIGENVALUES = Compute the matrix eigenvalues. 50648 MATRIX EIGENVECTORS = Compute the matrix eigenvectors. 50649 MATRIX EUCLID NORM = Compute the matrix Euclidean norm. 50650 MATRIX INVERSE = Compute a matrix inverse. 50651 MATRIX MINOR = Compute a matrix minor. 50652 MATRIX MULTIPLICAT = Perform a matrix multiplication. 50653 MATRIX NUMB OF COLU = Compute the number of columns in a matrix. 50654 MATRIX NUMB OF ROWS = Compute the number of rows in a matrix. 50655 MATRIX RANK = Compute the rank of a matrix. 50656 MATRIX SIMPLEX SOLU = Compute a matrix simplex solution. 50657 MATRIX SOLUTION = Solve a system of linear equations. 50658 MATRIX SPECTRAL NORM = Compute the matrix spectral norm. 50659 MATRIX SPECTRAL RADI = Compute the matrix spectral radius. 50660 MATRIX SUBMATRIX = Define a matrix submatrix. 50661 MATRIX SUBTRACTION = Perform a matrix subtraction. 50662 MATRIX TRACE = Compute a matrix trace. 50663 MATRIX TRANSPOSE = Compute a matrix transpose. 50664 CORRELATION MATRIX = Compute the correlation matrix of a matrix. 50665 VARIANCE-COVA MATRIX = Compute the variance-covariance matrix of a 50666 matrix. 50667 PRINCIPAL COMPONENTS = Compute the principal components of a 50668 matrix. 50669 SINGULAR VALUES = Compute the singular values of a matrix. 50670 SINGULAR VALUE DECOM = Compute the singular value decomposition of 50671 a matrix. 50672 50673Reference: 50674 "LINPACK User's Guide", Dongarra, Bunch, Moler, Stewart. Siam, 50675 1979. 50676 50677 "Numerical Recipes: The Art of Scientific Programming (FORTRAN 50678 Version)", Press, Flannery, Teukolsky, and Vetterling. Cambridge 50679 University Press, 1989 (chapter 2). 50680 50681Applications: 50682 Linear Algebra, Multivariate Analysis 50683 50684Implementation Date: 50685 93/8 50686 50687Program: 50688 . Generate a biplot (derived from the singular value factorization) 50689 . SOURCE: "THE BIPLOT AS A DIAGNOSTIC TOOL FOR MODELS OF TWO-WAY 50690 . TABLES", BRANDU, GABRIEL, TECHNOMETRICS, FEB. 1978. 50691 . DATA IS YIELDS OF COTTON, ROWS ARE VARIETY, COLUMNS ARE CENTER 50692 DIMENSION 100 COLUMNS 50693 READ MATRIX X 50694 1.55 1.26 1.41 1.78 50695 3.39 3.47 2.82 3.89 50696 1.95 1.91 1.74 2.29 50697 10.47 9.12 9.55 17.78 50698 1.45 1.51 1.41 1.70 50699 3.72 3.55 3.09 4.27 50700 4.47 4.07 3.98 4.47 50701 END OF DATA 50702 LET N = SIZE X1 50703 . 50704 FEEDBACK OFF 50705 LET P = MATRIX NUMBER OF COLUMNS X 50706 LOOP FOR K = 1 1 P 50707 LET X^K = LOG10(X^K) 50708 END OF LOOP 50709 LET SUM1 = 0 50710 LOOP FOR K = 1 1 P 50711 LET TEMP = SUM X^K 50712 LET SUM1 = SUM1 + TEMP 50713 END OF LOOP 50714 LET GMEAN = SUM1/(N*P) 50715 LET X = MATRIX SUBTRACTION X GMEAN 50716 LET U S V = SINGULAR VALUE FACTORIZATION X 50717 LET DENOM = MATRIX EUCLIDEAN NORM X 50718 LET S1 = S(1) 50719 LET S2 = S(2) 50720 LET GF = (S1**2 + S2**2)/DENOM**2 50721 . 50722 LET B = MATRIX TRANSPOSE V 50723 LET U1 = U1*SQRT(S1) 50724 LET U2 = U2*SQRT(S2) 50725 LET B1 = B1*SQRT(S1) 50726 LET B2 = B2*SQRT(S2) 50727 . 50728 LET TAG = SEQUENCE 1 1 N 50729 LET TAG2 = SEQUENCE 1 1 P 50730 CHARACTER CIRCLE SQUARE 50731 CHARACTER FILL SOLID ALL 50732 LINE BLANK ALL 50733 TITLE BIPLOT 50734 X1LABEL GOODNESS OF FIT = ^GF 50735 LEGEND FILL SOLID 50736 LEGEND FONT SIMPLEX 50737 LEGEND 1 SQUA() - COLUMN MARKERS 50738 LEGEND 2 CIRC() - ROW MARKERS 50739 . 50740 PLOT U2 U1 AND 50741 PLOT B2 B1 50742 LEGEND 1 50743 LEGEND 2 50744 LIMITS FREEZE 50745 PRE-ERASE OFF 50746 CHARACTER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 50747 CHARACTER OFFSET 1.2 0 ALL 50748 PLOT U2 U1 TAG 50749 PLOT B2 B1 TAG2 50750 50751-----SININT (LET)-------------------------------- 50752 50753SININT 50754 50755Name: 50756 SININT (LET) 50757 50758Type: 50759 Library Function 50760 50761Purpose: 50762 Compute the sine integral. 50763 50764Description: 50765 The sine integral is defined as: 50766 Si(X) = INTEGRAL(SIN(t)/t)dt 50767 where the integral is taken from 0 to x. 50768 50769Syntax: 50770 LET <y2> = SININT(<x>) <SUBSET/EXCEPT/FOR qualification> 50771 where <x> is a number, variable, or parameter; 50772 <y2> is a variable or a parameter (depending on what <x> is 50773 where the computed cosine integral values are stored; 50774 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 50775 50776Examples: 50777 LET A = SININT(0.1) 50778 LET A = SININT(-0.1) 50779 LET X2 = SININT(X) 50780 50781Note: 50782 DATAPLOT uses the routine SICIEI written by Irene Stegum and 50783 Ruth Zucker of NIST (see the REFERENCE section below). 50784 50785Note: 50786 Library functions are distinguished from let subcommands 50787 in the following ways. 50788 1) Functions enclose the input value in parenthesis. Let 50789 subcommands use spaces. 50790 2) Functions can accept (and return) either parameters 50791 (i.e., single values) or variables (i.e., an array of 50792 values) while let subcommands are specific in which they 50793 accept as input and what they return as output. 50794 3) Functions can accept expressions while let subcommands 50795 do not. For example, the following is legal: 50796 LET Y2 = ABS(Y1-INT(Y1)) 50797 For let subcommands, you typically have to do something 50798 like the following: 50799 LET YTEMP = Y**2 + 8 50800 LET A = SUM YTEMP 50801 50802Default: 50803 None 50804 50805Synonyms: 50806 None 50807 50808Related Commands: 50809 COSHINT = Compute the hyperbolic cosine integral. 50810 COSINT = Compute the cosine integral. 50811 SINHINT = Compute the hyperbolic sine integral. 50812 EXPINTN = Compute the exponential integral of order N. 50813 LOGINT = Compute the logarithmic integral. 50814 DAWSON = Compute Dawson's integral. 50815 50816Reference: 50817 "SICIEI: Automatic Computing Methods for Special FUnctions. Part 50818 III. The Sine, Cosine, Exponential Integrals and Related 50819 Functions", Stegum and Zucker, Journal of Research of the National 50820 Bureau of Standards, 80B(2), 1976. 50821 50822 "Handbook of Mathematical Functions, Applied Mathematics Series, 50823 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 50824 1964 (chapter 5). 50825 50826Applications: 50827 Special Functions 50828 50829Implementation Date: 50830 94/9 50831 50832Program: 50833 TITLE AUTOMATIC 50834 PLOT SININT(X) FOR X = -10 0.1 10 50835 50836-----SIZE (LET)--------------------------------------------------- 50837 50838SIZE 50839 50840Name: 50841 SIZE (LET) 50842 50843Type: 50844 Let Subcommand 50845 50846Purpose: 50847 Compute the number of elements in a variable. 50848 50849Syntax: 50850 LET <par> = SIZE <x1> <SUBSET/EXCEPT/FOR qualification> 50851 where <x1> is the variable for which the size is to be computed; 50852 <par> is a parameter where the size is saved; 50853 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 50854 50855Examples: 50856 LET N = SIZE Y1 50857 50858Default: 50859 None 50860 50861Synonyms: 50862 NUMBER 50863 COUNT 50864 50865Related Commands: 50866 SEQUENCE = Generate a sequence of numbers. 50867 PATTERN = Generate numbers with a specific pattern. 50868 50869Applications: 50870 Data Management 50871 50872Implementation Date: 50873 Pre-1987 50874 50875Program: 50876 XX 50877 50878-----SKEWNESS OUTLIER TEST------------------------------------ 50879 50880SKEWNESS OUTLIER TEST 50881 50882Name: 50883 SKEWNESS OUTLIER TEST 50884 50885Type: 50886 Analysis Command 50887 50888Purpose: 50889 Perform the skewness test for univariate outliers from a normal 50890 distribution. 50891 50892Description: 50893 The ASTM E178-16a standard for detecting outliers from a univariate 50894 normal distribution includes the skewness outlier test. 50895 50896 The test statistic is the adjusted Fisher-Pearson skewness 50897 coefficient 50898 50899 g1 = n*SUM[i=1 to n][(x(i)-xbar)**2]/((n-1)*(n-2)*s**2) 50900 50901 with n, xbar and s denoting the sample size, the sample mean 50902 and the sample standard deviation, respectively. 50903 50904 The critical values are obtained via simulation. The ASTM standard 50905 provides table values for n = 3 to 50 and alpha levels of 0.10, 0.05 50906 and 0.01. Linear interpolation is used for values of n not given in 50907 the table. Alternatively, you can perform a dynamic simulation 50908 to obtain the critical values. 50909 50910 To specify the method used to compute the critical value, enter 50911 one of the following commands (the default is ASTM) 50912 50913 SET SKEW OUTLIER TEST CRITICAL VALUES ASTM 50914 SET SKEW OUTLIER TEST CRITICAL VALUES SIMULATION 50915 50916 If n > 50, the simulation method will be used. 50917 50918Syntax 1: 50919 SKEWNESS OUTLIER TEST <y> <SUBSET/EXCEPT/FOR qualification> 50920 where <y> is the response variable being tested; 50921 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 50922 50923Syntax 2: 50924 MULTIPLE SKEWNESS OUTLIER TEST <y1> ... <yk> 50925 <SUBSET/EXCEPT/FOR qualification> 50926 where <y1> ... <yk> is a list of up to k response variables; 50927 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 50928 50929 This syntax performs the skewness outlier test on <y1>, then on 50930 <y2>, and so on. Up to 30 response variables can be specified. 50931 50932 Note that the syntax 50933 50934 MULTIPLE SKEWNESS OUTLIER TEST Y1 TO Y4 50935 50936 is supported. This is equivalent to 50937 50938 MULTIPLE SKEWNESS OUTLIER TEST Y1 Y2 Y3 Y4 50939 50940Syntax 3: 50941 REPLICATED SKEWNESS OUTLIER TEST <y> <x1> ... <xk> 50942 <SUBSET/EXCEPT/FOR qualification> 50943 where <y> is the response variable; 50944 <x1> ... <xk> is a list of up to k group-id variables; 50945 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 50946 50947 This syntax performs a cross-tabulation of <x1> ... <xk> and performs 50948 a skewness outlier test for each unique combination of cross-tabulated 50949 values. For example, if X1 has 3 levels and X2 has 2 levels, there 50950 will be a total of 6 skewness outlier tests performed. 50951 50952 Up to six group-id variables can be specified. 50953 50954 Note that the syntax 50955 50956 REPLICATED SKEWNESS OUTLIER TEST Y X1 TO X4 50957 50958 is supported. This is equivalent to 50959 50960 REPLICATED SKEWNESS OUTLIER TEST Y X1 X2 X3 X4 50961 50962Examples: 50963 SKEWNESS OUTLIER TEST Y1 50964 MULTIPLE SKEWNESS OUTLIER TEST Y1 Y2 Y3 50965 REPLICATED SKEWNESS OUTLIER TEST Y X1 X2 50966 SKEWNESS OUTLIER TEST Y1 SUBSET TAG > 2 50967 50968Note: 50969 Tests for outliers are dependent on knowing the distribution of the 50970 data. The skewness outlier test assumes that the data come from an 50971 approximately normal distribution. For this reason, it is strongly 50972 recommended that the skewness outlier test be complemented with a 50973 normal probability test. If the data are not approximately normally 50974 distributed, then the skewness outlier test may be detecting the 50975 non-normality of the data rather than the presence of an outlier. 50976 50977Note: 50978 You can specify the number of digits in the skewness outlier test 50979 output with the command 50980 50981 SET WRITE DECIMALS <value> 50982 50983Note: 50984 The SKEWNESS OUTLIER TEST command automatically saves the following 50985 parameters: 50986 50987 STATVAL = the value of the test statistic 50988 STATDCF = the CDF value of the test statistic 50989 PVALUE = the p-value of the test statistic 50990 CUTOFF80 = the 80 percent point of the reference distribution 50991 CUTOFF90 = the 90 percent point of the reference distribution 50992 CUTOFF95 = the 95 percent point of the reference distribution 50993 CUTOF975 = the 97.5 percent point of the reference distribution 50994 CUTOFF99 = the 99 percent point of the reference distribution 50995 50996 The STATCDF and PVALUE are only saved when the simulation method 50997 is used to obtain critical values. If the ASTM method is used to 50998 obtain critical values, the CUTOFF80 and CUTOF975 values are not 50999 saved. 51000 51001 If the MULTIPLE or REPLICATED option is used, these values will 51002 be written to the file "dpst1f.dat" instead. 51003 51004Note: 51005 In addition to the SKEWNESS OUTLIER TEST command, the following 51006 commands can also be used: 51007 51008 LET A = SKEWNESS OUTLIER TEST Y 51009 LET A = SKEWNESS OUTLIER TEST CDF Y 51010 LET A = SKEWNESS OUTLIER TEST PVALUE Y 51011 LET A = SKEWNESS OUTLIER TEST INDEX Y 51012 51013 LET ALPHA = <value> 51014 LET A = SKEWNESS OUTLIER TEST CRITICAL VALUE Y 51015 51016 The SKEWNESS OUTLIER TEST, SKEWNESS OUTLIER TEST CDF, and 51017 SKEWNESS OUTLIER TEST PVALUE return the values of the test statistic, 51018 the cdf of the test statistic and the pvalue of the test statistic, 51019 respectively. For the SKEWNESS OUTLIER TEST CDF and 51020 SKEWNESS OUTLIER TEST PVALUE commands, the simulation method will be 51021 used. Otherwise, the method specified by the 51022 SET SKEWNESS OUTLIER TEST CRITICAL VALUE command will be used. 51023 51024 The SKEWNESS OUTLIER TEST INDEX returns the row index of the most 51025 extreme value in the response variable. The most extreme value is 51026 defined as the value furtherest from the mean. 51027 51028 The SKEWNESS OUTLIER TEST CRITICAL VALUE returns the critical value 51029 for the specified value of ALPHA. If ALPHA is not specified, it will 51030 be set to 0.05. Note that if the ASTM method is specified for the 51031 critical values, only a few select values for alpha are supported 51032 (0.01, 0.05 and 0.10). 51033 51034 In addition to the above LET command, built-in statistics are 51035 supported for 30+ different commands (enter HELP STATISTICS 51036 for details). 51037 51038Default: 51039 The ASTM method is used to obtain critical values 51040 51041Synonyms: 51042 None 51043 51044Related Commands: 51045 KURTOSIS OUTLIER TEST = Perform the kurtosis outlier test. 51046 GRUBBS TEST = Perform the Grubbs outlier test. 51047 DAVID TEST = Perform the David outlier test. 51048 TIETJEN-MOORE TEST = Perform the Tietjen-Moore outlier 51049 test. 51050 EXTREME STUDENTIZED DEVIATE = Perform the generalized extreme 51051 studentized deviate outlier test. 51052 DIXON TEST = Perform the Dixon outlier test. 51053 SKEWNESS OUTLIER TEST = Perform the skewness outlier test. 51054 KURTOSIS OUTLIER TEST = Perform the kurtosis outlier test. 51055 ANDERSON DARLING TEST = Perform the Anderson-Darling test for 51056 normality. 51057 WILK SHAPIRO TEST = Perform the Wilk-Shapiro test for 51058 normality. 51059 PROBABILITY PLOT = Generates a probability plot. 51060 HISTOGRAM = Generate a histogram. 51061 BOX PLOT = Generate a box plot. 51062 51063Reference: 51064 E178 - 16A (2016), "Standard Practice for Dealing with Outlying 51065 Observations", ASTM International, 100 Barr Harbor Drive, 51066 PO Box C700, West Conshohocken, PA 19428-2959, USA. 51067 51068 Ferguson, T.S. (1961), "On the Rejection of Outliers," Fourth 51069 Berkeley Symposium on Mathematical Statistics and Probability, 51070 edited by Jerzy Neyman, University of California Press, Berkeley 51071 and Los Angeles, CA. 51072 51073 Ferguson, T.S. (1961), "Rules for Rejection of Outliers," Revue 51074 Inst. Int. de Stat., RINSA, Vol. 29, No. 3, pp. 29-43. 51075 51076Applications: 51077 Outlier Detection 51078 51079Implementation Date: 51080 2019/10 51081 51082Program: 51083 . Step 1: Read the data (from ASTM E-178 document) 51084 . 51085 read y 51086 3.73 51087 3.59 51088 3.94 51089 4.13 51090 3.04 51091 2.22 51092 3.23 51093 4.05 51094 4.11 51095 2.02 51096 end of data 51097 set write decimals 3 51098 . 51099 . Step 2: Compute the statistics 51100 . 51101 let stat = skew outlier test y 51102 set skew outlier test critical values astm 51103 let cv1 = skew outlier test critical value y 51104 set skew outlier test critical values simulation 51105 let cv2 = skew outlier test critical value y 51106 . 51107 let pval = skew outlier test pvalue y 51108 let statcdf = skew outlier test cdf y 51109 let iindx = skew outlier test index y 51110 . 51111 print stat cv1 cv2 pval statcdf iindx 51112 . 51113 set skew outlier test critical values astm 51114 skewness outlier test y 51115 set skew outlier test critical values simulation 51116 skewness outlier test y 51117 51118-----SKEWNESS (LET)--------------------------------------------------- 51119 51120SKEWNESS 51121 51122Name: 51123 SKEWNESS (LET) 51124 51125Type: 51126 Let Subcommand 51127 51128Purpose: 51129 Compute the skewness (or standardized third central moment) of a 51130 variable. 51131 51132Description: 51133 Skewness measures the lack of symmetry in a variable. The 51134 formula for the Fisher-Pearson skewness coefficient is: 51135 51136 g1 = (SUM[i=1 to n][(X(i)-Xbar)**3/N))/s**3] 51137 51138 where xbar, s, and N are the sample mean, the sample standard 51139 deviation, and the sample size, respectively. Note that in 51140 computing the skewness, the standard deviation is computed using 51141 n in the denominator rather than n - 1. 51142 51143 The adjusted Fisher-Pearson skewness coefficient is: 51144 51145 G1 = (SQRT(N*(N-1))/(N-1))*(SUM[i=1 to n][(X(i)-Xbar)**3/N))/s**3] 51146 51147 This provides a correction factor to adjust for the sample size. 51148 This adjustment factor approaches 1 as the sample size gets 51149 large. 51150 51151 In Dataplot, you can specify that the adjusted form of the 51152 statistic be computed by entering the command 51153 51154 SET SKEWNESS DEFINITION ADJUSTED FISHER-PEARSON 51155 51156 To reset the unadjusted skewness statistic, enter 51157 51158 SET SKEWNESS DEFINITION FISHER-PEARSON 51159 51160 There are many alternative definitions of skewness in the 51161 literature. Dataplot supports the following two additional 51162 definitions of skewness. 51163 51164 The Galton skewness (also known as Bowley's skewness) is defined as 51165 51166 Galton skewness = (Q1 + Q3 - 2*Q2)/(Q3 - Q1) 51167 51168 where Q1 is the lower quartile, Q3 is the upper quartile, and 51169 Q2 is the median. 51170 51171 The Pearson 2 skewness coefficient is defined as 51172 51173 Sk2 = 3*(Ybar - Ymed)/s 51174 51175 where Ymed is the sample median. 51176 51177Syntax 1: 51178 LET <par> = SKEWNESS <y> <SUBSET/EXCEPT/FOR qualification> 51179 where <y> is the response variable; 51180 <par> is a parameter where the skewness is saved; 51181 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 51182 51183 This syntax computes the Fisher-Pearson skewness. 51184 51185Syntax 2: 51186 LET <par> = GALTON SKEWNESS <y> <SUBSET/EXCEPT/FOR qualification> 51187 where <y> is the response variable; 51188 <par> is a parameter where the skewness is saved; 51189 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 51190 51191 This syntax computes the Galton skewness. 51192 51193Syntax 3: 51194 LET <par> = PEARSON TWO SKEWNESS <y> <SUBSET/EXCEPT/FOR qualification> 51195 where <y> is the response variable; 51196 <par> is a parameter where the skewness is saved; 51197 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 51198 51199 This syntax computes the Pearson two skewness. 51200 51201Examples: 51202 LET A = SKEWNESS Y1 51203 LET A = GALTON SKEWNESS Y1 51204 LET A = PEARSON TWO SKEWNESS Y1 51205 51206Note: 51207 The skewness for a normal distribution is zero. Symmetric data 51208 should have a skewness near zero. Negative values for the skewness 51209 indicate data that are skewed left and positive values for the 51210 skewness indicate data that are skewed right. By skewed left, we 51211 mean that the left tail is long relative to the right tail. 51212 Similarly, skewed right means that the right tail is long relative 51213 to the left tail. Note that if the data are multi-modal, then this 51214 may affect the sign of the skewness. 51215 51216 Measurement data is often bounded below (e.g., the measurement 51217 must be positive) but not above. This type of data will 51218 frequently exhibit right skewness. 51219 51220Note: 51221 Dataplot statistics can be used in a number of commands. For 51222 details, enter 51223 51224 HELP STATISTICS 51225 51226Default: 51227 None 51228 51229Synonyms: 51230 STANDARDIZED THIRD CENTRAL MOMENT 51231 STANDARDIZED 3RD CENTRAL MOMENT 51232 PEARSON 2 SKEWNESS 51233 PEARSON TYPE TWO SKEWNESS 51234 PEARSON TYPE 2 SKEWNESS 51235 51236Related Commands: 51237 MEAN = Compute mean of a variable. 51238 STANDARD DEVIATION = Compute the standard deviation of a variable. 51239 KURTOSIS = Compute the Kurtosis of a variable. 51240 51241Applications: 51242 Data Analysis 51243 51244Implementation Date: 51245 Pre-1987 51246 2013/04: Added adjusted Fisher-Pearson skewness 51247 2014/12: Added Galton skewness 51248 2014/12: Added Pearson two skewness 51249 51250Program: 51251 skip 25 51252 read weibbury.dat y 51253 . 51254 let s1 = skewness y 51255 set skewness definition adjusted fisher pearson 51256 let s2 = skewness y 51257 let s3 = galton skewness y 51258 let s4 = pearson two skewness y 51259 . 51260 set write decimals 4 51261 print s1 s2 s3 s4 51262 51263-----SKEWNESS PLOT----------------------------------------------- 51264 51265SKEWNESS PLOT 51266 51267Name: 51268 SKEWNESS PLOT 51269 51270Type: 51271 Graphics Command 51272 51273Purpose: 51274 Generates a skewness plot. 51275 51276Description: 51277 A skewness plot is a plot consisting of subsample skewnesss versus 51278 subsample index. The subsample skewness is the cube root of the 51279 standardized third central moment of the data in the subsample. 51280 The skewness plot is used to answer the question-- "Does the 51281 subsample skewness change over different subsamples?". It consists 51282 of: 51283 Vertical axis = subsample skewness; 51284 Horizontal axis = subsample index. 51285 The skewness plot yields 2 traces: 51286 1. a subsample skewness trace; and 51287 2. a full-sample skewness reference line. 51288 Like usual, the appearance of these 2 traces is 51289 controlled by the first 2 settings of the LINES, 51290 CHARACTERS, SPIKES, BARS, and similar attributes. 51291 51292Syntax: 51293 SKEWNESS PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 51294 where <y> is the response (= dependent) variable; 51295 <x> is the subsample identifier variable (this variable 51296 appears on the horizontal axis); 51297 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 51298 51299Examples: 51300 SKEWNESS PLOT Y X 51301 SKEWNESS PLOT Y X1 51302 51303Default: 51304 None 51305 51306Synonyms: 51307 None 51308 51309Related Commands: 51310 CHARACTERS = Sets the type for plot char. 51311 LINES = Sets the type for plot lines. 51312 KURTOSIS PLOT = Generates a kurtosis plot. 51313 VARIANCE PLOT = Generates a variance plot. 51314 STANDARD DEVIATION PLOT = Generates a standard deviation plot. 51315 RANGE PLOT = Generates a range plot 51316 MEAN PLOT = Generates a mean plot. 51317 MEDIAN PLOT = Generates a median plot. 51318 BOX PLOT = Generates a box plot. 51319 S CHART = Generates a standard deviation 51320 control chart. 51321 PLOT = Generates a data or function plot. 51322 51323Applications: 51324 Quality Control 51325 51326Implementation Date: 51327 88/2 51328 51329Program: 51330 SKIP 25 51331 READ GEAR.DAT Y X 51332 LINE BLANK DASH 51333 CHARACTER X BLANK 51334 XTIC OFFSET 0.2 0.2 51335 Y1LABEL SKEWNESS 51336 X1LABEL SAMPLE ID 51337 TITLE AUTOMATIC 51338 SKEWNESS PLOT Y X 51339 51340-----SKIP------------------------------------------------------- 51341 51342SKIP 51343 51344Name: 51345 SKIP 51346 51347Type: 51348 Support Command 51349 51350Purpose: 51351 Specifies the number of lines at the beginning of a file that 51352 should be skipped over during subsequent READ and SERIAL READ 51353 commands. 51354 51355Description: 51356 This gives the analyst a convenient method of skipping over 51357 non-data lines (consisting, for example, of descriptive text) 51358 which may exist at the beginning of a data file. 51359 51360Syntax 1: 51361 SKIP <num> 51362 where <num> is an integer number or parameter that specifies the 51363 desired number of lines to be skipped during subsequent 51364 READs and SERIAL READs. 51365 51366Syntax 2: 51367 SKIP AUTOMATIC 51368 51369 This syntax skips until a line beginning with "---" is 51370 found. Note that most of the built-in Dataplot data files 51371 follow this convention. 51372 51373Examples: 51374 SKIP 10 51375 SKIP 3 51376 SKIP 0 51377 SKIP 51378 51379Note: 51380 SKIP with no arguments reverts the number of lines to be skipped 51381 to 0. 51382 51383Default: 51384 The default number of lines to be skipped is 0. 51385 51386Synonyms: 51387 SKIP <N> is identical in function to ROW LIMITS <N> INFINITY. 51388 51389Related Commands: 51390 READ = Carries out a column-wise input of data. 51391 SERIAL READ = Carries out a row-wise input of data. 51392 ROW LIMITS = Specifies the start and stop row for subsequent 51393 READ commands. 51394 51395Applications: 51396 Data Input 51397 51398Implementation Date: 51399 Pre-1987. The SKIP AUTOMATIC option was added 1997/12. 51400 51401Program: 51402 SKIP 25 51403 READ BERGER1.DAT Y X 51404 FIT Y X 51405 51406-----SLACDF (LET)-------------------------------- 51407 51408SLACDF 51409 51410Name: 51411 SLACDF (LET) 51412 51413Type: 51414 Library Function 51415 51416Purpose: 51417 Compute the slash cumulative distribution function. 51418 51419Description: 51420 The standard slash distribution has the following 51421 probability density function: 51422 51423 f(x) = (NORPDF(0) - NORPDF(X))/(X**2) X <> 0 51424 = 0.5*NORPDF(0) X = 0 51425 51426 The slash cumulative distribution function is computed 51427 by numerically integrating the slash probability density 51428 function. 51429 51430 The most common use of the slash distribution is in 51431 simulation studies. It is a useful distribution in this 51432 context because it has heavier tails than a normal distribution, 51433 but it is not as pathological as the Cauchy distribution. 51434 51435Syntax: 51436 LET <y> = SLACDF(<x>) <SUBSET/EXCEPT/FOR qualification> 51437 where <x> is a variable, a number, or a parameter; 51438 <y> is a variable or a parameter (depending on what <x> is) 51439 where the computed slash cdf value is stored; 51440 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 51441 51442Examples: 51443 LET A = SLACDF(3) 51444 LET X2 = SLACDF(X1) 51445 51446Note: 51447 Dataplot uses the DQAGI routine from the Quadpack library 51448 to perform the numerical integration. 51449 51450Note: 51451 Library functions are distinguished from let subcommands 51452 in the following ways. 51453 1) Functions enclose the input value in parenthesis. Let 51454 subcommands use spaces. 51455 2) Functions can accept (and return) either parameters 51456 (i.e., single values) or variables (i.e., an array of 51457 values) while let subcommands are specific in which they 51458 accept as input and what they return as output. 51459 3) Functions can accept expressions while let subcommands 51460 do not. For example, the following is legal: 51461 LET Y2 = ABS(Y1-INT(Y1)) 51462 For let subcommands, you typically have to do something 51463 like the following: 51464 LET YTEMP = Y**2 + 8 51465 LET A = SUM YTEMP 51466 51467Default: 51468 None 51469 51470Synonyms: 51471 None 51472 51473Related Commands: 51474 SLAPDF = Compute the slash probability density function. 51475 SLAPPF = Compute the slash percent point function. 51476 NORPDF = Compute the normal probability density function. 51477 LOGPDF = Compute the logistic probability density function. 51478 CAUPDF = Compute the Cauchy probability density function. 51479 RANDOM NUMBERS = Generate random numbers from 60+ univariate 51480 distributions. 51481 51482Reference: 51483 "Continuous Univariate Distributions: Volume 1", 2nd. Ed., 51484 Johnson, Kotz, and Balakrishnan, John Wiley, 1994, 51485 (page 63). 51486 51487Applications: 51488 Simulation 51489 51490Implementation Date: 51491 2004/1 51492 51493Program: 51494 TITLE SLASH CUMULATIVE DISTRIBUTION FUNCTION 51495 PLOT SLACDF(X) FOR X = -10 0.01 10 51496 51497-----SLAPDF (LET)-------------------------------- 51498 51499SLAPDF 51500 51501Name: 51502 SLAPDF (LET) 51503 51504Type: 51505 Library Function 51506 51507Purpose: 51508 Compute the slash probability density function. 51509 51510Description: 51511 The slash distribution has the following probability density 51512 function: 51513 51514 f(x) = (NORPDF(0) - NORPDF(X))/(X**2) X <> 0 51515 = 0.5*NORPDF(0) X = 0 51516 51517 The most common use of the slash distribution is in 51518 simulation studies. It is a useful distribution in this 51519 context because it has heavier tails than a normal distribution, 51520 but it is not as pathological as the Cauchy distribution. 51521 51522Syntax: 51523 LET <y> = SLAPDF(<x>) <SUBSET/EXCEPT/FOR qualification> 51524 where <x> is a variable, a number, or a parameter; 51525 <y> is a variable or a parameter (depending on what <x> is) 51526 where the computed slash pdf value is stored; 51527 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 51528 51529Examples: 51530 LET A = SLAPDF(3) 51531 LET X2 = SLAPDF(X1) 51532 51533Note: 51534 You can generate random numbers from a slash distribution 51535 with the following command: 51536 51537 LET Y = SLASH RANDOM NUMBERS FOR I = 1 1 N 51538 51539Note: 51540 Library functions are distinguished from let subcommands 51541 in the following ways. 51542 1) Functions enclose the input value in parenthesis. Let 51543 subcommands use spaces. 51544 2) Functions can accept (and return) either parameters 51545 (i.e., single values) or variables (i.e., an array of 51546 values) while let subcommands are specific in which they 51547 accept as input and what they return as output. 51548 3) Functions can accept expressions while let subcommands 51549 do not. For example, the following is legal: 51550 LET Y2 = ABS(Y1-INT(Y1)) 51551 For let subcommands, you typically have to do something 51552 like the following: 51553 LET YTEMP = Y**2 + 8 51554 LET A = SUM YTEMP 51555 51556Default: 51557 None 51558 51559Synonyms: 51560 None 51561 51562Related Commands: 51563 SLACDF = Compute the slash cumulative distribution 51564 function. 51565 SLAPPF = Compute the slash percent point function. 51566 NORPDF = Compute the normal probability density function. 51567 LOGPDF = Compute the logistic probability density function. 51568 CAUPDF = Compute the Cauchy probability density function. 51569 RANDOM NUMBERS = Generate random numbers from 60+ univariate 51570 distributions. 51571 51572Reference: 51573 "Continuous Univariate Distributions: Volume 1", 2nd. Ed., 51574 Johnson, Kotz, and Balakrishnan, John Wiley, 1994, 51575 (page 63). 51576 51577Applications: 51578 Simulation 51579 51580Implementation Date: 51581 2003/3 51582 51583Program: 51584 TITLE SLASH PDF 51585 PLOT SLAPDF(X) FOR X = -10 0.01 10 51586 51587-----SLAPPF (LET)-------------------------------- 51588 51589SLAPPF 51590 51591Name: 51592 SLAPPF (LET) 51593 51594Type: 51595 Library Function 51596 51597Purpose: 51598 Compute the slash percent point function. 51599 51600Description: 51601 The standard slash distribution has the following 51602 probability density function: 51603 51604 f(x) = (NORPDF(0) - NORPDF(X))/(X**2) X <> 0 51605 = 0.5*NORPDF(0) X = 0 51606 51607 The slash cumulative distribution function is computed 51608 by numerically integrating the slash probability density 51609 function. The slash percent point function is computed 51610 by numerically inverting the slash cumulative distribution 51611 function. 51612 51613 The most common use of the slash distribution is in 51614 simulation studies. It is a useful distribution in this 51615 context because it has heavier tails than a normal distribution, 51616 but it is not as pathological as the Cauchy distribution. 51617 51618Syntax: 51619 LET <y> = SLAPPF(<p>) <SUBSET/EXCEPT/FOR qualification> 51620 where <p> is a variable, a number, or a parameter in the range 51621 [0,1]; 51622 <y> is a variable or a parameter (depending on what <p> is) 51623 where the computed slash ppf value is stored; 51624 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 51625 51626Examples: 51627 LET A = SLAPPF(0.95) 51628 LET X2 = SLAPPF(P1) 51629 51630Note: 51631 Library functions are distinguished from let subcommands 51632 in the following ways. 51633 1) Functions enclose the input value in parenthesis. Let 51634 subcommands use spaces. 51635 2) Functions can accept (and return) either parameters 51636 (i.e., single values) or variables (i.e., an array of 51637 values) while let subcommands are specific in which they 51638 accept as input and what they return as output. 51639 3) Functions can accept expressions while let subcommands 51640 do not. For example, the following is legal: 51641 LET Y2 = ABS(Y1-INT(Y1)) 51642 For let subcommands, you typically have to do something 51643 like the following: 51644 LET YTEMP = Y**2 + 8 51645 LET A = SUM YTEMP 51646 51647Default: 51648 None 51649 51650Synonyms: 51651 None 51652 51653Related Commands: 51654 SLACDF = Compute the slash cumulative distribution 51655 function. 51656 SLAPDF = Compute the slash probability density function. 51657 NORPDF = Compute the normal probability density function. 51658 LOGPDF = Compute the logistic probability density function. 51659 CAUPDF = Compute the Cauchy probability density function. 51660 RANDOM NUMBERS = Generate random numbers from 60+ univariate 51661 distributions. 51662 51663Reference: 51664 "Continuous Univariate Distributions: Volume 1", 2nd. Ed., 51665 Johnson, Kotz, and Balakrishnan, John Wiley, 1994, 51666 (page 63). 51667 51668Applications: 51669 Simulation 51670 51671Implementation Date: 51672 2004/1 51673 51674Program: 51675 TITLE SLASH PERCENT POINT FUNCTION 51676 PLOT SLAPPF(P) FOR P = 0.01 0.01 0.99 51677 51678-----SLEEP------------------------------------------------------- 51679 51680SLEEP 51681 51682Name: 51683 SLEEP 51684 51685Type: 51686 Support Command 51687 51688Purpose: 51689 This command pauses for a specified number of seconds. 51690 51691Description: 51692 The primary application of this command is to put a 51693 pause in a macro after a plot. This allows you to view 51694 individual plots in a multi-plot macro without having to 51695 enter carriage returns as you would with the PAUSE command. 51696 51697 This is a system dependent command. It is currently 51698 supported for Unix and Windows 95/98/NT. 51699 51700Syntax: 51701 SLEEP <n> 51702 where <n> specifies the number of seconds the pause will 51703 last. 51704 51705Examples: 51706 PLOT X**2 FOR X = 1 1 9 51707 SLEEP 5 51708 51709Default: 51710 None 51711 51712Synonyms: 51713 None 51714 51715Related Commands: 51716 SYSTEM = Enter an operating system command within a 51717 Dataplot session. 51718 CD = Change the current directory 51719 PAUSE = Wait for a carriage return before continuing. 51720 51721Applications: 51722 Interactive Usage 51723 51724Implementation Date: 51725 1997/9 51726 51727Program: 51728 PLOT X**2 FOR X = 1 1 9 51729 SLEEP 5 51730 51731-----SLOCDF (LET)-------------------------------- 51732 51733SLOCDF 51734 51735Name: 51736 SLOCDF (LET) 51737 51738Type: 51739 Library Function 51740 51741Purpose: 51742 Compute the slope cumulative distribution function 51743 with shape parameter alpha. 51744 51745Description: 51746 The standard slope distribution has the following 51747 cumulative distribution function: 51748 51749 F(x;alpha) = alpha*x + (1-alpha)*x**2 51750 0 <= x <= 1, 0 <= alpha <= 2 51751 51752 with alpha denoting the shape parameter. 51753 51754 This distribution can be extended with lower and upper 51755 bound parameters. If a and b denote the lower and upper 51756 bounds, respectively, then the location and scale 51757 parameters are: 51758 51759 location = a 51760 scale = b - a 51761 51762 The general form of the distribution can then be found 51763 by using the relation 51764 51765 F(x;alpha,a,b) = F((x-a)/(b-a);alpha,0,1) 51766 51767Syntax: 51768 LET <y> = SLOCDF(<x>,<alpha>,<a>,<b>) 51769 <SUBSET/EXCEPT/FOR qualification> 51770 where <x> is a number, parameter, or variable containing 51771 values in the interval (a,b); 51772 <y> is a variable or a parameter (depending on what 51773 <x> is) where the computed slope cdf value 51774 is stored; 51775 <alpha> is a positive number, parameter, or variable that 51776 specifies the shape parameter; 51777 <a> is a number, parameter, or variable that 51778 specifies the lower limit; 51779 <b> is a number, parameter, or variable that 51780 specifies the upper limit; 51781 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 51782 51783 If <a> and <b> are omitted, they default to 0 and 1, 51784 respectively. 51785 51786Examples: 51787 LET A = SLOCDF(0.3,0.2) 51788 LET Y = SLOCDF(X,0.5,0,5) 51789 PLOT SLOCDF(X,2,0,3) FOR X = 0 0.01 3 51790 51791Note: 51792 Library functions are distinguished from let subcommands 51793 in the following ways. 51794 1) Functions enclose the input value in parenthesis. Let 51795 subcommands use spaces. 51796 2) Functions can accept (and return) either parameters 51797 (i.e., single values) or variables (i.e., an array of 51798 values) while let subcommands are specific in which they 51799 accept as input and what they return as output. 51800 3) Functions can accept expressions while let subcommands 51801 do not. For example, the following is legal: 51802 LET Y2 = ABS(Y1-INT(Y1)) 51803 For let subcommands, you typically have to do something 51804 like the following: 51805 LET YTEMP = Y**2 + 8 51806 LET A = SUM YTEMP 51807 51808Default: 51809 None 51810 51811Synonyms: 51812 None 51813 51814Related Commands: 51815 SLOPDF = Compute the slope probability density function. 51816 SLOPPF = Compute the slope percent point function. 51817 TSSPDF = Compute the two-sided slope probability density function. 51818 OGIPDF = Compute the ogive probability density function. 51819 TOPPDF = Compute the Topp and Leone probability density function. 51820 RGTPDF = Compute the generalized reflected slope 51821 probability density function. 51822 GTLPDF = Compute the generalized slope probability 51823 density function. 51824 TSPPDF = Compute the two-sided power probability density 51825 function. 51826 BETPDF = Compute the alpha probability density function. 51827 TRIPDF = Compute the triangular probability density function. 51828 TRAPDF = Compute the trapezoid probability density function. 51829 UNIPDF = Compute the uniform probability density function. 51830 POWPDF = Compute the power probability density function. 51831 JSBPDF = Compute the Johnson SB probability density function. 51832 51833Reference: 51834 Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Alpha: 51835 Other Continuous Families of Distributions with Bounded 51836 Support and Applications", World Scientific, chapter 8. 51837 51838Applications: 51839 Distributional Modeling 51840 51841Implementation Date: 51842 2007/10 51843 51844Program: 51845 LABEL CASE ASIS 51846 TITLE CASE ASIS 51847 TITLE OFFSET 2 51848 . 51849 MULTIPLOT 2 2 51850 MULTIPLOT CORNER COORDINATES 0 0 100 95 51851 MULTIPLOT SCALE FACTOR 2 51852 . 51853 LET ALPHA = 0.5 51854 TITLE Alpha = ^alpha 51855 PLOT SLOCDF(X,ALPHA) FOR X = 0 0.01 1 51856 . 51857 LET ALPHA = 1 51858 TITLE Alpha = ^alpha 51859 PLOT SLOCDF(X,ALPHA) FOR X = 0 0.01 1 51860 . 51861 LET ALPHA = 1.5 51862 TITLE Alpha = ^alpha 51863 PLOT SLOCDF(X,ALPHA) FOR X = 0 0.01 1 51864 . 51865 LET ALPHA = 2 51866 TITLE Alpha = ^alpha 51867 PLOT SLOCDF(X,ALPHA) FOR X = 0 0.01 1 51868 . 51869 END OF MULTIPLOT 51870 . 51871 JUSTIFICATION CENTER 51872 MOVE 50 97 51873 TEXT Slope Cumulative Distribution Functions 51874 51875-----SLOPDF (LET)-------------------------------- 51876 51877SLOPDF 51878 51879Name: 51880 SLOPDF (LET) 51881 51882Type: 51883 Library Function 51884 51885Purpose: 51886 Compute the slope probability density function 51887 with shape parameter alpha. 51888 51889Description: 51890 The standard slope distribution has the following 51891 probability density function: 51892 51893 f(x;alpha) = alpha + 2*(1-alpha)*x 51894 0 <= x <= 1, 0 <= alpha <= 2 51895 51896 with alpha denoting the shape parameter. 51897 51898 This distribution can be extended with lower and upper 51899 bound parameters. If a and b denote the lower and upper 51900 bounds, respectively, then the location and scale 51901 parameters are: 51902 51903 location = a 51904 scale = b - a 51905 51906 The general form of the distribution can then be found 51907 by using the relation 51908 51909 f(x;alpha,a,b) = f((x-a)/(b-a);alpha,0,1)/(b-a) 51910 51911Syntax: 51912 LET <y> = SLOPDF(<x>,<alpha>,<a>,<b>) 51913 <SUBSET/EXCEPT/FOR qualification> 51914 where <x> is a number, parameter, or variable containing 51915 values in the interval (a,b); 51916 <y> is a variable or a parameter (depending on what 51917 <x> is) where the computed slope pdf value 51918 is stored; 51919 <alpha> is a positive number, parameter, or variable that 51920 specifies the shape parameter; 51921 <a> is a number, parameter, or variable that 51922 specifies the lower limit; 51923 <b> is a number, parameter, or variable that 51924 specifies the upper limit; 51925 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 51926 51927 If <a> and <b> are omitted, they default to 0 and 1, 51928 respectively. 51929 51930Examples: 51931 LET A = SLOPDF(0.3,0.2) 51932 LET Y = SLOPDF(X,0.5,0,5) 51933 PLOT SLOPDF(X,2,0,3) FOR X = 0 0.01 3 51934 51935Note: 51936 Slope random numbers, probability plots, and goodness of 51937 fit tests can be generated with the commands: 51938 51939 LET ALPHA = <value> 51940 LET A = <value> 51941 LET B = <value> 51942 LET Y = SLOPE RANDOM NUMBERS FOR I = 1 1 N 51943 SLOPE PROBABILITY PLOT Y 51944 SLOPE PROBABILITY PLOT Y2 X2 51945 SLOPE PROBABILITY PLOT Y3 XLOW XHIGH 51946 SLOPE KOLMOGOROV SMIRNOV GOODNESS OF FIT Y 51947 SLOPE CHI-SQUARE GOODNESS OF FIT Y2 X2 51948 SLOPE CHI-SQUARE GOODNESS OF FIT Y3 XLOW XHIGH 51949 51950 The following commands can be used to estimate the alpha 51951 shape parameter for the slope distribution: 51952 51953 LET ALPHA1 = <value> 51954 LET ALPHA2 = <value> 51955 SLOPE PPCC PLOT Y 51956 SLOPE PPCC PLOT Y2 X2 51957 SLOPE PPCC PLOT Y3 XLOW XHIGH 51958 SLOPE KS PLOT Y 51959 SLOPE KS PLOT Y2 X2 51960 SLOPE KS PLOT Y3 XLOW XHIGH 51961 51962 The default values for ALPHA1 and ALPHA2 are 0.05 and 2. 51963 51964 The probability plot can then be used to estimate the 51965 lower and upper limits (lower limit = PPA0, 51966 upper limit = PPA0 + PPA1). 51967 51968 For the ks plot, we can fix the location and scale. 51969 This is equivalent to assuming that the lower and 51970 upper limits are known (e.g., we could use the 51971 data minimum and maximum as the lower and upper 51972 limit values). Given that the lower and upper 51973 limits are LOWLIM and UPPLIM, enter the commands 51974 51975 LET KSLOC = LOWLIM 51976 LET KSSCALE = UPPLIM - LOWLIM 51977 51978 The ppcc plot is invariant to location and scale, 51979 so we cannot fix the lower and upper limits. 51980 51981 The BOOTSTRAP DISTRIBUTION command can be used to find 51982 uncertainty intervals for the ppcc plot and ks plot. 51983 51984Note: 51985 Library functions are distinguished from let subcommands 51986 in the following ways. 51987 1) Functions enclose the input value in parenthesis. Let 51988 subcommands use spaces. 51989 2) Functions can accept (and return) either parameters 51990 (i.e., single values) or variables (i.e., an array of 51991 values) while let subcommands are specific in which they 51992 accept as input and what they return as output. 51993 3) Functions can accept expressions while let subcommands 51994 do not. For example, the following is legal: 51995 LET Y2 = ABS(Y1-INT(Y1)) 51996 For let subcommands, you typically have to do something 51997 like the following: 51998 LET YTEMP = Y**2 + 8 51999 LET A = SUM YTEMP 52000 52001Default: 52002 None 52003 52004Synonyms: 52005 None 52006 52007Related Commands: 52008 SLOCDF = Compute the slope cumulative distribution 52009 function. 52010 SLOPPF = Compute the slope percent point function. 52011 TSSPDF = Compute the two-sided slope probability density function. 52012 OGIPDF = Compute the ogive probability density function. 52013 TOPPDF = Compute the Topp and Leone probability density function. 52014 RGTPDF = Compute the generalized reflected slope 52015 probability density function. 52016 GTLPDF = Compute the generalized slope probability 52017 density function. 52018 TSPPDF = Compute the two-sided power probability density 52019 function. 52020 BETPDF = Compute the alpha probability density function. 52021 TRIPDF = Compute the triangular probability density function. 52022 TRAPDF = Compute the trapezoid probability density function. 52023 UNIPDF = Compute the uniform probability density function. 52024 POWPDF = Compute the power probability density function. 52025 JSBPDF = Compute the Johnson SB probability density function. 52026 52027Reference: 52028 Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Alpha: 52029 Other Continuous Families of Distributions with Bounded 52030 Support and Applications", World Scientific, chapter 8. 52031 52032Applications: 52033 Distributional Modeling 52034 52035Implementation Date: 52036 2007/10 52037 52038Program 1: 52039 LABEL CASE ASIS 52040 TITLE CASE ASIS 52041 TITLE OFFSET 2 52042 . 52043 MULTIPLOT 2 2 52044 MULTIPLOT CORNER COORDINATES 0 0 100 95 52045 MULTIPLOT SCALE FACTOR 2 52046 . 52047 LET ALPHA = 0.5 52048 TITLE Alpha = ^alpha 52049 PLOT SLOPDF(X,ALPHA) FOR X = 0 0.01 1 52050 . 52051 LET ALPHA = 1 52052 TITLE Alpha = ^alpha 52053 PLOT SLOPDF(X,ALPHA) FOR X = 0 0.01 1 52054 . 52055 LET ALPHA = 1.5 52056 TITLE Alpha = ^alpha 52057 PLOT SLOPDF(X,ALPHA) FOR X = 0 0.01 1 52058 . 52059 LET ALPHA = 2 52060 TITLE Alpha = ^alpha 52061 PLOT SLOPDF(X,ALPHA) FOR X = 0 0.01 1 52062 . 52063 END OF MULTIPLOT 52064 . 52065 JUSTIFICATION CENTER 52066 MOVE 50 97 52067 TEXT Slope Probability Density Functions 52068 52069Program 2: 52070 let alpha = 1.2 52071 let y = slope rand numb for i = 1 1 200 52072 . 52073 let alphasav = alpha 52074 slope ppcc plot y 52075 just center 52076 move 50 5 52077 let alpha = shape 52078 text maxppcc = ^maxppcc, Alpha = ^alpha 52079 move 50 2 52080 text Alphasav = ^alphasav 52081 . 52082 char x 52083 line blank 52084 slope prob plot y 52085 move 50 5 52086 text PPA0 = ^ppa0, PPA1 = ^ppa1 52087 move 50 2 52088 let upplim = ppa0 + ppa1 52089 text Lower Limit = ^ppa0, Upper Limit = ^upplim 52090 char blank 52091 line solid 52092 . 52093 let ksloc = ppa0 52094 let ksscale = upplim 52095 slope kolm smir goodness of fit y 52096 52097-----SLOPE (LET)-------------------------------- 52098 52099SLOPE 52100 52101Name: 52102 SLOPE (LET) 52103 52104Type: 52105 Library Function 52106 52107Purpose: 52108 Return the slope between two points. 52109 52110Description: 52111 Given two points, (X1,Y1) and (X2,Y2), the slope is defined as 52112 52113 m = (Y2-Y1)/(X2-X1) 52114 52115Syntax: 52116 LET <y> = SLOPE(<x1>,<y1>,<x2>,<y2>) 52117 <SUBSET/EXCEPT/FOR qualification> 52118 where <x1> is a variable or a parameter containing the x coordinates 52119 of the first point; 52120 <y1> is a variable or a parameter containing the y coordinates 52121 of the first point; 52122 <x2> is a variable or a parameter containing the x coordinates 52123 of the second point; 52124 <y2> is a variable or a parameter containing the y coordinates 52125 of the second point; 52126 <y> is a variable or a parameter (depending on what the input 52127 arguments are) where the computed slope values are stored; 52128 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 52129 52130Examples: 52131 LET A = SLOPE(0,0,10,15) 52132 LET A = SLOPE(X1,Y1,X2,Y2) 52133 52134Note: 52135 Library functions are distinguished from let subcommands 52136 in the following ways. 52137 1) Functions enclose the input value in parenthesis. Let 52138 subcommands use spaces. 52139 2) Functions can accept (and return) either parameters 52140 (i.e., single values) or variables (i.e., an array of 52141 values) while let subcommands are specific in which they 52142 accept as input and what they return as output. 52143 3) Functions can accept expressions while let subcommands 52144 do not. For example, the following is legal: 52145 LET Y2 = ABS(Y1-INT(Y1)) 52146 For let subcommands, you typically have to do something 52147 like the following: 52148 LET YTEMP = Y**2 + 8 52149 LET A = SUM YTEMP 52150 52151Default: 52152 None 52153 52154Synonyms: 52155 None 52156 52157Related Commands: 52158 DPNTLINE = Compute the perpindicular distance between a point 52159 and a line defined by a point and a slope. 52160 POINTS IN POLYGON = Determine whether points are in the interior 52161 of a convex polygon. 52162 CONVEX HULL = Determine the convex hull of a set of points. 52163 TRANSFORM POINTS = Perform location, scale, and rotation 52164 transformation for a set of points. 52165 EXTREME POINTS = Determine the extreme points of a set of points. 52166 LINE INTERSECTIONS = Determine the intersection points for a set of 52167 lines. 52168 PARALLEL LINE = Determine the coordinates for a point that defines 52169 a parallel line determined by a point and a line 52170 defined by two points. 52171 PERPINDICULAR LINE = Determine the coordinates for a point that defines 52172 a perpindicular line determined by a point and a 52173 line defined by two points. 52174 52175Applications: 52176 Computational Geometry 52177 52178Implementation Date: 52179 2013/01 52180 52181Program: 52182 skip 25 52183 read convhull.dat x y 52184 . 52185 let y2 x2 = 2d convex hull y x 52186 let xtemp = x2(1) 52187 let ytemp = y2(1) 52188 let y2 = combine y2 ytemp 52189 let x2 = combine x2 xtemp 52190 let x3 = x2 52191 let y3 = y2 52192 let n = size y2 52193 let nm1 = n - 1 52194 retain x2 y2 for i = 1 1 nm1 52195 retain x3 y3 for i = 2 1 n 52196 let slope = slope(x2,y2,x3,y3) 52197 . 52198 set write decimals 4 52199 print x2 y2 x3 y3 slope 52200 52201-----SLOPPF (LET)-------------------------------- 52202 52203SLOPPF 52204 52205Name: 52206 SLOPPF (LET) 52207 52208Type: 52209 Library Function 52210 52211Purpose: 52212 Compute the slope percent point function with shape 52213 parameter alpha. 52214 52215Description: 52216 The standard slope distribution has the following 52217 percent point function: 52218 52219 G(p;alpha) = p alpha = 1 52220 = {-alpha + 52221 SQRT(alpha**2 + 4*p*(1-alpha))}/ 52222 (2*(1-alpha)) alpha <> 1 52223 52224 0 <= p <= 1, 0 <= alpha <= 2 52225 52226 with alpha denoting the shape parameter. 52227 52228 This distribution can be extended with lower and upper 52229 bound parameters. If a and b denote the lower and upper 52230 bounds, respectively, then the location and scale 52231 parameters are: 52232 52233 location = a 52234 scale = b - a 52235 52236 The general form of the distribution can then be found 52237 by using the relation 52238 52239 G(p;alpha,a,b) = a + (b-a)*G(p;alpha,0,1) 52240 52241Syntax: 52242 LET <y> = SLOPPF(<p>,<alpha>,<a>,<b>) 52243 <SUBSET/EXCEPT/FOR qualification> 52244 where <p> is a number, parameter, or variable containing 52245 values in the interval (0,1); 52246 <y> is a variable or a parameter (depending on what 52247 <p> is) where the computed slope ppf value 52248 is stored; 52249 <alpha> is a positive number, parameter, or variable that 52250 specifies the shape parameter; 52251 <a> is a number, parameter, or variable that 52252 specifies the lower limit; 52253 <b> is a number, parameter, or variable that 52254 specifies the upper limit; 52255 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 52256 52257 If <a> and <b> are omitted, they default to 0 and 1, 52258 respectively. 52259 52260Examples: 52261 LET A = SLOPPF(0.95,0.2) 52262 LET Y = SLOPPF(X,0.5,0,5) 52263 PLOT SLOPPF(P,2,0,3) FOR P = 0 0.01 1 52264 52265Note: 52266 Library functions are distinguished from let subcommands 52267 in the following ways. 52268 1) Functions enclose the input value in parenthesis. Let 52269 subcommands use spaces. 52270 2) Functions can accept (and return) either parameters 52271 (i.e., single values) or variables (i.e., an array of 52272 values) while let subcommands are specific in which they 52273 accept as input and what they return as output. 52274 3) Functions can accept expressions while let subcommands 52275 do not. For example, the following is legal: 52276 LET Y2 = ABS(Y1-INT(Y1)) 52277 For let subcommands, you typically have to do something 52278 like the following: 52279 LET YTEMP = Y**2 + 8 52280 LET A = SUM YTEMP 52281 52282Default: 52283 None 52284 52285Synonyms: 52286 None 52287 52288Related Commands: 52289 SLOCDF = Compute the slope cumulative distribution function. 52290 SLOPDF = Compute the slope probability density function. 52291 TSSPDF = Compute the two-sided slope probability density function. 52292 OGIPDF = Compute the ogive probability density function. 52293 TOPPDF = Compute the Topp and Leone probability density function. 52294 RGTPDF = Compute the generalized reflected slope 52295 probability density function. 52296 GTLPDF = Compute the generalized slope probability 52297 density function. 52298 TSPPDF = Compute the two-sided power probability density 52299 function. 52300 BETPDF = Compute the alpha probability density function. 52301 TRIPDF = Compute the triangular probability density function. 52302 TRAPDF = Compute the trapezoid probability density function. 52303 UNIPDF = Compute the uniform probability density function. 52304 POWPDF = Compute the power probability density function. 52305 JSBPDF = Compute the Johnson SB probability density function. 52306 52307Reference: 52308 Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Alpha: 52309 Other Continuous Families of Distributions with Bounded 52310 Support and Applications", World Scientific, chapter 8. 52311 52312Applications: 52313 Distributional Modeling 52314 52315Implementation Date: 52316 2007/10 52317 52318Program: 52319 LABEL CASE ASIS 52320 TITLE CASE ASIS 52321 TITLE OFFSET 2 52322 . 52323 MULTIPLOT 2 2 52324 MULTIPLOT CORNER COORDINATES 0 0 100 95 52325 MULTIPLOT SCALE FACTOR 2 52326 . 52327 LET ALPHA = 0.5 52328 TITLE Alpha = ^alpha 52329 PLOT SLOPPF(P,ALPHA) FOR P = 0 0.01 1 52330 . 52331 LET ALPHA = 1 52332 TITLE Alpha = ^alpha 52333 PLOT SLOPPF(P,ALPHA) FOR P = 0 0.01 1 52334 . 52335 LET ALPHA = 1.5 52336 TITLE Alpha = ^alpha 52337 PLOT SLOPPF(P,ALPHA) FOR P = 0 0.01 1 52338 . 52339 LET ALPHA = 2 52340 TITLE Alpha = ^alpha 52341 PLOT SLOPPF(P,ALPHA) FOR P = 0 0.01 1 52342 . 52343 END OF MULTIPLOT 52344 . 52345 JUSTIFICATION CENTER 52346 MOVE 50 97 52347 TEXT Slope Percent Point Functions 52348 52349-----SMALLEST (LET)------------------------------------- 52350 52351SMALLEST 52352 52353Name: 52354 SMALLEST (LET) 52355 52356Type: 52357 Let Subcommand 52358 52359Purpose: 52360 Extract the smallest elements of a variable. 52361 52362Description: 52363 This is a generalization of the MINIMUM command. However, instead of 52364 returning the single smallest value, it returns the user specified 52365 number of smallest values. 52366 52367 The values will be returned in sorted order. If the requested number 52368 of smallest values is less than 1, then an error will be returned. If 52369 the requested number of smallest values is greater than the number of 52370 observations in the response variable, then the full response variable 52371 will be returned in sorted order. 52372 52373Syntax: 52374 LET <y> = SMALLEST <x> <nval> <SUBSET/EXCEPT/FOR> 52375 where <x> is a response variable; 52376 <nval> is a number or parameter that specifies how 52377 many values to extract; 52378 <y> is a variable that contains the smallest values. 52379 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 52380 52381Examples: 52382 LET NVAL = 3 52383 LET Y = SMALLEST X NVAL 52384 52385 LET Y = SMALLEST X 3 52386 LET Y = SMALLEST X 5 52387 LET Y = SMALLEST X 5 FOR I = 1 1 500 52388 52389Default: 52390 None 52391 52392Synonyms: 52393 None 52394 52395Related Commands: 52396 LARGEST = Return the largest values in a variable. 52397 MAXIMUM = Return the maximum value of a variable. 52398 MINIMUM = Return the minimum value of a variable. 52399 52400Applications: 52401 Data Transformation 52402 52403Implementation Date: 52404 2018/10 52405 52406Program: 52407 let y = normal random numbers for i = 1 1 100 52408 let nval = 5 52409 let yout = smallest y nval 52410 set write decimals 3 52411 print yout 52412 52413-----SMOOTH------------------------------------------------------- 52414 52415SMOOTH 52416 52417Name: 52418 ... SMOOTH 52419 52420Type: 52421 Analysis Command 52422 52423Purpose: 52424 Carries out 52425 1) least squares smoothing; 52426 2) moving average type smoothing; 52427 2) robust smoothing. 52428 52429Description: 52430 These are data analysis techniques for producing a "smooth" set of 52431 values from a time series which has been contaminated with noise. 52432 For least squares smoothing, the analyst can specify the 52433 1) degree (default = 1); and 52434 2) width (default = 3) 52435 of the smoothing function. Any smoothing function from degree 0 to 52436 degree 5 may be used (moving average smoothing is mathematically 52437 equivalent to both degree 0 and degree 1 smoothing). To specify 52438 the desired degree, the POLYNOMIAL DEGREE command should be used 52439 prior to the SMOOTH command. Alternatively (and more commonly) the 52440 desired degree can be specified as the first word of the SMOOTH 52441 command. Thus 52442 POLYNOMIAL DEGREE 3 52443 SMOOTH Y 52444 can be shortened to 52445 CUBIC SMOOTH Y 52446 To specify the width of the least squares smoothing function, the 52447 FILTER WIDTH command should be used prior to the SMOOTH command. 52448 The filter width must be odd. For robust smoothing, the 3RSR 52449 smoother (developed by John Tukey) is used. For the 3RSR smoother, 52450 the filter width is always 3 (and so the FILTER WIDTH command is 52451 not needed). The 3RSR smoother involves 4 steps: 52452 1) computes 3-term moving medians; 52453 2) computes 3-term medians of the 3-term medians repeatedly 52454 until no change; 52455 3) applies a "splitting" process; 52456 4) repeats the splitting process until no change. 52457 See the Tukey book for complete details of the robust smoothing. 52458 52459Syntax 1: 52460 <d> SMOOTH <y> <SUBSET/EXCEPT/FOR qualification> 52461 where <d> is the specification of the desired degree: 52462 CONSTANT or ZERO-DEGREE 52463 LINEAR or FIRST-DEGREE 52464 QUADRATIC or SECOND-DEGREE 52465 CUBIC or THIRD-DEGREE 52466 QUARTIC or FOURTH-DEGREE 52467 QUINTIC or FIFTH-DEGREE 52468 <y> is the variable under analysis; 52469 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 52470 52471Syntax 2: 52472 ROBUST SMOOTH <y> <SUBSET/EXCEPT/FOR qualification> 52473 <y> is the variable under analysis; 52474 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 52475 52476Syntax 3: 52477 <stat> SMOOTH <y> <SUBSET/EXCEPT/FOR qualification> 52478 where <stat> is the specification of the type of smoothing: 52479 MOVING AVERAGE 52480 MOVING MEDIAN 52481 MOVING MIDMEAN 52482 MOVING MIDRANGE 52483 MOVING UPPER QUARTILE 52484 MOVING LOWER QUARTILE 52485 MOVING MAXIMUM 52486 MOVING MINIMUM 52487 MOVING TRIANGLE 52488 MOVING HAMMING; 52489 <y> is the variable under analysis; 52490 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 52491 52492Examples: 52493 LINEAR SMOOTH Y 52494 QUADRATIC SMOOTH TEMP 52495 CUBIC SMOOTH V 52496 ROBUST SMOOTH CONC 52497 MOVING MEDIAN SMOOTH Y 52498 52499Note: 52500 The smoothed values are stored in the internal variable PRED. The 52501 internal variable RES contains the difference between the observed 52502 values (i.e., the raw data) and the smoothed values. 52503 52504Note: 52505 See the sources under the REFERENCE section for the mathematical 52506 details of the various type of smoothing operations. 52507 52508Note: 52509 The least squares SMOOTH command assumes equispaced data. The 52510 LOWESS SMOOTH command performs locally weighted least squares 52511 smoothing and can be used for non-equispaced data. 52512 52513Default: 52514 For least squares smoothing, the default is degree 1 and filter 52515 width 3 (that is, moving average smoothing of width 3). 52516 52517Synonyms: 52518 MOVING AVERAGE SMOOTH is identical to LINEAR SMOOTH. 52519 52520Related Commands: 52521 POLYNOMIAL DEGREE = Sets the degree for least squares smoothing. 52522 FILTER WIDTH = Sets the filter width for least squares 52523 smoothing. 52524 LOWESS SMOOTH = Carries out a locally weighted least squares 52525 smoothing. 52526 FIT = Carries out a least squares fit. 52527 52528References: 52529 "Introduction to Numerical Analysis", F. B. Hildebrand, Dover 52530 Press, (pp. 295-302, especially 301). 52531 52532 "A First Course in Numerical Analysis", Anthony Ralston, 52533 (pp. 250-254). 52534 52535 "Smoothing and Differentiation of Data by Simplified Least Squares 52536 Procedures", A. Savitsky M. J. E. Golay, Analytical Chemistry, 52537 July, 1964, (pp. 1627-1639). 52538 52539 "Exploratory Data Analysis", John Tukey, Addison-Wesley, 1977. 52540 52541Applications: 52542 XX 52543 52544Implementation Date: 52545 XX 52546 52547Program: 52548 SKIP 25 52549 READ MAVRO.DAT Y 52550 LET N = SIZE Y 52551 LET X = SEQUENCE 1 1 N 52552 . 52553 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 52554 TITLE AUTOMATIC 52555 CHARACTER SIZE 1.2 52556 CHAR X BLANK 52557 LINES BLANK SOLID 52558 PLOT Y 52559 TITLE LEAST SQUARES CUBIC SMOOTH 52560 CAPTURE SMOOTH_OUT.DAT 52561 CUBIC SMOOTH Y 52562 PLOT Y PRED VS X 52563 ROBUST SMOOTH Y 52564 TITLE ROBUST SMOOTH 52565 PLOT Y PRED VS X 52566 MOVING MEDIAN SMOOTH Y 52567 END OF CAPTURE 52568 TITLE MOVING MEDIAN SMOOTH 52569 PLOT Y PRED VS X 52570 END OF MULTIPLOT 52571 52572-----SN (LET)---------------------------------------------- 52573 52574SN 52575 52576Name: 52577 SN (LET) 52578 52579Type: 52580 Library Function 52581 52582Purpose: 52583 Compute the Jacobi elliptic function sn. 52584 52585Description: 52586 The Jacobi elliptic function sn is defined as: 52587 sn(u,k)=SIN(phi) 52588 where phi is the amplitude and is defined as: 52589 u = INTEGRAL(1./SQRT(1-k*sin(theta)*sin(theta)))dtheta 52590 where INTEGRAL is the integral from 0 to phi. 52591 52592 The algorithm DATAPLOT uses takes MC=1-k**2 as its second 52593 argument rather than k. Be aware that other routines take k**2 52594 as the second argument (e.g., IMSL, NAG, and mathematica). If 52595 you want to use k**2, enter something like the following: 52596 LET K2 = <value> 52597 LET MC = 1 - K2 52598 52599Syntax: 52600 LET <a> = SN(<u>,<mc>) <SUBSET/EXCEPT/FOR qualification> 52601 where <u> is a number, parameter, or variable; 52602 <mc> is a number, parameter, or variable; 52603 <a> is a variable or a parameter (depending on what <u> 52604 and <mc> are) where the computed values are stored; 52605 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 52606 52607Examples: 52608 LET A = SN(2,1) 52609 LET A = SN(X,0.5) 52610 LET X2 = SN(9,0) 52611 52612Note: 52613 The Jacobi elliptic functions are computed using a Fortran 52614 translation of the Algol-60 procedure given by Bulirsch (see the 52615 REFERENCE section below). 52616 52617Note: 52618 DATAPLOT computes the Jacobi elliptic functions sn, cn, and dn. 52619 An additional 9 functions can be computed from these: 52620 cd(u,k) = cn(u,k)/dn(u,k) 52621 sd(u,k) = sn(u,k)/dn(u,k) 52622 nd(u,k) = 1/dn(u,k) 52623 dc(u,k) = dn(u,k)/cn(u,k) 52624 nc(u,k) = 1/cn(u,k) 52625 sc(u,k) = sn(u,k)/cn(u,k) 52626 ns(u,k) = 1/sn(u,k) 52627 ds(u,k) = dn(u,k)/sn(u,k) 52628 cs(u,k) = cn(u,k)/sn(u,k) 52629 52630Note: 52631 Library functions are distinguished from let subcommands 52632 in the following ways. 52633 1) Functions enclose the input value in parenthesis. Let 52634 subcommands use spaces. 52635 2) Functions can accept (and return) either parameters 52636 (i.e., single values) or variables (i.e., an array of 52637 values) while let subcommands are specific in which they 52638 accept as input and what they return as output. 52639 3) Functions can accept expressions while let subcommands 52640 do not. For example, the following is legal: 52641 LET Y2 = ABS(Y1-INT(Y1)) 52642 For let subcommands, you typically have to do something 52643 like the following: 52644 LET YTEMP = Y**2 + 8 52645 LET A = SUM YTEMP 52646 52647Default: 52648 None 52649 52650Synonyms: 52651 None 52652 52653Related Commands: 52654 CN = Compute the Jacobi elliptic function cn. 52655 DN = Compute the Jacobi elliptic function dn. 52656 PEQ = Compute the real component of the Weirstrass elliptic 52657 function (equianharmonic case). 52658 PEQI = Compute the complex component of the Weirstrass elliptic 52659 function (equianharmonic case). 52660 PLEM = Compute the real component of the Weirstrass elliptic 52661 function (lemniscatic case). 52662 PLEMI = Compute the complex component of the Weirstrass elliptic 52663 function (lemniscatic case). 52664 RC = Compute the Carlson degenerate elliptic integral. 52665 RF = Compute the Carlson elliptic integral of the first kind. 52666 RD = Compute the Carlson elliptic integral of the second kind. 52667 RJ = Compute the Carlson elliptic integral of the third kind. 52668 ELLIPC1 = Compute the Legendre complete elliptic integral of the 52669 first kind. 52670 ELLIPC2 = Compute the Legendre complete elliptic integral of the 52671 second kind. 52672 ELLIP1 = Compute the Legendre elliptic integral of the first 52673 kind. 52674 ELLIP2 = Compute the Legendre elliptic integral of the second 52675 kind. 52676 ELLIP3 = Compute the Legendre's elliptic integral of the third 52677 kind. 52678 52679Reference: 52680 "Numerical Calculation of Elliptic Integrals and Elliptic 52681 Functions", Bulirsch, Numerische Mathematik, vol. 7, 1965 52682 (pp. 78-90). 52683 52684 "Handbook of Mathematical Functions, Applied Mathematics Series, 52685 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 52686 1964 (chapter 16). 52687 52688Applications: 52689 Special Functions 52690 52691Implementation Date: 52692 94/11 52693 52694Program: 52695 TITLE JACOBI ELLIPTIC FUNCTIONS 52696 LET MC = 0.5 52697 LINE SOLID DASH DOT 52698 PLOT SN(X,MC) FOR X = -10 0.1 10 AND 52699 PLOT CN(X,MC) FOR X = -10 0.1 10 AND 52700 PLOT DN(X,MC) FOR X = -10 0.1 10 52701 52702-----SNCDF (LET)-------------------------------- 52703 52704SNCDF 52705 52706Name: 52707 SNCDF (LET) 52708 52709Type: 52710 Library Function 52711 52712Purpose: 52713 Compute the skew-normal cumulative distribution function. 52714 52715Description: 52716 The skew-normal distribution has the following probability density 52717 function: 52718 52719 f(x,lambda)=2*NORCDF(lambda*x)*NORPDF(x) 52720 -infinity < x, lambda < infinity 52721 52722 For lambda = 0, the skew-normal reduces to a normal distribution. 52723 As lambda goes to infinity, the skew-normal tends to the 52724 half-normal distribution. 52725 52726 The cumulative distribution function is computed by numerically 52727 integrating the skew-normal density function. 52728 52729 The standard skew-normal distribution can be generalized with 52730 location and scale parameters. 52731 52732Syntax: 52733 LET <y> = SNCDF(<x>,<lambda>,<loc>,<scale>) 52734 <SUBSET/EXCEPT/FOR qualification> 52735 where <x> is a variable or a parameter; 52736 <lambda> is a number of parameter that specifies the 52737 value of the shape parameter; 52738 <loc> is an optional number or parameter that specifies the 52739 value of the location parameter; 52740 <scale> is an optional positive number or parameter that 52741 specifies the value of the scale parameter; 52742 <y> is a variable or a parameter (depending on what <x> is) 52743 where the computed skew-normal cdf value is stored; 52744 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 52745 52746Examples: 52747 LET A = SNCDF(3,1) 52748 LET A = SNCDF(A1,LAMBDA) 52749 LET X2 = SNCDF(X1,0.5) 52750 52751Note: 52752 Dataplot uses the DQAGI subroutine of Piessens and De Doncker 52753 from the Quadpack library of integration routines. 52754 52755Note: 52756 Library functions are distinguished from let subcommands 52757 in the following ways. 52758 1) Functions enclose the input value in parenthesis. Let 52759 subcommands use spaces. 52760 2) Functions can accept (and return) either parameters 52761 (i.e., single values) or variables (i.e., an array of 52762 values) while let subcommands are specific in which they 52763 accept as input and what they return as output. 52764 3) Functions can accept expressions while let subcommands 52765 do not. For example, the following is legal: 52766 LET Y2 = ABS(Y1-INT(Y1)) 52767 For let subcommands, you typically have to do something 52768 like the following: 52769 LET YTEMP = Y**2 + 8 52770 LET A = SUM YTEMP 52771 52772Default: 52773 None 52774 52775Synonyms: 52776 None 52777 52778Related Commands: 52779 SNPDF = Compute the skew-normal probability density function. 52780 SNPPF = Compute the skew-normal percent point function. 52781 NORPDF = Compute the normal density function. 52782 CHIPDF = Compute the chi probability density function. 52783 CHSPDF = Compute the chi-square probability density function. 52784 WEIPDF = Compute the Weibull probability density function. 52785 52786Reference: 52787 "A Class of Distributions Which Includes the Normal Ones", 52788 Azzalini, Scandinavian Journal of Statistics, 12, 171-178. 52789 52790 "Continuous Univariate Distributions: Volume I", Second Edition, 52791 Johnson, Kotz, and Balakrishnan, Wiley, 1994, p. 454. 52792 52793Applications: 52794 Distributional Analysis, Bayesian Analysis 52795 52796Implementation Date: 52797 1/2004 52798 52799Program: 52800 MULTIPLOT 2 2 52801 MULTIPLOT CORNER COORDINATES 0 0 100 100 52802 TITLE SKEW-NORMAL: LAMBDA = 0 52803 PLOT SNCDF(X,0) FOR X = -5 0.1 5 52804 TITLE SKEW-NORMAL: LAMBDA = 1 52805 PLOT SNCDF(X,1) FOR X = -5 0.1 5 52806 TITLE SKEW-NORMAL: LAMBDA = 5 52807 PLOT SNCDF(X,5) FOR X = -5 0.1 5 52808 TITLE SKEW-NORMAL: LAMBDA = 10 52809 PLOT SNCDF(X,10) FOR X = -5 0.1 5 52810 END OF MULTIPLOT 52811 52812-----SNPDF (LET)-------------------------------- 52813 52814SNPDF 52815 52816Name: 52817 SNPDF (LET) 52818 52819Type: 52820 Library Function 52821 52822Purpose: 52823 Compute the skew-normal probability density function. 52824 52825Description: 52826 The skew-normal distribution has the following probability density 52827 function: 52828 52829 f(x,lambda)=2*NORCDF(lambda*x)*NORPDF(x) 52830 -infinity < x, lambda < infinity 52831 52832 For lambda = 0, the skew-normal reduces to a normal distribution. 52833 As lambda goes to infinity, the skew-normal tends to the 52834 half-normal distribution. 52835 52836 The standard skew-normal distribution can be generalized with 52837 location and scale parameters. 52838 52839Syntax: 52840 LET <y> = SNPDF(<x>,<lambda>,<loc>,<scale>) 52841 <SUBSET/EXCEPT/FOR qualification> 52842 where <x> is a variable or a parameter; 52843 <lambda> is a number of parameter that specifies the 52844 value of the shape parameter; 52845 <loc> is an optional number or parameter that specifies the 52846 value of the location parameter; 52847 <scale> is an optional positive number or parameter that 52848 specifies the value of the scale parameter; 52849 <y> is a variable or a parameter (depending on what <x> is) 52850 where the computed skew-normal pdf value is stored; 52851 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 52852 52853Examples: 52854 LET A = SNPDF(3,1) 52855 LET A = SNPDF(A1,LAMBDA) 52856 LET X2 = SNPDF(X1,0.5) 52857 52858Note: 52859 Library functions are distinguished from let subcommands 52860 in the following ways. 52861 1) Functions enclose the input value in parenthesis. Let 52862 subcommands use spaces. 52863 2) Functions can accept (and return) either parameters 52864 (i.e., single values) or variables (i.e., an array of 52865 values) while let subcommands are specific in which they 52866 accept as input and what they return as output. 52867 3) Functions can accept expressions while let subcommands 52868 do not. For example, the following is legal: 52869 LET Y2 = ABS(Y1-INT(Y1)) 52870 For let subcommands, you typically have to do something 52871 like the following: 52872 LET YTEMP = Y**2 + 8 52873 LET A = SUM YTEMP 52874 52875Default: 52876 None 52877 52878Synonyms: 52879 None 52880 52881Related Commands: 52882 SNCDF = Compute the skew-normal cumulative distribution function. 52883 SNPPF = Compute the skew-normal percent point function. 52884 NORPDF = Compute the normal density function. 52885 CHIPDF = Compute the chi probability density function. 52886 CHSPDF = Compute the chi-square probability density function. 52887 WEIPDF = Compute the Weibull probability density function. 52888 52889Reference: 52890 "A Class of Distributions Which Includes the Normal Ones", 52891 Azzalini, Scandinavian Journal of Statistics, 12, 171-178. 52892 52893 "Continuous Univariate Distributions: Volume I", Second Edition, 52894 Johnson, Kotz, and Balakrishnan, Wiley, 1994, p. 454. 52895 52896Applications: 52897 Distributional Analysis, Bayesian Analysis 52898 52899Implementation Date: 52900 1/2004 52901 52902Program: 52903 MULTIPLOT 2 2 52904 MULTIPLOT CORNER COORDINATES 0 0 100 100 52905 TITLE SKEW-NORMAL: LAMBDA = 0 52906 PLOT SNPDF(X,0) FOR X = -5 0.1 5 52907 TITLE SKEW-NORMAL: LAMBDA = 1 52908 PLOT SNPDF(X,1) FOR X = -5 0.1 5 52909 TITLE SKEW-NORMAL: LAMBDA = 5 52910 PLOT SNPDF(X,5) FOR X = -5 0.1 5 52911 TITLE SKEW-NORMAL: LAMBDA = 10 52912 PLOT SNPDF(X,10) FOR X = -5 0.1 5 52913 END OF MULTIPLOT 52914 52915-----SNPPF (LET)-------------------------------- 52916 52917SNPPF 52918 52919Name: 52920 SNPPF (LET) 52921 52922Type: 52923 Library Function 52924 52925Purpose: 52926 Compute the skew-normal percent point function. 52927 52928Description: 52929 The skew-normal distribution has the following probability density 52930 function: 52931 52932 f(x,lambda)=2*NORCDF(lambda*x)*NORPDF(x) 52933 -infinity < x, lambda < infinity 52934 52935 For lambda = 0, the skew-normal reduces to a normal distribution. 52936 As lambda goes to infinity, the skew-normal tends to the 52937 half-normal distribution. 52938 52939 The skew-normal percent point function is computed by numerically 52940 inverting the skew-normal cumulative distribution function (which 52941 in turn is computed by numerically integrating the skew-normal 52942 density function). 52943 52944 The standard skew-normal distribution can be generalized with 52945 location and scale parameters. 52946 52947Syntax: 52948 LET <y> = SNPPF(<p>,<lambda>,<loc>,<scale>) 52949 <SUBSET/EXCEPT/FOR qualification> 52950 where <p> is a variable or a parameter in the range (0,1); 52951 <lambda> is a number of parameter that specifies the 52952 value of the shape parameter; 52953 <loc> is an optional number or parameter that specifies the 52954 value of the location parameter; 52955 <scale> is an optional positive number or parameter that 52956 specifies the value of the scale parameter; 52957 <y> is a variable or a parameter (depending on what <x> is) 52958 where the computed skew-normal ppf value is stored; 52959 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 52960 52961Examples: 52962 LET A = SNPPF(0.95,1) 52963 LET A = SNPPF(A1,LAMBDA) 52964 LET X = SNPPF(P1,0.5) 52965 52966Note: 52967 Library functions are distinguished from let subcommands 52968 in the following ways. 52969 1) Functions enclose the input value in parenthesis. Let 52970 subcommands use spaces. 52971 2) Functions can accept (and return) either parameters 52972 (i.e., single values) or variables (i.e., an array of 52973 values) while let subcommands are specific in which they 52974 accept as input and what they return as output. 52975 3) Functions can accept expressions while let subcommands 52976 do not. For example, the following is legal: 52977 LET Y2 = ABS(Y1-INT(Y1)) 52978 For let subcommands, you typically have to do something 52979 like the following: 52980 LET YTEMP = Y**2 + 8 52981 LET A = SUM YTEMP 52982 52983Default: 52984 None 52985 52986Synonyms: 52987 None 52988 52989Related Commands: 52990 SNCDF = Compute the skew-normal cumulative distribution function. 52991 SNPDF = Compute the skew-normal probability density function. 52992 NORPDF = Compute the normal density function. 52993 CHIPDF = Compute the chi probability density function. 52994 CHSPDF = Compute the chi-square probability density function. 52995 WEIPDF = Compute the Weibull probability density function. 52996 52997Reference: 52998 "A Class of Distributions Which Includes the Normal Ones", 52999 Azzalini, Scandinavian Journal of Statistics, 12, 171-178. 53000 53001 "Continuous Univariate Distributions: Volume I", Second Edition, 53002 Johnson, Kotz, and Balakrishnan, Wiley, 1994, p. 454. 53003 53004Applications: 53005 Distributional Analysis, Bayesian Analysis 53006 53007Implementation Date: 53008 1/2004 53009 53010Program: 53011 MULTIPLOT 2 2 53012 MULTIPLOT CORNER COORDINATES 0 0 100 100 53013 TITLE SKEW-NORMAL: LAMBDA = 0 53014 PLOT SNPPF(P,0) FOR P = 0.01 0.01 0.99 53015 TITLE SKEW-NORMAL: LAMBDA = 1 53016 PLOT SNPPF(P,1) FOR P = 0.01 0.01 0.99 53017 TITLE SKEW-NORMAL: LAMBDA = 5 53018 PLOT SNPPF(P,5) FOR P = 0.01 0.01 0.99 53019 TITLE SKEW-NORMAL: LAMBDA = 10 53020 PLOT SNPPF(P,10) FOR P = 0.01 0.01 0.99 53021 END OF MULTIPLOT 53022 53023-----SN SCALE (LET)------------------------------- 53024 53025SN SCALE 53026 53027Name: 53028 SN SCALE (LET) 53029 53030Type: 53031 Let Subcommand 53032 53033Purpose: 53034 Compute the Sn scale estimate for a variable. 53035 53036Description: 53037 Mosteller and Tukey (see Reference section below) define 53038 two types of robustness: 53039 53040 1) resistance means that changing a small part, even by a 53041 large amount, of the data does not cause a large change 53042 in the estimate 53043 53044 2) robustness of efficiency means that the statistic has 53045 high efficiency in a variety of situations rather than 53046 in any one situation. Efficiency means that the estimate 53047 is close to optimal estimate given that we know what 53048 distribution that the data comes from. A useful measure 53049 of efficiency is: 53050 53051 Efficiency = (lowest variance feasible)/ 53052 (actual variance) 53053 53054 Many statistics have one of these properties. However, 53055 it can be difficult to find statistics that are both 53056 resistant and have robustness of efficiency. 53057 53058 The most common estimate of scale, the standard deviation, 53059 is the most efficient estimate of scale if the data come from 53060 a normal distribution. However, the standard deviation is 53061 not robust in the sense that changing even one value can 53062 dramatically change the computed value of the standard deviation 53063 (i.e., poor resistance). In addition, it does not have 53064 robustness of efficiency for non-normal data. 53065 53066 The median absolute deviation (MAD) and interquartile range are 53067 the two most commonly used robust alternatives to the standard 53068 deviation. The MAD in particular is a very robust scale 53069 estimator. However, the MAD has the following limitations: 53070 53071 1) It does not have particularly high efficiency for 53072 data that is in fact normal (37%). In comparison, the 53073 median has 64% efficiency for normal data. 53074 53075 2) The MAD statistic also has an implicit assumption of 53076 symmetry. That is, it measures the distance from a 53077 measure of central location (the median). 53078 53079 Rousseeuw and Croux proposed the Sn estimate of scale as an 53080 alternative to the MAD. It shares desirable robustness 53081 properties with MAD (50% breakdown point, bounded influence 53082 function). In addition, it has significantly better normal 53083 efficiency (58%) and it does not depend on symmetry. 53084 53085 The Sn scale estimate is defined as: 53086 53087 Sn = c*MEDIAN(i){MEDIAN(j)|x(i) - x(j)|} 53088 53089 That is, for each i we compute the median of 53090 {|x(i) - x(j)|; j = 1, ..., n}. The median of these n 53091 numbers is then the estimate of Sn. The constant c is 53092 determined to make Sn a consistent estimator. The value 53093 used is 1.1926 (this is the value needed to make Sn a 53094 consistent estimator for normal data). 53095 53096 The Sn statistic measures typical distances between values 53097 in contrast to the MAD and the standard deviation which 53098 measure the distance from a central location. This is why 53099 the Sn is appropriate for asymmetic distributions as well 53100 symmetric distributions. 53101 53102 The Rousseeuw and Croux article (see the Reference section 53103 below) discusses the properties of the Sn estimate in 53104 detail. 53105 53106Syntax: 53107 LET <par> = SN SCALE <y> <SUBSET/EXCEPT/FOR qualification> 53108 where <y> is the response variable; 53109 <par> is a parameter where the computed Sn scale 53110 statistic is stored; 53111 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 53112 53113Examples: 53114 LET A = SN SCALE Y1 53115 LET A = SN SCALE Y1 SUBSET TAG > 2 53116 53117Note: 53118 Dataplot uses code provided by Rousseeuw and Croux to compute 53119 the Sn estimate. This algorithm uses an efficient computational 53120 method for computing Sn. 53121 53122Note: 53123 The Rousseeuw and Croux article also proposes the Qn scale 53124 estimate. The article discusses the properties of both 53125 estimators in detail. 53126 53127Note: 53128 In addition, the Sn statistic is supported for the following 53129 plots and commands 53130 53131 SN SCALE PLOT Y X 53132 CROSS TABULATE SN SCALE PLOT Y X1 X2 53133 BOOTSTRAP SN SCALE PLOT Y 53134 JACKNIFE SN SCALE PLOT Y 53135 DEX SN SCALE PLOT Y X1 ... XK 53136 SN SCALE BLOCK PLOT Y X1 ... XK 53137 SN SCALE INFLUENCE CURVE Y 53138 SN SCALE INTERACTION PLOT Y X1 X2 53139 53140 TABULATE SN SCALE Y X 53141 CROSS TABULATE SN Y X1 X2 53142 LET Z = CROSS TABULATE SN SCALE Y X1 X2 53143 LET Y = MATRIX COLUMN SN SCALE M 53144 LET Y = MATRIX ROW SN SCALE M 53145 53146 53147Default: 53148 None 53149 53150Synonyms: 53151 None 53152 53153Related Commands: 53154 QN SCALE = Compute the Qn scale estimate of a 53155 variable. 53156 MEDIAN ABSOLUTE DEVIATION = Compute the median absolute 53157 deviation of a variable. 53158 INTERQUARTILE RANGE = Compute the interquartile range of 53159 a variable. 53160 STANDARD DEVIATION = Compute the standard deviation of a 53161 variable. 53162 DIFFERENCE OF SN = Compute the difference of the Sn 53163 scale estimates between two variables. 53164 STATISTIC PLOT = Generate a statistic versus subset 53165 plot. 53166 CROSS TABULATE PLOT = Generate a statistic versus subset 53167 plot (two subset variables). 53168 BOOTSTRAP PLOT = Generate a bootstrap plot for a 53169 statistic. 53170 53171Reference: 53172 "Alternatives to the Median Absolute Deviation", 53173 Peter J. Rousseuw and Christophe Croux, Journal of the American 53174 Statistical Association, December, 1993, Vol. 88, No. 424, 53175 pp. 1273-1283. 53176 53177 "Data Analysis and Regression: A Second Course in Statistics", 53178 Mosteller and Tukey, Addison-Wesley, 1977, pp. 203-209. 53179 53180Applications: 53181 Data Analysis 53182 53183Implementation Date: 53184 2003/4 53185 53186Program: 53187 MULTIPLOT 2 2 53188 MULTIPLOT CORNER COORDINATES 0 0 100 100 53189 MULTIPLOT SCALE FACTOR 2 53190 X1LABEL DISPLACEMENT 12 53191 . 53192 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 200 53193 LET SIGMA = 1 53194 LET Y2 = LOGNORMAL RANDOM NUMBERS FOR I = 1 1 200 53195 . 53196 BOOTSTRAP SAMPLES 500 53197 BOOTSTRAP SN SCALE PLOT Y1 53198 X1LABEL B025 = ^B025, B975=^B975 53199 HISTOGRAM YPLOT 53200 X1LABEL 53201 . 53202 BOOTSTRAP SN SCALE PLOT Y2 53203 X1LABEL B025 = ^B025, B975=^B975 53204 HISTOGRAM YPLOT 53205 . 53206 END OF MULTIPLOT 53207 JUSTIFICATION CENTER 53208 MOVE 50 96 53209 TEXT SN SCALE BOOTSTRAP: NORMAL 53210 MOVE 50 46 53211 TEXT SN SCALE BOOTSTRAP: LOGNORMAL 53212 53213-----SORT2 (LET)--------------------------------------------------- 53214 53215SORT2 53216 53217Name: 53218 SORT2 (LET) 53219 53220Type: 53221 Let Subcommand 53222 53223Purpose: 53224 Sort the elements of two, three, or four variables in ascending 53225 order. 53226 53227Description: 53228 The SORT command is used to sort a single variable. In some 53229 cases, it is desirable to sort based on more than one 53230 variable. Note that this only makes sense if some of the 53231 variables contain replication. For example, if you have 53232 one or more group variables, you might want to sort a 53233 response variable within common values of the group-id 53234 variables. 53235 53236 In the variable list, the sorts are performed from left 53237 to right. For example, if we are sorting the variables 53238 X and Y, we first sort the X variable (and carry the 53239 corresponding rows in Y). We then determine the distinct 53240 values in the X array. For each distinct value of X, 53241 we sort the corresponding rows in the Y variable. 53242 53243Syntax 1: 53244 LET <y1> <y2> = SORT2 <x1> <x2> 53245 <SUBSET/EXCEPT/FOR qualification> 53246 where <x1> is the first variable to be sorted; 53247 <x2> is the second variable to be sorted; 53248 <y1> is a variable where the sorted <x1> values are saved; 53249 <y2> is a variable where the sorted <x2> values are saved; 53250 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 53251 53252 This syntax is used for the case where we are sorting based 53253 on two variables. 53254 53255Syntax 2: 53256 LET <y1> <y2> <y3> = SORT3 <x1> <x2> <x3> 53257 <SUBSET/EXCEPT/FOR qualification> 53258 where <x1> is the first variable to be sorted; 53259 <x2> is the second variable to be sorted; 53260 <x3> is the third variable to be sorted; 53261 <y1> is a variable where the sorted <x1> values are saved; 53262 <y2> is a variable where the sorted <x2> values are saved; 53263 <y3> is a variable where the sorted <x3> values are saved; 53264 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 53265 53266 This syntax is used for the case where we are sorting based 53267 on three variables. 53268 53269Syntax 3: 53270 LET <y1> <y2> <y3> <y4> = SORT4 <x1> <x2> <x3> <x4> 53271 <SUBSET/EXCEPT/FOR qualification> 53272 where <x1> is the first variable to be sorted; 53273 <x2> is the second variable to be sorted; 53274 <x3> is the third variable to be sorted; 53275 <x4> is the fourth variable to be sorted; 53276 <y1> is a variable where the sorted <x1> values are saved; 53277 <y2> is a variable where the sorted <x2> values are saved; 53278 <y3> is a variable where the sorted <x3> values are saved; 53279 <y4> is a variable where the sorted <x4> values are saved; 53280 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 53281 53282 This syntax is used for the case where we are sorting based 53283 on four variables. 53284 53285Examples: 53286 LET X2 Y2 = SORT2 X Y 53287 LET Y1 Y2 Y3 = SORT3 X1 X2 X3 53288 LET Y1 Y2 Y3 Y4 = SORT3 X1 X2 X3 X4 53289 53290Note: 53291 Once data for specific replication has been extracted, 53292 DATAPLOT uses the QUICKSORT algorithm developed by Richard 53293 Singelton to perform the sort of a single variable. 53294 53295Note: 53296 By default, the values are sorted in ascending order. If 53297 you want to sort values in descending order, enter the 53298 command 53299 53300 SET SORT DIRECTION DESCENDING 53301 53302 Currently, all variables must be sorted in the same 53303 direction (i.e., either ascending or descending). 53304 53305Default: 53306 None 53307 53308Synonyms: 53309 None 53310 53311Related Commands: 53312 SORT = Sort the elements of a variable. 53313 SORTC = Sort the elements of a variable and carry one or 53314 more variables along. 53315 COCODE = Generate a cocoded variable. 53316 CODE = Generate a coded variable. 53317 SEQUENCE = Generate a sequence of numbers. 53318 PATTERN = Generate numbers with a specific pattern. 53319 RANK = Rank the elements of a variable. 53320 53321Reference: 53322 "Quicksort Algorithm", Richard Singelton, CACM, March, 1969. 53323 53324Applications: 53325 Data Management 53326 53327Implementation Date: 53328 2008/10 53329 53330Program 1: 53331 SKIP 25 53332 READ GEAR.DAT Y X 53333 LET X2 Y2 = SORT2 X Y 53334 SET WRITE DECIMALS 3 53335 PRINT X Y X2 Y2 53336 53337Program 2: 53338 SKIP 25 53339 READ RIPKEN.DAT Y X1 X2 X3 X4 53340 LET Z2 Z3 Y2 = SORT3 X2 X3 Y 53341 SET WRITE DECIMALS 3 53342 PRINT X2 X3 Y Z2 Z3 Y2 53343 LET Z2 Z3 Z4 Y2 = SORT4 X2 X3 X4 Y 53344 SET WRITE DECIMALS 3 53345 PRINT X2 X3 X4 Y Z2 Z3 Z4 Y2 53346 53347-----SORT (LET)--------------------------------------------------- 53348 53349SORT 53350 53351Name: 53352 SORT (LET) 53353 53354Type: 53355 Let Subcommand 53356 53357Purpose: 53358 Sort the elements of a variable in ascending order. 53359 53360Syntax: 53361 LET <resp> = SORT <y1> <SUBSET/EXCEPT/FOR qualification> 53362 where <y1> is the variable to be sorted (it is not changed); 53363 <resp> is a variable where the sorted values are saved; 53364 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 53365 53366Examples: 53367 LET YSORT = SORT Y1 53368 53369Note: 53370 DATAPLOT uses the QUICKSORT algorithm developed by Richard 53371 Singelton. 53372 53373Default: 53374 None 53375 53376Synonyms: 53377 None 53378 53379Related Commands: 53380 COCODE = Generate a cocoded variable. 53381 CODE = Generate a coded variable. 53382 SEQUENCE = Generate a sequence of numbers. 53383 PATTERN = Generate numbers with a specific pattern. 53384 RANK = Rank the elements of a variable. 53385 SORTC = Sort the elements of a variable and carry one or 53386 more variables along. 53387 53388Reference: 53389 "Quicksort Algorithm", Richard Singelton, CACM, March, 1969. 53390 53391Applications: 53392 XX 53393 53394Implementation Date: 53395 XX 53396 53397Program: 53398 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 53399 LET Y2 = SORT Y1 53400 53401-----SORT BY STATISTIC (LET)----------------------------------------- 53402 53403SORT BY STATISTIC (LET) 53404 53405Name: 53406 SORT BY STATISTIC (LET) 53407 53408Type: 53409 Let Subcommand 53410 53411Purpose: 53412 Sort the values of a group variable based on the values 53413 of a user-specified statistic for each group. 53414 53415Description: 53416 For plots based on a response variable and a corresponding 53417 group-id variable, it is often desirable to generate the 53418 plot sorted by the value of some statistic for each group. 53419 For example, you may want to generate a box plot ordered 53420 from the smallest median to the largest median. 53421 53422 In most cases, the sorting statistic will be a location 53423 statistic such as the mean, median, minimum, or maximum. 53424 However, Dataplot supports 40+ statistics for the sorting 53425 statistic. 53426 53427 The SORT BY command is a utility command that simplifies 53428 the generation of these sorted plots. Specifically, it can 53429 be used in conjunction with the following types of plots: 53430 53431 1) BOX PLOT 53432 2) <STATISTIC> PLOT 53433 3) PLOT Y X TAG (i.e., scatter plot with replication) 53434 53435 Given a response variable, Y, and a group-id variable, X, 53436 the SORT BY command computes the value of a specified 53437 statistic for each group and returns the following two 53438 variables: 53439 53440 1) An index variable which is the ranking of the 53441 computed statistic for each group (if there are five 53442 groups in the data, the index variable will have 53443 five elements). 53444 53445 2) A sorted group-id variable, X2, that is used in 53446 place of the original X variable in subsequent 53447 plots. 53448 53449Syntax: 53450 LET <x2> <index> = SORT BY <stat> <y> <x> 53451 <SUBSET/EXCEPT/FOR qualification> 53452 where <y> is the response variable; 53453 <x> is the group-id variable; 53454 <stat> is one of the following statistics: 53455 MEAN, MIDMEAN, MEDIAN, TRIMMED MEAN, WINSORIZED MEAN, 53456 GEOMETRIC MEAN, HARMONIC MEAN, HODGES LEHMAN, 53457 BIWEIGHT LOCATION, 53458 SUM, PRODUCT, SIZE (or NUMBER or SIZE), 53459 STANDARD DEVIATION, STANDARD DEVIATION OF MEAN, 53460 VARIANCE, VARIANCE OF THE MEAN, 53461 TRIMMED MEAN STANDARD ERROR, 53462 AVERAGE ABSOLUTE DEVIATION (or AAD), 53463 MEDIAN ABSOLUTE DEVIATION (or MAD), 53464 IQ RANGE, BIWEIGHT MIDVARIANCE, BIWEIGHT SCALE, 53465 PERCENTAGE BEND MIDVARIANCE, 53466 WINSORIZED VARIANCE, WINSORIZED STANDARD DEVIATION, 53467 RELATIVE STANDARD DEVIATION, RELATIVE VARIANCE, 53468 COEFFICIENT OF VARIATION, 53469 RANGE, MIDRANGE, MAXIMUM, MINIMUM, EXTREME, 53470 LOWER HINGE, UPPER HINGE, LOWER QUARTILE, UPPER QUARTILE, 53471 <FIRST/SECOND/THIRD/FOURTH/FIFTH/SIXTH/SEVENTH/EIGHTH/ 53472 NINTH/TENTH> DECILE, 53473 PERCENTILE, QUANTILE, QUANTILE STANDARD ERROR, 53474 SKEWNESS, KURTOSIS, NORMAL PPCC, 53475 AUTOCORRELATION, AUTOCOVARIANCE, 53476 SIN FREQUENCY, SIN AMPLITUDE, 53477 CP, CPK, CNPK, CPM, CC, 53478 EXPECTED LOSS, PERCENT DEFECTIVE, 53479 TAGUCHI SN0 (or SN), TAGUCHI SN+ (or SNL), 53480 TAGUCHI SN- (or SNS), TAGUCHI SN00 (or SN2); 53481 <x2> is a variable where the sorted group-id values are 53482 stored; 53483 <index> is a variable where the ranking of the statistic 53484 for each group are stored; 53485 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 53486 53487Examples: 53488 LET X2 INDX = SORT BY MEAN Y X 53489 LET X2 INDX = SORT BY MEIDAN Y X 53490 LET X2 INDX = SORT BY SD Y X 53491 LET X2 INDX = SORT BY MINIMUM Y X 53492 LET X2 INDX = SORT BY IQ RANGE Y X 53493 53494Note: 53495 These plots often have alphabetic tick mark labels. The 53496 following enhancements were made to simplify the use 53497 of alphabetic tick mark labels with sorted plots. 53498 53499 a) The TIC MARK LABEL FORMAT and TIC MARK LABEL CONTENT 53500 commands were previously augmented to allow numeric 53501 variables, group label variables, or the row label 53502 variable as the contents for the tick mark labels. 53503 Specifically, 53504 53505 LET LAB = DATA 50 40 30 20 10 0 53506 X1TIC MARK LABEL FORMAT VARIABLE 53507 X1TIC MARK LABEL CONTENT LAB 53508 53509 LET IG = GROUP LABELS A B C D E 53510 X1TIC MARK LABEL FORMAT GROUP LABEL 53511 X1TIC MARK LABEL CONTENT IG 53512 53513 X1TIC MARK LABEL FROMAT ROW LABELS 53514 53515 This has been enhanced to allow an index variable to 53516 be specified on the above TIC MARK LABEL CONTENT 53517 commands (the index variable is typically generated by 53518 a SORT BY <stat> command). The index variable specifies 53519 the order in which the tic mark labels will be generated. 53520 53521 So the above examples can be augmented by 53522 53523 LET X2 INDX = SORT BY MEAN Y X 53524 LET LAB = DATA 50 40 30 20 10 0 53525 X1TIC MARK LABEL FORMAT VARIABLE 53526 X1TIC MARK LABEL CONTENT LAB INDX 53527 53528 LET X2 INDX = SORT BY MEAN Y X 53529 LET IG = GROUP LABELS A B C D E 53530 X1TIC MARK LABEL FORMAT GROUP LABEL 53531 X1TIC MARK LABEL CONTENT IG INDX 53532 53533 LET X2 INDX = SORT BY MEAN Y X 53534 X1TIC MARK LABEL FROMAT ROW LABELS 53535 X1TIC MARK LABEL CONTENT INDX 53536 53537 Note that it is the values of INDX when the plot is 53538 generated, not when the TIC MARK LABEL CONTENT is 53539 entered, that will be used to sort the tick mark labels. 53540 53541 b) The LET ... = GROUP LABEL .... command was augmented in 53542 the following two ways. 53543 53544 i) You can specify literal strings for group labels. 53545 For example, 53546 53547 LET IG = GROUP LABEL BATCHSP()1 BATCHSP()2 ... 53548 BATCHSP()3 BATCHSP()4 53549 53550 The strings are separated by spaces. If you need to 53551 include a space in a particular string, use the 53552 SP() as in the above example. 53553 53554 ii) Pre-defined strings can be used to define a group 53555 label variable. For example, 53556 53557 LET IG = GROUP LABEL ST1 TO ST10 53558 53559 where ST1, ST2, ...., ST10 are previously defined 53560 strings. The TO syntax is useful in this context 53561 when the number of strings is large. 53562 53563 Dataplot's algorithm for parsing the GROUP LABEL command 53564 is: 53565 53566 i) Dataplot first checks the character variables file 53567 (HELP SET CONVERT CHARACTER for details). If the 53568 first name listed is found, Dataplot uses this 53569 character variable to define the group labels. 53570 53571 ii) If a character variable is not found, Dataplot 53572 checks all the listed names to see if they are 53573 previously defined strings. If they are, then 53574 Dataplot substitutes the values of these strings. 53575 53576 iii) If one or more of the names is not a previously 53577 defined string, then Dataplot treats all of the 53578 names as literal text strings. 53579 53580 53581Default: 53582 None 53583 53584Synonyms: 53585 None 53586 53587Related Commands: 53588 PLOT = Generate a plot. 53589 BOX PLOT = Generate a box plot. 53590 STATISTIC PLOT = Generate a statistic versus subset plot. 53591 TIC MARK LABEL FORMAT = Specify the format for tic mark labels. 53592 TIC MARK LABEL CONTENT = Specify the content for alphabetic 53593 tic mark labels. 53594 53595Applications: 53596 Data Analysis 53597 53598Implementation Date: 53599 2006/1: Original Implementation 53600 53601Program 1: 53602 skip 25 53603 read splett2.dat y x 53604 . 53605 let x2 indx = sort by median y x 53606 let ig = group label Tinius1 Tinius2 Satec Tokyo 53607 x1tic mark label case asis 53608 x1tic mark label format group labels 53609 x1tic mark label content ig indx 53610 . 53611 char box plot 53612 line box plot 53613 fences on 53614 . 53615 xlimits 1 4 53616 major xtic mark number 4 53617 minor xtic mark number 0 53618 xtic offset 0.5 0.5 53619 . 53620 title case asis 53621 title offset 2 53622 title Charpy V-NIST Notch Testing 53623 label case asis 53624 x1label Machine Manufacturer 53625 y1label Absorbed Energy 53626 . 53627 box plot y x2 53628 53629Program 2: 53630 set convert character on 53631 skip 25 53632 read draft69c.dat rank day month 53633 . 53634 let ig = group label month 53635 x1tic mark label format group label 53636 let xcode = character code month 53637 . 53638 major xtic mark number 12 53639 minor xtic mark number 0 53640 xlimits 1 12 53641 xtic offset 0.5 0.5 53642 . 53643 let xcode2 indx = sort by mean rank xcode 53644 x1tic mark label content ig indx 53645 . 53646 x1tic mark label size 1.5 53647 tic mark label case asis 53648 label case asis 53649 title case asis 53650 title displacement 2 53651 x1label Month 53652 y1label Draft Ranking 53653 title Mean Plot Ordered by Mean 53654 . 53655 mean plot rank xcode2 53656 53657Program 3: 53658 skip 25 53659 read splett2.dat y x 53660 . 53661 let ig = group label Tinius1 Tinius2 Satec Tokyo 53662 . 53663 char x blank 53664 line blank dash 53665 . 53666 xlimits 1 4 53667 major xtic mark number 4 53668 minor xtic mark number 0 53669 tic offset units screen 53670 tic offset 5 5 53671 . 53672 title offset 2 53673 multiplot corner coordinates 0 0 100 100 53674 multiplot 2 2 53675 multiplot scale factor 2 53676 . 53677 x1tic mark label format group label 53678 x1tic mark label content ig 53679 title Mean Plot (Unsorted) 53680 mean plot y x 53681 . 53682 title SD Plot (Unsorted) 53683 sd plot y x 53684 . 53685 title Mean Plot (Sorted by Mean) 53686 let x2 indx = sort by mean y x 53687 x1tic mark label content ig indx 53688 mean plot y x2 53689 . 53690 title SD Plot (Sorted by SD) 53691 let x2 indx = sort by sd y x 53692 x1tic mark label content ig indx 53693 sd plot y x2 53694 . 53695 end of multiplot 53696 53697Program 4: 53698 skip 25 53699 read gear.dat y x 53700 . 53701 char x all 53702 line solid all 53703 . 53704 xlimits 1 10 53705 major xtic mark number 10 53706 minor xtic mark number 0 53707 xtic offset 0.5 0.5 53708 . 53709 title offset 2 53710 multiplot corner coordinates 0 0 100 100 53711 multiplot 2 2 53712 multiplot scale factor 2 53713 . 53714 title Original Data 53715 plot y x x 53716 . 53717 title Sort by Mean 53718 let x2 indx = sort by mean y x 53719 x1tic mark label format variable 53720 x1tic mark label content indx 53721 plot y x2 x2 53722 . 53723 title Sort by Minimum 53724 let x2 indx = sort by minimum y x 53725 x1tic mark label content indx 53726 plot y x2 x2 53727 . 53728 title Sort by SD 53729 let x2 indx = sort by sd y x 53730 x1tic mark label content indx 53731 plot y x2 x2 53732 . 53733 end of multiplot 53734 53735-----SORTC (LET)--------------------------------------------------- 53736 53737SORTC 53738 53739Name: 53740 SORTC (LET) 53741 53742Type: 53743 Let Subcommand 53744 53745Purpose: 53746 Sort the elements of a variable in ascending order. In addition, 53747 carry one or more additional variables along when doing the sort 53748 (that is, the additional variables are sorted in the order of the 53749 first variable). 53750 53751Syntax: 53752 LET <resp> = SORTC <y1> <y2> ... <yn> 53753 <SUBSET/EXCEPT/FOR qualification> 53754 where <y1> is the variable to be sorted (it is not changed); 53755 <y2> ... <yn> is a list of variables to be carried along; 53756 <resp> is a variable where the sorted values are saved; 53757 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 53758 53759Examples: 53760 LET YSORT = SORT Y1 Y2 53761 LET YSORT = SORT Y1 Y2 Y3 Y4 53762 53763Note: 53764 DATAPLOT uses the QUICKSORT algorithm developed by Richard 53765 Singelton. 53766 53767Default: 53768 None 53769 53770Synonyms: 53771 None 53772 53773Related Commands: 53774 COCODE = Generate a cocoded variable. 53775 CODE = Generate a coded variable. 53776 SEQUENCE = Generate a sequence of numbers. 53777 PATTERN = Generate numbers with a specific pattern. 53778 RANK = Rank the elements of a variable. 53779 SORT = Sort the elements of a variable. 53780 53781Applications: 53782 XX 53783 53784Implementation Date: 53785 XX 53786 53787Program: 53788 XX 53789 53790-----SORT DIRECTION (SET)--------------------------------------- 53791 53792SORT DIRECTION 53793 53794Name: 53795 SORT DIRECTION (SET) 53796 53797Type: 53798 Set Subcommand 53799 53800Purpose: 53801 Specify whether sorts performed by SORT and SORTC generate 53802 ascending or descending sorts. 53803 53804Syntax: 53805 SET SORT DIRECTION <value> 53806 where <value> is ASCENDING or DESCENDING. 53807 53808Examples: 53809 SET SORT DIRECTION ASCENDING 53810 SET SORT DIRECTION DESCENDING 53811 53812Default: 53813 The default is ASCENDING. 53814 53815Synonyms: 53816 None 53817 53818Related Commands: 53819 SORT = Sort an array of numbers. 53820 SORTC = Sort an array of numbers and carry other arrays. 53821 53822Applications: 53823 Sorting 53824 53825Implementation Date: 53826 2000/1 53827 53828Program: 53829 LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 100 53830 LET Y2 = SORT Y 53831 SET SORT DIRECTION DESCENDING 53832 LET Y3 = SORT Y 53833 SET WRITE DECIMALS 3 53834 PRINT Y Y2 Y3 53835 53836-----SPACING------------------------------------------------------- 53837 53838SPACING 53839 53840Name: 53841 SPACING 53842 53843Type: 53844 Diagrammatic Graphics Command 53845 53846Purpose: 53847 Specifies whether text is drawn with fixed or proportional spacing. 53848 53849Description: 53850 Proportional spacing often has a neater appearance. However, fixed 53851 spacing is desirable when it is important to line up different 53852 portions of text. 53853 53854Syntax: 53855 SPACING <FIXED/PROPORTIONAL> 53856 where FIXED specifies fixed spacing and PROPORTIONAL specifies 53857 proportional spacing. 53858 53859Examples: 53860 SPACING FIXED 53861 SPACING PROPORTIONAL 53862 53863Note: 53864 This command only applies to software fonts. The spacing for 53865 hardware fonts is determined by the definition of the font and 53866 cannot be changed. Most hardware fonts are fixed space fonts. 53867 The exception is that most Postscript and QMS fonts are 53868 proportional space fonts. If fixed spacing is needed for 53869 Postscript, use the SET POSTSCRIPT FONT command to set one of the 53870 Courier fonts (all the rest are proportional). The SET QMS FONT 53871 command can be used to set the hardware font for QMS devices. 53872 See the documentation for the QMS device for a list of which fonts 53873 are fixed and which are proportional. 53874 53875Default: 53876 Proportional spacing is used by default. 53877 53878Synonyms: 53879 None 53880 53881Related Commands: 53882 TEXT = Writes a text string. 53883 FONT = Specify the font to use for text. 53884 53885Applications: 53886 XX 53887 53888Implementation Date: 53889 XX 53890 53891Program: 53892 VERTICAL SPACING 6 53893 CRLF ON 53894 MARGIN 10 53895 FONT DUPLEX 53896 SPACING PROPORTIONAL 53897 . 53898 HW 4 2 53899 MOVE 5 95 53900 TEXT JAPAN's 6-POINT PROGRAM FOR 53901 MOVE 5 89 53902 TEXT QUALITY MANUFACTURING 53903 MOVE 10 80 53904 HW 2.6 1.3 53905 TEXT CIRC() QUALITY AUDITS 53906 TEXT CIRC() COMPANY-WIDE QUALITY CONTROL (CWQC) 53907 TEXT CIRC() QUALITY TRAINING AND EDUCATION 53908 TEXT CIRC() APPLICATION OF STATISTICAL METHODS 53909 . 53910 SPACING FIXED 53911 . 53912 TEXT CIRC() QUALITY CIRCLE ACTIVITIES 53913 TEXT CIRC() NATION-WIDE QUALITY CONTROL PROMOTIONAL ACTIVITIES 53914 HW 2 1 53915 MOVE 5 10 53916 TEXT SOURCE: Q.C. TRENDS WINTER 1985, PAGES 22-23. 53917 53918-----SPEARMAN DISSIMILARITY (LET)-------------------------------- 53919 53920SPEARMAN DISSIMILARITY 53921 53922Name: 53923 SPEARMAN DISSIMILARITY (LET) 53924 SPEARMAN SIMILARITY (LET) 53925 53926Type: 53927 Let Subcommand 53928 53929Purpose: 53930 Compute the Spearman rank correlation coefficient transformed to a 53931 dissimilarity measure between two variables. 53932 53933Description: 53934 If the measurements in the two samples are replaced with their ranks 53935 (and average ranks in the case of ties) and the Pearson correlation 53936 coefficient (HELP CORRELATION for details) is computed, the result is 53937 the Spearman rho correlation coefficient. 53938 53939 The rank correlation is recommended in the following cases: 53940 53941 1) When the underlying data does not have a meaningful numerical 53942 measure, but it can be ranked; 53943 2) When the relationship between the two variables is not 53944 linear; 53945 3) When the normality assumption for two variables is not 53946 valid. 53947 53948 A perfect linear relationship yields a correlation coefficient of 53949 +1 (or -1 for a negative relationship) and no linear relationship 53950 yields a correlation coefficient of 0. 53951 53952 In some applications, such as clustering, it can be useful to 53953 transform the correlation coefficient to a dissimilarity measure. 53954 The transformation used here is 53955 53956 d = (1 - R)/2 53957 53958 This converts the correlation coefficient with values between -1 and 53959 1 to a score between 0 and 1. High positive correlation (i.e., very 53960 similar) results in a dissimilarity near 0 and high negative 53961 correlation (i.e., very dissimilar) results in a dissimilarity near 1. 53962 53963 If a similarity score is preferred, you can use 53964 53965 s = 1 - d 53966 53967 where d is defined as above. 53968 53969Syntax 1: 53970 LET <par> = SPEARMAN DISSIMILARITY <y1> <y2> 53971 <SUBSET/EXCEPT/FOR qualification> 53972 where <y1> is the first response variable; 53973 <y2> is the second response variable; 53974 <par> is a parameter where the computed Spearman dissimilarity 53975 is stored; 53976 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 53977 53978Syntax 2: 53979 LET <par> = SPEARMAN SIMILARITY <y1> <y2> 53980 <SUBSET/EXCEPT/FOR qualification> 53981 where <y1> is the first response variable; 53982 <y2> is the second response variable; 53983 <par> is a parameter where the computed Spearman similarity 53984 is stored; 53985 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 53986 53987Examples: 53988 LET A = SPEARMAN DISSIMILARITY Y1 Y2 53989 LET A = SPEARMAN DISSIMILARITY Y1 Y2 SUBSET TAG > 2 53990 LET A = SPEARMAN SIMILARITY Y1 Y2 53991 53992Note: 53993 The two variables must have the same number of elements. 53994 53995Default: 53996 None 53997 53998Synonyms: 53999 SPEARMAN DISTANCE is a synonym for SPEARMAN DISSIMILARITY 54000 54001Related Commands: 54002 RANK CORRELATION = Compute Spearman's rank correlation 54003 coefficient. 54004 CORRELATION = Compute the Pearson correlation of two 54005 variables. 54006 PEARSON DISSIMILARITY = Compute the dissimilarity of two variables 54007 based on Pearson correlation. 54008 KENDALL TAU DISSIMILARITY = Compute the dissimilarity of two variables 54009 based on Kendall's tau correlation. 54010 COSINE DISTANCE = Compute the cosine distance. 54011 MANHATTAN DISTANCE = Compute the Euclidean distance. 54012 EUCLIDEAN DISTANCE = Compute the Euclidean distance. 54013 MATRIX DISTANCE = Compute various distance metrics for a 54014 matrix. 54015 GENERATE MATRIX <stat> = Compute a matrix of pairwise statistic 54016 values. 54017 CLUSTER = Perform a cluster analysis. 54018 54019Reference: 54020 Kaufman and Rousseeuw (1990), "Finding Groups in Data: An 54021 Introduction To Cluster Analysis", Wiley. 54022 54023Applications: 54024 Clustering 54025 54026Implementation Date: 54027 2017/08: 54028 2018/10: SPEARMAN DISTANCE is a synonym for SPEARMAN DISSIMILARITY 54029 54030Program 1: 54031 SKIP 25 54032 READ BERGER1.DAT Y X 54033 LET CORR = RANK CORRELATION Y X 54034 LET D = SPEARMAN DISSIMILARITY Y X 54035 SET WRITE DECIMALS 4 54036 PRINT CORR D 54037 54038Program 2: 54039 SKIP 25 54040 READ IRIS.DAT Y1 Y2 Y3 Y4 54041 SET WRITE DECIMALS 3 54042 . 54043 LET M = GENERATE MATRIX SPEARMAN DISSIMILARITY Y1 Y2 Y3 Y4 54044 PRINT M 54045 54046Program 3: 54047 SKIP 25 54048 READ IRIS.DAT Y1 Y2 Y3 Y4 TAG 54049 . 54050 TITLE CASE ASIS 54051 TITLE OFFSET 2 54052 CASE ASIS 54053 TIC MARK OFFSET UNITS DATA 54054 YLIMITS 0 1 54055 MAJOR YTIC MARK NUMBER 6 54056 MINOR YTIC MARK NUMBER 1 54057 Y1TIC MARK LABEL DECIMAL 1 54058 XLIMITS 1 3 54059 MAJOR XTIC MARK NUMBER 3 54060 MINOR XTIC MARK NUMBER 0 54061 XTIC MARK OFFSET 0.3 0.3 54062 CHARACTER X BLANK 54063 LINES BLANK SOLID 54064 . 54065 MULTIPLOT CORNER COORDINATES 5 5 95 95 54066 MULTIPLOT SCALE FACTOR 2 54067 MULTIPLOT 2 3 54068 . 54069 TITLE Sepal Length vs Sepal Width 54070 SPEARMAN DISSIMILARITY PLOT Y1 Y2 TAG 54071 . 54072 TITLE Sepal Length vs Petal Length 54073 SPEARMAN DISSIMILARITY PLOT Y1 Y3 TAG 54074 . 54075 TITLE Sepal Length vs Petal Width 54076 SPEARMAN DISSIMILARITY PLOT Y1 Y4 TAG 54077 . 54078 TITLE Sepal Width vs Petal Length 54079 SPEARMAN DISSIMILARITY PLOT Y2 Y3 TAG 54080 . 54081 TITLE Sepal Width vs Petal Width 54082 SPEARMAN DISSIMILARITY PLOT Y2 Y4 TAG 54083 . 54084 TITLE Petal Length vs Petal Width 54085 SPEARMAN DISSIMILARITY PLOT Y3 Y4 TAG 54086 . 54087 END OF MULTIPLOT 54088 . 54089 JUSTIFICATION CENTER 54090 MOVE 50 5 54091 TEXT Species 54092 DIRECTION VERTICAL 54093 MOVE 5 50 54094 TEXT Spearman Rank Dissimilarity Coefficient 54095 DIRECTION HORIZONTAL 54096 54097-----SPECTRAL PLOT--------------------------------------------------- 54098 54099SPECTRAL PLOT 54100 54101Name: 54102 ... SPECTRAL PLOT 54103 54104Type: 54105 Graphics Command 54106 54107Purpose: 54108 Generates a spectral plot. 54109 54110Description: 54111 A spectral plot is a graphical data analysis technique for 54112 examining frequency-domain models for a single time series or for 54113 two time series. The spectral power function is a smoothed Fourier 54114 transform of the autocorrelation function. The spectral plot is a 54115 graphical technique for assessing autocorrelation and cyclic 54116 structure in time series. The frequency is plotted (on the 54117 horizontal axis) from 0 to 0.5 cycles per unit time where unit time 54118 is assumed to be 1 (i.e., unit time is the elapsed time between 54119 adjacent data values). The variance component at each frequency is 54120 plotted on the vertical axis. 54121 54122 From a data analysis point of view, the type of structure in the 54123 autocorrelation plot indicates the location of peaks in the 54124 spectral plot. The peaks in the spectral plot also indicate the 54125 dominant frequency for underlying cyclic models. Once the dominant 54126 peaks have been identified, the next step is typically to use other 54127 time series analysis techniques (such as the complex demodulation 54128 phase plots) to determine if this frequency is constant over the 54129 entire domain of the data, or to carry out a non-linear fit with an 54130 underlying cyclic model (see the documentation for COMPLEX 54131 DEMODULATION PLOT). 54132 54133 The axes depend on the type of spectral plot. The autospectral 54134 plot has the following: 54135 Vertical axis = power (= variable contribution); 54136 Horizontal axis = frequency (cycles per observation). 54137 Spectral plots are available in the following 9 types: 54138 1) spectral plot (= autospectral plot) 54139 2) cross-spectral plot 54140 3) co-spectral plot 54141 4) quadrature spectral plot 54142 5) coherency spectral plot 54143 6) amplitude spectral plot 54144 7) phase spectral plot 54145 8) gain spectral plot 54146 9) argand spectral plot 54147 54148Syntax 1: 54149 SPECTRAL PLOT <y1> <SUBSET/EXCEPT/FOR qualification> 54150 where <y1> is a response variable; 54151 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 54152 54153 This syntax is used for a single time series. 54154 54155Syntax 2: 54156 <keyword> PLOT <y1> <y2> <SUBSET/EXCEPT/FOR qualification> 54157 where <keyword> is one of the following: 54158 CROSS-SPECTRAL 54159 CO-SPECTRAL 54160 QUADRATURE SPECTRAL 54161 COHERENCY SPECTRAL 54162 AMPLITUDE SPECTRAL 54163 PHASE PSECTRAL 54164 ARGAND SPECTRAL; 54165 <y1> is the first response variable; 54166 <y2> is the second response variable; 54167 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 54168 54169 This syntax is used for two time series. 54170 54171Examples: 54172 SPECTRAL PLOT Y 54173 SPECTRAL PLOT Y2 SUBSET Y2 > 2 54174 CROSS-SPECTRAL PLOT Y1 Y2 54175 CO-SPECTRAL PLOT Y1 Y2 54176 QUADRATURE SPECTRAL PLOT Y1 Y2 54177 COHERENCY SPECTRAL PLOT Y1 Y2 54178 AMPLITUDE SPECTRAL PLOT Y1 Y2 54179 PHASE SPECTRAL PLOT Y1 Y2 54180 ARGAND SPECTRAL PLOT Y1 Y2 54181 54182Note: 54183 The SPECTRAL PLOT command assumes the data are equi-spaced and 54184 that there is no missing data. Any equi-spaced time series is 54185 intrinsically limited to detecting frequencies no larger than 0.5 54186 cycles per data point (this corresponds to the fact that the 54187 smallest detectable cycle in the data is 2 data points per cycle). 54188 54189Note: 54190 The spectral plot is essentially a "smoothed" periodogram. The 54191 smoothing is done in the frequency domain. There are several 54192 alternative methods for computing the spectrum estimates. DATAPLOT 54193 uses the algorithm from the Jenkins and Watts reference (pp. 382- 54194 383). 54195 54196Note: 54197 Spectral plots are often drawn with log scales to provide better 54198 resolution (enter LOG ON). Some analysts prefer to draw the plot 54199 as a solid connected lines while others prefer to draw it with 54200 spikes. Either way is straightforward to generate with the proper 54201 settings for the LINES and SPIKES commands. 54202 54203Default: 54204 None 54205 54206Synonyms: 54207 SPECTRUM is a synonym for SPECTRAL. 54208 The word PLOT is optional in the various SPECTRAL PLOT commands 54209 (e.g., SPECTRUM Y, CROSS-SPECTRUM Y1 Y2). 54210 AUTO SPECTRAL PLOT is a synonym for SPECTRAL PLOT. 54211 54212Related Commands: 54213 PERIODOGRAM = Generates a periodogram plot. 54214 CORRELATION PLOT = Generates a correlation plot. 54215 COMPLEX DEMOD PLOT = Generates a complex demodulation plot. 54216 LAG PLOT = Generates a lag plot. 54217 PLOT = Generates a data or function plot. 54218 4-PLOT = Generates 4-plot univariate analysis. 54219 CHARACTERS = Sets the types for plot characters. 54220 LINES = Sets the types for plot lines. 54221 LOG = Sets the log switches on/off. 54222 SPIKES = Sets the on/off switches for plot spikes. 54223 SUMMARY = Generates a table of summary statistics. 54224 LET = Generates sin/cos transformations (plus 54225 much more). 54226 FIT = Carries out a least squares fit. 54227 54228Reference: 54229 "Spectral Analysis and Its Applications", Jenkins and Watts. 54230 Holden-Day, 1968 (pp. 16-23). 54231 54232 "Fourier Analysis of Time Series", Peter Bloomfield, Wiley, 1976. 54233 54234Applications: 54235 Frequency Time Series Analysis 54236 54237Implementation Date: 54238 XX 54239 54240Program 1: 54241 SKIP 25 54242 READ LEW.DAT Y 54243 . 54244 MULTIPLOT 2 1; MULTIPLOT CORNER COORDINATES 0 0 100 100 54245 TITLE SPECTRAL PLOT; Y1LABEL POWER; X1LABEL FREQUENCY 54246 SPIKE ON; LINE BLANK 54247 SPECTRAL PLOT Y 54248 LOG ON 54249 SPIKE OFF; LINE SOLID 54250 SPECTRAL PLOT Y 54251 END OF MULTIPLOT 54252 54253Program 1: 54254 SKIP 25 54255 READ HAYES1.DAT JUNK Y1 Y2 54256 . 54257 MULTIPLOT 3 3; MULTIPLOT CORNER COORDINATES 0 0 100 100 54258 TITLE AUTOMATIC; Y1LABEL POWER; X1LABEL FREQUENCY 54259 LINE SOLID DOTTED 54260 CROSS-SPECTRAL PLOT Y1 Y2 54261 COSPECTRAL PLOT Y1 Y2 54262 QUADRATURE SPECTRAL PLOT Y1 Y2 54263 COHERENCY SPECTRAL PLOT Y1 Y2 54264 AMPLITUDE SPECTRAL PLOT Y1 Y2 54265 PHASE SPECTRAL PLOT Y1 Y2 54266 GAIN SPECTRAL PLOT Y1 Y2 54267 ARGAND SPECTRAL PLOT Y1 Y2 54268 END OF MULTIPLOT 54269 54270-----SPENCE (LET)-------------------------------- 54271 54272SPENCE 54273 54274Name: 54275 SPENCE (LET) 54276 54277Type: 54278 Library Function 54279 54280Purpose: 54281 Compute the Spence integral. 54282 54283Description: 54284 The Spence integral is defined as: 54285 F(x) = INTEGRAL(-LOG(1-Y)/Y) DY 54286 where INTEGRAL is the integral from 0 to x. 54287 54288 This is a form of Spence's integral due to K. Mitchell. It 54289 differs from the definition in the NBS Handbook of Mathematical 54290 Functions (see the REFERENCE section below). 54291 54292Syntax: 54293 LET <y> = SPENCE(<x>) <SUBSET/EXCEPT/FOR qualification> 54294 where <x> is a number, variable, or parameter; 54295 <y> is a variable or a parameter (depending on what <x> is 54296 where the computed SPENCE integral values are stored; 54297 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 54298 54299Examples: 54300 LET A = SPENCE(0.1) 54301 LET A = SPENCE(10) 54302 LET X2 = SPENCE(X) 54303 54304Note: 54305 DATAPLOT uses the routine DSPENC from the SLATEC Common 54306 Mathematical Library to compute this function. SLATEC is a large 54307 set of high quality, portable, public domain Fortran routines for 54308 various mathematical capabilities maintained by seven federal 54309 laboratories. 54310 54311Note: 54312 Library functions are distinguished from let subcommands 54313 in the following ways. 54314 1) Functions enclose the input value in parenthesis. Let 54315 subcommands use spaces. 54316 2) Functions can accept (and return) either parameters 54317 (i.e., single values) or variables (i.e., an array of 54318 values) while let subcommands are specific in which they 54319 accept as input and what they return as output. 54320 3) Functions can accept expressions while let subcommands 54321 do not. For example, the following is legal: 54322 LET Y2 = ABS(Y1-INT(Y1)) 54323 For let subcommands, you typically have to do something 54324 like the following: 54325 LET YTEMP = Y**2 + 8 54326 LET A = SUM YTEMP 54327 54328Default: 54329 None 54330 54331Synonyms: 54332 None 54333 54334Related Commands: 54335 LOGINT = Compute the logarithmic integral. 54336 EXPINT1 = Compute the exponential integral of order 1. 54337 EXPINTN = Compute the exponential integral of order N. 54338 EXPINTE = Compute the principla value of the exponential 54339 integral. 54340 ERF = Compute the error function. 54341 SININT = Compute the sine integral. 54342 COSINT = Compute the cosine integral. 54343 54344Reference: 54345 "Handbook of Mathematical Functions, Applied Mathematics Series, 54346 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 54347 1964 (page 1004). 54348 54349 Article by K. Mitchell in the Philosophical Magazine, 40, p. 351, 54350 (1949). 54351 54352Applications: 54353 Special Functions 54354 54355Implementation Date: 54356 94/9 54357 54358Program: 54359 TITLE AUTOMATIC 54360 PLOT SPENCE(X) FOR X = -10 0.1 10 54361 54362-----SPIKE------------------------------------------------------- 54363 54364SPIKE 54365 54366Name: 54367 SPIKE 54368 54369Type: 54370 Plot Control Command 54371 54372Purpose: 54373 Specifies if a spike will be drawn at the plot points of each 54374 trace on subsequent plots. 54375 54376Description: 54377 A spike is a vertical line from the plot point to the spike base 54378 (most typically the x axis). 54379 54380 DATAPLOT can draw a trace as a character or plot symbol at each 54381 point, as a connected line, as a spike from the point to a base, 54382 as a bar from the plot point to a base, or as any combination of 54383 the above. The choice is determined by the BAR, SPIKE, CHARACTER, 54384 and LINE commands. The switches for these commands work 54385 independently of each other. 54386 54387 Spikes are commonly used in time series plots. They are also 54388 useful in showing deviation from a common value such as the mean 54389 or median. They are also used to generate dot charts. Dot charts 54390 are an alternative bar charts recommended by Bill Cleveland in the 54391 books listed in the REFERENCE section below. 54392 54393Syntax: 54394 SPIKE <ON/OFF> <ON/OFF> <ON/OFF> etc. 54395 where ON specifies that the trace is to be drawn with spikes and 54396 OFF specifies that it is not. Up to 100 spike types can 54397 be specified. 54398 54399Examples: 54400 SPIKE ON OFF ON OFF 54401 SPIKE ON ALL 54402 SPIKE ALL ON 54403 SPIKE 54404 54405Note: 54406 Dot charts are typically drawn vertically rather than horizontally. 54407 This can done with either the SPIKE DIRECTION or the HORIZONTAL 54408 SWITCH command. 54409 54410Note: 54411 It is common with dot charts to want alphabetic labels. The TIC 54412 MARK LABEL FORMAT, TIC MARK LABEL CONTENT, and TIC OFFSET commands 54413 can be used for this purpose. 54414 54415Note: 54416 The SPIKE command with no arguments sets the spike type to blank 54417 for all traces. The SPIKE command with the word ALL before or 54418 after the specified type assigns that spike type to all traces; 54419 thus SPIKE ON ALL or SPIKE ALL ON plots spikes for all traces. 54420 54421Default: 54422 No spikes are drawn (i.e., all OFF). 54423 54424Synonyms: 54425 None 54426 54427Related Commands: 54428 PLOT = Generates a data or function plot. 54429 SPIKE BASE = Sets the base locations for plot spikes. 54430 SPIKE COLOR = Sets the colors for plot spikes. 54431 SPIKE DIRECTION = Sets the directions for plot spikes. 54432 SPIKE LINE = Sets the line types for plot spikes. 54433 SPIKE THICKNESS = Sets the line thicknesses for plot spikes. 54434 54435Reference: 54436 "Elements of Graphing Data" by William S. Cleveland, Wadsworth 54437 Advanced Books and Software, 1985. 54438 54439 "Visualizing Data", William S. Cleveland, Hobart Press, 1993. 54440 54441Applications: 54442 Presentation Graphics 54443 54444Implementation Date: 54445 XX 54446 54447Program 1: 54448 SKIP 25 54449 READ BOXJE142.DAT YIELD 54450 . 54451 TITLE TIME SERIES PLOT 54452 Y1LABEL YIELD 54453 X1LABEL SEQUENCE NUMBER 54454 XLIMITS 0 70 54455 XTIC OFFSET 2 2 54456 LET N = SIZE YIELD 54457 LET X = DATA 1 N 54458 LET A = MEAN YIELD 54459 LET Y = DATA A A 54460 CHARACTER OFF 54461 SPIKE ON 54462 SPIKE BASE A 54463 LINE BLANK 54464 PLOT YIELD AND 54465 PLOT Y X 54466 54467Program 2: 54468 READ STRING S1 S2 S3 S4 S5 S6 S7 54469 ALABAMA ALASKA ARIZONA ARKANSAS CALIFORNIA SP()COLORADO CONNETICUIT 54470 READ STRING S8 S9 S10 S11 S12 S13 S14 54471 DELAWARE WASHINGTONSP()DC FLORIDA GEORGIA HAWAII IDAHO ILLINOIS 54472 READ STRING S15 S16 S17 S18 S19 S20 S21 S22 54473 INDIANA IOWA KANSAS KENTUCKY LOUSIANA MAINE MARYLAND MASSACHUSETS 54474 READ STRING S23 S24 S25 S26 S27 S28 S29 54475 MICHIGAN MINNESOTA MISSISSIPPI MISSOURI MONTANA NEBRASKA NEVADA 54476 READ STRING S30 S31 S32 S33 54477 NEWSP()HAMPSHIRE NEWSP()JERSEY NEWSP()MEXICO NEWSP()YORK 54478 READ STRING S34 S35 S36 S37 S38 54479 NORTHSP()CAROLINA NORTHSP()DAKOTA OHIO OKLAHOMA OREGON 54480 READ STRING S39 S40 S41 S42 54481 PENNSYLVANIA RHODESP()ISLAND SOUTHSP()CAROLINA SOUTHSP()DAKOTA 54482 READ STRING S43 S44 S45 S46 S47 S48 S49 S50 S51 54483 TENNESSEE TEXAS UTAH VERMONT VIRGINIA WASHINGTON WESTSP()VIRGINIA 54484 READ STRING S50 S51 54485 WISCONSIN WYOMING 54486 . 54487 SKIP 25 54488 COLUMN LIMITS 5 30 54489 READ MURDER86.DAT RATE 54490 . 54491 TITLE DOT CHART WITH ONE VARIABLE 54492 Y1TIC MARK LABEL OFF; YTIC SIZE 0.5 54493 YLIMITS 1 51; YTIC OFFSET 1 1 54494 MAJOR YTIC MARK NUMBER 51; MINOR YTIC MARK NUMBER 0 54495 X1LABEL MURDER RATE (PER 100,000); XLIMITS 0 30; XTIC OFFSET 0 2 54496 HORIZONTAL SWITCH ON 54497 CHARACTER CIRCLE; CHARACTER FILL ON; CHARACTER HW 0.8 0.7 54498 LINE BLANK 54499 SPIKE ON 54500 SPIKE LINE DOT 54501 LET INDX = SEQUENCE 1 1 51 54502 LET RATE2 = SORTC RATE INDX 54503 PLOT RATE2 54504 HEIGHT 0.7; JUSTIFICATION RIGHT 54505 LET INC = (90-20)/52; LET YPOS = 19.7; LET XPOS = 14 54506 LOOP FOR K = 1 1 51 54507 LET YPOS = YPOS + INC 54508 LET J = INDX(K) 54509 MOVE XPOS YPOS; TEXT ^S^J 54510 END OF LOOP 54511 54512-----SPIKE BASE------------------------------------------------------- 54513 54514SPIKE BASE 54515 54516Name: 54517 SPIKE BASE 54518 54519Type: 54520 Plot Control Command 54521 54522Purpose: 54523 Specifies the base location for spikes on plots. 54524 54525Description: 54526 A spike is a vertical line from the base number to the plot point. 54527 Spike bases are specified by trace. 54528 54529Syntax: 54530 SPIKE BASES <number> <number> <number> etc. 54531 where <number> is a number or parameter that specifies the desired 54532 spike base. Up to 100 spike bases can be specified. 54533 54534Examples: 54535 SPIKE BASES 0. 0. 10. 54536 SPIKE BASES 20. 20. 20. 54537 SPIKE BASES 0. ALL 54538 SPIKE BASES ALL 0. 54539 SPIKE BASES 54540 54541Note: 54542 The SPIKE BASE command with no arguments sets the spike base to 0.0 54543 for all traces. The SPIKE BASE command with the word ALL before or 54544 after the specified base assigns that spike base to all traces; 54545 thus SPIKE BASE 0.0 ALL or SPIKE BASE ALL 0.0 uses a base of 0.0 54546 for all traces. 54547 54548Note: 54549 The BAR BASE, SPIKE, CHARACTER, and LINE switch all work 54550 independently of each other. That is, a plot point can be a line, 54551 a character, a spike or a bar or any combination of the above. 54552 54553Default: 54554 All spike bases are 0.0. 54555 54556Synonyms: 54557 None 54558 54559Related Commands: 54560 PLOT = Generates a data or function plot. 54561 SPIKE = Sets the on/off switches for plot spikes. 54562 SPIKE COLOR = Sets the colors for plot spikes. 54563 SPIKE DIRECTION = Sets the directions for plot spikes. 54564 SPIKE LINE = Sets the line types for plot spikes. 54565 SPIKE THICKNESS = Sets the line thicknesses for plot spikes. 54566 54567References: 54568 "Elements of Graphing Data" by William S. Cleveland, Wadsworth 54569 Advanced Books and Software, 1985. 54570 54571 "Visualizing Data", William S. Cleveland, Hobart Press, 1993. 54572 54573Applications: 54574 Presentation Graphics 54575 54576Implementation Date: 54577 XX 54578 54579Program: 54580 SKIP 25 54581 READ ELNINO.DAT Y YEAR MONTH 54582 . 54583 SPIKE ON 54584 LINE BLANK 54585 LET A = MEAN Y 54586 SPIKE BASE A 54587 X1LABEL MEAN PLOT 54588 Y1LABEL SOUTHERN OSCILLATION INDEX 54589 XLIMITS 1 12 54590 XTIC OFFSET 1 1 54591 MAJOR XTIC MARK NUMBER 12 54592 MINOR XTIC MARK NUMBER 0 54593 X1TIC MARK LABEL FORMAT ALPHA 54594 X1TIC MARK LABEL CONTENTS JAN FEB MARCH APRIL MAY JUNE JULY AUG ... 54595 SEP OCT NOV DEC 54596 MEAN PLOT Y MONTH 54597 54598-----SPIKE COLOR------------------------------------------------------- 54599 54600SPIKE COLOR 54601 54602Name: 54603 SPIKE COLOR 54604 54605Type: 54606 Plot Control Command 54607 54608Purpose: 54609 Specifies the colors used to draw spikes on subsequent plots. 54610 54611Description: 54612 A spike is a vertical line from the plot point to the spike base 54613 (most typically the x axis). Spikes are specified by trace. That 54614 is, all points belonging to the same trace are drawn with the same 54615 spike attributes. 54616 54617Syntax: 54618 SPIKE COLOR <color> <color> <color> etc. 54619 where <color> is a character string that specifies the desired 54620 color. Up to 100 spike colors can be specified. 54621 54622Examples: 54623 SPIKE COLOR RED BLUE GREEN 54624 SPIKE COLORS BLACK ALL 54625 SPIKE COLORS ALL RED 54626 SPIKE COLORS 54627 54628Note: 54629 The SPIKE COLOR command with no arguments sets the spike color to 54630 default for all traces. The SPIKE COLOR command with the word ALL 54631 before or after the specified type assigns that color to all 54632 traces; thus SPIKE COLOR RED ALL or SPIKE LINE ALL RED plots spikes 54633 with red lines for all traces. 54634 54635Note: 54636 The BAR, SPIKE, CHARACTER, and LINE switch all work independently 54637 of each other. That is, a plot point can be a line, a character, 54638 a spike or a bar or any combination of the above. 54639 54640Default: 54641 All spikes are drawn with black lines. 54642 54643Synonyms: 54644 SPIKE PATTERN 54645 54646Related Commands: 54647 PLOT = Generates a data or function plot. 54648 SPIKE = Sets the on/off switches for plot spikes. 54649 SPIKE BASE = Sets the base locations for plot spikes. 54650 SPIKE DIRECTION = Sets the directions for plot spikes. 54651 SPIKE LINE = Sets the line types for plot spikes. 54652 SPIKE THICKNESS = Sets the line thicknesses for plot spikes. 54653 54654References: 54655 "Elements of Graphing Data" by William S. Cleveland, Wadsworth 54656 Advanced Books and Software, 1985. 54657 54658 "Visualizing Data", William S. Cleveland, Hobart Press, 1993. 54659 54660Applications: 54661 Presentation Graphics 54662 54663Implementation Date: 54664 XX 54665 54666Program: 54667 LET CARTER = DATA 66 30 11 43 44 41 35 82 54 36 54668 LET REAGAN = DATA 26 54 84 47 51 51 52 14 36 55 54669 LET X = DATA 1 2 3 5 6 7 8 10 11 12 54670 . 54671 TIC MARK LABEL FORMAT ALPHA; YLIMITS 1 12; YTIC OFFSET 1 1 54672 Y1TIC LABEL CONTENT DEMOCRATS INDEPENDENTS REPUBLICANS SP() ... 54673 EAST SOUTH MIDWEST WEST SP() BLACKS HISPANICS WHITES SP() 54674 MINOR Y1TIC MARK NUMBER 0 54675 X1LABEL PERCENT 54676 XLIMITS -100 100 54677 MAJOR XTIC MARK NUMBER 11; MINOR XTIC MARK NUMBER 1 54678 XTIC MARK LABEL CONTENT 100 80 60 40 20 0 20 40 60 80 100 54679 . 54680 LINE BLANK BLANK SOLID 54681 SPIKE ON ON OFF; SPIKE THICKNESS 0.5 ALL; SPIKE DIRECTION H ALL 54682 SPIKE COLOR G25 G75 54683 TITLE DEMONSTRATE SPIKE COLOR COMMAND 54684 LEGEND 1 CARTER; LEGEND 1 COORDINATES 17 85 54685 LEGEND 2 REAGAN; LEGEND 2 COORDINATES 83 85; LEGEND 2 JUST RIGHT 54686 . 54687 LET CART2 = -CARTER 54688 LET XJUNK = DATA 0.5 12.5; LET YJUNK = DATA 0 0 54689 PLOT X VS REAGAN AND 54690 PLOT X VS CART2 AND 54691 PLOT XJUNK YJUNK 54692 54693-----SPIKE DIRECTION------------------------------------------------- 54694 54695SPIKE DIRECTION 54696 54697Name: 54698 SPIKE DIRECTION 54699 54700Type: 54701 Plot Control Command 54702 54703Purpose: 54704 Specifies if a spike will be drawn horizontally or vertically 54705 on subsequent plots. 54706 54707Description: 54708 A spike is a vertical line from the plot point to the spike base. 54709 Vertical spikes are drawn from the x-axis to the plot point while 54710 horizontal spikes are drawn from the y-axis to the plot point. 54711 54712Syntax: 54713 SPIKE DIRECTIONS <H/V> <H/V> <H/V> etc. 54714 where H specifies the spike is drawn horizontally while V specifies 54715 that the spike is drawn vertically. Up to 100 spike 54716 directions can be specified. 54717 54718Examples: 54719 SPIKE DIRECTIONS H H 54720 SPIKE DIRECTIONS V V 54721 SPIKE DIRECTIONS V ALL 54722 SPIKE DIRECTIONS ALL V 54723 SPIKE DIRECTIONS 54724 54725Note: 54726 The HORIZONTAL SWITCH command can also be used to generate 54727 horizontal bars. This command is more general in that all plot 54728 elements are drawn horizontally (SPIKE DIRECTION only does the 54729 spikes). It also exchanges the x and y data values before 54730 plotting (the BAR DIRECTION command does not do this). 54731 54732Note: 54733 Horizontal spikes are typically combined with a portrait page 54734 orientation to generate publication quality bar dot graphs. 54735 54736Note: 54737 The SPIKE DIRECTION command with no arguments sets the spike 54738 direction to vertical for all spikes. The SPIKE DIRECTION command 54739 with the word ALL before or after the specified direction assigns 54740 that spike direction to all traces; thus SPIKE DIRECTION H ALL or 54741 SPIKE DIRECTION ALL H plots all spikes horizontally. 54742 54743Note: 54744 The BAR, SPIKE, CHARACTER, and LINE switch all work independently 54745 of each other. That is, a plot point can be a line, a character, 54746 a spike or a bar or any combination of the above. 54747 54748Default: 54749 All spikes are drawn vertically. 54750 54751Synonyms: 54752 None 54753 54754Related Commands: 54755 PLOT = Generates a data or function plot. 54756 HORIZONTAL SWITCH = Specifies whether a plot is drawn horizontally 54757 or vertically. 54758 SPIKE = Sets the on/off switches for plot spikes. 54759 SPIKE BASE = Sets the base locations for plot spikes. 54760 SPIKE COLOR = Sets the colors for plot spikes. 54761 SPIKE LINE = Sets the line types for plot spikes. 54762 SPIKE THICKNESS = Sets the line thicknesses for plot spikes. 54763 54764References: 54765 "Elements of Graphing Data" by William S. Cleveland, Wadsworth 54766 Advanced Books and Software, 1985. 54767 54768 "Visualizing Data", William S. Cleveland, Hobart Press, 1993. 54769 54770Applications: 54771 Presentation Graphics 54772 54773Implementation Date: 54774 XX 54775 54776Program: 54777 LET CARTER = DATA 66 30 11 43 44 41 35 82 54 36 54778 LET REAGAN = DATA 26 54 84 47 51 51 52 14 36 55 54779 LET X = DATA 1 2 3 5 6 7 8 10 11 12 54780 . 54781 TIC MARK LABEL FORMAT ALPHA; YLIMITS 1 12; YTIC OFFSET 1 1 54782 Y1TIC LABEL CONTENT DEMOCRATS INDEPENDENTS REPUBLICANS SP() ... 54783 EAST SOUTH MIDWEST WEST SP() BLACKS HISPANICS WHITES SP() 54784 MINOR Y1TIC MARK NUMBER 0 54785 X1LABEL PERCENT 54786 XLIMITS -100 100 54787 MAJOR XTIC MARK NUMBER 11; MINOR XTIC MARK NUMBER 1 54788 XTIC MARK LABEL CONTENT 100 80 60 40 20 0 20 40 60 80 100 54789 . 54790 LINE BLANK BLANK SOLID 54791 SPIKE ON ON OFF 54792 SPIKE DIRECTION H ALL 54793 CHARACTER CIRCLE CIRCLE; CHARACTER FILL ON ON 54794 CHARACTER HW 1 0.75 ALL 54795 TITLE DOT CHART WITH HORIZONTAL DIRECTION 54796 LEGEND 1 CARTER; LEGEND 1 COORDINATES 17 85 54797 LEGEND 2 REAGAN; LEGEND 2 COORDINATES 83 85; LEGEND 2 JUST RIGHT 54798 . 54799 LET CART2 = -CARTER 54800 LET XJUNK = DATA 0.5 12.5; LET YJUNK = DATA 0 0 54801 PLOT X VS REAGAN AND 54802 PLOT X VS CART2 AND 54803 PLOT XJUNK YJUNK 54804 54805-----SPIKE LINE------------------------------------------------------- 54806 54807SPIKE LINE 54808 54809Name: 54810 SPIKE LINE 54811 54812Type: 54813 Plot Control Command 54814 54815Purpose: 54816 Specifies the line patterns used to draw spikes on subsequent 54817 plots. 54818 54819Description: 54820 A spike is a vertical line from the plot point to the spike base 54821 (most typically the x axis). Spikes are specified by trace. That 54822 is, all points belonging to the same trace are drawn with the same 54823 spike attributes. 54824 54825Syntax: 54826 SPIKE LINE <type> <type> <type> etc. 54827 where <type> is a character string that specifies the desired line 54828 type. Up to 100 spike line types can be specified. 54829 54830Examples: 54831 SPIKE LINE SOLID DASH DOT 54832 SPIKE LINES SOLID ALL 54833 SPIKE LINES ALL SOLID 54834 SPIKE LINES 54835 54836Note: 54837 The SPIKE LINE command with no arguments sets the spike type to 54838 solid for all traces. The SPIKE LINE command with the word ALL 54839 before or after the specified type assigns that pattern line type 54840 to all traces; thus SPIKE LINE SOLID ALL or SPIKE LINE ALL SOLID 54841 plots spike patterns with solid lines for all traces. 54842 54843Note: 54844 The BAR, SPIKE, CHARACTER, and LINE switch all work independently 54845 of each other. That is, a plot point can be a line, a character, 54846 a spike or a bar or any combination of the above. 54847 54848Default: 54849 All spikes are drawn with solid lines. 54850 54851Synonyms: 54852 SPIKE PATTERN 54853 54854Related Commands: 54855 PLOT = Generates a data or function plot. 54856 SPIKE = Sets the on/off switches for plot spikes. 54857 SPIKE BASE = Sets the base locations for plot spikes. 54858 SPIKE COLOR = Sets the colors for plot spikes. 54859 SPIKE DIRECTION = Sets the directions for plot spikes. 54860 SPIKE THICKNESS = Sets the line thicknesses for plot spikes. 54861 54862References: 54863 "Elements of Graphing Data" by William S. Cleveland, Wadsworth 54864 Advanced Books and Software, 1985. 54865 54866 "Visualizing Data", William S. Cleveland, Hobart Press, 1993. 54867 54868Applications: 54869 Presentation Graphics 54870 54871Implementation Date: 54872 XX 54873 54874Program: 54875 LET CARTER = DATA 66 30 11 43 44 41 35 82 54 36 54876 LET REAGAN = DATA 26 54 84 47 51 51 52 14 36 55 54877 LET X = DATA 1 2 3 5 6 7 8 10 11 12 54878 . 54879 TIC MARK LABEL FORMAT ALPHA; YLIMITS 1 12; YTIC OFFSET 1 1 54880 Y1TIC LABEL CONTENT DEMOCRATS INDEPENDENTS REPUBLICANS SP() ... 54881 EAST SOUTH MIDWEST WEST SP() BLACKS HISPANICS WHITES SP() 54882 MINOR Y1TIC MARK NUMBER 0 54883 X1LABEL PERCENT; XLIMITS -100 100 54884 MAJOR XTIC MARK NUMBER 11; MINOR XTIC MARK NUMBER 1 54885 XTIC MARK LABEL CONTENT 100 80 60 40 20 0 20 40 60 80 100 54886 . 54887 LINE BLANK BLANK SOLID 54888 CHARACTER CIRCLE CIRCLE; CHARACTER FILL ON ON 54889 CHARACTER HW 1 0.75 ALL 54890 SPIKE ON ON OFF; SPIKE DIRECTION H ALL 54891 SPIKE LINE DASH DASH 54892 TITLE DEMONSTRATE SPIKE LINE COMMAND 54893 LEGEND 1 CARTER; LEGEND 1 COORDINATES 17 85 54894 LEGEND 2 REAGAN; LEGEND 2 COORDINATES 83 85; LEGEND 2 JUST RIGHT 54895 . 54896 LET CART2 = -CARTER 54897 LET XJUNK = DATA 0.5 12.5; LET YJUNK = DATA 0 0 54898 PLOT X VS REAGAN AND 54899 PLOT X VS CART2 AND 54900 PLOT XJUNK YJUNK 54901 54902-----SPIKE THICKNESS-------------------------------------------------- 54903 54904SPIKE THICKNESS 54905 54906Name: 54907 SPIKE THICKNESS 54908 54909Type: 54910 Plot Control Command 54911 54912Purpose: 54913 Specifies the thickness of lines used to draw spikes on subsequent 54914 plots. 54915Description: 54916 A spike is a vertical line from the plot point to the spike base 54917 (most typically the x axis). Spikes are specified by trace. That 54918 is, all points belonging to the same trace are drawn with the same 54919 spike attributes. 54920 54921 Line thickness is specified as a percentage of the vertical 54922 height of the device. Line widths are typically between 0.1 and 54923 0.3. 54924 54925Syntax: 54926 SPIKE THICKNESSS <thickness> <thickness> <thickness> etc. 54927 where <thickness> is a number or parameter that specifies the 54928 desired line thickness. Up to 100 spike thicknesses can 54929 be specified. 54930 54931Examples: 54932 SPIKE THICKNESSS 0.1 0.2 0.1 0.2 54933 SPIKE THICKNESSS 0.2 0.2 0.1 54934 SPIKE THICKNESSS 0.1 ALL 54935 SPIKE THICKNESSS ALL 0.1 54936 SPIKE THICKNESSS 54937 54938Note: 54939 The SPIKE THICKNESS command with no arguments sets the spike line 54940 thickness to default for all traces. The SPIKE THICKNESS command 54941 with the word ALL before or after the specified thickness assigns 54942 that spike line thickness to all spikes; thus SPIKE THICKNESS 0.1 54943 ALL or SPIKE THICKNESS ALL 0.1 draws spikes with a line thickness 54944 of 0.1 for all traces on the plot. 54945 54946Note: 54947 The SPIKE, BAR, CHARACTER, and LINE switch all work independently 54948 of each other. That is, a plot point can be a line, a character, 54949 a spike, a bar, or any combination of the above. 54950 54951Default: 54952 All spikes are drawn with a line width of 0.1. 54953 54954Synonyms: 54955 None 54956 54957Related Commands: 54958 PLOT = Generates a data or function plot. 54959 SPIKE = Sets the on/off switches for plot spikes. 54960 SPIKE BASE = Sets the base locations for plot spikes. 54961 SPIKE COLOR = Sets the colors for plot spikes. 54962 SPIKE DIRECTION = Sets the directions for plot spikes. 54963 SPIKE LINE = Sets the line types for plot spikes. 54964 54965References: 54966 "Elements of Graphing Data" by William S. Cleveland, Wadsworth 54967 Advanced Books and Software, 1985. 54968 54969 "Visualizing Data", William S. Cleveland, Hobart Press, 1993. 54970 54971Applications: 54972 Presentation Graphics 54973 54974Implementation Date: 54975 XX 54976 54977Program: 54978 LET CARTER = DATA 66 30 11 43 44 41 35 82 54 36 54979 LET REAGAN = DATA 26 54 84 47 51 51 52 14 36 55 54980 LET X = DATA 1 2 3 5 6 7 8 10 11 12 54981 . 54982 TIC MARK LABEL FORMAT ALPHA; YLIMITS 1 12; YTIC OFFSET 1 1 54983 Y1TIC LABEL CONTENT DEMOCRATS INDEPENDENTS REPUBLICANS SP() ... 54984 EAST SOUTH MIDWEST WEST SP() BLACKS HISPANICS WHITES SP() 54985 MINOR Y1TIC MARK NUMBER 0 54986 X1LABEL PERCENT 54987 XLIMITS -100 100 54988 MAJOR XTIC MARK NUMBER 11; MINOR XTIC MARK NUMBER 1 54989 XTIC MARK LABEL CONTENT 100 80 60 40 20 0 20 40 60 80 100 54990 . 54991 LINE BLANK BLANK SOLID 54992 SPIKE ON ON OFF; SPIKE DIRECTION H ALL 54993 SPIKE THICKNESS 0.5 ALL 54994 TITLE DEMONSTRATE SPIKE THICKNESS COMMAND 54995 LEGEND 1 CARTER; LEGEND 1 COORDINATES 17 85 54996 LEGEND 2 REAGAN; LEGEND 2 COORDINATES 83 85; LEGEND 2 JUST RIGHT 54997 . 54998 LET CART2 = -CARTER 54999 LET XJUNK = DATA 0.5 12.5; LET YJUNK = DATA 0 0 55000 PLOT X VS REAGAN AND 55001 PLOT X VS CART2 AND 55002 PLOT XJUNK YJUNK 55003 55004-----SPHRHRMR (LET)-------------------------------- 55005 55006SPHRHRMR 55007 55008Name: 55009 SPHRHRMR (LET) 55010 55011Type: 55012 Library Function 55013 55014Purpose: 55015 Compute the spherical harmonic function of order N and degree M. 55016 55017Description: 55018 The spherical harmonic function is related to the associated 55019 Legendre function as follows: 55020 Yn,m(theta,phi) = SQRT((2n+1)*(n-m)!/(4*PI*(n+m)!))* 55021 Pn,m(cos(theta))*EXP(i*m*phi) 55022 where Pn,m is the associated Legendre polynomial. See the 55023 documentation for the LEGENDRE command for a description of 55024 Legendre polynomials and associated Legendre polynomials. 55025 55026 DATAPLOT use the NORMP set of routines from the Slatec library to 55027 compute the normalized associated Legendre polynomials. These are 55028 then transformed in an appropriate manner to obtain the spherical 55029 harmonic value. These routines use a technique called extended 55030 range arithmetic to avoid underflow and overflow problems. 55031 However, DATAPLOT stores the result as a single precision real 55032 number. If it is unable to do so, it prints an error message. 55033 55034Syntax 1: 55035 LET <y> = SPHRHRMR(<theta>,<phi>,<n>,<m>) 55036 <SUBSET/EXCEPT/FOR qualification> 55037 where <theta> is a number, parameter, or variable in the range 55038 (-PI,PI); 55039 <phi> is a number, parameter, or variable in the range 55040 (-PI,PI); 55041 <n> is a non-negative integer number, parameter, or variable 55042 that specifies the order of the Legendre polynomial; 55043 <m> is a non-negative integer number, parameter, or variable 55044 that specifies the degree of the Legendre polynomial; 55045 <y> is a variable or a parameter (depending on what <x> is) 55046 where the computed spherical harmonic value is stored; 55047 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 55048 55049 This syntax computes the real component of the spherical harmonic 55050 function. 55051 55052Syntax 2: 55053 LET <y> = SPHRHRMC(<theta>,<phi>,<n>,<m>) 55054 <SUBSET/EXCEPT/FOR qualification> 55055 where <theta> is a number, parameter, or variable in the range 55056 (-PI,PI); 55057 <phi> is a number, parameter, or variable in the range 55058 (-PI,PI); 55059 <n> is a non-negative integer number, parameter, or variable 55060 that specifies the order of the Legendre polynomial; 55061 <m> is a non-negative integer number, parameter, or variable 55062 that specifies the degree of the Legendre polynomial; 55063 <y> is a variable or a parameter (depending on what <x> is) 55064 where the computed spherical harmonic value is stored; 55065 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 55066 55067 This syntax computes the complex component of the spherical 55068 harmonic function. 55069 55070Examples: 55071 DEGREES; LET AR = SPHRHRMR(45,60,5,2); LET AC = SPHRMRC(45,60,5,2) 55072 DEGREES; LET AR = SPHRHRMR(T,P,5,2); LET AC = SPHRMRC(T,P,5,2) 55073 DEGREES; LET AR = SPHRHRMR(T,P,N,M); LET AC = SPHRMRC(T,P,N,M) 55074 55075Note: 55076 Spherical harmonics are often specified with an angular input 55077 value. If your input value is in terms of the (-1,1) interval, 55078 use the command 55079 LET TNEW = ARCCOS(T) 55080 LET PNEW = ARCCOS(P) 55081 and then use TNEW and PNEW as the input arguments to the spherical 55082 harmonic functions. 55083 55084 By default, the angle is specified in radians. Enter the command 55085 DEGREES to specify degree units. 55086 55087Note: 55088 Library functions are distinguished from let subcommands 55089 in the following ways. 55090 1) Functions enclose the input value in parenthesis. Let 55091 subcommands use spaces. 55092 2) Functions can accept (and return) either parameters 55093 (i.e., single values) or variables (i.e., an array of 55094 values) while let subcommands are specific in which they 55095 accept as input and what they return as output. 55096 3) Functions can accept expressions while let subcommands 55097 do not. For example, the following is legal: 55098 LET Y2 = ABS(Y1-INT(Y1)) 55099 For let subcommands, you typically have to do something 55100 like the following: 55101 LET YTEMP = Y**2 + 8 55102 LET A = SUM YTEMP 55103 55104Default: 55105 None 55106 55107Synonyms: 55108 None 55109 55110Related Commands: 55111 LEGENDRE = Compute the Legendre polynomial of order N. 55112 CHEBT = Compute the Chebychev polynomial first kind, order N. 55113 CHEBU = Compute the Chebychev polynomial second kind, order N. 55114 HERMITE = Compute the Hermite polynomial of order N. 55115 JACOBIPE = Compute the Jacobi polynomial of order N. 55116 ULTRASPH = Compute the ultrasperical polynomial of order N. 55117 LAGUERRE = Compute the Laguerre polynomial of order N. 55118 55119Reference: 55120 "Extended-Range Arithmetic and Normalized Legendre Polynomials", 55121 Smith, Olver, and Lozier, ACM Transactions On Mathematical 55122 Software, Vol. 7, No. 1, March, 1981 (pp. 93-105). 55123 55124 "Associated Legendre Functions on the Cut", Smith, and Olver, 55125 Journal of Computational Physics, Vol. 51, No. 3, September, 1983, 55126 (pp. 502-518). 55127 55128 "Handbook of Mathematical Functions, Applied Mathematics Series, 55129 Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 55130 1964 (chapter 22). 55131 55132Applications: 55133 Mathematics 55134 55135Implementation Date: 55136 95/7 55137 55138Program: 55139 TITLE CASE ASIS; LABEL CASE ASIS; LINE SOLID DASH 55140 DEGREES 55141 Y1LABEL Y(theta,phi,n,m) 55142 X1LABEL THETA (phi = 60, n = 5) 55143 X2LABEL SOLID = Real Component 55144 X3LABEL DASH = Complex Component 55145 TITLE Spherical Harmonics (m = 2) 55146 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 55147 PLOT SPHRHRMR(X,60,5,2) FOR X = 1 1 89 AND 55148 PLOT SPHRHRMC(X,60,5,2) FOR X = 1 1 89 55149 TITLE Spherical Harmonics (m = 3) 55150 PLOT SPHRHRMR(X,60,5,3) FOR X = 1 1 89 AND 55151 PLOT SPHRHRMC(X,60,5,3) FOR X = 1 1 89 55152 TITLE Spherical Harmonics (m = 4) 55153 PLOT SPHRHRMR(X,60,5,4) FOR X = 1 1 89 AND 55154 PLOT SPHRHRMC(X,60,5,4) FOR X = 1 1 89 55155 TITLE Spherical Harmonics (m = 5) 55156 PLOT SPHRHRMR(X,60,5,5) FOR X = 1 1 89 AND 55157 PLOT SPHRHRMC(X,60,5,5) FOR X = 1 1 89 55158 END OF MULTIPLOT 55159 55160-----SPLINE FIT------------------------------------------------------- 55161 55162SPLINE FIT 55163 55164Name: 55165 ... SPLINE FIT 55166 55167Type: 55168 Analysis Command 55169 55170Purpose: 55171 Carries out a B-spline fit. 55172 55173Description: 55174 A spline fit is a data analysis technique for estimating (via the 55175 least squares criterion) the parameters in a spline polynomial 55176 model. It is commonly used to fit curves that have different 55177 shapes in different areas of the horizontal axis variable. Knot 55178 points are defined to delineate these different regions. Separate 55179 spline polynomials are fit in these different areas. The 55180 distinction of spline fits is that the fitted curve will be smooth 55181 at the knot points. 55182 55183Syntax 1: 55184 <degree> SPLINE FIT <y> <x> <x2> <SUBSET/EXCEPT/FOR qualification> 55185 where <degree> is the degree of the spline fit: 55186 LINEAR (or 1ST or FIRST) 55187 QUADRATIC (or 2ND or SECOND) 55188 CUBIC (or 3RD or THIRD ) (the default) 55189 QUARTIC (or 4TH or FOURTH) 55190 QUINTIC (or 5TH or FIFTH) 55191 SEXTIC (or 6TH or SIXTH) 55192 SEPTIC (or 7TH or SEVENTH) 55193 OCTIC (or 8TH or EIGHTH) 55194 NONIC (or 9TH or NINTH) 55195 DEXIC (or 10TH or TENTH); 55196 <y> is the response (vertical axis) variable; 55197 <x> is the independent (horizontal axis) variable; 55198 <x2> is the knots variable; 55199 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 55200 55201Syntax 2: 55202 <degree> SPLINE FIT <y> <x> <SUBSET/EXCEPT/FOR qualification> 55203 where <degree> is the degree of the spline fit (same choices as for 55204 syntax 1); 55205 <y> is the response (vertical axis) variable; 55206 <x> is the independent (horizontal axis) variable; 55207 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 55208 55209 With this syntax, the knots variable is specified with the KNOTS 55210 command before doing the SPLINE FIT command. 55211 55212Examples: 55213 SPLINE FIT Y X X2 55214 CUBIC SPLINE FIT Y X K 55215 55216Note: 55217 The knots variable contains the values along the X axis which 55218 define the end points of sub-domains (a separate spline is fit in 55219 each sub-domain). The individual points are "splined" together at 55220 these knot points. 55221 55222Note: 55223 The values for the spline fit are placed in the internal variable 55224 PRED. The residuals (the difference between the fitted values and 55225 the raw data) are placed in the internal variable RES. 55226 55227Note: 55228 A maximum of 50 knot points can be defined. 55229 55230Note: 55231 Cubic splines are the most commonly used. Degrees above 3 are 55232 rarely used. 55233 55234Default: 55235 Cubic splines (i.e., degree 3). 55236 55237Synonyms: 55238 None 55239 55240Related Commands: 55241 KNOTS = Specify the knots variable for a spline fit. 55242 FIT = Compute a least squares fit. 55243 LOWESS = Compute a locally weighted least squares. 55244 SMOOTH = Perform a smoothing of a variable. 55245 55246Reference: 55247 "...", Wold, Technometrics, 1974, page 2. 55248 55249 "Numerical Recipes", Press, Flannery, Teukolsky, Vetterling, 55250 Cambridge Press, 1989 (chapter 3). 55251 55252Applications: 55253 Fitting 55254 55255Implementation Date: 55256 Pre-1987 55257 55258Program: 55259 LET X = DATA 1 2 3 4 5 6 7 8 9 10 55260 LET Y = DATA 1 2 3 4 5 5.1 5.2 5.3 5.4 5.5 55261 . 55262 LET KNOT(1) = 5 55263 CAPTURE SPLINE_OUT.DAT 55264 LINEAR SPLINE FIT Y X KNOT 55265 END OF CAPTURE 55266 CHARACTER CIRCLE BLANK 55267 LINE BLANK SOLID 55268 CHARACTER FILL ON 55269 CHARACTER SIZE 1.2 55270 TITLE LINEAR SPLINE FIT 55271 PLOT Y PRED VS X 55272 55273-----SPREAD LOCATION PLOT-------------------------------------- 55274 55275SPREAD LOCATION PLOT 55276 55277Name: 55278 SPREAD LOCATION PLOT 55279 55280Type: 55281 Graphics Command 55282 55283Purpose: 55284 Generates a spread location plot. 55285 55286Description: 55287 The spread-location (s-l) plot is a robust alternative to 55288 the homoscedasticity plot. 55289 55290 Given a response variable Y and a group-id variable X, 55291 the homoscedasticity plot is the group standard deviations 55292 versus the group means. This is a graphical measure of 55293 how the spread (variability) changes as the location changes 55294 across groups. This is basically a graphical test for 55295 the assumption of homogeneous variances across samples. 55296 55297 The s-l plot has the square roots of the absolute value of 55298 the Y(i) minus their group medians on the vertical axis and 55299 the group medians on the horizontal axis. A reference line 55300 connects the group medians. This provides a more robust 55301 measure of how the spread changes as the location changes. 55302 55303 The basic idea can be applied to other measure of location 55304 and spread. That is, some measure of spread (or variability) 55305 is plotted on the vertical axis and some measure of location 55306 is plotted on the horizontal axis. Although Dataplot only 55307 supports the HOMOSCEDASTICITY PLOT and the SPREAD LOCATION 55308 PLOT directly, it should be straight forward to implement 55309 other alternatives as macros. 55310 55311 When setting the LINE and CHARACTER commands, the reference 55312 line is the first trace and the data starts with trace 2 55313 (each group is identified as a unique trace). That is, to 55314 draw the data points as circles and the reference line as a 55315 solid line, do something like the following 55316 55317 CHARACTER CIRCLE ALL 55318 CHARACTER BLANK 55319 LINE BLANK ALL 55320 LINE SOLID 55321 SPREAD LOCATION PLOT Y X 55322 55323Syntax: 55324 SPREAD LOCATION PLOT <y> <tag> <SUBSET/EXCEPT/FOR qualification> 55325 where <y> is a response variable; 55326 <tag> is a group identifier variable; 55327 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 55328 55329Examples: 55330 SPREAD LOCATION PLOT Y1 TAG 55331 SPREAD LOCATION PLOT Y1 TAG SUBSET TAG > 2 55332 55333Default: 55334 None 55335 55336Synonyms: 55337 None 55338 55339References: 55340 "Visualizing Data", Cleveland, William S., Hobart Press, 1993. 55341 55342Related Commands: 55343 LINES = Sets the type for plot lines. 55344 CHARACTER = Sets the type for plot characters. 55345 HOMOSCEDATICITY PLOT = Generates a homoscedasticity plot. 55346 BOX PLOT = Generates a box plot. 55347 PLOT = Generates a data or function plot. 55348 LEVENES TEST = Perform Levenes test for homogeneity 55349 of variances. 55350 55351 BARTLET TEST = Perform Bartlet;s test for homogeneity 55352 of variances. 55353Applications: 55354 Exploratory Data Analysis 55355 55356Implementation Date: 55357 2000/1 55358 55359Program: 55360 SKIP 25 55361 READ SPLETT2.DAT Y MACHINE 55362 TIC OFFSET UNITS DATA 55363 XTIC OFFSET 0.5 0.5 55364 YTIC OFFSET 0.2 0.2 55365 YTIC MARK DECIMAL 1 55366 CHARACTER BLANK 1 2 3 4 55367 LINE SOLID BLANK BLANK BLANK BLANK 55368 TITLE AUTOMATIC 55369 Y1LABEL SPREAD 55370 X1LABEL LOCATION 55371 SPREAD LOCATION PLOT Y MACHINE 55372 55373-----SQRT (LET)------------------------------------------------ 55374 55375SQRT 55376 55377Name: 55378 SQRT (LET) 55379 55380Type: 55381 Library Function 55382 55383Purpose: 55384 Compute the square root of a non-negative number. 55385 55386Syntax: 55387 LET <y2> = SQRT(<y1>) <SUBSET/EXCEPT/FOR qualification> 55388 where <y1> is a variable or a parameter containing non-negative 55389 decimal number(s); 55390 <y2> is a variable or a parameter (depending on what <y1> is) 55391 where the computed square roots are stored; 55392 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 55393 55394Examples: 55395 LET A = SQRT(14.2835,1) 55396 LET A = SQRT(A1,2) 55397 LET X2 = SQRT(X1,1) 55398 LET X2 = SQRT(X1-4,2) 55399 55400Note: 55401 Library functions are distinguished from let subcommands 55402 in the following ways. 55403 1) Functions enclose the input value in parenthesis. Let 55404 subcommands use spaces. 55405 2) Functions can accept (and return) either parameters 55406 (i.e., single values) or variables (i.e., an array of 55407 values) while let subcommands are specific in which they 55408 accept as input and what they return as output. 55409 3) Functions can accept expressions while let subcommands 55410 do not. For example, the following is legal: 55411 LET Y2 = ABS(Y1-INT(Y1)) 55412 For let subcommands, you typically have to do something 55413 like the following: 55414 LET YTEMP = Y**2 + 8 55415 LET A = SUM YTEMP 55416 55417Default: 55418 None 55419 55420Synonyms: 55421 None 55422 55423Related Commands: 55424 ABS = Compute the absolute value of a number. 55425 EXP = Compute the exponential of a number. 55426 MOD = Compute the modulo function. 55427 MIN = Compute the minimum of two numbers. 55428 MAX = Compute the maximum of two numbers. 55429 DIM = Compute the positive difference of two numbers. 55430 IND = Compute the mathematical indicator function. 55431 55432Applications: 55433 XX 55434 55435Implementation Date: 55436 XX 55437 55438Program: 55439 TITLE PLOT SQUARE ROOT FUNCTION 55440 PLOT SQRT(X) FOR X = 0 .1 9.9 55441 55442-----SQUARED RANKS TEST----------------------------------------- 55443 55444SQUARED RANKS 55445 55446Name: 55447 SQUARED RANKS 55448 55449Type: 55450 Analysis Command 55451 55452Purpose: 55453 Perform a squared ranks test that k samples have equal variances. 55454 55455Description: 55456 The F test is the standard parameteric test for testing the 55457 equality of variances for the two sample case. The squared 55458 ranks test is a nonparametric test for either the two sample 55459 case or the case of k groups. 55460 55461 The assumptions for using this test are 55462 55463 1. The k samples are random samples from their respective 55464 populations. 55465 55466 2. The k samples are mutually independent. 55467 55468 3. The measurement is scale is at least interval (i.e., 55469 the data can be ranked). 55470 55471 More formally, 55472 55473 H0: The samples are identically distributed except for 55474 possibly different means 55475 HA: At least two of the variances are not equal 55476 Test Statistic: 55477 55478 T = (1/D**2)*{SUM[i=1 to k][S(i)**2/n(i)] - N*SBAR**2} 55479 55480 where 55481 55482 S(i) = sum of squared ranks in subsample i 55483 n(i) = number of observations in subsample i 55484 D**2 = (1/(N-1))*{SUM[i=1 to N][R(i)**4] - N*SBAR**2} 55485 SBAR = (1/N)*SUM[j=1 to k][S(k)] 55486 = (1/N)*SUM[i=1 to N][S(k)] 55487 R(i) = rank of observation i 55488 55489 For the 2-sample case, the test statistic is 55490 55491 T1 = {T - N1*SBAR**2}/ 55492 SQRT{(N1*N2)/(N*(N-1))}*SUM[i=1 to N][R(i)**4] - 55493 (N1*N2/(N-1))*(SBAR)**2} 55494 55495 Significance Level: alpha 55496 Critical Region: For the k sample case 55497 55498 T1 > CHIPPF(ALPHA,K-1) 55499 55500 where CHIPPF is the chi-square percent point 55501 function. 55502 55503 For the 2 sample case, 55504 55505 T1 > NORPPF(1 - ALPHA/2) 55506 T1 < NORPPF(ALPHA/2) 55507 55508 where CHIPPF is the chi-square percent point 55509 function. 55510 55511 Conclusion: Reject the null hypothesis if the test 55512 statistic is in the critical region. 55513 55514Syntax 1: 55515 <LOWER TAILED/UPPER TAILED> SQUARED RANKS <y> <x> 55516 <SUBSET/EXCEPT/FOR qualification> 55517 where <LOWER TAILED/UPPER TAILED> is an optional keyword for the 55518 two sample case; 55519 <y> is the response (= dependent) variable; 55520 <x> is the factor (= independent) variable; 55521 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 55522 55523 The LOWER TAILED and UPPER TAILED options are only available 55524 for the two sample case. Only one can be specified and if 55525 neither is entered a two-tailed test will be performed. 55526 55527Syntax 2: 55528 MULTIPLE SQUARED RANKS <y1> ... <yk> 55529 <SUBSET/EXCEPT/FOR qualification> 55530 where <LOWER TAILED/UPPER TAILED> is an optional keyword for the 55531 two sample case; 55532 <y1> ... <yk> is a list of 1 to 30 response variables; 55533 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 55534 55535 This syntax is used for the case when the data for each group is 55536 stored in a separate variable. This syntax accepts matrix arguments. 55537 55538 The LOWER TAILED and UPPER TAILED options are only available 55539 for the two sample case. Only one can be specified and if 55540 neither is entered a two-tailed test will be performed. 55541 55542Examples: 55543 SQUARED RANKS TEST Y X 55544 SQUARED RANKS TEST Y X SUBSET X = 1 TO 4 55545 MULTIPLE SQUARED RANKS TEST Y1 Y2 Y3 Y4 55546 MULTIPLE SQUARED RANKS TEST Y1 TO Y4 55547 LOWER TAILED SQUARED RANKS TEST Y1 Y2 55548 UPPER TAILED SQUARED RANKS TEST Y1 Y2 55549 55550Note: 55551 For the k sample case and if the hypothesis of identical distributions 55552 is rejected, you can perform a multiple comparisons procedure to 55553 determine which pairs of populations tend to differ. 55554 55555 The populations i and j seem to have different variances if the 55556 following inequality is satisfied: 55557 55558 |S(i)/N(i) - S(j)/n(j)| > TPPF(1-(alpha/2))* 55559 SQRT(D**2**(N-1-T1)/(N-k))* 55560 SQRT((1/N(i)) + (1/N(j))) 55561 55562 with TPPF and T1 denoting the t percent point function with N - k 55563 degrees of freedom and the Kruskal-Wallis test statistic, 55564 respectively. 55565 55566Note: 55567 The following statistics are also supported: 55568 55569 LET A = SQUARED RANKS TEST Y 55570 LET A = SQUARED RANKS TEST CDF Y 55571 LET A = SQUARED RANKS TEST PVALUE Y 55572 LET A = SQUARED RANKS TEST LOWER TAILED PVALUE Y 55573 LET A = SQUARED RANKS TEST UPPER TAILED PVALUE Y 55574 55575 Enter HELP STATISTICS to see what commands can use these 55576 statistics. 55577 55578Default: 55579 None 55580 55581Synonyms: 55582 SQUARED RANKS is a synonym for SQUARED RANKS TEST 55583 55584Related Commands: 55585 KLOTZ TEST = Perform two sample test for equal variances. 55586 KRUSKAL WALLIS TEST = Perform Kruskal Wallis test for equal 55587 locations. 55588 ANOVA = Perform an analysis of variance. 55589 MEDIAN TEST = Perform a median test for equal variances. 55590 BLOCK PLOT = Generate a block plot. 55591 DEX ... PLOT = Generates a dex plot for a statistic. 55592 T TEST = Performs a t test. 55593 55594Reference: 55595 W. J. Conover, (1999). "Practical Nonparameteric Statistics", 55596 Third Edition, Wiley, pp. 300-310. 55597 55598Applications: 55599 Nonparametric Analysis 55600 55601Implementation Date: 55602 2011/6 55603 55604Program: 55605 . Step 1: Read Data (example 1 from pp. 304-305 of Conover) 55606 . 55607 let y1 = data 10.8 11.1 10.4 10.1 11.3 55608 let y2 = data 10.8 10.5 11.0 10.9 10.8 10.7 10.8 55609 . 55610 . Step 2: Data with more than 2 groups 55611 . 55612 let z1 = data 0.7 1 2 1.4 0.5 0.8 1 1.1 1.9 1.2 1.5 55613 let z2 = data 1.7 2.1 -0.4 0 1 1.1 0.9 2.3 1.3 0.4 0.5 55614 let z3 = data 0.9 0.9 1 0 0.1 -0.6 2.2 -0.3 0.6 2.4 2.5 55615 . 55616 . Step 3: Convert to form needed for "statistic" command 55617 . 55618 let y x = stacked y1 y2 55619 let zy zx = stacked z1 z2 z3 55620 set write decimals 4 55621 . 55622 . Step 2: Check the statistic 55623 . 55624 . stat = 5.192, pvalue = 0.0754 55625 . 55626 let stat = squared rank test zy zx 55627 let pval = squared rank test pvalue zy zx 55628 let cdf = squared rank test cdf zy zx 55629 print stat cdf pval 55630 pause 55631 . 55632 let stat2 = squared rank test y x 55633 let cdf2 = squared rank test cdf y x 55634 let pval2 = squared rank test pvalue y x 55635 let pvallt = squared rank test lower tailed pvalue y x 55636 let pvalut = squared rank test upper tailed pvalue y x 55637 print stat2 cdf2 pval2 pvallt pvalut 55638 . 55639 squared rank test y1 y2 55640 55641-----SRACDF (LET)-------------------------------- 55642 55643SRACDF 55644 55645Name: 55646 SRACDF (LET) 55647 55648Type: 55649 Library Function 55650 55651Purpose: 55652 Compute the studentized range cumulative distribution 55653 function with degrees of freedom parameter V and number of 55654 samples parameter R. 55655 55656Description: 55657 The studentized range is defined as: 55658 55659 Q = Range/Standard Deviation 55660 55661 The studentized range is used in constructing confidence 55662 intervals for tests of multiple comparisons in analysis 55663 of variance problems. 55664 55665 The parameter V must be >= 1 and R must be >= 2. Note 55666 that for the most common uses of this distribution 55667 R is usually set to V + 1. 55668 55669Syntax: 55670 LET <y> = SRACDF(<x>,<v>,<r>) <SUBSET/EXCEPT/FOR qualification> 55671 where <x> is a variable or a parameter where the studentized 55672 range will be computed (<x> > 0); 55673 <y> is a variable or a parameter (depending on what <x> is) 55674 where the computed studentized range cdf values are 55675 stored; 55676 <v> is a number or parameter that specifies the degrees 55677 of freedom parameter (<v> >= 1); 55678 <r> is a number or parameter that specifies the sample 55679 size parameter (<r> >= 2); 55680 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 55681 55682Examples: 55683 LET A = SRACDF(3,10,11) 55684 LET A = SRACDF(A1,22,23) 55685 LET X2 = SRACDF(X1,V,R) 55686 55687Note: 55688 This command is implemented using the Algorithm AS 190, 55689 prtrng, from Applied Statistics (1983), Vol. 32, No. 2. 55690 It incorporates modifications from Applied Statistics, 55691 (1985) Vol. 34, (1). 55692 55693Note: 55694 Library functions are distinguished from let subcommands 55695 in the following ways. 55696 1) Functions enclose the input value in parenthesis. Let 55697 subcommands use spaces. 55698 2) Functions can accept (and return) either parameters 55699 (i.e., single values) or variables (i.e., an array of 55700 values) while let subcommands are specific in which they 55701 accept as input and what they return as output. 55702 3) Functions can accept expressions while let subcommands 55703 do not. For example, the following is legal: 55704 LET Y2 = ABS(Y1-INT(Y1)) 55705 For let subcommands, you typically have to do something 55706 like the following: 55707 LET YTEMP = Y**2 + 8 55708 LET A = SUM YTEMP 55709 55710Default: 55711 None 55712 55713Synonyms: 55714 None 55715 55716Related Commands: 55717 SRAPPF = Compute the studentized range percent point function. 55718 ANOVA = Perform an analysis of variance. 55719 CHSPDF = Compute the chi-square probability density function. 55720 CHSPPF = Compute the chi-square percent point function. 55721 CHSCDF = Compute the chi-square cumulative distribution function. 55722 FCDF = Compute the F cumulative distribution function. 55723 FPDF = Compute the F probability density function. 55724 FPPF = Compute the F percent point function. 55725 NORCDF = Compute the normal cumulative distribution function. 55726 NORPDF = Compute the normal probability density function. 55727 NORPPF = Compute the normal percent point function. 55728 TCDF = Compute the T cumulative distribution function. 55729 TPDF = Compute the T probability density function. 55730 TPPF = Compute the T percent point function. 55731 55732Applications: 55733 Analysis of Variance 55734 55735Implementation Date: 55736 1999/3 55737 55738Program: 55739 TITLE AUTOMATIC 55740 MULTIPLOT CORNER COORDINATES 5 5 95 95 55741 MULTIPLOT 2 2 55742 PLOT SRACDF(X,4,5) FOR X = 0.01 0.01 10 55743 PLOT SRACDF(X,9,10) FOR X = 0.01 0.01 10 55744 PLOT SRACDF(X,19,20) FOR X = 0.01 0.01 10 55745 PLOT SRACDF(X,29,30) FOR X = 0.01 0.01 10 55746 END OF MULTIPLOT 55747 55748-----SRAPPF (LET)-------------------------------- 55749 55750SRAPPF 55751 55752Name: 55753 SRAPPF (LET) 55754 55755Type: 55756 Library Function 55757 55758Purpose: 55759 Compute the studentized range percent point function with 55760 degrees of freedom parameter V and number of samples 55761 parameter R. 55762 55763Description: 55764 The studentized range is defined as: 55765 55766 Q = Range/Standard Deviation 55767 55768 The studentized range is used in constructing confidence 55769 intervals for tests of multiple comparisons in analysis 55770 of variance problems. 55771 55772 The parameter V must be >= 1 and R must be >= 2. Note 55773 that for the most common uses of this distribution 55774 R is usually set to V + 1. 55775 55776 This function is only supported for values in the range 55777 0.90 to 0.99. 55778 55779Syntax: 55780 LET <y> = SRAPPF(<p>,<v>,<r>) <SUBSET/EXCEPT/FOR qualification> 55781 where <p> is a variable or a parameter where the studentized 55782 range percent point will be computed 55783 (0.90 <= <p> <= 0.99); 55784 <y> is a variable or a parameter (depending on what <x> is) 55785 where the computed studentized range cdf values are 55786 stored; 55787 <v> is a number or parameter that specifies the degrees 55788 of freedom parameter (<v> >= 1); 55789 <r> is a number or parameter that specifies the sample 55790 size parameter (<r> >= 2); 55791 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 55792 55793Examples: 55794 LET A = SRAPPF(0.90,10,11) 55795 LET A = SRAPPF(0.95,22,23) 55796 LET X2 = SRAPPF(0.99,V,R) 55797 55798Note: 55799 This command is implemented using the Algorithm AS 190, 55800 qrtrng, from Applied Statistics (1983), Vol. 32, No. 2. 55801 It incorporates modifications from Applied Statistics, 55802 (1985) Vol. 34, (1). 55803 55804Note: 55805 Library functions are distinguished from let subcommands 55806 in the following ways. 55807 1) Functions enclose the input value in parenthesis. Let 55808 subcommands use spaces. 55809 2) Functions can accept (and return) either parameters 55810 (i.e., single values) or variables (i.e., an array of 55811 values) while let subcommands are specific in which they 55812 accept as input and what they return as output. 55813 3) Functions can accept expressions while let subcommands 55814 do not. For example, the following is legal: 55815 LET Y2 = ABS(Y1-INT(Y1)) 55816 For let subcommands, you typically have to do something 55817 like the following: 55818 LET YTEMP = Y**2 + 8 55819 LET A = SUM YTEMP 55820 55821Default: 55822 None 55823 55824Synonyms: 55825 None 55826 55827Related Commands: 55828 SRACDF = Compute the studentized range cumulative distribution 55829 function. 55830 ANOVA = Perform an analysis of variance. 55831 CHSPDF = Compute the chi-square probability density function. 55832 CHSPPF = Compute the chi-square percent point function. 55833 CHSCDF = Compute the chi-square cumulative distribution function. 55834 FCDF = Compute the F cumulative distribution function. 55835 FPDF = Compute the F probability density function. 55836 FPPF = Compute the F percent point function. 55837 NORCDF = Compute the normal cumulative distribution function. 55838 NORPDF = Compute the normal probability density function. 55839 NORPPF = Compute the normal percent point function. 55840 TCDF = Compute the T cumulative distribution function. 55841 TPDF = Compute the T probability density function. 55842 TPPF = Compute the T percent point function. 55843 55844Applications: 55845 Analysis of Variance 55846 55847Implementation Date: 55848 1999/3 55849 55850Program: 55851 TITLE AUTOMATIC 55852 MULTIPLOT CORNER COORDINATES 5 5 95 95 55853 MULTIPLOT 2 2 55854 PLOT SRAPPF(P,4,5) FOR P = 0.90 0.01 0.99 55855 PLOT SRAPPF(P,9,10) FOR P = 0.90 0.01 0.99 55856 PLOT SRAPPF(P,19,20) FOR P = 0.90 0.01 0.99 55857 PLOT SRAPPF(P,29,30) FOR P = 0.90 0.01 0.99 55858 END OF MULTIPLOT 55859 55860-----STACK------------------------------------------------------- 55861 55862STACK 55863 55864Name: 55865 STACK 55866 55867Type: 55868 LET Subcommand 55869 55870Purpose: 55871 Convert a set of response variables to a single response 55872 variable and a group-id variable. 55873 55874Description: 55875 Many commands in Dataplot expect the data to be in the 55876 form of a single response variable and a group-id variable 55877 (e.g., BOX PLOT, MEAN PLOT, SD PLOT, TABULATE). However, many 55878 data files will contain grouped data in a form where each group 55879 is stored as a separate response variable. 55880 55881 The STACK command provides a convenient method for converting 55882 from the multi-column form to the single response variable 55883 with group-id variable form. 55884 55885Syntax: 55886 LET <y2> <x2> = STACK <x1> ... <xk> 55887 <SUBSET/EXPCEPT/FOR qualification> 55888 where <x1> ... <xk> is a set of one or more response variables 55889 (they do not have to be of equal size); 55890 <y2> is the variable to contain <x1> ... <xk> in a 55891 single response variable; 55892 <x2> is the variable to contain the group-id variable; 55893 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 55894 55895Examples: 55896 LET Y2 X2 = STACK Z1 Z2 Z3 Z4 Z5 55897 55898Default: 55899 None. 55900 55901Synonyms: 55902 None 55903 55904Related Commands: 55905 EXTEND = Extends a variable by another variable. 55906 LET = Creates, transforms, etc. a variable. 55907 MEAN PLOT = Generate a mean plot. 55908 BOX PLOT = Generate a box plot. 55909 TABULATE = Peform a tabulation. 55910 UNSTACK = Create multiple response variables from a response 55911 variable and an associated group-id variable. 55912 55913Applications: 55914 Data Management 55915 55916Implementation Date: 55917 2003/5 55918 55919Program: 55920 SKIP 25 55921 READ MONTGOME.DAT Y1 Y2 Y3 55922 . 55923 LET Z2 X2 = STACK Y1 Y2 Y3 55924 . 55925 XTIC OFFSET 0.5 0.5 55926 LET NVAR = 3 55927 XLIMITS 1 NVAR 55928 MAJOR XTIC MARK NUMBER NVAR 55929 MINOR XTIC MARK NUMBER 0 55930 MAJOR XTIC MARK NUMBER NVAR 55931 X1TIC MARK LABEL FORMAT ALPHA 55932 X1TIC MARK LABEL CONTENT LARGE MEDIUM SMALL 55933 . 55934 MULTIPLOT SCALE FACTOR 1.5 55935 MULTIPLOT CORNER COORDINATES 0 0 100 100 55936 MULTIPLOT 2 2 55937 CHARACTER X BLANK 55938 LINE BLANK SOLID 55939 Y1LABEL MEAN (PERCENTAGE CLASSIFICATION) 55940 MEAN PLOT Z2 X2 55941 Y1LABEL SD (PERCENTAGE CLASSIFICATION) 55942 SD PLOT Z2 X2 55943 LINES BOX PLOT 55944 CHARACTER BOX PLOT 55945 FENCES ON 55946 Y1LABEL (PERCENTAGE CLASSIFICATION) 55947 BOX PLOT Z2 X2 55948 END OF MULTIPLOT 55949 55950-----STANDARD DEVIATION (LET)----------------------------------------- 55951 55952STANDARD DEVIATION 55953 55954Name: 55955 STANDARD DEVIATION (LET) 55956 55957Type: 55958 Let Subcommand 55959 55960Purpose: 55961 Compute the standard deviation of a variable. 55962 55963Description: 55964 The standard deviation is a common measure of the spread of a 55965 distribution or variable. The formula is: 55966 SD = SQRT(SUM(Xi - Xmean)**2/(N-1)) 55967 55968Syntax: 55969 LET <par> = STANDARD DEVIATION <y> 55970 <SUBSET/EXCEPT/FOR qualification> 55971 where <y> is the variable for which the standard deviation is to 55972 be computed; 55973 <par> is a parameter where the computed standard deviation 55974 is saved; 55975 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 55976 55977Examples: 55978 LET SD = STANDARD DEVIATION Y1 55979 LET SD = STANDARD DEVIATION Y1 SUBSET TAG > 2 55980 55981Default: 55982 None 55983 55984Synonyms: 55985 None 55986 55987Related Commands: 55988 MEAN = Compute the mean of a variable. 55989 RANGE = Compute the range of a variable. 55990 VARIANCE = Compute the variance of a variable. 55991 WEIGHTED STAND DEVI = Compute the weighted standard deviation of 55992 a variable. 55993 55994Applications: 55995 Data Analysis 55996 55997Implementation Date: 55998 Pre-1987 55999 56000Program: 56001 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 56002 LET SD = STANDARD DEVIATION Y1 56003 56004-----SD CONFIDENCE LIMITS-------------------------------------- 56005 56006SD CONFIDENCE LIMITS 56007 56008Name: 56009 SD CONFIDENCE LIMITS 56010 56011Type: 56012 Analysis Command 56013 56014Purpose: 56015 Generates a confidence interval for the standard deviation. 56016 56017Description: 56018 Given a sample of n observations with standard deviation s, the 56019 two-sided confidence interval for the standard deviation is 56020 56021 lower confidence limit = s*SQRT((n-1)/CHSPPF(1-alpha/2;n-1)) 56022 upper confidence limit = s*SQRT((n-1)/CHSPPF(alpha/2;n-1)) 56023 56024 with CHSPPF denoting the percent point function of the chi-square 56025 distribution. In these formulas, alpha is less than 0.5 (i.e., 56026 for a 95% confidence interval, we are using alpha = 0.05). 56027 56028 The one-sided lower confidence limit is 56029 56030 lower confidence limit = s*SQRT((n-1)/CHSPPF(1-alpha;n-1)) 56031 56032 The one-sided upper confidence limit is 56033 56034 upper confidence limit = s*SQRT((n-1)/CHSPPF(alpha;n-1)) 56035 56036 This confidence interval is based on the assumption that 56037 the underlying data is approximately normally distributed. 56038 The confidence interval for the standard deviation is highly 56039 sensitive to non-normality in the data. It is recommended 56040 that the original data be tested for normality before using 56041 these normal based intervals. If the data is not approximately 56042 normal, an alternative is to use the command 56043 56044 BOOTSTRAP STANDARD DEVIATION PLOT Y 56045 56046Syntax 1: 56047 <LOWER/UPPER> SD CONFIDENCE LIMITS <y> 56048 <SUBSET/EXCEPT/FOR qualification> 56049 where <y> is the response variable; 56050 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56051 56052 If LOWER is specified, a one-sided lower confidence limit is 56053 returned. If UPPER is specified, a one-sided upper confidence 56054 limit is returned. If neither is specified, a two-sided limit 56055 is returned. 56056 56057 This syntax supports matrix arguments for the response variable. 56058 56059Syntax 2: 56060 MULTIPLE <LOWER/UPPER> SD CONFIDENCE LIMITS <y1> ... <yk> 56061 <SUBSET/EXCEPT/FOR qualification> 56062 where <y1> .... <yk> is a list of 1 to 30 response variables; 56063 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56064 56065 This syntax will generate a confidence interval for each of 56066 the response variables. The word MULTIPLOT is optional. That is, 56067 56068 MULTIPLE SD CONFIDENCE LIMITS Y1 Y2 Y3 56069 56070 is equivalent to 56071 56072 SD CONFIDENCE LIMITS Y1 Y2 Y3 56073 56074 If LOWER is specified, a one-sided lower confidence limit is 56075 returned. If UPPER is specified, a one-sided upper confidence 56076 limit is returned. If neither is specified, a two-sided limit 56077 is returned. 56078 56079 This syntax supports matrix arguments for the response variables. 56080 56081Syntax 3: 56082 REPLICATED <LOWER/UPPER> SD CONFIDENCE LIMITS <y> <x1> ... <xk> 56083 <SUBSET/EXCEPT/FOR qualification> 56084 where <y> is the response variable; 56085 <x1> .... <xk> is a list of 1 to 6 group-id variables; 56086 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56087 56088 This syntax performs a cross-tabulation of the <x1> ... <xk> 56089 and generates a confidence interval for each unique combination 56090 of the cross-tabulated values. For example, if X1 has 3 levels 56091 and X2 has 2 levels, six confidence intervals will be generated. 56092 56093 If LOWER is specified, a one-sided lower confidence limit is 56094 returned. If UPPER is specified, a one-sided upper confidence 56095 limit is returned. If neither is specified, a two-sided limit 56096 is returned. 56097 56098 This syntax does not support matrix arguments. 56099 56100Examples: 56101 SD CONFIDENCE LIMITS Y1 56102 SD CONFIDENCE LIMITS Y1 SUBSET TAG > 2 56103 MULTIPLE SD CONFIDENCE LIMITS Y1 TO Y5 56104 REPLICATED SD CONFIDENCE LIMITS Y X 56105 56106Note: 56107 As noted above, the confidence interval for the standard 56108 deviation is very sensitive to non-normality in the data. 56109 Bonett (2006) has proposed an interval that is nearly exact when 56110 the data is normally distributed and provides good performance 56111 for moderately non-normal data. The interval for the variance (for 56112 the standard deviation, take the square root of these values) is 56113 56114 EXP{LOG(c*s**2) - z(alpha/2)*se} < sigma**2 < 56115 EXP{LOG(c*s**2) + z(alpha/2)*se} 56116 56117 where 56118 56119 s = sample standard deviation 56120 c = n/(n - z(alpha/2)) 56121 z = the normal percent point function 56122 se = the standard error 56123 = c*SQRT[(gamma4hat - (n-3)/n))/(n-1)] 56124 gam4hat = an adjusted estimate of kurtosis 56125 = N*SUM[i=1 to n][(x(i) - m)**4/ 56126 (SUM[i=1 to n][(x(i) - xbar)**2])**2 56127 m = trimmed mean with trim proportion equal 56128 to 1/(2*SQRT(n-4)) 56129 56130 The use of the trimmed mean reduces the bias of the 56131 kurtosis estimate for heavy tailed and skewed data. 56132 56133 The justification and derivation of this interval is given 56134 in Bonett's paper. 56135 56136 To request that the Bonett interval be generated, enter 56137 56138 SET BONETT STANDARD DEVIATION CONFIDENCE LIMITS ON 56139 56140 Based on simulation studies by Bonett, this interval results 56141 in greatly improved coverage properties for moderately 56142 non-normal data. For more extreme non-normality, large 56143 sample sizes may be required to obtain good coverage 56144 properties. Often a transformation to reduce skewness 56145 (which may reduce the heavy tailedness as well), such as 56146 the LOG or square root, can significantly reduce the sample 56147 size required to obtain good coverage properties. 56148 56149 Bonett also suggests that improved estimates for the kurtosis can 56150 significantly improve the coverage properties. Bonett's example is 56151 quality control applications where much historical data is frequently 56152 available. If a prior estimate of kurtosis is available, then the 56153 above formula pools this prior estimate with the kurtosis estimate 56154 from the data using 56155 56156 gamma4hat = (n0*gam4(0) + n*gam4hat)/(n0 + n) 56157 56158 with gam4(0) and n0 denoting the prior estimate of kurtosis 56159 and the associated sample size, respectively. Bonett gives 56160 guidance on pooling multiple estimates of kurtosis based on 56161 several small samples (it is often the case in quality control 56162 applications that a large number of small samples are available). 56163 56164 In Dataplot, you can specify a prior estimate of kurtosis by 56165 entering the commands 56166 56167 LET KURTOSIS = <value> 56168 LET N0 = <value> 56169 56170 Niwitpong and Kirdwichai (2008) suggested two modifications to 56171 Bonett's interval to improve the coverage for data that are 56172 skewed and heavy tailed. Specifically, the following modifications 56173 are made to Bonett's interval 56174 56175 1. Use the median instead of the trimmed mean to compute 56176 the sample kurtosis. 56177 56178 2. Use the t percent point function rather than the normal 56179 percent point function. 56180 56181 This interval will be more conservative than the original 56182 Bonett data. Based on simulation studies in their paper, these 56183 adjustments can improve the nominal coverage for data that are 56184 skewed. However, it may be overly conservative for data that 56185 are only moderately non-normal. 56186 56187 To use the Niwitpong and Kirdwichai adjusted interval, enter 56188 56189 SET BONETT STANDARD DEVIATION CONFIDENCE LIMITS ADJUSTED ON 56190 56191Note: 56192 A table of confidence limits is printed for alpha levels of 56193 50.0, 80.0, 90.0, 95.0, 99.0, and 99.9. 56194 56195Note: 56196 In addition to the STANDARD DEVIATION CONFIDENCE LIMIT command, the 56197 following commands can also be used: 56198 56199 LET ALPHA = 0.05 56200 56201 LET A = LOWER STANDARD DEVIATION CONFIDENCE LIMIT Y 56202 LET A = UPPPER STANDARD DEVIATION CONFIDENCE LIMIT Y 56203 LET A = LOWER BONETT STANDARD DEVIATION CONFIDENCE LIMIT Y 56204 LET A = UPPPER BONETT STANDARD DEVIATION CONFIDENCE LIMIT Y 56205 LET A = ONE SIDED LOWER STANDARD DEVIATION CONFIDENCE LIMIT Y 56206 LET A = ONE SIDED UPPER STANDARD DEVIATION CONFIDENCE LIMIT Y 56207 56208 LET A = SUMMARY LOWER STANDARD DEVIATION CONFIDENCE LIMIT YSD N 56209 LET A = SUMMARY UPPPER STANDARD DEVIATION CONFIDENCE LIMIT YSD N 56210 LET A = SUMMARY ONE SIDED LOWER STANDARD DEVIATION CONFIDENCE LIMIT 56211 YSD N 56212 LET A = SUMMARY ONE SIDED UPPER STANDARD DEVIATION CONFIDENCE LIMIT 56213 YSD N 56214 56215 The first command specifies the significance level. The next six 56216 commands are used when you have raw data. The last four commands are 56217 used when only summary data (standard deviation, sample size) is 56218 available. 56219 56220 In addition to the above LET command, built-in statistics are 56221 supported for about 20 different commands (enter HELP STATISTICS 56222 for details). 56223 56224Default: 56225 None 56226 56227Synonyms: 56228 STANDARD DEVIATION CONFIDENCE INTERVAL is a synonym for 56229 STANDARD DEVIATION CONFIDENCE LIMITS 56230 56231 SD CONFIDENCE LIMIT is a synonym for STANDARD DEVIATION CONFIDENCE 56232 LIMIT 56233 56234Related Commands: 56235 SD PREDICTION LIMITS = Generate a prediction limit for the 56236 standard deviation. 56237 CONFIDENCE LIMITS = Generate a confidence limit for the mean. 56238 PREDICTION LIMITS = Generate prediction limits for the mean. 56239 PREDICTION BOUNDS = Generate prediction limits to cover all 56240 new observations. 56241 TOLERANCE LIMITS = Generate a tolerance limit. 56242 56243Reference: 56244 Hahn and Meeker (1991), "Statistical Intervals: A Guide for 56245 Practitioners," Wiley, pp. 55-56. 56246 56247 Bonett (2006), "Approximate Confidence Interval for Standard 56248 Deviation of Nonnormal Distributions", Computational Statistics 56249 and Data Analysis, Vol. 50, pp. 775 - 782. 56250 56251 Niwitpong and Kirdwichai (2008), "Adjusted Bonett Confidence 56252 Interval for Standard Deviation of Non-Normal Distributions", 56253 Thailand Statistician, Vol. 6, No. 1, pp. 1-6. 56254 56255Applications: 56256 Confirmatory Data Analysis 56257 56258Implementation Date: 56259 2013/04 56260 2017/12: Support for Bonett intervals 56261 56262Program 1: 56263 SKIP 25 56264 READ ZARR13.DAT Y 56265 SET WRITE DECIMALS 5 56266 . 56267 SD CONFIDENCE LIMITS Y 56268 LOWER SD CONFIDENCE LIMITS Y 56269 UPPER SD CONFIDENCE LIMITS Y 56270 56271Program 2: 56272 SKIP 25 56273 READ GEAR.DAT Y X 56274 LET NNEW = 3 56275 . 56276 REPLICATED SD CONFIDENCE LIMITS Y X 56277 56278Program 3: 56279 . Following example from Hahn and Meeker's book. 56280 . 56281 let ymean = 50.10 56282 let ysd = 1.31 56283 let n1 = 5 56284 let alpha = 0.05 56285 . 56286 set write decimals 5 56287 let slow1 = summary lower sd confidence limits ysd n1 56288 let supp1 = summary upper sd confidence limits ysd n1 56289 let slow2 = summary one sided lower sd confidence limits ysd n1 56290 let supp2 = summary one sided upper sd confidence limits ysd n1 56291 print slow1 supp1 slow2 supp2 56292 56293Program 4: 56294 . Step 1: Read the data (example from Bonett paper) 56295 . 56296 let y = data 15.83 16.01 16.24 16.42 15.33 15.44 16.88 16.31 56297 . 56298 . Step 2: Compute the statistics 56299 . 56300 set write decimals 4 56301 let ysd = standard deviation y 56302 let lcl = lower bonett standard deviation confidence limit y 56303 let ucl = upper bonett standard deviation confidence limit y 56304 print ysd lcl ucl 56305 . 56306 set bonett standard deviation confidence limit on 56307 standard deviation confidence limits y 56308 56309-----STANDARD DEVIATION OF THE MEAN (LET)---------------------------- 56310 56311STANDARD DEVIATION OF THE MEAN 56312 56313Name: 56314 STANDARD DEVIATION OF THE MEAN (LET) 56315 56316Type: 56317 Let Subcommand 56318 56319Purpose: 56320 Compute the standard deviation of the mean of a variable. 56321 56322Description: 56323 The standard deviation of the mean is: 56324 sd of mean = s/SQRT(N) 56325 where s is the standard deviation of the variable. 56326 56327Syntax: 56328 LET <par> = STANDARD DEVIATION OF THE MEAN <y> 56329 <SUBSET/EXCEPT/FOR qualification> 56330 where <y> is the variable for which the standard deviation of the 56331 mean is to be computed; 56332 <par> is a parameter where the computed standard deviation 56333 of the mean is saved; 56334 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56335 56336Examples: 56337 LET SD = STANDARD DEVIATION OF THE MEAN Y1 56338 LET SD = STANDARD DEVIATION OF THE MEAN Y1 SUBSET TAG > 2 56339 56340Default: 56341 None 56342 56343Synonyms: 56344 None 56345 56346Related Commands: 56347 MEAN = Compute the mean of a variable. 56348 STAND DEVI = Compute the standard deviation of a variable. 56349 56350Applications: 56351 XX 56352 56353Implementation Date: 56354 XX 56355 56356Program: 56357 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 56358 LET SD = STANDARD DEVIATION OF THE MEAN Y1 56359 56360-----STANDARD DEVIATION PLOT------------------------------------- 56361 56362STANDARD DEVIATION PLOT 56363 56364Name: 56365 STANDARD DEVIATION PLOT 56366 56367Type: 56368 Graphics Command 56369 56370Purpose: 56371 Generates a standard deviation plot. 56372 56373Description: 56374 A standard deviation plot is a plot consisting of subsample 56375 standard deviations versus subsample index. The subsample standard 56376 deviation is the standard deviation (with divisor ni-1) of the data 56377 in the subsample. The standard deviation plot is used to answer 56378 the question--"Does the subsample variation change over different 56379 subsamples?". It consists of: 56380 Vertical axis = subsample standard deviation; 56381 Horizontal axis = subsample index. 56382 The standard deviation plot yields 2 traces; 56383 1. a subsample standard deviation trace; and 56384 2. a full-sample standard deviation reference line. 56385 Like usual, the appearance of these 2 traces is 56386 controlled by the first 2 settings of the LINES, 56387 CHARACTERS, SPIKES, BARS, and similar attributes. 56388 56389Syntax: 56390 STANDARD DEVIATION PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 56391 where <y> is the response (= dependent) variable; 56392 <x> is the subsample identifier variable (this variable 56393 appears on the horizontal axis); 56394 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56395 56396Examples: 56397 STANDARD DEVIATION PLOT Y X 56398 STANDARD DEVIATION PLOT Y X1 56399 56400Default: 56401 None 56402 56403Synonyms: 56404 SD PLOT 56405 S PLOT 56406 56407Related Commands: 56408 CHARACTERS = Sets the type for plot char. 56409 LINES = Sets the type for plot lines. 56410 VARIANCE PLOT = Generates a variance plot. 56411 STAN DEVI OF MEAN PLOT = Generates standard deviation of the mean 56412 plot. 56413 RANGE PLOT = Generates a range plot. 56414 MEAN PLOT = Generates a mean plot. 56415 MEDIAN PLOT = Generates a median plot. 56416 BOX PLOT = Generates a box plot. 56417 S CHART = Generates a standard deviation 56418 control chart. 56419 PLOT = Generates a data or function plot. 56420 56421Applications: 56422 Quality Control 56423 56424Implementation Date: 56425 88/2 56426 56427Program: 56428 SKIP 25 56429 READ GEAR.DAT DIAMETER BATCH 56430 LINE BLANK DASH 56431 CHARACTER X BLANK 56432 XTIC OFFSET 0.2 0.2 56433 Y1LABEL STANDARD DEVIATION 56434 X1LABEL BATCH 56435 TITLE STANDARD DEVIATION PLOT 56436 STANDARD DEVIATION PLOT DIAMETER BATCH 56437 56438-----STANDARD DEVIATION OF THE MEAN PLOT------------------------- 56439 56440STANDARD DEVIATION OF THE MEAN PLOT 56441 56442Name: 56443 STANDARD DEVIATION OF THE MEAN PLOT 56444 56445Type: 56446 Graphics Command 56447 56448Purpose: 56449 Generates a standard deviation of the mean plot. 56450 56451Description: 56452 A standard deviation of the mean plot consists of subsample 56453 standard deviations of the mean versus subsample index. The 56454 subsample standard deviation of the mean is the subsample standard 56455 deviation divided by the square root of the subsample size. The 56456 standard deviation of the mean plot is used to answer the 56457 question--"Does the subsample variation of the mean change over 56458 different subsamples?". It consists of: 56459 Vertical axis = subsample standard deviation; 56460 Horizontal axis = subsample index. 56461 The standard deviation of the mean plot yields 2 traces: 56462 1. a subsample standard deviation of the mean trace; 56463 2. a full-sample standard deviation of the mean reference line. 56464 Like usual, the appearance of these 2 traces is 56465 controlled by the first 2 settings of the LINES, 56466 CHARACTERS, SPIKES, BARS, and similar attributes. 56467 56468Syntax: 56469 STANDARD DEVIATION OF THE MEAN PLOT <y> <x> 56470 <SUBSET/EXCEPT/FOR/qualification> 56471 where <y> is the response (= dependent) variable; 56472 <x> is the subsample identifier variable (this variable 56473 appears on the horizontal axis); 56474 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56475 56476Examples: 56477 STANDARD DEVIATION OF THE MEAN PLOT Y X 56478 STANDARD DEVIATION OF THE MEAN PLOT Y X1 56479 56480Default: 56481 None 56482 56483Synonyms: 56484 STANDARD DEVIATION OF MEAN PLOT 56485 SDM PLOT 56486 56487Related Commands: 56488 CHARACTERS = Sets the type for plot char. 56489 LINES = Sets the type for plot lines. 56490 STANDARD DEVIATION PLOT = Generates a standard deviation plot. 56491 VARIANCE PLOT = Generates a variance plot. 56492 VARIANCE OF MEAN PLOT = Generates variance of the mean plot. 56493 RANGE PLOT = Generates a range plot. 56494 MEAN PLOT = Generates a mean plot. 56495 MEDIAN PLOT = Generates a median plot. 56496 BOX PLOT = Generates a box plot. 56497 S CHART = Generates a standard deviation control 56498 chart. 56499 PLOT = Generates a data or function plot. 56500 56501Applications: 56502 Quality Control 56503 56504Implementation Date: 56505 88/2 56506 56507Program: 56508 SKIP 25 56509 READ GEAR.DAT DIAMETER BATCH 56510 LINE BLANK DASH 56511 CHARACTER X BLANK 56512 XTIC OFFSET 0.2 0.2 56513 Y1LABEL STANDARD DEVIATION OF THE MEAN 56514 X1LABEL BATCH 56515 TITLE STANDARD DEVIATION OF THE MEAN PLOT 56516 STANDARD DEVIATION OF THE MEAN PLOT DIAMETER BATCH 56517 56518-----SD PREDICTION LIMITS-------------------------------------- 56519 56520SD PREDICTION LIMITS 56521 56522Name: 56523 SD PREDICTION LIMITS 56524 56525Type: 56526 Analysis Command 56527 56528Purpose: 56529 Generates a prediction interval for the standard deviation of one 56530 or more new observations given a previous sample. 56531 56532Description: 56533 Given a sample of n observations with standard deviation s, the 56534 two-sided prediction interval to contain the standard deviation 56535 of m new indpendent, identically distributed observations is 56536 56537 lower prediction limit = s*SQRT(1/F(1-alpha/2;n-1,m-1)) 56538 upper prediction limit = s*SQRT(F(1-alpha/2;n-1,m-1)) 56539 56540 with F denoting the percent point function of the F distribution. 56541 56542 The one-sided lower prediction limit is 56543 56544 lower prediction limit = s*SQRT(1/F(1-alpha;n-1,m-1)) 56545 56546 The one-sided upper prediction limit is 56547 56548 upper prediction limit = s*SQRT(F(1-alpha;n-1,m-1)) 56549 56550 In this formula, the only value from the new observations is the 56551 sample size. That is, it can be applied before the new data is 56552 actually collected. The number of observations for the new sample 56553 is entered with the command 56554 56555 LET NNEW = <value> 56556 56557 If NNEW is not defined, then a value of 1 is used. 56558 56559 This prediction interval is based on the assumption that 56560 the underlying data is approximately normally distributed. 56561 The prediction interval for the standard deviation is highly 56562 sensitive to non-normality in the data. It is recommended 56563 that the original data be tested for normality before using 56564 these normal based intervals. 56565 56566Syntax 1: 56567 <LOWER/UPPER> <LOGNORMAL/BOXCOX> SD PREDICTION LIMITS <y> 56568 <SUBSET/EXCEPT/FOR qualification> 56569 where <y> is the response variable; 56570 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56571 56572 If LOWER is specified, a one-sided lower prediction limit is 56573 returned. If UPPER is specified, a one-sided upper prediction 56574 limit is returned. If neither is specified, a two-sided limit 56575 is returned. 56576 56577 If the keyword LOGNORMAL is present, the log of the data will be 56578 taken, then the normal prediction limits will be computed, and then 56579 the computed normal lower and upper limits will be exponentiated to 56580 obtain the lognormal prediction limtis. 56581 56582 Similarly, if the keyword BOXCOX is present, a Box-Cox transformation 56583 to normality will be applied to the data before computing the normal 56584 prediction limits. The computed lower and upper limits will then 56585 be transformed back to the original scale. 56586 56587 This syntax supports matrix arguments for the response variable. 56588 56589Syntax 2: 56590 MULTIPLE <LOWER/UPPER> <LOGNORMAL/BOXCOX> SD PREDICTION LIMITS 56591 <y1> ... <yk> 56592 <SUBSET/EXCEPT/FOR qualification> 56593 where <y1> .... <yk> is a list of 1 to 30 response variables; 56594 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56595 56596 This syntax will generate a prediction interval for each of 56597 the response variables. The word MULTIPLOT is optional. That is, 56598 56599 MULTIPLE SD PREDICTION LIMITS Y1 Y2 Y3 56600 56601 is equivalent to 56602 56603 SD PREDICTION LIMITS Y1 Y2 Y3 56604 56605 If LOWER is specified, a one-sided lower prediction limit is 56606 returned. If UPPER is specified, a one-sided upper prediction 56607 limit is returned. If neither is specified, a two-sided limit 56608 is returned. 56609 56610 If the keyword LOGNORMAL is present, the log of the data will be 56611 taken, then the normal prediction limits will be computed, and then 56612 the computed normal lower and upper limits will be exponentiated to 56613 obtain the lognormal prediction limtis. 56614 56615 Similarly, if the keyword BOXCOX is present, a Box-Cox transformation 56616 to normality will be applied to the data before computing the normal 56617 prediction limits. The computed lower and upper limits will then 56618 be transformed back to the original scale. 56619 56620 This syntax supports matrix arguments for the response variables. 56621 56622Syntax 3: 56623 REPLICATED <LOWER/UPPER> <LOGNORMAL/BOXCOX> 56624 SD PREDICTION LIMITS <y> <x1> ... <xk> 56625 <SUBSET/EXCEPT/FOR qualification> 56626 where <y> is the response variable; 56627 <x1> .... <xk> is a list of 1 to 6 group-id variables; 56628 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56629 56630 This syntax performs a cross-tabulation of the <x1> ... <xk> 56631 and generates a prediction interval for each unique combination 56632 of the cross-tabulated values. For example, if X1 has 3 levels 56633 and X2 has 2 levels, six prediction intervals will be generated. 56634 56635 If LOWER is specified, a one-sided lower prediction limit is 56636 returned. If UPPER is specified, a one-sided upper prediction 56637 limit is returned. If neither is specified, a two-sided limit 56638 is returned. 56639 56640 If the keyword LOGNORMAL is present, the log of the data will be 56641 taken, then the normal prediction limits will be computed, and then 56642 the computed normal lower and upper limits will be exponentiated to 56643 obtain the lognormal prediction limtis. 56644 56645 Similarly, if the keyword BOXCOX is present, a Box-Cox transformation 56646 to normality will be applied to the data before computing the normal 56647 prediction limits. The computed lower and upper limits will then 56648 be transformed back to the original scale. 56649 56650 This syntax does not support matrix arguments. 56651 56652Examples: 56653 SD PREDICTION LIMITS Y1 56654 SD PREDICTION LIMITS Y1 SUBSET TAG > 2 56655 MULTIPLE SD PREDICTION LIMITS Y1 TO Y5 56656 REPLICATED SD PREDICTION LIMITS Y X 56657 56658Note: 56659 A table of prediction limits is printed for alpha levels of 56660 50.0, 80.0, 90.0, 95.0, 99.0, and 99.9. 56661 56662Note: 56663 In addition to the STANDARD DEVIATION PREDICTION LIMIT command, the 56664 following commands can also be used: 56665 56666 LET ALPHA = 0.05 56667 LET NNEW = <value> 56668 56669 LET A = LOWER STANDARD DEVIATION PREDICTION LIMIT Y 56670 LET A = UPPPER STANDARD DEVIATION PREDICTION LIMIT Y 56671 LET A = ONE SIDED LOWER STANDARD DEVIATION PREDICTION LIMIT Y 56672 LET A = ONE SIDED UPPER STANDARD DEVIATION PREDICTION LIMIT Y 56673 56674 LET A = SUMMARY LOWER STANDARD DEVIATION PREDICTION LIMIT YSD N 56675 LET A = SUMMARY UPPPER STANDARD DEVIATION PREDICTION LIMIT YSD N 56676 LET A = SUMMARY ONE SIDED LOWER STANDARD DEVIATION PREDICTION LIMIT 56677 YSD N 56678 LET A = SUMMARY ONE SIDED UPPER STANDARD DEVIATION PREDICTION LIMIT 56679 YSD N 56680 56681 The first 2 commands specify the significance level and the number 56682 of new observations. The next 4 commands are used when you have raw 56683 data. The last 4 commands are used when only summary data (standard 56684 deviation, sample size) is available. 56685 56686 In addition to the above LET command, built-in statistics are 56687 supported for about 20 different commands (enter HELP STATISTICS 56688 for details). 56689 56690Default: 56691 None 56692 56693Synonyms: 56694 STANDARD DEVIATION PREDICTION INTERVAL is a synonym for 56695 STANDARD DEVIATION PREDICTION LIMITS 56696 56697 SD PREDICTION LIMIT is a synonym for STANDARD DEVIATION PREDICTION 56698 LIMIT 56699 56700Related Commands: 56701 SD CONFIDENCE LIMITS = Generate a confidence limit for the 56702 standard deviation. 56703 PREDICTION LIMITS = Generate prediction limits for the mean. 56704 PREDICTION BOUNDS = Generate prediction limits to cover all 56705 new observations. 56706 CONFIDENCE LIMITS = Generate a confidence limit for the mean. 56707 TOLERANCE LIMITS = Generate a tolerance limit. 56708 56709Reference: 56710 Hahn and Meeker (1991), "Statistical Intervals: A Guide for 56711 Practitioners", Wiley, pp. 61-62. 56712 56713Applications: 56714 Confirmatory Data Analysis 56715 56716Implementation Date: 56717 2013/04 56718 2014/06: Support for LOGNORMAL and BOXCOX options 56719 56720Program 1: 56721 SKIP 25 56722 READ ZARR13.DAT Y 56723 SET WRITE DECIMALS 5 56724 LET NNEW = 5 56725 . 56726 SD PREDICTION LIMITS Y 56727 LOWER SD PREDICTION LIMITS Y 56728 UPPER SD PREDICTION LIMITS Y 56729 56730Program 2: 56731 SKIP 25 56732 READ GEAR.DAT Y X 56733 SET WRITE DECIMALS 5 56734 LET NNEW = 3 56735 . 56736 REPLICATED SD PREDICTION LIMITS Y X 56737 56738Program 3: 56739 . Following example from Hahn and Meeker's book. 56740 . 56741 let ymean = 50.10 56742 let ysd = 1.31 56743 let n1 = 5 56744 let nnew = 3 56745 let alpha = 0.05 56746 . 56747 set write decimals 5 56748 let slow1 = summary lower sd prediction limits ysd n1 56749 let supp1 = summary upper sd prediction limits ysd n1 56750 let slow2 = summary one sided lower sd prediction limits ysd n1 56751 let supp2 = summary one sided upper sd prediction limits ysd n1 56752 print slow1 supp1 slow2 supp2 56753 56754-----STANDARDIZE (LET)----------------------------------------- 56755 56756STANDARDIZE 56757 56758Name: 56759 STANDARDIZE (LET) 56760 56761Type: 56762 Let Subcommand 56763 56764Purpose: 56765 Standardize, i.e., subtract the mean and divide by the 56766 standard deviation, a variable. 56767 56768Description: 56769 In many applications, it is desirable to standardize the 56770 data values. 56771 56772 This command provides additional flexibility in that either 56773 one or two group id variables can also be specified. That is, 56774 if one group id variable is given, the mean and standard 56775 deviation is computed for each group and the data values 56776 are standardized by the corresponding group mean and standard 56777 deviation. Likewise, if two group variables are specified, 56778 then a mean and standard deviaiton are computed for each cell 56779 of the cross tabulation and the data values are standardized 56780 by the corresponding cell mean and standard deviaition. 56781 56782 You can specify several alternative measures to the mean for 56783 the location statistic and several alternative measures to 56784 the standard deviaition for the scale statistic. See the 56785 Note below for details. In addition, you can choose to 56786 standardize only by location (i.e., subtract the mean but 56787 do not divide by the standard deviation) or only by scale. 56788 56789 You can also specifically specify a z-score or u-score. 56790 A z-score subtracts the mean and divides by the standard 56791 deviation (i.e,, it scales to a standard normal distribution). 56792 Similarly, the u-score subtracts the minimum and divides by 56793 the range. That is, it creates a standard uniform random 56794 variable (i.e., the data is scaled to a range between 0 and 1). 56795 If a z-score or u-score is explicitly requested, the 56796 settings for the SET LOCATION STATISTIC and SET SCALE STATISTIC 56797 (see Note below) are ignored. 56798 56799Syntax 1: 56800 LET <var> = STANDARDIZE <y> <SUBSET/EXCEPT/FOR qualification> 56801 where <y> is the response variable; 56802 <var> is a variable where the standardized values are stored; 56803 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56804 56805 This syntax standardizes (with respect to both location and 56806 scale) the variable with no groups. 56807 56808Syntax 2: 56809 LET <var> = LOCATION STANDARDIZE <y> 56810 <SUBSET/EXCEPT/FOR qualification> 56811 where <y> is the response variable; 56812 <var> is a variable where the standardized values are stored; 56813 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56814 56815 This syntax standardizes the variable (with respect to location 56816 only) with no groups. 56817 56818Syntax 3: 56819 LET <var> = SCALE STANDARDIZE <y> 56820 <SUBSET/EXCEPT/FOR qualification> 56821 where <y> is the response variable; 56822 <var> is a variable where the standardized values are stored; 56823 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56824 56825 This syntax standardizes the variable (with respect to scale 56826 only) with no groups. 56827 56828Syntax 4: 56829 LET <var> = ZSCORE <y> <SUBSET/EXCEPT/FOR qualification> 56830 where <y> is the response variable; 56831 <var> is a variable where the standardized values are stored; 56832 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56833 56834 This syntax specifically computes a z-score. 56835 56836Syntax 5: 56837 LET <var> = USCORE <y> <SUBSET/EXCEPT/FOR qualification> 56838 where <y> is the response variable; 56839 <var> is a variable where the standardized values are stored; 56840 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56841 56842 This syntax specifically computes a u-score. 56843 56844Syntax 6: 56845 LET <var> = STANDARDIZE <y> <x1> <SUBSET/EXCEPT/FOR qualification> 56846 where <y> is the response variable; 56847 <x1> is a group id variable; 56848 <var> is a variable where the standardized values are stored; 56849 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56850 56851 This syntax standardizes (with respect to both location and 56852 scale) the variable with one group variable. 56853 56854Syntax 7: 56855 LET <var> = LOCATION STANDARDIZE <y> <x1> 56856 <SUBSET/EXCEPT/FOR qualification> 56857 where <y> is the response variable; 56858 <x1> is a group id variable; 56859 <var> is a variable where the standardized values are stored; 56860 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56861 56862 This syntax standardizes the variable (with respect to location 56863 only) with one group variable. 56864 56865Syntax 8: 56866 LET <var> = SCALE STANDARDIZE <y> <x1> 56867 <SUBSET/EXCEPT/FOR qualification> 56868 where <y> is the response variable; 56869 <x1> is a group id variable; 56870 <var> is a variable where the standardized values are stored; 56871 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56872 56873 This syntax standardizes the variable (with respect to scale 56874 only) with one group variable. 56875 56876Syntax 9: 56877 LET <var> = ZSCORE <y> <x1> <SUBSET/EXCEPT/FOR qualification> 56878 where <y> is the response variable; 56879 <x1> is a group id variable; 56880 <var> is a variable where the standardized values are stored; 56881 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56882 56883 This syntax computes a z-score with one group variable. 56884 56885Syntax 10: 56886 LET <var> = USCORE <y> <x1> <SUBSET/EXCEPT/FOR qualification> 56887 where <y> is the response variable; 56888 <x1> is a group id variable; 56889 <var> is a variable where the standardized values are stored; 56890 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56891 56892 This syntax computes a u-score with one group variable. 56893 56894Syntax 11: 56895 LET <var> = STANDARDIZE <y> <x1> <x2> 56896 <SUBSET/EXCEPT/FOR qualification> 56897 where <y> is the response variable; 56898 <x1> is the first group id variable; 56899 <x2> is the second group id variable; 56900 <var> is a variable where the standardized values are stored; 56901 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56902 56903 This syntax standardizes (with respect to both location and 56904 scale) the variable with two group variable. 56905 56906Syntax 12: 56907 LET <var> = LOCATION STANDARDIZE <y> <x1> <x2> 56908 <SUBSET/EXCEPT/FOR qualification> 56909 where <y> is the response variable; 56910 <x1> is a group id variable; 56911 <x2> is the second group id variable; 56912 <var> is a variable where the standardized values are stored; 56913 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56914 56915 This syntax standardizes the variable (with respect to location 56916 only) with two group variable. 56917 56918Syntax 13: 56919 LET <var> = SCALE STANDARDIZE <y> <x1> <x2> 56920 <SUBSET/EXCEPT/FOR qualification> 56921 where <y> is the response variable; 56922 <x1> is a group id variable; 56923 <x2> is the second group id variable; 56924 <var> is a variable where the standardized values are stored; 56925 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56926 56927 This syntax standardizes the variable (with respect to scale 56928 only) with two group variable. 56929 56930Syntax 14: 56931 LET <var> = ZSCORE <y> <x1> <x2> <SUBSET/EXCEPT/FOR qualification> 56932 where <y> is the response variable; 56933 <x1> is a group id variable; 56934 <x2> is the second group id variable; 56935 <var> is a variable where the standardized values are stored; 56936 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56937 56938 This syntax computes a z-score with two group variables. 56939 56940Syntax 15: 56941 LET <var> = USCORE <y> <x1> <x2> <SUBSET/EXCEPT/FOR qualification> 56942 where <y> is the response variable; 56943 <x1> is a group id variable; 56944 <x2> is the second group id variable; 56945 <var> is a variable where the standardized values are stored; 56946 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 56947 56948 This syntax computes a u-score with two group variables. 56949 56950Examples: 56951 LET Y2 = STANDARDIZE Y1 56952 LET Y2 = LOCATION STANDARDIZE Y1 56953 LET Y2 = LOCATION STANDARDIZE Y1 X1 56954 LET Y2 = LOCATION STANDARDIZE Y1 X1 X2 56955 56956 SET LOCATION STATISTIC MEDIAN 56957 SET SCALE STATISTIC MAD 56958 LET Y2 = STANDARDIZE Y1 X1 X2 56959 56960Note: 56961 The most common application of this command is to standardize 56962 using the mean as the location measure and the standard 56963 deviation as the scale measure. Several alternative measures 56964 are allowed. 56965 56966 To set the location measure, enter the command 56967 56968 SET LOCATION STATISTIC <MEAN/MEDIAN/MIDMEAN/TRIMMED MEAN/ 56969 WINSORIZED MEAN/MIDRANGE/ 56970 HARMONIC MEAN/GEOMETRIC MEAN> 56971 56972 To set the scale measure, enter the command 56973 56974 SET SCALE STATISTIC <SD/MAD/AAD/INTERQUARTILE RANGE/ 56975 GEOMETRIC STANDARD DEVIATION/ 56976 SN SCALE/QN SCALE> 56977 56978 Here, SD is the standard deviation, MAD is the median absolute 56979 deviation, and AAD is the average absolute deviation. 56980 56981 Note the using the ZSCORE or USCORE syntax overrides the settings 56982 specified by these SET commands. That is, ZSCORE always uses the 56983 mean and standard deviation and USCORE always uses the minimum and 56984 the range. 56985 56986Default: 56987 The default location statistic is the mean and the default 56988 scale statistic is the standard deviation. 56989 56990Synonyms: 56991 IQ RANGE is a synonym for INTERQUARTILE RANGE. 56992 56993Related Commands: 56994 MEAN PLOT = Generate a mean vs. subset plot. 56995 SD PLOT = Generate a standard deviation vs. subset plot. 56996 TABULATE = Compute group statistics (one group variable). 56997 CROSS TABULATE = Compute group statistics (two group variables). 56998 MEDIAN = Compute the median. 56999 MIDDMEAN = Compute the midmean. 57000 TRIMMED MEAN = Compute the trimmed mean. 57001 SD = Compute the standard deviation. 57002 AAD = Compute the average absolute deviation. 57003 MAD = Compute the median absolute deviation. 57004 57005Applications: 57006 Data Analysis 57007 57008Implementation Date: 57009 2001/3: Initial Implementation 57010 57011 2001/9: Add support for following: 57012 1) Additional location statistics: MINIMUM, HARMONIC MEAN, 57013 GEOMETRIC MEAN, WINSORIZED MEAN, MIDRANGE 57014 2) Additional scale statistics: IQ RANGE, GEOMETRIC SD 57015 3) Support for USCORE 57016 4) Support for SCALE STANDARDIZE 57017 2003/5: Added support for SN SCALE, QN SCALE 57018 57019Program 1: 57020 SKIP 25 57021 READ GEAR.DAT Y X 57022 LET Y2 = STANDARDIZE Y X 57023 57024Program 2: 57025 SKIP 25 57026 READ GEAR.DAT Y X 57027 LET Y2 = LOCATION STANDARDIZE Y X 57028 57029Program 3: 57030 SKIP 25 57031 READ GEAR.DAT Y X 57032 SET LOCATION STATISTIC MEDIAN 57033 SET SCALE STATISTIC MAD 57034 LET Y2 = STANDARDIZE Y X 57035 57036Program 4: 57037 SKIP 25 57038 READ RIPKEN.DAT Y X1 X2 57039 LET Y2 = STANDARDIZE Y X1 X2 57040 57041-----STANDARD INPUT (SET)--------------------------------------- 57042 57043STANDARD INPUT 57044 57045Name: 57046 STANDARD INPUT (SET) 57047 57048Type: 57049 Set Subcommand 57050 57051Purpose: 57052 Specify the name of a file that will be equivalenced to 57053 standard input. 57054 57055Description: 57056 By default, Dataplot reads commands from standard input (in Fortran, 57057 this is typically unit 5). The SET STANDARD INPUT is used to specify 57058 the name of a file to read from when input is expected from standard 57059 input. 57060 57061 In it's simplest usage, this is essentially equivalent to using a 57062 CALL command (this is demonstrated in the Program 1 and Program 2 57063 sections below). 57064 57065 However, the SET STANDARD INPUT is typically used in a different 57066 context than the CALL command. Specifcally, it is motivated by 57067 the idea of having an external program control the input to 57068 Dataplot in a dynamic fashion. 57069 57070 For example, suppose you have a Python script and you would like that 57071 script to use Dataplot to perform a certain analysis. Suppose 57072 further that the user of the Python script has interactive control 57073 over what analysis he would like Dataplot to perform and when 57074 he would like that analysis performed. A typical sequence would 57075 then be 57076 57077 1. The Python script initiates Dataplot and has Dataplot 57078 execute the commands 57079 57080 SET MAXIMUM COUNTER STANDARD INPUT 0 57081 SET DELAY STANDARD INPUT 2 57082 SET STANDARD INPUT POLL file.dp 57083 57084 When the POLL CLOSE option is used, Dataplot does the 57085 following 57086 57087 a. Check for the existence of the file. If the file 57088 exists, then execute the commands in "file.dp" (the 57089 file name does not have to be "file.dp"). 57090 57091 b. If the file does not exist, wait for a specified 57092 time and then check for the existence of the file 57093 again. Repeat until the file is found. 57094 57095 The wait time is specified by the SET DELAY STANDARD 57096 INPUT command. The value is specified in seconds. 57097 If this command is not given, the default value is 2. 57098 The SET MAXIMUM COUNTER STANDARD INPUT command can 57099 be used to specify a maximum number of iterations. 57100 If this command is omitted or a value of 0 is given, 57101 then Dataplot will keep repeating until the file is 57102 found. 57103 57104 If the POLL option is omitted, then Dataplot will check 57105 for the existence of the file only once. If the file 57106 is not found, nothing is done and standard input is restored 57107 to unit 5. 57108 57109 2. The last line of the "file.dp" file will typically contain one 57110 of the following lines 57111 57112 SET STANDARD INPUT 57113 SET STANDARD INPUT CLOSE 57114 SET STANDARD INPUT CLOSE POLL 57115 57116 where 57117 57118 a. The SET STANDARD INPUT command closes "file.dp" and reverts 57119 standard input back to the terminal. The "file.dp" file is 57120 not deleted. 57121 57122 b. The SET STANDARD INPUT CLOSE command close and deletes the 57123 "file.dp" file. Standard input reverts back to the 57124 terminal. 57125 57126 This option is useful when the external program will not 57127 subsequently send additional commands to Dataplot. 57128 57129 c. The SET STANDARD INPUT CLOSE POLL command close and deletes 57130 the "file.dp" file. However, it resumes polling mode. That 57131 is, it effectively enters the command 57132 57133 SET STANDARD INPUT POLL file.dp 57134 57135 This option is used when the external program expects to 57136 subsequently send additonal commands to Dataplot. 57137 57138 The external program is not limited to Python. A similar sequence 57139 can be used within Perl, Tcl/TK, or any number of other programs. 57140 57141Syntax 1: 57142 SET STANDARD INPUT <fname> 57143 where <fname> is a file name. 57144 57145 This syntax equates standard input to <fname>. It will only 57146 search for the existence of <fname> one time. 57147 57148Syntax 2: 57149 SET STANDARD INPUT 57150 57151 This syntax closes the file equated to standard input and reverts 57152 standard input back to the terminal. 57153 57154Syntax 3: 57155 SET STANDARD INPUT POLL <fname> 57156 where <fname> is a file name. 57157 57158 This syntax equates standard input to <fname>. It will continually 57159 search for the existence of <fname> (based on the SET MAXIMUM 57160 COUNTER STANDARD INPUT and SET DELAY STANDARD INPUT commands). 57161 57162Syntax 4: 57163 SET STANDARD INPUT CLOSE <fname> 57164 where <fname> is a file name. 57165 57166 This syntax closes and deletes the <fname> file and reverts standard 57167 input back to the terminal. 57168 57169Syntax 5: 57170 SET STANDARD INPUT POLL CLOSE <fname> 57171 where <fname> is a file name. 57172 57173 This syntax closes and deletes the <fname> file and reverts POLL 57174 mode for <fname>. 57175 57176Examples: 57177 SET STANDARD INPUT commands.dp 57178 SET STANDARD INPUT POLL commands.dp 57179 57180Note: 57181 SET RESUME POLL is a synonym for SET STANDARD INPUT POLL. However, 57182 no file name is entered. The previously defined file name (from 57183 the most recent SET STANDARD INPUT POLL command) will be used. 57184 57185Default: 57186 None 57187 57188Synonyms: 57189 SET SUSPEND POLL is a synonym for SET STANDARD INPUT. 57190 SET POLL SUSPEND is a synonym for SET STANDARD INPUT. 57191 SET POLL RESUME is a synonym for SET RESUME POLL. 57192 57193Related Commands: 57194 CALL = Execute the commands from an external file. 57195 57196Applications: 57197 Program Control 57198 57199Implementation Date: 57200 2016/01 57201 57202Program 1: 57203 . Put these lines in the external file 57204 . 57205 . stdin.dp 57206 . 57207 . These commands will be executed by the Program 2 example. 57208 . 57209 print "in file stdin.dp" 57210 let a = 3 57211 let b = 4 57212 set standard input 57213 57214Program 2: 57215 . Execute the commands in file stdin.dp 57216 . 57217 set standard input stdin.dp 57218 57219-----STANDARDIZED THIRD CENTRAL MOMENT (LET)------------------------ 57220 57221STANDARDIZED THIRD CENTRAL MOMENT 57222 57223Name: 57224 STANDARDIZED THIRD CENTRAL MOMENT (LET) 57225 57226Type: 57227 Let Subcommand 57228 57229Purpose: 57230 Compute the standardized third central moment (or skewness) of a 57231 variable. 57232 57233Description: 57234 The skewness measures the lack of symmetry in a variable. The 57235 formula is: 57236 skew = (SUM(Xi-Xmean)**3/(N-1))/s**3 57237 where s is the standard deviation and N is the number of 57238 observations. 57239 57240Syntax: 57241 LET <par> = STANDARDIZED THIRD CENTRAL MOMENT <x1> 57242 <SUBSET/EXCEPT/FOR qualification> 57243 where <x1> is the variable for which the skewnes is to be computed; 57244 <par> is a parameter where the skewness is saved; 57245 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 57246 57247Examples: 57248 LET N = STANDARDIZED THIRD CENTRAL MOMENT Y1 57249 57250Default: 57251 None 57252 57253Synonyms: 57254 SKEWNESS 57255 STANDARDIZED 3RD CENTRAL MOMENT 57256 57257Related Commands: 57258 MEAN = Compute mean of a variable. 57259 STAND DEVI = Compute the standard deviation of a variable. 57260 KURTOSIS = Compute the Kurtosis of a variable. 57261 57262Applications: 57263 XX 57264 57265Implementation Date: 57266 XX 57267 57268Program: 57269 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 57270 LET SKEW = STANDARDIZED THIRD CENTRAL MOMENT Y1 57271 57272-----STANDARDIZED FOURTH CENTRAL MOMENT (LET)----------------------- 57273 57274STANDARDIZED FOURTH CENTRAL MOMENT 57275 57276Name: 57277 STANDARDIZED FOURTH CENTRAL MOMENT (LET) 57278 57279Type: 57280 Let Subcommand 57281 57282Purpose: 57283 Compute the standardized fourth central moment of a variable. 57284 57285Description: 57286 The formula is: 57287 F = (SUM(X-XMEAN)**4/(N-1))/XSD**4 57288 where X is the sample variable, XMEAN is the mean of X, XSD is the 57289 standard deviation of X, and N is the sample size. This statistic 57290 (also called the kurtosis) is the measure of the "fatness" of the 57291 distribution. The higher the kurtosis, the more spread out the 57292 distribution is. 57293 57294Syntax: 57295 LET <par> = STANDARDIZED FOURTH CENTRAL MOMENT <resp> 57296 <SUBSET/EXCEPT/FOR qualification> 57297 where <resp> is the variable for which the fourth central moment is 57298 to be computed; 57299 <par> is a parameter where the calculated fourth central 57300 moment is stored; 57301 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 57302 57303Examples: 57304 LET A1 = STANDARDIZED FOURTH CENTRAL MOMENT Y1 57305 57306Default: 57307 None 57308 57309Synonyms: 57310 KURTOSIS 57311 57312Related Commands: 57313 SEQUENCE = Generate a sequence of numbers. 57314 PATTERN = Generate numbers with a specific pattern. 57315 MEAN = Compute the mean of a variable. 57316 STAND DEVIATION = Compute the standard deviation of a variable. 57317 SKEWNESS = Compute the skewness of a variable. 57318 VARIANCE = Compute the variance of a variable. 57319 57320Applications: 57321 XX 57322 57323Implementation Date: 57324 XX 57325 57326Program: 57327 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 57328 LET A1 = STANDARDIZED FOURTH CENTRAL MOMENT Y1 57329 57330-----STAR PLOT--------------------------------------------------- 57331 57332STAR PLOT 57333 57334Name: 57335 STAR PLOT 57336 57337Type: 57338 Graphics Command 57339 57340Purpose: 57341 Generates a star plot. 57342 57343Description: 57344 A star plot is a graphical data analysis technique for examining 57345 the relative behavior of all variables in a multivariate data set. 57346 The star plot consists of a sequence of equi-angular spokes 57347 (radii). Each spoke represents a different variable in the 57348 multivariate data set. An individual star plot examines the 57349 behavior of all such variables but only for a specified subset of 57350 the data (e.g., looking at all the attributes of car performance, 57351 but only for a particular car, such as Chevrolet). The total 57352 length of a given spoke is uniformly set to unity for sake of 57353 reference. The "data length" of a given spoke is proportional to 57354 the magnitude of the variable for the subset relative to the 57355 maximum magnitude of the variable across all subsets. Thus we are 57356 looking at the ratio of the "local" value of the variable to the 57357 "global" maximum of the variable. An interconnecting line cutting 57358 across each spoke at the "data length" gives the star plot its 57359 unique appearance and name. 57360 57361Syntax: 57362 STAR PLOT <y1> <y2> ... <yk> <SUBSET/EXCEPT/FOR qualification> 57363 where <y1> is the first response variable; 57364 <y2> is the second response variable; 57365 <yk> is the last response variable; 57366 and where the <SUBSET/EXCEPT/FOR qualification> must be given. 57367 It is not optional for this command as it is for most other 57368 DATAPLOT commands. 57369 57370Examples: 57371 STAR PLOT Y1 Y2 Y3 Y4 Y5 SUBSET AUTO 4 57372 STAR PLOT Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 SUBSET STATE 25 57373 57374Note: 57375 A few variations of the star plot exist, all of which DATAPLOT 57376 can easily handle by judicious use of the components in the LINES 57377 command. For example, suppose there are k variables in the star 57378 plot (and so k spokes), then 57379 1) element 1 of LINES controls the appearance of the 57380 interconnecting line (this is usually SOLID); 57381 2) the next k elements of LINES controls the appearance of the 57382 spokes from the origin out to the interconnecting line 57383 (some analysts prefer this to be SOLID, others prefer this 57384 to be DOTTED); 57385 3) the following k elements of LINES controls the appearance 57386 of the spokes from the interconnecting line out to the 57387 uniform end of the spoke (some analysts prefer this to be 57388 SOLID, others prefer this to be DOTTED, others prefer this 57389 to be BLANKed out). 57390 When using the LINES command in this context, note the convenient 57391 abbreviations SO for SOLID, DO for DOTTED, DA for DASHED, BL for 57392 BLANK, etc., as in LINES SO DO DO DO DO DO BL BL BL BL BL which 57393 for a 5-variable star plot, would set the interconnecting line to 57394 SOLID, the inner part of the spokes to DOTTED, and BLANK out the 57395 outer part of the spokes. 57396 57397Note: 57398 The generation of multiple star plots per page is typical (one 57399 star plot for each subset of interest). This is easily done in 57400 DATAPLOT by using the STAR PLOT command in conjunction with the 57401 MULTIPLOT and LOOP commands. The following generates 50 star 57402 plots on the same page with each star plot consisting of 6 57403 variables (spokes): 57404 MULTIPLOT 5 10 57405 LOOP FOR K = 1 1 50 57406 STAR PLOT Y1 Y2 Y3 Y4 Y5 Y6 SUBSET STATE K 57407 END OF LOOP 57408 57409Default: 57410 None 57411 57412Synonyms: 57413 None 57414 57415Related Commands: 57416 PROFILE PLOT = Generates a (multivariate) profile plot. 57417 ANDREWS PLOT = Generates an Andrews plot. 57418 SYMBOL PLOT = Generates a symbol plot. 57419 LINES = Sets the type for plot lines. 57420 MULTIPLOT = Allows multiple plots per page. 57421 LOOP = Starts a loop (iteration). 57422 END OF LOOP = Terminates a loop. 57423 ^ = Allows string and value substitution. 57424 57425Reference: 57426 "Graphical Methods for Data Analysis", Chambers, Cleveland, 57427 Kleiner, and Tukey. Wadsworth, 1983 (pp. 160-161). 57428 57429Applications: 57430 Multivariate Analysis 57431 57432Implementation Date: 57433 88/3 57434 57435Program: 57436 TITLE 57437 FEEDBACK OFF 57438 DIMENSION 100 COLUMNS 57439 SKIP 25 57440 COLUMN LIMITS 20 132 57441 READ AUTO79.DAT Y1 TO Y9 57442 LET N = SIZE Y1; LET CAR = SEQUENCE 1 1 N 57443 . 57444 COLUMN LIMITS 1 19; SKIP 0 57445 LOOP FOR K = 1 1 25 57446 LET K1 = 25+K; ROW LIMITS K1 K1; READ STRING AUTO79.DAT S^K 57447 END OF LOOP 57448 . 57449 MULTIPLOT 5 5; MULTIPLOT CORNER COORDINATES 0 0 100 100 57450 FRAME CORNER COORDINATES 15 10 95 95 57451 . 57452 LEGEND 1 COORDINATES 55 5 57453 LEGEND JUSTIFICATION CENTER 57454 LEGEND SIZE 4 57455 LOOP FOR K = 1 1 25 57456 LEGEND 1 ^S^K 57457 STAR PLOT Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 SUBSET CAR K 57458 END OF LOOP 57459 END OF MULTIPLOT 57460 57461-----<dist> ANDERSON DARLING---------------------------------------- 57462 57463STATISTIC ANDERSON DARLING 57464 57465Name: 57466 <dist> ANDERSON DARLING 57467 57468Type: 57469 LET Subcommand 57470 57471Purpose: 57472 Compute the Anderson-Darling (A-D) goodness of fit statistic for a 57473 specified distribution for a response variable. 57474 57475Description: 57476 The Anderson-Darling test is a goodness of fit statistic (see the 57477 documentation for the GOODNESS OF FIT command for details). 57478 57479 Although this value is normally determined using the GOODNESS OF FIT 57480 command, for a limited number of distributions you can also generate 57481 this as a statistic LET subcommand. The advantage in this case is 57482 that you can use it with any of the commands that support built-in 57483 statistics (e.g., the STATISTIC PLOT or the TABULATION command). For 57484 example, if you have groups of data, you can use the TABULATE or 57485 STATISTIC PLOT commands to easily compare the goodness of fit across 57486 the groups. 57487 57488 In order to compute the Anderson-Darling statistic, the distribution 57489 parameters are first computed using maximum likelihood. This command 57490 can also return the maximum likelihood estimates. 57491 57492 This command is only supported for a subset of the distributions for 57493 which the Anderson-Darling statistic is supported with the GOODNESS 57494 OF FIT command. See the Note section below for a list of 57495 distributions supported by this command. 57496 57497Syntax 1: 57498 LET <par> = <dist> ANDERSON DARLING <y> 57499 <SUBSET/EXCEPT/FOR qualification> 57500 where <y> is a response variable; 57501 <dist> is one of the supported distributions listed below; 57502 <par> is the parameter where the AD value is saved; 57503 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 57504 57505 This syntax is used for the case where there are no shape parameters. 57506 57507Syntax 2: 57508 LET <par> = <dist> ANDERSON DARLING STATISTIC <y> 57509 <SUBSET/EXCEPT/FOR qualification> 57510 where <y> is a response variable; 57511 <dist> is one of the supported distributions listed below; 57512 <par> is the parameter where the AD value is saved; 57513 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 57514 57515 This syntax is used for those distributions that have a shape 57516 parameter. When the distribution has a shape parameter, then the word 57517 STATISTIC is required to distinguish this command from the 57518 ANDERSON DARLING PLOT command. Specifically it is used to distinguish 57519 the following two cases 57520 57521 WEIBULL ANDERSON DARLING PLOT Y 57522 WEIBULL ANDERSON DARLING STATISTIC PLOT Y X 57523 57524 The first command is the Weibull Anderson Darling plot (i.e., a plot 57525 of the Anderson-Darling goodness of fit across values of the shape 57526 parameter) while the second command plots the Anderson Darling statistic 57527 for Y for each group in X. 57528 57529Syntax 3: 57530 LET <par> = <dist> ANDERSON DARLING LOCATION <y> 57531 <SUBSET/EXCEPT/FOR qualification> 57532 where <y> is a response variable; 57533 <dist> is one of the supported distributions listed below; 57534 <par> is the parameter where the location value is saved; 57535 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 57536 57537 This syntax returns the estimate of the location parameter rather 57538 than the AD value. Not all supported distributions have a location 57539 parameter. 57540 57541Syntax 4: 57542 LET <par> = <dist> ANDERSON DARLING SCALE <y> 57543 <SUBSET/EXCEPT/FOR qualification> 57544 where <y> is a response variable; 57545 <dist> is one of the supported distributions listed below; 57546 <par> is the parameter where the scale value is saved; 57547 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 57548 57549 This syntax returns the estimate of the scale parameter rather 57550 than the AD value. 57551 57552Syntax 5: 57553 LET <par> = <dist> ANDESON DARLING SHAPE <y> 57554 <SUBSET/EXCEPT/FOR qualification> 57555 where <y> is a response variable; 57556 <dist> is one of the supported distributions listed below; 57557 <par> is the parameter where the shape value is saved; 57558 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 57559 57560 This syntax returns the estimate of the shape parameter rather 57561 than the Anderson-Darling statistic. Not all supported distributions 57562 have a shape parameter. 57563 57564Examples: 57565 LET A = NORMAL ANDERSON DARLING Y 57566 LET A = NORMAL ANDERSON DARLING LOCATION Y 57567 LET A = NORMAL ANDERSON DARLING SCALE Y 57568 57569 LET A = LOGISTIC ANDERSON DARLING Y 57570 57571 LET A = WEIBULL ANDERSON DARLING STATISTIC Y 57572 LET A = WEIBULL ANDERSON DARLING SCALE Y 57573 LET A = WEIBULL ANDERSON DARLING SHAPE Y 57574 57575Note: 57576 The following location/scale distributions are supported. 57577 57578 LET A = DOUBLE EXPONENTIAL ANDERSON DARLING Y 57579 LET A = EXPONENTIAL ANDERSON DARLING Y 57580 LET A = GUMBEL ANDERSON DARLING Y 57581 LET A = LOGISTIC ANDERSON DARLING Y 57582 LET A = MAXWELL ANDERSON DARLING Y 57583 LET A = NORMAL ANDERSON DARLING Y 57584 LET A = RAYLEIGH ANDERSON DARLING Y 57585 LET A = UNIFORM ANDERSON DARLING Y 57586 57587 The Maxwell and Rayleigh support the 2-parameter case rather than 57588 the 1-parameter case (i.e., the location parameter will be 57589 estimated). 57590 57591 For the uniform distribution, the scale parameter will actually 57592 return the upper limit parameter. 57593 57594 In addition, the following distributions with a single shape 57595 parameter are supported. 57596 57597 LET A = BURR TYPE 10 ANDERSON DARLING STATISTIC Y 57598 LET A = FATIGUE LIFE ANDERSON DARLING STATISTIC Y 57599 LET A = FRECHET ANDERSON DARLING STATISTIC Y 57600 LET A = GAMMA ANDERSON DARLING STATISTIC Y 57601 LET A = GEOMETRIC EXTREME EXPONENTIAL ANDERSON DARLING STATISTIC Y 57602 LET A = INVERTED GAMMA ANDERSON DARLING STATISTIC Y 57603 LET A = LOGISTIC EXPONENTIAL ANDERSON DARLING STATISTIC Y 57604 LET A = LOGNORMAL ANDERSON DARLING STATISTIC Y 57605 LET A = WEIBULL ANDERSON DARLING STATISTIC Y 57606 57607 Note that the above support the 2-parameter form of the distribution 57608 (i.e., the scale and shape parameters are estimated from the data 57609 and the location parameter is set to zero). 57610 57611Note: 57612 The distribution parameters are estimated using maximum likelihood. 57613 For several distributions, you can choose an alternative estimation 57614 method using the command 57615 57616 SET DISTRIBUTIONAL FIT TYPE <value> 57617 57618 where <value> can be one of the following 57619 57620 ML - use the default maximum likelihood 57621 (available for all supported 57622 distributions) 57623 MOMENT - use the moment estimates, available for 57624 uniform, Gumbel, 2-par Maxwell, 57625 2-par gamma, 2-par inverted gamma, 57626 2-par fatigue life 57627 MODIFIED MOMENT - use the modified moment estimates, 57628 available for 2-par Rayleigh 57629 57630Note: 57631 Dataplot statistics can be used in 20+ commands. For details, enter 57632 57633 HELP STATISTICS 57634 57635Default: 57636 None 57637 57638Synonyms: 57639 AD is a synonym for ANDERSON DARLING 57640 57641Related Commands: 57642 GOODNESS OF FIT = Perform a distributional goodness of fit test. 57643 MAXIMUM LIKELIHOOD = Perform maximum likelihood to estimate 57644 distributional parameters. 57645 STATISTIC PPCC = Compute the ppcc value for a specified 57646 distribution. 57647 STATISTIC PLOT = Generates a statistic versus subset plot. 57648 TABULATE = Compute a statistic based on a cross-tabulation. 57649 PPCC PLOT = Generates a probability plot correlation 57650 coefficient plot. 57651 PROBABILITY PLOT = Generates a probability plot. 57652 57653Reference: 57654 Stephens, M. A. (1974), "EDF Statistics for Goodness of Fit and 57655 Some Comparisons," Journal of the American Statistical Association, 57656 Vol. 69, pp. 730-737. 57657 57658 Stephens, M. A. (1976), "Asymptotic Results for Goodness-of-Fit 57659 Statistics with Unknown Parameters," Annals of Statistics, 57660 Vol. 4, pp. 357-369. 57661 57662 Stephens, M. A. (1977), "Goodness of Fit for the Extreme Value 57663 Distribution," Biometrika, Vol. 64, pp. 583-588. 57664 57665 Stephens, M. A. (1977), "Goodness of Fit with Special Reference to 57666 Tests for Exponentiality," Technical Report No. 262, Department of 57667 Statistics, Stanford University, Stanford, CA. 57668 57669 Stephens, M. A. (1979), "Tests of Fit for the Logistic Distribution 57670 Based on the Empirical Distribution Function," Biometrika, Vol. 66, 57671 pp. 591-595. 57672 57673Applications: 57674 Distributional Modeling 57675 57676Implementation Date: 57677 2015/2 57678 57679Program 1: 57680 . Step 1: Read the data 57681 . 57682 skip 25 57683 read nor.dat y1 57684 read exp.dat y2 57685 read weibbury.dat y3 57686 read lgn.dat y4 57687 read gamma.dat y5 57688 read frechet.dat y6 57689 let y x = stack y1 y2 y3 y4 y5 y6 57690 skip 0 57691 . 57692 case asis 57693 label case asis 57694 title case asis 57695 title offset 2 57696 multiplot corner coordinates 2 2 98 98 57697 multiplot scale factor 2 57698 . 57699 . Step 2: Plot normal a-d statistic 57700 . 57701 multiplot 2 2 57702 y1label Anderson-Darling Statistic 57703 x3label Datasets 57704 xlimits 1 6 57705 major xtic mark number 6 57706 minor xtic mark number 0 57707 x1tic mark offset 0.5 0.5 57708 x1tic mark label format alpha 57709 x1tic mark label content NOR.DAT sp()cr()sp()cr()EXP.DAT WEIBBURY.DAT ... 57710 sp()cr()sp()cr()LGN.DAT GAMMA.DAT sp()cr()sp()cr()FRECHET.DAT 57711 x1tic mark label size 1.2 57712 y1label displacement 12 57713 ylimits 0 1 57714 character X 57715 line blank 57716 . 57717 title Normal AD 57718 normal anderson darling plot y x 57719 . 57720 ylimits 57721 y1label Location 57722 title Normal AD Location 57723 normal anderson darling location plot y x 57724 . 57725 y1label Scale 57726 title Normal AD Scale 57727 normal anderson darling scale plot y x 57728 . 57729 . Step 3: Location/Scale distributions 57730 . 57731 multiplot 2 2 57732 label 57733 . 57734 ylimits 0 1 57735 title Normal AD 57736 normal anderson darling plot y x 57737 . 57738 ylimits 0 6 57739 title Exponential AD 57740 exponential anderson darling plot y x 57741 ylimits 0 1000 57742 title Double Exponential AD 57743 double exponential anderson darling plot y x 57744 ylimits 0 1.5 57745 title Gumbel (Maximum) 57746 gumbel anderson darling plot y x 57747 . 57748 end of multiplot 57749 . 57750 justification center 57751 move 50 3 57752 text Datasets 57753 direction vertical 57754 move 2 50 57755 text Anderson-Darling Statistic 57756 direction horizontal 57757 . 57758 multiplot 2 2 57759 x1tic mark label format numeric 57760 label 57761 . 57762 ylimits 0 20 57763 title Uniform AD 57764 uniform anderson darling plot y x 57765 . 57766 ylimits 0 1 57767 title Maxwell AD 57768 maxwell anderson darling plot y x 57769 . 57770 ylimits 0 10 57771 title Rayleigh AD 57772 rayleigh anderson darling plot y x 57773 . 57774 ylimits 0 1 57775 title Logistic 57776 logistic anderson darling plot y x 57777 . 57778 end of multiplot 57779 . 57780 justification center 57781 move 50 3 57782 text Datasets 57783 direction vertical 57784 move 2 50 57785 text Anderson-Darling Statistic 57786 direction horizontal 57787 57788Program 2: 57789 . Step 1: Read the data 57790 . 57791 skip 25 57792 read nor.dat y1 57793 read exp.dat y2 57794 read weibbury.dat y3 57795 read lgn.dat y4 57796 read gamma.dat y5 57797 read frechet.dat y6 57798 let y x = stack y1 y2 y3 y4 y5 y6 57799 skip 0 57800 . 57801 case asis 57802 title case asis 57803 title offset 2 57804 . 57805 xlimits 1 6 57806 major xtic mark number 6 57807 minor xtic mark number 0 57808 x1tic mark offset 0.5 0.5 57809 x1tic mark label size 1.5 57810 character X 57811 line blank 57812 . 57813 . Step 3: Weibull, Lognormal, Gamma, Fatigue Life 57814 . 57815 multiplot corner coordinates 2 2 98 98 57816 multiplot scale factor 2 57817 multiplot 2 2 57818 x1tic mark label format numeric 57819 label 57820 . 57821 ylimits 0 1 57822 title Weibull AD 57823 weibull anderson darling statistic plot y x 57824 . weibull ad statistic plot y x 57825 . 57826 ylimits 0 1 57827 title Lognormal AD 57828 lognormal anderson darling statistic plot y x 57829 ylimits 57830 . 57831 . Note that gamma has problem with datasets 1 and 4 57832 . 57833 ylimits 0 1 57834 title Gamma AD 57835 gamma anderson darling statistic plot y x subset x 2 3 5 6 57836 . 57837 ylimits 0 2 57838 title Fatigue Life AD 57839 fatigue life anderson darling statistic plot y x 57840 . 57841 end of multiplot 57842 . 57843 justification center 57844 move 50 3 57845 text Datasets 57846 direction vertical 57847 move 2 50 57848 text Anderson-Darling Statistic 57849 direction horizontal 57850 57851-----SET STATISTIC MISSING VALUE (SET)---------------------------------- 57852 57853STATISTIC MISSING VALUE 57854 57855Name: 57856 SET STATISTIC MISSING VALUE (SET) 57857 57858Type: 57859 Set Subcommand 57860 57861Purpose: 57862 Specify a numeric value that will interpreted as a missing 57863 value when computing one of the built-in statistics. 57864 57865Description: 57866 Data will often contain missing values. In computing built-in 57867 statistics with the LET sub-commands, you can define a value that will 57868 be interpreted as a missing value. Data that are equal to this 57869 missing value will be omitted from the computation of the statistic. 57870 57871 In computing a simple statistic LET sub-command such as 57872 57873 LET A = MEAN Y 57874 57875 it is relatively easy to omit missing values with a SUBSET clause. 57876 For example 57877 57878 LET A = MEAN Y SUBSET Y <> -99999 57879 57880 You can also do this with the commands 57881 57882 SET STATISTIC MISSING VALUE -99999 57883 LET A = MEAN Y SUBSET Y 57884 57885 Although in this simple case there is no need to use the 57886 SET STATISTIC MISSING VALUE, there are 20+ commands (such as 57887 CROSS TABULATE, STATISTIC PLOT) that utilize the built-in statistics. 57888 In these cases, using the SET STATISTIC MISSING VALUE can be more 57889 convenient than using the SUBSET clause. 57890 57891 Enter HELP STATISTICS for a list of built-in statistics and the 57892 commands that can utilize them. 57893 57894Syntax: 57895 SET STATISTIC MISSING VALUE <value> 57896 where <value> is a number or parameter that specifies a value that 57897 will be interpreted as a missing value code. 57898 57899Examples: 57900 SET STATISTIC MISSING VALUE -9999 57901 SET STATISTIC MISSING VALUE -1 57902 57903Note: 57904 In addition to built-in statistic LET sub-commands, the following 57905 commands also recognize the SET STATISTIC MISSING VALUE command 57906 57907 MANTEL HAENSZEL TEST 57908 ODDS RATIO CHI-SQUARE TEST 57909 ODDS RATIO INDEPENDENCE TEST 57910 LET ... = WEIBULL MOMENT ESTIMATE 57911 LET ... = LOGNORMAL MOMENT ESTIMATE 57912 LET ... = GAMMA MOMENT ESTIMATE 57913 LET ... = INVERSE GAUSSIAN MOMENT ESTIMATE 57914 LET ... = VARIABLE TO MATRIX 57915 LET ... = STANDARDIZE 57916 57917Default: 57918 The missing value is set to minimum real value on the machine (this 57919 can be determined with a PROBE CPUMIN command). 57920 57921Synonyms: 57922 None 57923 57924Related Commands: 57925 STATISTICS = List built-in statistics and commands 57926 that can utilize them. 57927 MANTEL HAENSZEL = Perform a Mantel-Haenszel test. 57928 WEIBULL MOMENT ESTIMATE = Compute Weibull parameter estimates based 57929 on moments. 57930 57931Applications: 57932 Terminal usage 57933 57934Implementation Date: 57935 2007/04 57936 57937Program 1: 57938 read matrix m 57939 2 4 7 -9999 57940 2 -9999 2 3 57941 1 2 -9999 3 57942 end of data 57943 . 57944 set statistic missing value -9999 57945 . 57946 let meanv = matrix row mean m 57947 . 57948 set write decimals 3 57949 print meanv 57950 57951Program 2: 57952 let n1 = 105 57953 let n2 = 192 57954 let n3 = 145 57955 let n = n1 + n2 + n3 57956 let x = 3 for i = 1 1 n 57957 let x = 1 for i = 1 1 n1 57958 let istrt = n1 + 1 57959 let istop = n1 + n2 57960 let x = 2 for i = istrt 1 istop 57961 . 57962 set statistic missing value -99 57963 . 57964 . Group 1 values 57965 . 57966 let y1 = 0 for i = 1 1 n 57967 let y2 = 0 for i = 1 1 n 57968 let y1 = 1 for i = 1 1 81 57969 let y2 = 1 for i = 1 1 34 57970 . 57971 . Group 2 values (have unequal samples here, so fill 57972 . with missing values 57973 . 57974 let istrt = n1 + 1 57975 let istop1 = istrt + 118 - 1 57976 let istop2 = istrt + 69 - 1 57977 let y1 = 1 for i = istrt 1 istop1 57978 let y2 = 1 for i = istrt 1 istop2 57979 let istrt2 = n1 + 174 + 1 57980 let istop2 = n1 + n2 57981 let y2 = -99 for i = istrt2 1 istop2 57982 . 57983 . Group 3 values 57984 . 57985 let istrt = n1 + n2 + 1 57986 let istop1 = istrt + 82 - 1 57987 let istop2 = istrt + 52 - 1 57988 let y1 = 1 for i = istrt 1 istop1 57989 let y2 = 1 for i = istrt 1 istop2 57990 . 57991 set statistic missing value -99 57992 . 57993 odds ratio chi-square test y1 y2 x 57994 57995-----STATISTIC BLOCK----------------------------------------------------- 57996 57997STATISTIC BLOCK 57998 57999Name: 58000 statISTIC BLOCK 58001 58002Type: 58003 Analysis Command 58004 58005Purpose: 58006 Defines a statistic via a group of Dataplot commands. 58007 58008Description: 58009 Dataplot supports a large number of built-in statistics (enter 58010 HELP statISTICS for a complete list). For example, 58011 58012 LET A = MEAN Y 58013 LET A = STANDARD DEVIATION Y 58014 LET A = CORRELATION Y1 Y2 58015 58016 Built-in statistics can be used in the following commands 58017 58018 1. LET A = <stat> 58019 2. <stat> STATISTIC PLOT 58020 3. CROSS TABULATE <stat> STATISTIC PLOT 58021 4. FLUCTUATION PLOT <stat> 58022 5. <stat> BLOCK PLOT 58023 6. BOOTSTRAP <stat> PLOT 58024 7. JACKNIFE <stat> PLOT 58025 8. DEX <stat> PLOT 58026 9. <stat> INFLUENCE CURVE 58027 10. CROSS TABULATE <stat> 58028 11. POSITIONAL TABULATION <stat> 58029 12. LET V = MATRIX COLUMN <stat> 58030 13. LET V = MATRIX ROW <stat> 58031 14. LET A = MATRIX GRAND <stat> 58032 15. LET M = MATRIX PARTITION <stat> 58033 16. LET V = CROSS TABULATE <stat> 58034 17. LET V = CROSS TABULATE CUMULATIVE <stat> 58035 18. LET V = SORT BY <stat> 58036 19. LET YOUT = MOVING <stat> 58037 20. LET YOUT = CUMULATIVE <stat> 58038 21. <STAT> INTERACTION PLOT 58039 58040 Although Dataplot provides a large number of built-in statistics, 58041 there may be situations where you would like to define a statistic 58042 not already supported by Dataplot. Statistic blocks were introduced 58043 to address this limitation. Statistic blocks allow you to define 58044 statistics using various Dataplot LET subcommands. 58045 58046 Statistic blocks are created using the CAPTURE syntax. For 58047 example, 58048 58049 CAPTURE STATISTIC BLOCK ONE ZZZZMEAN A Y 58050 LET N = SIZE Y 58051 LET YSUM = SUM Y 58052 LET A = YSUM/N 58053 END OF CAPTURE 58054 58055 The statistic block contains the following components 58056 58057 1. CAPTURE STATISTIC BLOCK - this initiates the creation 58058 of the statistic block. The CAPTURE command is typically 58059 used to direct Dataplot output to a file. However, in this 58060 case it saves the specified commands in an internal 58061 structure that can be accessed later. 58062 58063 2. ONE - up to three statistic blocks can be defined. In this 58064 example, "ONE" specifies that this is statistic block one. 58065 You can redefine these three statistic blocks as often as 58066 you need in a Dataplot session. 58067 58068 3. ZZZZMEAN - this is the name of the statistic block. This is 58069 the name that will be used to execute the statistic block in 58070 subsequent commands. This follows the rules for other 58071 Dataplot names (i.e., up to eight alphanumeric characters). 58072 58073 Note that this name should not be the same as one of Dataplot's 58074 built-in statistics. 58075 58076 4. A - this is name of the parameter that will contain the 58077 response for the statistic block. This is the value that 58078 is typically defined in the last line of the statistic block. 58079 For statistic blocks, the response must be a parameter. If 58080 the response is a variable, an error will be returned. 58081 58082 5. Y - this is the response variable for which the statistic is 58083 being computed. You can specify from one to three response 58084 variables. 58085 58086 The following Dataplot commands can be included in a statistic block: 58087 58088 1. LET ... = PATTERN ... 58089 2. LET ... = DATA ... 58090 3. LET ... = ... RANDOM NUMBERS ... 58091 4. ARITHMETIC OPERATIONS 58092 5. STATISTIC LET SUB-COMMANDS 58093 6. MATH LET SUB-COMMANDS 58094 The following MATH LET sub-commands are not allowed: 58095 58096 a. MATRIX sub-commands 58097 b. DERIVATIVE 58098 c. NUMERICAL DERIVATIVE 58099 d. INTEGRAL 58100 e. RUNGE-KUTTA 58101 f. OPTIMIZE 58102 g. ROOTS 58103 58104 The arithmetic operations and statistics LET sub-commands are of 58105 particular interest. Commands that are not supported are not added 58106 to the statistic block during the CAPTURE operation. Up to 30 58107 commands can be saved to a given statistic block. 58108 58109Syntax 1: 58110 CAPTURE STATISTIC BLOCK <one/two/three> <name> <resp> <variable list> 58111 where <one/two/three> specifies which statistic block is being created; 58112 <name> is the name of the statistic block; 58113 <resp> is the name of parameter that is the result of the 58114 statistic block; 58115 and where <variable list> is a list of 1 to 3 variable names that are 58116 used to compute the statistic. 58117 58118 This syntax is used to create the contents of a statistic block. 58119 58120Syntax 2: 58121 LIST STATISTIC BLOCK <one/two/three> 58122 where <one/two/three> specifies which statistic block is being listed. 58123 58124 This syntax is used to list the contents of a statistic block. 58125 58126Examples: 58127 capture statistic block one zzzzsd a y 58128 let n = size y 58129 let ysum = sum y 58130 let ymean = ysum/n 58131 let y2 = (y - ymean)**2 58132 let y2sum = sum y2 58133 let a = sqrt(y2sum/(n-1)) 58134 end of capture 58135 58136Note: 58137 Error checking (e.g., matching parenthesis, valid number of 58138 arguments for a built-in function) is performed when the statistic 58139 block is evaluated, not when it is created. 58140 58141Note: 58142 There may be cases where you cannot create the needed statistic even 58143 with the STATISTIC BLOCK command. The LET ... = EXECUTE ... command 58144 can be used to run an external prorgram. That is, your statistic 58145 block can use the EXECUTE command to compute the desired statistic. 58146 You can create the external program in whatever language is most 58147 convenient for your application. The basic requirement is that the 58148 resulting external file can be run from the command line and that it 58149 can read from standard input and write to standard output. 58150 58151 This is demonstrated in the Program 2 example below. 58152 58153Default: 58154 None 58155 58156Synonyms: 58157 None 58158 58159Related Commands: 58160 LET = Carries out a variety of operations on variables, 58161 parameters, and functions. 58162 LET FUNCTION = Define a function. 58163 FUNCTION BLOCK = Define a function block. 58164 EXECUTE = Run an external program. 58165 CAPTURE = Re-direct Dataplot output to an external file. 58166 58167Applications: 58168 Statistics 58169 58170Implementation Date: 58171 2016/08 58172 58173Program 1: 58174 skip 25 58175 read gear.dat y x 58176 skip 0 58177 . 58178 . Step 2: Define the statistic block 58179 . 58180 capture statistic block one zzzzsd a y 58181 let n = size y 58182 let ysum = sum y 58183 let ymean = ysum/n 58184 let y2 = (y - ymean)**2 58185 let y2sum = sum y2 58186 let a = sqrt(y2sum/(n-1)) 58187 end of capture 58188 . 58189 xlimits 1 10 58190 major xtic mark number 10 58191 x1tic mark offset 0.5 0.5 58192 x1label Batch 58193 y1label SD of Batch 58194 line blank 58195 char X 58196 . 58197 multiplot corner coordinates 2 2 98 98 58198 multiplot scale factor 2 58199 multiplot 2 1 58200 title automatic 58201 . 58202 zzzzsd plot y x 58203 sd plot y x 58204 . 58205 end of multiplot 58206 58207Program 2: 58208 . Step 1: Read the data 58209 . 58210 skip 25 58211 read gear.dat y x 58212 skip 0 58213 . 58214 . Step 2: Create and compile the Fortran code 58215 . 58216 capture script exec.for 58217 program test 58218 c 58219 c For this simple example, read in a data set and 58220 c compute the mean and standard deviation. 58221 c 58222 real x(10000) 58223 c 58224 xmean=0.0 58225 xsd=0.0 58226 nval=0 58227 read(*,*,end=19,err=9020)nval 58228 c 58229 sum1=0.0 58230 do 10 i=1,min(nval,10000) 58231 read(*,*,end=19,err=9020)x(i) 58232 sum1=sum1 + x(i) 58233 10 continue 58234 19 continue 58235 if(nval.ge.1)then 58236 xmean=sum1/real(nval) 58237 endif 58238 c 58239 if(nval.gt.1)then 58240 sum1=0.0 58241 do 20 i=1,nval 58242 sum1=sum1 + (x(i)-xmean)**2 58243 20 continue 58244 xsd=sqrt(sum1/real(nval-1)) 58245 endif 58246 c 58247 c Now write sd to standard output 58248 c 58249 9020 continue 58250 write(*,*)xsd 58251 c 58252 stop 58253 end 58254 end of capture 58255 . 58256 system gfortran -o exec.exe exec.for 58257 . 58258 . Step 3: Define the statistic block 58259 . 58260 capture statistic block one zzzzsd a y 58261 let ztemp = execute ./exec.exe y 58262 let a = ztemp(1) 58263 end of capture 58264 . 58265 xlimits 1 10 58266 major xtic mark number 10 58267 x1tic mark offset 0.5 0.5 58268 x1label Batch 58269 y1label SD of Batch 58270 line blank 58271 char X 58272 . 58273 multiplot corner coordinates 2 2 98 98 58274 multiplot scale factor 2 58275 multiplot 2 1 58276 title automatic 58277 . 58278 zzzzsd plot y x 58279 sd plot y x 58280 . 58281 end of multiplot 58282 58283-----STATISTIC PLOT--------------------------------------------------- 58284 58285STATISTIC PLOT 58286 58287Name: 58288 ... STATISTIC PLOT 58289 58290Type: 58291 Graphics Command 58292 58293Purpose: 58294 Generates a statistic versus index plot for a given statistic. 58295 58296Description: 58297 A statistic plot consists of subsample statistic versus subsample 58298 index. The subsample statistic is the value of some statistic for 58299 the data in the subsample. The statistic plot is used to answer the 58300 question--"Does the subsample statistic change over different 58301 subsamples?". The plot consists of: 58302 58303 Vertical axis = subsample statistic; 58304 Horizontal axis = subsample index. 58305 58306 The statistic plot yields 2 traces: 58307 58308 1. a subsample statistic trace; and 58309 2. a full-sample statistic reference line. 58310 58311 The appearance of these two traces is controlled by the first two 58312 settings of the LINES, CHARACTERS, SPIKES, BARS, and similar 58313 attributes. 58314 58315Syntax 1: 58316 <stat> STATISTIC PLOT <y1> ... <yk> <x> 58317 <SUBSET/EXCEPT/FOR qualification> 58318 where <stat> is one of Dataplot's supported statistics; 58319 <y1> ... <yk> is a list of 1 to 3 response variables 58320 (<stat> determines how many response variables); 58321 <x> is the subsample identifier variable (this variable 58322 appears on the horizontal axis); 58323 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 58324 58325 For a list of supported statistics, enter 58326 58327 HELP STATISTICS 58328 58329Syntax 2: 58330 <stat> STATISTIC PLOT <y1> ... <yk> <x> 58331 <SUBSET/EXCEPT/FOR qualification> 58332 where <stat> is one of Dataplot's supported statistics; 58333 <y1> ... <yk> is a list of 1 to 30 response variables; 58334 <x> is the subsample identifier variable (this variable 58335 appears on the horizontal axis); 58336 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 58337 58338 This syntax is used for multiple response variables. See the 58339 Note section below for details on this syntax. 58340 58341Syntax 3: 58342 <stat> STATISTIC TAG PLOT <y> <x> <tag> 58343 <SUBSET/EXCEPT/FOR qualification> 58344 where <stat> is one of Dataplot's supported statistics; 58345 <y1> ... <yk> is a list of 1 to 3 response variables 58346 (<stat> determines how many response variables); 58347 <x> is the subsample identifier variable (this variable 58348 appears on the horizontal axis); 58349 <tag> is group-id variable; 58350 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 58351 58352 For this syntax, there are two group variables. The <x> 58353 variable is used as in syntax 1. That is, this variable 58354 is used to define the sub-groups for computing the statistic. 58355 In syntax 1, there are two plot traces created. The first 58356 contains the statistic value for each group and the second 58357 contains the statistic for the full data set. With this 58358 syntax, the <tag> variable is used to define groups with the 58359 same plot attributes. For example, if <tag> contains three 58360 distinct values (1, 2, and 3), there will be four plot traces 58361 created. The first trace is for groups (<x>) where the 58362 corresponding <tag> value is 1, the second trace is where the 58363 corresponding <tag> value is 2, the third trace is where the 58364 corresponding <tag> value is 3, and the fourth trace is 58365 the statistic for the full data set. 58366 58367 The <tag> value should be the same for all rows in a 58368 group defined by <x>. However, if this is not the case, 58369 the <tag> value corresponding to the first row in <x> for 58370 that group will be used. 58371 58372 This syntax is used to highlight certain groups. For 58373 example, groups that denote potential outliers might be 58374 highlighted in a different color. 58375 58376 This syntax is demonstrated in the Program 3 example. 58377 58378Examples: 58379 MEAN PLOT Y X 58380 STANDARD DEVIATION PLOT Y X1 58381 MEAN PLOT Y1 TO Y5 X 58382 MEAN TAG PLOT Y X TAG 58383 58384Note: 58385 A number of the subcommands (e.g., MEAN PLOT) are documented 58386 individually. 58387 58388Note: 58389 Although DATAPLOT supports this command for a large number of 58390 statistics, there may be cases where you want it for another one. 58391 The following example shows how to compute the rank correlation 58392 (assume Y1 and Y2 are the response variables and TAG is the group 58393 identifier). 58394 58395 LET TAGDIST = DISTINCT TAG 58396 LET NGROUP = SIZE TAGDIST 58397 LOOP FOR K = 1 1 NGROUP 58398 LET IGROUP TAGDIST(K) 58399 LET A = RANK CORRELATION Y1 Y2 SUBSET TAG = IGROUP 58400 LET YNEW(K) = A 58401 LET XNEW(K) = K 58402 END OF LOOP 58403 LET A = RANK CORRELATION Y1 Y2 58404 LET YNEW2 = DATA A A 58405 LET XNEW2 = DATA 1 NGROUP 58406 PLOT YNEW XNEW AND 58407 PLOT YNEW2 XNEW2 58408 58409 This basic idea can be easily adapted to other statistics (even ones 58410 that are not built-in to DATAPLOT). It can also be adapted to 58411 statistics requiring any arbitrary number of variables to compute. 58412 58413 The 2016/08 version of Dataplot added the STATISTIC BLOCK 58414 command that can be used to define a statistic. 58415 58416Note: 58417 The 2009/05 version of Dataplot updated the <stat> PLOT command to 58418 support multiple response variables (Syntax 2). For example, 58419 58420 MEAN PLOT Y1 TO Y4 X 58421 58422 That is, for each distinct value of X, there are now 4 means 58423 plotted instead of just one. 58424 58425 The following commands can be used to control the appearance of 58426 the plot: 58427 58428 SET STATISTIC PLOT FORMAT <DEX/OVERLAY> 58429 SET STATISTIC PLOT SUMMARY <VARIABLE/GROUP> 58430 58431 If the FORMAT option is set to OVERLAY and the SUMMARY option 58432 is set to VARIABLE, this is equivalent to the following: 58433 58434 YLIMITS ... 58435 PRE-ERASE OFF 58436 ERASE 58437 MEAN PLOT Y1 X 58438 MEAN PLOT Y2 X 58439 MEAN PLOT Y3 X 58440 MEAN PLOT Y4 X 58441 PRE-ERASE ON 58442 58443 That is, there will be a curve corresponding to each response 58444 variable and there will be a reference line corresponding to 58445 each variable. 58446 58447 If the FORMAT option is set to DEX, then this plot uses a 58448 format similar to the DEX <stat> PLOT command. That is, for 58449 each distinct value of X, there will be curve connecting the 58450 mean values for the 4 response variables. 58451 58452 If the SUMMARY option is set to GROUP, there will be a single 58453 reference curve. At each distinct value of X, a single overall 58454 mean is computed for all 4 of the response variables. 58455 58456 In addition, the following option is added to this command: 58457 58458 <stat> <zscore/uscore> PLOT 58459 58460 If ZSCORE is given, then a z-score transformation (subtract the 58461 mean and then divide by the standard deviation) is computed 58462 on each response variable first. If USCORE is given, then a 58463 u-score transformation (subtract the minimum and divide by the 58464 range) is computed on each column. Note these z-score and 58465 u-score transformations apply to the entire response variable, not 58466 to each distinct group within the response variable. 58467 58468Note: 58469 By default, Dataplot draws a reference line where the vertical 58470 axis coordinate is the value of the statistic for all of the 58471 data. 58472 58473 For some statistics (e.g., STANDARD DEVIATION and other scale 58474 statistics), this may not be particularly meaningful. Alternatively 58475 you can specify either the mean or the median value of the 58476 statistic over the groups. For example, if you are generating 58477 a standard deviation plot and you have 10 groups, you can 58478 specify that the reference line be drawn at the mean (or the 58479 median) of the 10 computed standard deviations. 58480 58481 To specify what reference line is drawn, enter 58482 58483 SET STATISTIC PLOT REFERENCE LINE <OVERALL/AVERAGE/MEDIAN> 58484 58485 where OVERALL is the value of the statistic for all of the data, 58486 AVERAGE is the mean of the statistic over the groups, and 58487 MEDIAN is the median of the statistic over the groups. 58488 58489 The default is OVERALL. 58490 58491Default: 58492 None 58493 58494Synonyms: 58495 On most of the commands, the word STATISTIC is optional and is 58496 usually omitted (e.g., the mean plot is documented under MEAN PLOT 58497 rather than MEAN STATISTIC PLOT). 58498 58499Related Commands: 58500 CHARACTERS = Sets the type for plot characters. 58501 LINES = Sets the type for plot lines. 58502 BOX PLOT = Generates a box plot. 58503 CONTROL CHART = Generates a control chart. 58504 PLOT = Generates a data or function plot. 58505 SUMMARY = Computes various statistics for a 58506 variable. 58507 STATISTIC BLOCK = Define a new statistic. 58508 58509Applications: 58510 Exploratory Data Analysis 58511 58512Implementation Date: 58513 1988/02 58514 2009/04: support for multiple response variables 58515 2015/04: added SET STATISTIC PLOT REFERENCE LINE 58516 2018/02: support for a tag variable (Syntax 3) 58517 58518 The list of supported statistics has been regulary updated 58519 since the original 1988/2 implementation. 58520 58521Program 1: 58522 SKIP 25 58523 READ GEAR.DAT DIAMETER BATCH 58524 . 58525 TITLE AUTOMATIC 58526 TITLE OFFSET 2 58527 MULTIPLOT 2 2 58528 MULTIPLOT CORNER COORDINATES 3 0 100 100 58529 MULTIPLOT SCALE FACTOR 2 58530 X1LABEL DISPLACEMENT 14 58531 Y1LABEL DISPLACEMENT 12 58532 TIC MARK LABEL SIZE 1.8 58533 . 58534 XTIC OFFSET 1 1 58535 X1LABEL BATCH 58536 LINE BLANK SOLID 58537 CHARACTER X BLANK 58538 Y1LABEL MEAN 58539 TITLE MEAN PLOT 58540 MEAN PLOT DIAMETER BATCH 58541 Y1LABEL STANDARD DEVIATION 58542 TITLE SD PLOT 58543 STANDARD DEVIATION PLOT DIAMETER BATCH 58544 Y1LABEL RELATIVE STANDARD DEVIATION 58545 TITLE RELSD PLOT 58546 RELSD PLOT DIAMETER BATCH 58547 Y1LABEL RANGE 58548 TITLE RANGE PLOT 58549 RANGE PLOT DIAMETER BATCH 58550 . 58551 END OF MULTIPLOT 58552 58553Program 2: 58554 skip 25 58555 read iris.dat y1 to y4 x 58556 . 58557 title case asis 58558 title offset 2 58559 label case asis 58560 y1label Mean 58561 x1label Group-ID 58562 xlimits 1 3 58563 major xtic mark number 3 58564 minor xtic mark number 0 58565 xtic offset 0.6 0.6 58566 ytic offset 1 1 58567 . 58568 set stat plot format dex 58569 set stat plot summary vari 58570 title sp()Case 1: Format = DEX, Summary = Variable 58571 line color black black black blue red green cyan 58572 mean plot y1 to y4 x 58573 title sp()Case 1b: Z-Score - Format = DEX, Summary = Variable 58574 mean zscore plot y1 to y4 x 58575 . 58576 set stat plot format dex 58577 set stat plot summary group 58578 title sp()Case 2: Format = DEX, Summary = Group 58579 mean plot y1 to y4 x 58580 title sp()Case 2: Z-Score - Format = DEX, Summary = Group 58581 mean zscore plot y1 to y4 x 58582 . 58583 set stat plot format overlay 58584 set stat plot summary group 58585 line color blue red green cyan 58586 line so so so so bl 58587 char bl bl bl bl x 58588 title sp()Case 3: Format = Overlay, Summary = Group 58589 mean plot y1 to y4 x 58590 title sp()Case 3: Z-Score Format = Overlay, Summary = Group 58591 mean zscore plot y1 to y4 x 58592 . 58593 set stat plot format overlay 58594 set stat plot summary variable 58595 line so all 58596 char bl all 58597 line color blue red green cyan blue red green cyan 58598 title sp()Case 4: Format = Overlay, Summary = Variable 58599 mean plot y1 to y4 x 58600 title sp()Case 4: Z-Score - Format = Overlay, Summary = Variable 58601 mean zscore plot y1 to y4 x 58602 58603Program 3: 58604 . Name: meantag.dp 58605 . Purpose: Test "tag" option on statistic plot case 58606 . 58607 . Step 0: Define output devices 58608 . 58609 let string fplot = meantag.ps 58610 set ipl1na ^fplot 58611 call checksys.dp 58612 . 58613 . Step 1: Read the data 58614 . 58615 skip 25 58616 read gear.dat y x 58617 skip 0 58618 let tag = sequence 1 10 1 2 for i = 1 1 100 58619 . 58620 . Step 2: Define plot control settings 58621 . 58622 case asis 58623 label case asis 58624 title case asis 58625 title offset 2 58626 . 58627 xlimits 1 10 58628 major x1tic mark number 10 58629 minor x1tic mark number 0 58630 tic offset units data 58631 x1tic mark offset 0.5 0.5 58632 . 58633 title Mean Plot of GEAR.DAT 58634 y1label Mean Diameter 58635 x1label Batch 58636 . 58637 . Step 3: Generate the plot without tags 58638 . 58639 character circle blank 58640 character fill on 58641 character hw 1.0 0.75 all 58642 line blank solid 58643 mean plot y x 58644 . 58645 . Step 4: Generate the plot with tags 58646 . 58647 character circle circle blank 58648 character fill on on 58649 character hw 1.0 0.75 all 58650 character color blue red 58651 line blank blank solid 58652 . 58653 . mean tag plot y x tag 58654 mean character plot y x tag 58655 58656-----<dist> PPCC------------------------------------------------ 58657 58658STATISTIC PPCC 58659 58660Name: 58661 <dist> PPCC 58662 58663Type: 58664 LET Subcommand 58665 58666Purpose: 58667 Compute the probability plot correlation coefficient (also 58668 called the ppcc) value for a variable for a specified distribution. 58669 58670Description: 58671 The ppcc value is the correlation coefficient of the straight line 58672 fitted to a probability plot (see the documentation for PPCC PLOT for 58673 details). 58674 58675 Although this value is normally determined using either a probability 58676 plot or a ppcc plot, for a limited number of distributions you can 58677 also generate this as a statistic LET subcommand. The advantage in 58678 this case is that you can use it with any of the commands that 58679 support built-in statistics (e.g., the STATISTIC PLOT or the 58680 TABULATION command). 58681 58682 This command was updated 2013/02 in the following ways. 58683 58684 1. In addition to the PPCC value, you can now extract the 58685 estimates of the location and scale parameters based on 58686 the probability plot. See Syntax 2 and Syntax 3 below. 58687 58688 2. For certain one and two shape parameter distritutions, you 58689 can extract the shape parameter based on the 58690 PPCC plot/probability plot method. 58691 58692 In using these commands, the shape parameter can be 58693 be handled in one of two ways. 58694 58695 a. You can assume a fixed shape parameter. For example, 58696 58697 LET GAMMA = 2.6 58698 WEIBULL PPCC STATISTIC PLOT Y X 58699 58700 This command will plot the ppcc value for a Weibull 58701 distribution with a shape parameter of 2.6 for the 58702 groups defined by the X variable. 58703 58704 b. No shape parameter will be pre-defined. 58705 58706 In the example above, if GAMMA is not pre-defined then 58707 the shape parameter will be estimated using the PPCC 58708 plot method (this is done in the background) for each 58709 distinct group. 58710 58711 See the Note section below for a list of supported 58712 distributions. 58713 58714Syntax 1: 58715 LET <par> = <dist> PPCC <y> <SUBSET/EXCEPT/FOR qualification> 58716 where <y> is a response variable; 58717 <dist> is one of the distributions listed in the Note section 58718 below; 58719 <par> is the parameter where the ppcc value is saved; 58720 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 58721 58722Syntax 2: 58723 LET <par> = <dist> PPCC LOCATION <y> 58724 <SUBSET/EXCEPT/FOR qualification> 58725 where <y> is a response variable; 58726 <dist> is one of the distributions described in the Note 58727 section below; 58728 <par> is the parameter where the location value is 58729 saved; 58730 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 58731 58732 This syntax returns the estimate of the location parameter rather 58733 than the PPCC value. 58734 58735Syntax 3: 58736 LET <par> = <dist> PPCC SCALE <y> 58737 <SUBSET/EXCEPT/FOR qualification> 58738 where <y> is a response variable; 58739 <dist> is one of the distributions described in the Note 58740 section below; 58741 <par> is the parameter where the normal location value is 58742 saved; 58743 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 58744 58745 This syntax returns the estimate of the location parameter rather 58746 than the PPCC value. 58747 58748Syntax 4: 58749 LET <par> = <dist> PPCC STATISTIC <y> 58750 <SUBSET/EXCEPT/FOR qualification> 58751 where <y> is a response variable; 58752 <dist> is one of the distributions with shape parameters 58753 described in the Note section below; 58754 <par> is the parameter where the normal ppcc value is saved; 58755 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 58756 58757 When the distribution has a shape parameter, then the word 58758 STATISTIC is required to distinguish this command from the 58759 PPCC PLOT command. Specifically the following can conflict 58760 58761 WEIBULL PPCC PLOT Y 58762 WEIBULL PPCC STATISTIC PLOT Y X 58763 58764 The first command is the Weibull PPCC plot while the second 58765 command plots the PPCC value for Y for each group in X. 58766 58767Syntax 5: 58768 LET <par> = <dist> PPCC SHAPE <y> 58769 <SUBSET/EXCEPT/FOR qualification> 58770 where <y> is a response variable; 58771 <dist> is one of the distributions with a single shape 58772 parameters described in the Note section below; 58773 <par> is the parameter where the normal ppcc value is saved; 58774 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 58775 58776 This syntax returns the estimate of the shape parameter rather 58777 than the PPCC value. 58778 58779Syntax 6: 58780 LET <par> = <dist> PPCC SHAPE ONE <y> 58781 <SUBSET/EXCEPT/FOR qualification> 58782 where <y> is a response variable; 58783 <dist> is one of the distributions with two shape 58784 parameters described in the Note section below; 58785 <par> is the parameter where the normal ppcc value is saved; 58786 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 58787 58788 This syntax returns the estimate of the first shape parameter 58789 rather than the PPCC value. 58790 58791Syntax 7: 58792 LET <par> = <dist> PPCC SHAPE TWO <y> 58793 <SUBSET/EXCEPT/FOR qualification> 58794 where <y> is a response variable; 58795 <dist> is one of the distributions with two shape 58796 parameters described in the Note section below; 58797 <par> is the parameter where the normal ppcc value is saved; 58798 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 58799 58800 This syntax returns the estimate of the second shape parameter 58801 rather than the PPCC value. 58802 58803Examples: 58804 LET A = LOGISTIC PPCC Y 58805 LET A = DOUBLE EXPONENTIAL PPCC Y SUBSET Y > -3 58806 58807Note: 58808 The following location/scale distributions are supported. 58809 58810 LET A = ANGLIT PPCC Y 58811 LET A = ARCSINE PPCC Y 58812 LET A = CAUCHY PPCC Y 58813 LET A = COSINE PPCC Y 58814 LET A = DOUBLE EXPONENTIAL PPCC Y 58815 LET A = EXPONENTIAL PPCC Y 58816 LET A = HALF CAUCHY PPCC Y 58817 LET A = HALF NORMAL PPCC Y 58818 LET A = HYPERBOLIC SECANT PPCC Y 58819 LET A = LOGISTIC PPCC Y 58820 LET A = MAXWELL PPCC Y 58821 LET A = MAXIMUM GUMBEL PPCC Y 58822 LET A = MINIMUM GUMBEL PPCC Y 58823 LET A = MAXWELL PPCC Y 58824 LET A = NORMAL PPCC Y 58825 LET A = RAYLEIGH PPCC Y 58826 LET A = SEMICIRCULAR PPCC Y 58827 LET A = SLASH PPCC Y 58828 LET A = UNIFORM PPCC Y 58829 58830 In addition, the following distributions with a single shape 58831 parameter are supported. If you want a fixed value of the 58832 shape parameter, you can specify it as shown here: 58833 58834 LET GAMMA = <value> 58835 LET A = WEIBULL PPCC STATISTIC Y 58836 LET A = 2PARAMETER WEIBULL PPCC STATISTIC Y 58837 58838 LET GAMMA = <value> 58839 LET A = INVERTED WEIBULL PPCC STATISTIC Y 58840 58841 LET GAMMA = <value> 58842 LET A = GAMMA PPCC STATISTIC Y 58843 58844 LET GAMMA = <value> 58845 LET A = WALD PPCC STATISTIC Y 58846 58847 LET GAMMA = <value> 58848 LET A = FATIGUE LIFE PPCC STATISTIC Y 58849 58850 LET GAMMA = <value> 58851 LET A = GENERALIZED PARETO PPCC STATISTIC Y 58852 58853 LET SIGMA = <value> 58854 LET A = LOGNORMAL PPCC STATISTIC Y 58855 58856 LET LAMBDA = <value> 58857 LET A = TUKEY LAMBDA PPCC STATISTIC Y 58858 58859 LET G = <value> 58860 LET A = G PPCC STATISTIC Y 58861 58862 In addition, the following distribution with two shape 58863 parameters is supported. If you want fixed values of the 58864 shape parameters, you can specify it as shown here: 58865 58866 LET G = <value> 58867 LET H = <value> 58868 LET A = G AND H PPCC STATISTIC Y 58869 58870Note: 58871 Dataplot statistics can be used in a number of commands. For 58872 details, enter 58873 58874 HELP STATISTICS 58875 58876Default: 58877 None 58878 58879Synonyms: 58880 None 58881 58882Related Commands: 58883 STATISTIC PLOT = Generates a statistic versus subset plot. 58884 CROSS TABULATE = Compute a statistic based on a cross-tabulation. 58885 PPCC PLOT = Generates a probability plot correlation 58886 coefficient plot. 58887 PROBABILITY PLOT = Generates a probability plot. 58888 58889Reference: 58890 James J. Filliben (1975), "The Probability Plot Correlation Coefficient 58891 Test for Normality," Technometrics, Vol. 17, No. 1. 58892 58893Applications: 58894 Exploratory Data Analysis 58895 58896Implementation Date: 58897 2011/06 58898 2013/02: Support for location, scale and shape parameters 58899 2013/02: Support for additional distributions 58900 2015/02: Support for g distribution 58901 2016/06: Support for 2-parameter Weibull 58902 58903Program 1: 58904 SKIP 25 58905 READ GEAR.DAT Y X 58906 . 58907 LABEL CASE ASIS 58908 Y1LABEL Correlation 58909 X1LABEL Batch 58910 Y1LABEL DISPLACEMENT 15 58911 X1LABEL DISPLACEMENT 12 58912 TITLE CASE ASIS 58913 TITLE OFFSET 2 58914 XLIMITS 1 10 58915 X1TIC MARK OFFSET 0.5 0.5 58916 Y1LIMITS 0.92 0.99 58917 TIC MARK OFFSET UNITS DATA 58918 LINE BLANK SOLID 58919 CHARACTER X BLANK 58920 . 58921 MULTIPLOT CORNER COORDIANTES 2 2 98 98 58922 MULTIPLOT SCALE FACTOR 2 58923 MULTIPLOT 2 2 58924 . 58925 TITLE Normal PPCC Values 58926 NORMAL PPCC PLOT Y X 58927 TITLE Logistic PPCC Values 58928 LOGISTIC PPCC PLOT Y X 58929 TITLE Double Exponential PPCC Values 58930 DOUBLE EXPONENTIAL PPCC PLOT Y X 58931 TITLE Uniform PPCC Values 58932 UNIFORM PPCC PLOT Y X 58933 . 58934 END OF MULTIPLOT 58935 58936Program 2: 58937 skip 25 58938 read gear.dat y x 58939 . 58940 tic mark offset units screen 58941 tic mark offset 5 5 58942 char X 58943 line blank 58944 . 58945 multiplot scale factor 2 58946 multiplot corner coordinates 5 5 95 95 58947 . 58948 y1label displacement 16 58949 x1label displacement 12 58950 title offset 2 58951 label case asis 58952 title automatic 58953 x1label Batch 58954 . 58955 multiplot 2 2 58956 y1label Correlation 58957 normal ppcc statistic plot y x 58958 y1label Location 58959 normal ppcc location plot y x 58960 y1label Scale 58961 normal ppcc scale plot y x 58962 char X all 58963 line blank all 58964 y1label Raw Data 58965 plot y x x 58966 end of multiplot 58967 58968-----STCDF (LET)-------------------------------- 58969 58970STCDF 58971 58972Name: 58973 STCDF (LET) 58974 58975Type: 58976 Library Function 58977 58978Purpose: 58979 Compute the skew-t cumulative distribution function. 58980 58981Description: 58982 The skew-t distribution has the following probability density 58983 function: 58984 58985 f(x,nu,lambda)=2*TCDF(lambda*x*SQRT((1+nu)/(x**2+nu)),nu+1)* 58986 TPDF(x,nu) -infinity < x, lambda < infinity 58987 58988 For lambda = 0, the skew-t reduces to a t distribution. 58989 As lambda goes to infinity, the skew-t tends to the 58990 folded-t distribution. 58991 58992 The cumulative distribution is computed by numerically 58993 integrating the skew-t probability density function. 58994 58995 The standard skew-t distribution can be generalized with 58996 location and scale parameters. 58997 58998Syntax: 58999 LET <y> = STCDF(<x>,<nu>,<lambda>) 59000 <SUBSET/EXCEPT/FOR qualification> 59001 where <x> is a variable or a parameter; 59002 <nu> is a number of parameter that specifies the 59003 value of the degrees of freedom shape parameter; 59004 <lambda> is a number of parameter that specifies the 59005 value of the skewness shape parameter; 59006 <y> is a variable or a parameter (depending on what <x> is) 59007 where the computed skew-t cdf value is stored; 59008 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 59009 59010Examples: 59011 LET A = STCDF(3,5,1) 59012 LET A = STCDF(A1,DF,LAMBDA) 59013 LET X2 = STCDF(X1,NU,0.5) 59014 59015Note: 59016 Library functions are distinguished from let subcommands 59017 in the following ways. 59018 1) Functions enclose the input value in parenthesis. Let 59019 subcommands use spaces. 59020 2) Functions can accept (and return) either parameters 59021 (i.e., single values) or variables (i.e., an array of 59022 values) while let subcommands are specific in which they 59023 accept as input and what they return as output. 59024 3) Functions can accept expressions while let subcommands 59025 do not. For example, the following is legal: 59026 LET Y2 = ABS(Y1-INT(Y1)) 59027 For let subcommands, you typically have to do something 59028 like the following: 59029 LET YTEMP = Y**2 + 8 59030 LET A = SUM YTEMP 59031 59032Default: 59033 None 59034 59035Synonyms: 59036 None 59037 59038Related Commands: 59039 STPDF = Compute the skew-t probability density function. 59040 STPPF = Compute the skew-t percent point function. 59041 SNPDF = Compute the skew-normal probability density function. 59042 TPDF = Compute the t probability density function. 59043 FTPDF = Compute the folded t probability density function. 59044 NORPDF = Compute the normal density function. 59045 CHSPDF = Compute the chi-square probability density function. 59046 59047Reference: 59048 "A Class of Distributions Which Includes the Normal Ones", 59049 Azzalini, Scandinavian Journal of Statistics, 12, 171-178. 59050 59051 "Log-Skew-Normal and Log-Skew-t Distributions as Models for 59052 Familiy Income Data", Azzalini and Dal Cappello, 59053 unpublished paper downloaded from Azzallini web site. 59054 59055Applications: 59056 Distributional Modeling 59057 59058Implementation Date: 59059 1/2004 59060 59061Program: 59062 MULTIPLOT 2 2 59063 MULTIPLOT CORNER COORDINATES 0 0 100 100 59064 TITLE SKEW-T (NU=3): LAMBDA = 0 59065 PLOT STCDF(X,3,0) FOR X = -5 0.1 5 59066 TITLE SKEW-T (NU=3): LAMBDA = 1 59067 PLOT STCDF(X,3,1) FOR X = -5 0.1 5 59068 TITLE SKEW-T (NU=3): LAMBDA = 5 59069 PLOT STCDF(X,3,5) FOR X = -5 0.1 5 59070 TITLE SKEW-T (NU=3): LAMBDA = 10 59071 PLOT STCDF(X,3,10) FOR X = -5 0.1 5 59072 END OF MULTIPLOT 59073 59074-----STEM AND LEAF PLOT----------------------------------------------- 59075 59076STEM AND LEAF PLOT 59077 59078Name: 59079 STEM AND LEAF PLOT 59080 59081Type: 59082 Graphics Command 59083 59084Purpose: 59085 Generates a stem and leaf plot. 59086 59087Description: 59088 A stem and leaf plot is a graphical data analysis technique for 59089 summarizing the distributional information of a variable. It is 59090 similar to a histogram, but it preserves the original numeric 59091 values in the data. As such, it is an effective alternative to 59092 the histogram for small to moderate size data sets. It is not 59093 recommended for large data sets. 59094 59095Syntax: 59096 STEM AND LEAF PLOT <x> <SUBSET/EXCEPT/FOR qualification> 59097 where <x> is the variable of raw data values; 59098 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 59099 59100Examples: 59101 STEM AND LEAF PLOT TEMP 59102 59103Note: 59104 Although the stem and leaf plot is a graphics command, the 59105 plot is generated as alphanumeric output, not as graphics output. 59106 This means that if device 2 is on, the stem and leaf plot is not 59107 generated in the plot file DPPL1F.DAT. The CAPTURE command can 59108 be used to direct the stem and leaf output to a text file. 59109 59110Default: 59111 None 59112 59113Synonyms: 59114 None 59115 59116Related Commands: 59117 FREQUENCY PLOT = Generates a frequency plot. 59118 HISTOGRAM = Generates a histogram. 59119 PIE CHART = Generates a pie chart. 59120 PERCENT POINT PLOT = Generates a percent point plot. 59121 PROBABILITY PLOT = Generates a probability plot. 59122 PPCC PLOT = Generates probability plot correlation 59123 coefficient plot. 59124 CAPTURE = Redirect alphanumeric output to a file. 59125 59126Applications: 59127 Exploratory Data Analysis 59128 59129Implementation Date: 59130 Pre-1987 59131 59132Program: 59133 SKIP 25 59134 READ GEAR.DAT DIAMETER 59135 . 59136 CAPTURE STEM_LEAF_OUT.DAT 59137 STEM AND LEAF PLOT DIAMETER 59138 END OF CAPTURE 59139 59140 The following output is generated: 59141 59142 97 : 59143 98 : 01244 59144 98 : 788 59145 99 : 00111123344444 59146 99 : 5555566666666666666677777788888888888889999 59147 00 : 000000000122222222224444 59148 00 : 56666699 59149 01 : 03 59150 01 : 8 59151 59152-----STATUS------------------------------------------------------- 59153 59154STATUS 59155 59156Name: 59157 STATUS 59158 59159Type: 59160 Support Command 59161 59162Purpose: 59163 Prints the current character types, line type variable names, 59164 parameter values, functions, etc. 59165 59166Syntax 1: 59167 STATUS 59168 59169 This lists all status information. 59170 59171Syntax 2: 59172 STATUS <keyword> 59173 where <keyword> is one of the following: 59174 MACHINE - print host name and machine constants 59175 FILE - print DATAPLOT file names 59176 ARROWS - print current ARROW settings 59177 SEGMENTS - print current SEGMENT settings 59178 LEGENDS - print current LEGEND settings 59179 BOXES - print current BOX settings 59180 SPIKES - print current SPIKE settings 59181 BARS - print current BAR settings 59182 DIMENSION - print current dimension settings 59183 CHARACTERS - print current CHARACTER settings 59184 LINES - print current LINE settings 59185 VARIABLES - print information on currently defined 59186 variables 59187 PARAMETERS - print information on currently defined 59188 parameters 59189 FUNCTIONS - print the currently defined functions 59190 MATRICES - print information on currently defined 59191 matrices. 59192 59193Syntax 3: 59194 STATUS VARIABLES <a> 59195 where <a> is a single alphabetic character. 59196 59197 This syntax displays all variables beginning with the letter 59198 <a>. For example, STATUS VARIABLES X displays all variables 59199 beginning with the letter X. This can be useful when you have 59200 created a large number of variables. 59201 59202Syntax 4: 59203 GUI STATUS VARIABLE 59204 59205 This is a special form of the command that is sent by the Tcl/Tk 59206 scripts for the Dataplot Graphical User Interface (GUI). If this 59207 command is entered directly by the Dataplot user, it is equivalent 59208 to entering a STATUS VARIABLES command. 59209 59210 The command 59211 59212 SET GUI FEEDBACK <ON/OFF> 59213 59214 is used to set the FEEDBACK switch for this command. 59215 59216Examples: 59217 STATUS 59218 STATUS VARIABLES 59219 STATUS VARIABLES X 59220 STATUS V X 59221 STATUS PARAMETERS 59222 59223Note: 59224 If the variable status is requested, the following information will 59225 be written to "dpst1f.dat". 59226 59227 59228 1) Line 1 will contain the number of currently defined variables. 59229 59230 2) For each currently defined variable, the succeeding lines will 59231 contain 59232 59233 a) The variable name 59234 b) The number of observations 59235 c) The number of distinct observations 59236 d) The first 10 distinct values 59237 59238Default: 59239 None 59240 59241Synonyms: 59242 LS is a synonym for STATUS 59243 59244Related Commands: 59245 RESET = Reset DATAPLOT internal parameters, variables, 59246 functions, and switches to their default values. 59247 59248Applications: 59249 Interactive Usage 59250 59251Implementation Date: 59252 Pre-1987 59253 1991/12: Support for STATUS <keyword> syntax 59254 2010/07: Support for Syntax 3 59255 2010/09: Added LS as a synonym 59256 2014/11: Write variable list to dpst1f.dat 59257 2015/12: Additional info to dpst1f.dat 59258 59259Program: 59260 SKIP 25 59261 READ BERGER1.DAT Y X BAT 59262 STATUS VARIABLES 59263 59264-----STEP (LET)-------------------------------- 59265 59266STEP 59267 59268Name: 59269 STEP (LET) 59270 59271Type: 59272 Library Function 59273 59274Purpose: 59275 Return the integer portion of a number or variable rounded to 59276 positive integer. 59277 59278Syntax: 59279 LET <y2> = STEP(<y1>) <SUBSET/EXCEPT/FOR qualification> 59280 where <y1> is a variable or a parameter; 59281 <y2> is a variable or a parameter (depending on what <y1> 59282 is) where the computed integer values are stored; 59283 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 59284 59285Examples: 59286 LET A = STEP(2.83) 59287 LET A = STEP(A1) 59288 LET X2 = STEP(X1) 59289 LET X2 = STEP(X1-4.2) 59290 59291Note: 59292 Library functions are distinguished from let subcommands 59293 in the following ways. 59294 1) Functions enclose the input value in parenthesis. Let 59295 subcommands use spaces. 59296 2) Functions can accept (and return) either parameters 59297 (i.e., single values) or variables (i.e., an array of 59298 values) while let subcommands are specific in which they 59299 accept as input and what they return as output. 59300 3) Functions can accept expressions while let subcommands 59301 do not. For example, the following is legal: 59302 LET Y2 = ABS(Y1-INT(Y1)) 59303 For let subcommands, you typically have to do something 59304 like the following: 59305 LET YTEMP = Y**2 + 8 59306 LET A = SUM YTEMP 59307 59308Default: 59309 None 59310 59311Synonyms: 59312 FLOOR 59313 59314Related Commands: 59315 CEIL = Compute the integer value rounded to positive infinity. 59316 INT = Compute the integer value rounded to zero. 59317 SIGN = Compute the sign of a number. 59318 FRACT = Compute the fractional portion of number. 59319 MSD = Compute the most significant digit of a number. 59320 ROUND = Round to the closest integer of a number. 59321 59322Applications: 59323 Elementary function 59324 59325Implementation Date: 59326 95/4 59327 59328Program: 59329 LET Y1 = SEQUENCE -5 0.1 5 59330 LET Y2 = STEP(Y1) 59331 PRINT Y1 Y2 59332 59333-----STOP------------------------------------------------------- 59334 59335STOP 59336 59337Name: 59338 STOP 59339 59340Type: 59341 Support Command 59342 59343Purpose: 59344 Terminates a DATAPLOT run. 59345 59346Syntax: 59347 STOP 59348 59349Examples: 59350 STOP 59351 59352Default: 59353 None 59354 59355Synonyms: 59356 EXIT, END, HALT, QUIT 59357 59358Related Commands: 59359 XX 59360 59361Applications: 59362 Interactive Usage 59363 59364Implementation Date: 59365 Pre-1987 59366 59367Program: 59368 XX 59369 59370-----STPDF (LET)-------------------------------- 59371 59372STPDF 59373 59374Name: 59375 STPDF (LET) 59376 59377Type: 59378 Library Function 59379 59380Purpose: 59381 Compute the skew-t probability density function. 59382 59383Description: 59384 The skew-t distribution has the following probability density 59385 function: 59386 59387 f(x,nu,lambda)=2*TCDF(lambda*x*SQRT((1+nu)/(x**2+nu)),nu+1)* 59388 TPDF(x,nu) -infinity < x, lambda < infinity 59389 59390 For lambda = 0, the skew-t reduces to a t distribution. 59391 As lambda goes to infinity, the skew-t tends to the 59392 folded-t distribution. 59393 59394 The standard skew-t distribution can be generalized with 59395 location and scale parameters. 59396 59397Syntax: 59398 LET <y> = STPDF(<x>,<nu>,<lambda>) 59399 <SUBSET/EXCEPT/FOR qualification> 59400 where <x> is a variable or a parameter; 59401 <nu> is a number of parameter that specifies the 59402 value of the degrees of freedom shape parameter; 59403 <lambda> is a number of parameter that specifies the 59404 value of the skewness shape parameter; 59405 <y> is a variable or a parameter (depending on what <x> is) 59406 where the computed skew-t pdf value is stored; 59407 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 59408 59409Examples: 59410 LET A = STPDF(3,5,1) 59411 LET A = STPDF(A1,DF,LAMBDA) 59412 LET X2 = STPDF(X1,NU,0.5) 59413 59414Note: 59415 Library functions are distinguished from let subcommands 59416 in the following ways. 59417 1) Functions enclose the input value in parenthesis. Let 59418 subcommands use spaces. 59419 2) Functions can accept (and return) either parameters 59420 (i.e., single values) or variables (i.e., an array of 59421 values) while let subcommands are specific in which they 59422 accept as input and what they return as output. 59423 3) Functions can accept expressions while let subcommands 59424 do not. For example, the following is legal: 59425 LET Y2 = ABS(Y1-INT(Y1)) 59426 For let subcommands, you typically have to do something 59427 like the following: 59428 LET YTEMP = Y**2 + 8 59429 LET A = SUM YTEMP 59430 59431Default: 59432 None 59433 59434Synonyms: 59435 None 59436 59437Related Commands: 59438 STCDF = Compute the skew-t cumulative distribution function. 59439 STPPF = Compute the skew-t percent point function. 59440 SNPDF = Compute the skew-normal probability density function. 59441 TPDF = Compute the t probability density function. 59442 FTPDF = Compute the folded t probability density function. 59443 NORPDF = Compute the normal density function. 59444 CHSPDF = Compute the chi-square probability density function. 59445 59446Reference: 59447 "A Class of Distributions Which Includes the Normal Ones", 59448 Azzalini, Scandinavian Journal of Statistics, 12, 171-178. 59449 59450 "Log-Skew-Normal and Log-Skew-t Distributions as Models for 59451 Familiy Income Data", Azzalini and Dal Cappello, 59452 unpublished paper downloaded from Azzallini web site. 59453 59454Applications: 59455 Distributional Modeling 59456 59457Implementation Date: 59458 1/2004 59459 59460Program: 59461 MULTIPLOT 2 2 59462 MULTIPLOT CORNER COORDINATES 0 0 100 100 59463 TITLE SKEW-T (NU=3): LAMBDA = 0 59464 PLOT STPDF(X,3,0) FOR X = -5 0.1 5 59465 TITLE SKEW-T (NU=3): LAMBDA = 1 59466 PLOT STPDF(X,3,1) FOR X = -5 0.1 5 59467 TITLE SKEW-T (NU=3): LAMBDA = 5 59468 PLOT STPDF(X,3,5) FOR X = -5 0.1 5 59469 TITLE SKEW-T (NU=3): LAMBDA = 10 59470 PLOT STPDF(X,3,10) FOR X = -5 0.1 5 59471 END OF MULTIPLOT 59472 59473-----STPPF (LET)-------------------------------- 59474 59475STPPF 59476 59477Name: 59478 STPPF (LET) 59479 59480Type: 59481 Library Function 59482 59483Purpose: 59484 Compute the skew-t percent point function. 59485 59486Description: 59487 The skew-t distribution has the following probability density 59488 function: 59489 59490 f(x,nu,lambda)=2*TCDF(lambda*x*SQRT((1+nu)/(x**2+nu)),nu+1)* 59491 TPDF(x,nu) -infinity < x, lambda < infinity 59492 59493 For lambda = 0, the skew-t reduces to a t distribution. 59494 As lambda goes to infinity, the skew-t tends to the 59495 folded-t distribution. 59496 59497 The skew-t percent point function is computed numerically 59498 (by inverting the skew-t cdf function with the bisection 59499 method). 59500 59501 The standard skew-t distribution can be generalized with 59502 location and scale parameters. 59503 59504Syntax: 59505 LET <y> = STPPF(<p>,<nu>,<lambda>) 59506 <SUBSET/EXCEPT/FOR qualification> 59507 where <p> is a variable or a parameter in the range [0,1]; 59508 <nu> is a number of parameter that specifies the 59509 value of the degrees of freedom shape parameter; 59510 <lambda> is a number of parameter that specifies the 59511 value of the skewness shape parameter; 59512 <y> is a variable or a parameter (depending on what <p> is) 59513 where the computed skew-t ppf value is stored; 59514 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 59515 59516Examples: 59517 LET A = STPPF(0.95,5,1) 59518 LET A = STPPF(A1,DF,LAMBDA) 59519 LET X2 = STPPF(P1,NU,0.5) 59520 59521Note: 59522 Library functions are distinguished from let subcommands 59523 in the following ways. 59524 1) Functions enclose the input value in parenthesis. Let 59525 subcommands use spaces. 59526 2) Functions can accept (and return) either parameters 59527 (i.e., single values) or variables (i.e., an array of 59528 values) while let subcommands are specific in which they 59529 accept as input and what they return as output. 59530 3) Functions can accept expressions while let subcommands 59531 do not. For example, the following is legal: 59532 LET Y2 = ABS(Y1-INT(Y1)) 59533 For let subcommands, you typically have to do something 59534 like the following: 59535 LET YTEMP = Y**2 + 8 59536 LET A = SUM YTEMP 59537 59538Default: 59539 None 59540 59541Synonyms: 59542 None 59543 59544Related Commands: 59545 STCDF = Compute the skew-t cumulative distribution function. 59546 STPDF = Compute the skew-t probability density function. 59547 SNPDF = Compute the skew-normal probability density function. 59548 TPDF = Compute the t probability density function. 59549 FTPDF = Compute the folded t probability density function. 59550 NORPDF = Compute the normal density function. 59551 CHSPDF = Compute the chi-square probability density function. 59552 59553Reference: 59554 "A Class of Distributions Which Includes the Normal Ones", 59555 Azzalini, Scandinavian Journal of Statistics, 12, 171-178. 59556 59557 "Log-Skew-Normal and Log-Skew-t Distributions as Models for 59558 Familiy Income Data", Azzalini and Dal Cappello, 59559 unpublished paper downloaded from Azzallini web site. 59560 59561Applications: 59562 Distributional Modeling 59563 59564Implementation Date: 59565 1/2004 59566 59567Program: 59568 MULTIPLOT 2 2 59569 MULTIPLOT CORNER COORDINATES 0 0 100 100 59570 TITLE SKEW-T (NU=3): LAMBDA = 0 59571 PLOT STPPF(P,3,0) FOR P = 0.01 0.01 0.99 59572 TITLE SKEW-T (NU=3): LAMBDA = 1 59573 PLOT STPPF(P,3,1) FOR P = 0.01 0.01 0.99 59574 TITLE SKEW-T (NU=3): LAMBDA = 5 59575 PLOT STPPF(P,3,5) FOR P = 0.01 0.01 0.99 59576 TITLE SKEW-T (NU=3): LAMBDA = 10 59577 PLOT STPPF(P,3,10) FOR P = 0.01 0.01 0.99 59578 END OF MULTIPLOT 59579 59580-----STREAM READ------------------------------------------------------- 59581 59582STREAM READ 59583 59584Name: 59585 STREAM READ 59586 59587Type: 59588 Support Command 59589 59590Purpose: 59591 Read data and perform certain computations for data sets that 59592 are too large to read into memory. 59593 59594Description: 59595 Dataplot was designed primarily for interactive usage. For this reason, 59596 it reads all data into memory. The current default is to have a 59597 workspace that accomodates 10 columns with 1,500,000 rows (you can 59598 re-dimension to obtain more columns at the expense of fewer rows, however 59599 you cannot increase the maximum number of rows). 59600 59601 With the advent of "big data", there are more data files that cannot be 59602 read into Dataplot's available memory. For these data files, there are 59603 several things that can potentially be done 59604 59605 1. For some platforms, if you have a large amount of memory you may 59606 be able to build a version of Dataplot that raises the maximum 59607 number of rows. For example, on a Linux system with 64MB of RAM, 59608 we were able to build a version that supports a maximum of 59609 10,000,000 rows. Contact Alan Heckert if you need assistance 59610 with this. 59611 59612 2. The STREAM READ command was added. This command uses one pass 59613 algorithms to do a number of things. 59614 59615 a. You can create a new file that uses SET WRITE FORMAT. This 59616 is typically done once so that you can use SET READ FORMAT on 59617 subsequent reading of the data file (this can substantially 59618 speed up processing of these large files). 59619 59620 b. You can generate various summary statistics either for the 59621 full data set or for groups in the data. 59622 59623 c. You can generate cross tabulation statistics (up to 4 cross 59624 tabulation variables can be specified). 59625 59626 d. You can create various types of distance or similarity 59627 (e.g., Euclidean distances, correlation) matrices either for 59628 the full data set or for cross tabulations of the data. 59629 59630 Distance and similarity matrices are often used for various 59631 types of multivariate analysis. 59632 59633 e. You can generate approximate percentiles either for the full 59634 data set or for cross tabulations of the data. Based on this, 59635 you can perform distributional modeling for a single variable 59636 or distributional comparisons between variables (e.g., 59637 quantile quantile plots, bihistograms, two sample KS tests, 59638 and so on). 59639 59640 Although Dataplot may not be able to read many of these large 59641 data sets into memory, the STREAM READ command does allow you to 59642 perform certain types of exploratory analyses on these large data 59643 sets. 59644 59645Syntax 1: 59646 STREAM READ WRITE <file> <x1> <x2> ... <xk> 59647 where <file> is the name of the file to read; 59648 and where <x1>, <x2>, ... <xk> is a list of variables to read. 59649 59650 This version of the command is used to read the input file and to 59651 write a new version of the data using a specified Fortran-like format. 59652 59653 This command is useful in the following way. Large data files can 59654 take a long time to read. If you can use the SET READ FORMAT command 59655 to read the data, this can significantly speed up the reading of the 59656 data. For example, reading the data set used by the example programs 59657 below used 24.7 cpu seconds on a Linux machine running CentOS. 59658 Performing the same read on the same platform with a SET READ FORMAT 59659 required 0.6 cpu seconds. Cpu times will vary depending on the 59660 hardware and operating system, but this is indicative of the relative 59661 performance improvement that can be obtained by using the SET READ 59662 FORMAT command. This example file is not particularly large 59663 (361,920 rows). The speed improvement becomes even more important 59664 when we start dealing with multiple millions of rows. 59665 59666 Often large data sets will initially not be in a format where the 59667 SET READ FORMAT can be used. So this command can be used once, with 59668 the SET WRITE FORMAT command, to create a new version of the file that 59669 is formatted in a way that the SET READ FORMAT can be used. This new 59670 file is then used for subsequent Dataplot sessions that use this data. 59671 59672Syntax 2: 59673 STREAM READ GROUP STATISTICS <stat> <file> <x1> <x2> ... <xk> 59674 where <stat> is one of Dataplot's supported univariate statistics; 59675 <file> is the name of the file to read; 59676 and where <x1>, <x2>, ... <xk> is a list of variables to read. 59677 59678 This syntax will read the file a user-specified number of rows at a 59679 time. It will then replace those rows with the specified statistic. 59680 That is, the original data will be replaced with the specified 59681 statistic for fixed intervals of the data. 59682 59683 For example, you can read 1,000 rows, compute (and save) the mean 59684 for those 1,000 rows for each variable, then repeat for the next 59685 1,000 rows. That is, the original data will be replaced with the 59686 means of fixed intervals of the data. 59687 59688 To specify the number of rows to read at a time, enter 59689 59690 SET STREAM READ SIZE <value> 59691 59692 Alternatively, you can specify one of the variabes to define 59693 the group (i.e., when the value of the specified variable 59694 changes, this denotes the start of a new group). For this 59695 option, enter 59696 59697 SET STREAM READ GROUP VARIBLE <var-name> 59698 59699 This capability is motivated by the desire to handle large data 59700 sets that may exceed Dataplot's storage limits. This command 59701 allows you to compute some basic statistics (mean, minimum, 59702 maximum, standard deviation, and so on) for slices of the data. 59703 Often, some useful exploratory analysis can be performed on this 59704 compressed data. 59705 59706 To see a list of supported univariate statistics, enter 59707 59708 HELP STATISTICS 59709 59710Syntax 3: 59711 STREAM READ DEFAULT STATISTICS <file> <x1> <x2> ... <xk> 59712 where <file> is the name of te file to read; 59713 and where <x1>, <x2>, ... <xk> is a list of variables to read. 59714 59715 This is a variant of Syntax 2 that allows a default set of statistics 59716 to be computed on a single pass of the data. 59717 59718 This computes the statistic for slices of the data as in Syntax 2 59719 (it uses the SET STREAM READ SIZE and SET STREAM READ GROUP VARIABLE 59720 commands as in Syntax 2). 59721 59722 The following statistics are computed: 59723 59724 1. VALUE OF LAST ROW OF GROUP 59725 2. GROUP-ID 59726 3. SIZE 59727 4. MINIMUM 59728 5. MAXIMUM 59729 6. MEAN 59730 7. STANDARD DEVIATION 59731 8. SKEWNESS 59732 9. KURTOSIS 59733 10. MEDIAN 59734 11. INTERQUARTILE RANGE 59735 12. RANGE 59736 13. AUTOCORRELATION 59737 14. LOWER QUARTILE 59738 15. UPPER QUARTILE 59739 16. 0.01 QUANTILE 59740 17. 0.05 QUANTILE 59741 18. 0.10 QUANTILE 59742 19. 0.90 QUANTILE 59743 20. 0.95 QUANTILE 59744 21. 0.99 QUANTILE 59745 59746 For this syntax, a tag variable (TAGSTAT) will be created that 59747 defines the statistic (i.e., each row of TAGSTAT contains a 59748 value from 1 to 21). TAGSTAT can be used to exract the desired 59749 statistic for each group. 59750 59751 If a group variable was specified, that variable will contain the 59752 group-id. For example, if X is the group id variable and it has 59753 3 groups with values of 1, 2, and 3, then the X will have a value of 59754 1 in rows 1 to 21, a value of 2 in rows 22 to 42, and a value of 3 59755 in rows 43 to 63. 59756 59757Syntax 4: 59758 STREAM READ FULL STATISTICS <file> <x1> <x2> ... <xk> 59759 where <file> is the name of the file to read; 59760 and where <x1>, <x2>, ... <xk> is a list of variables to read. 59761 59762 This syntax will compute the following statistics using 1-pass 59763 algorithms for all of the data: 59764 59765 1. COUNT 59766 2. MINIMUM 59767 3. MAXIMUM 59768 4. MEAN 59769 5. STANDARD DEVIATION 59770 6. SKEWNESS 59771 7. KURTOSIS 59772 8. RANGE 59773 59774 Each of the <x1> ... <xk> will have 8 rows containing the above 59775 eight statistics for each column read. 59776 59777Syntax 5: 59778 STREAM READ CROSS TABULATE <file> <var-list> 59779 where <file> is the name of the file to read; 59780 and where <x1>, <x2>, ... <xk> is a list of variables to read. 59781 59782 This is similar to syntax 4. However, instead of computing 59783 the statistics for the full data set, it will compute them for 59784 cross tabulations of the data. 59785 59786 You can specify from one to four cross-tabulation variables 59787 with the commands 59788 59789 SET STREAM READ CROSS TABULATE VARIABLE ONE <name> 59790 SET STREAM READ CROSS TABULATE VARIABLE TWO <name> 59791 SET STREAM READ CROSS TABULATE VARIABLE THREE <name> 59792 SET STREAM READ CROSS TABULATE VARIABLE FOUR <name> 59793 59794 With this syntax, the following nine statistics will be computed 59795 for each cross-tabulation cell 59796 59797 1. COUNT 59798 2. MINIMUM 59799 3. MAXIMUM 59800 4. MEAN 59801 5. STANDARD DEVIATION 59802 6. SKEWNESS 59803 7. KURTOSIS 59804 8. RANGE 59805 9. NUMBER OF MISSING VALUES 59806 59807 For this syntax, a tag variable (TAGSTAT) will be created that 59808 defines the statistic (i.e., each row of TAGSTAT contains a 59809 value from 1 to 9). TAGSTAT can be used to exract the desired 59810 statistic for each group. 59811 59812 For each cell, 9 rows will be generated. The variables defined as 59813 cross tabulation variables will simply have their value for that 59814 cell for all 9 rows. For the variables that are not defined as 59815 cross tabulation variables, the 9 rows will contain the values of 59816 the above 9 statistics. 59817 59818Syntax 6: 59819 STREAM READ <metric> <file> <x1> <x2> ... <xk> 59820 where <file> is the name of the file to read; 59821 <metric> is one of the measures defined below; 59822 and where <x1>, <x2>, ... <xk> is a list of variables to read. 59823 59824 With this option, the STREAM READ will return a distance, similarity, 59825 covariance, or correlation matrix. The raw data is not saved. For 59826 example, 59827 59828 STREAM READ CORRELATION FILE.DAT Y1 Y2 Y3 59829 59830 will return the 3 variables Y1, Y2, and Y3 where each of these variables 59831 will contain 3 rows. For example, Y2(3) contains the correlation between 59832 the second response column and the third response column. 59833 59834 The <metric> option can be any of the following 59835 59836 EUCLIDEAN DISTANCE 59837 MANHATTAN DISTANCE 59838 CHEBYCHEV DISTANCE 59839 CANBERRA DISTANCE 59840 HAMMING DISTANCE 59841 COSINE DISTANCE 59842 COSINE SIMILARITY 59843 ANGULAR COSINE DISTANCE 59844 ANGULAR COSINE SIMILARITY 59845 COVARIANCE 59846 CORRELATION 59847 59848 This syntax will ignore character fields. If you do not want some fields 59849 in the file to be included, you can do something like the following 59850 59851 LET ITYPE = DATA 1 1 1 0 1 59852 SET STREAM READ VARIABLE TYPE ITYPE 59853 59854 These commands specify that fields 1, 2, 3, and 5 will be included while 59855 field 4 will be excluded. This can be useful if some of the fields are 59856 categorical variables where distance and covariance/correlation do not 59857 make sense. 59858 59859Syntax 7: 59860 STREAM READ CROSS TABULATE <metric> <file> <x1> <x2> ... <xk> 59861 where <file> is the name of the file to read; 59862 <metric> is one of measures specified in Syntax 6; 59863 and where <x1>, <x2>, ... <xk> is a list of variables to read. 59864 59865 This is similar to Syntax 6. However, the metric will be 59866 computed separately for each cross tabulation cell. 59867 59868 The cross tabulation variables are specified as in Syntax 5. This 59869 syntax also creates a TAGSTAT variable. However, in this case the 59870 TAGSTAT variable is the "cell id" value. 59871 59872 For each cell, the number of rows generated will be equal to the 59873 number of columns used to compute the distance metric (i.e., the cross 59874 tabulation variables or variables omitted by the SET STREAM READ 59875 VARIABLE TYPE command). The variables defined as cross tabulation 59876 variables will simply have their value for that cell for all the rows. 59877 59878Syntax 8: 59879 STREAM READ PERCENTILES <file> <x1> <x2> ... <xk> 59880 where <file> is the name of the file to read; 59881 and where <x1>, <x2>, ... <xk> is a list of variables to read. 59882 59883 This syntax will replace the raw data with a user-specified number 59884 of approximate percentiles. To specify the number of equally spaced 59885 percentiles to generate, enter the command 59886 59887 SET STREAM READ NUMBER OF PERCENTILES <value> 59888 59889 where <value> is one of 9, 99, 999, or 9999. The default is 999. 59890 The minimum and maximum values are also saved. So if the number of 59891 percentiles is 999, 1001 points will be returned. 59892 59893 Dataplot uses the extended P2 algorithm (the P2 algorithm was 59894 originally proposed by Jain and Chlamtac and was extended for 59895 multiple percentiles by Raatikanien). This algorithm requires 59896 2*m+3 points where m is the desired number of percentiles. 59897 So if the number of values read is less than or equal to 2*m+3, 59898 Dataplot returns the original data (in sorted order). If the 59899 number of points is greater than this, then the approximate 59900 percentiles are returned. 59901 59902Syntax 9: 59903 STREAM READ CROSS TABULATE PERCENTILES <file> <x1> <x2> ... <xk> 59904 where <file> is the name of the file to read; 59905 and where <x1>, <x2>, ... <xk> is a list of variables to read. 59906 59907 This is similar to Syntax 8. However, the percentiles will be 59908 computed separately for each cross tabulation cell. 59909 59910 The cross tabulation variables are specified as in Syntax 5. This 59911 syntax also creates a TAGSTAT variable. However, in this case the 59912 TAGSTAT variable is the "cell id" value. 59913 59914 For each cell, the number of rows generated will be equal to the 59915 number of percentiles requested. The variables defined as cross 59916 tabulation variables will simply have their value for that cell for 59917 all the rows. 59918 59919Examples: 59920 SET WRITE FORMAT 10E15.7 59921 STREAM READ WRITE BIG.DAT X1 TO X10 59922 59923 SET STREAM READ SIZE 100 59924 STREAM READ GROUP STATISTIC MEAN BIG.DAT X1 TO X10 59925 STREAM READ GROUP STATISTIC STANDARD DEVIATION BIG.DAT X1 TO X10 59926 STREAM READ DEFAULT STATISTICS BIG.DAT X1 TO X10 59927 59928 STREAM READ FULL STATISTICS BIG.DAT X1 TO X10 59929 STREAM READ CROSS TABULATE BIG.DAT X1 TO X10 59930 59931Note: 59932 For the WRITE and CROSS TABULATE cases, character variables 59933 will be automatically converted to categorical variables. For 59934 the GROUP STATISITC, DEFAULT STATISTIC, FULL STATISTIC, and 59935 PERCENTILE cases, character variables will still be ignored. 59936 59937 If you would like to save the character strings from the 59938 character variables as group labels, enter the command 59939 59940 SET STREAM READ GROUP LABEL ON 59941 59942 If you have specified a column to be the row label variable 59943 using the SET ROW LABEL COLUMN command, this variable will 59944 not be converted to a numeric variable and group labels will 59945 not be created. 59946 59947Note: 59948 When computing statistics, missing values (as specified by the 59949 SET READ MISSING VALUE command) will be omitted. 59950 59951Note: 59952 Note that the STREAM READ command has a number of limitations compared 59953 to the standard READ command. 59954 59955 1. Functions/strings, parameters, matrices, and images are not 59956 supported. 59957 59958 2. Reading from the clipboard is not supported. 59959 59960 3. Automatic name detection is not supported. 59961 59962 4. The STREAM READ command is restricted to files (i.e., reading 59963 from the terminal is not supported). 59964 59965Default: 59966 None 59967 59968Synonyms: 59969 None 59970 59971Related Commands: 59972 READ = Read variables from a file or the terminal. 59973 SERIAL READ = Perform a serial read. 59974 READ FUNCTION = Read a function. 59975 READ MATRIX = Read a matrix. 59976 READ PARAMETER = Read a parameter. 59977 READ STRING = Read a string. 59978 READ IMAGE = Read an image format into numeric arrays. 59979 READ STACKED VARIABLE = Read a list of variables into a single 59980 response variable and a group-id variable. 59981 SET READ FORMAT = Define a FORTRAN style format for reads. 59982 DATA (LET) = Enter data values into a variable. 59983 CLIPBOARD = Various commands for reading from the 59984 system clipboard. 59985 59986References: 59987 Jain and Chlamtac (1985), "The P^2 Algorithm for Dynamic Calculation 59988 of Quantiles and Histograms without Storing Observations," 59989 Communications of the ACM, 28, No. 10, pp. 1076-1085. 59990 59991 Raatikanien (1987), "Simultaneous Estimation of Several Percentiles," 59992 Simulation, pp. 159-164. 59993 59994Applications: 59995 Data Input 59996 59997Implementation Date: 59998 2016/07: Original implementation 59999 2018/07: Interpret character variables as categorical numeric 60000 variables for the WRITE and CROSS TABULATE cases 60001 2018/07: Support for CROSS TABULATION 60002 2018/07: Omit missing values when computing statistics 60003 2018/07: Option to automatically create group labels from character 60004 data 60005 2018/07: Allow specification of a "row label" column 60006 2018/07: Support for DISTANCE metrics 60007 2018/08: Support for CROSS TABULATION for DISTANCE metrics 60008 2018/08: Support for PERCENTILE and CROSS TABULATE PERCENTILE 60009 60010Program 1: 60011 . Step 1: Demonstrate the group statistic option of stream read 60012 . 60013 skip 25 60014 set read format 3F7.0 60015 set stream read group variable rowid 60016 stream read group statistics mean elliottr.dat redcolme rowid colid 60017 . 60018 . Step 2: Generate plot of column means 60019 . 60020 title offset 2 60021 title case asis 60022 label case asis 60023 . 60024 title Column Means for Red Pixels for ELLIOTTR.DAT 60025 y1label Column Mean 60026 x1label Row 60027 . 60028 plot redcolme vs rowid 60029 . 60030 . Step 3: Reset read settings 60031 . 60032 skip 0 60033 set read format 60034 60035Program 2: 60036 . Step 1: Demonstrate the default statistic option of stream read 60037 . 60038 skip 25 60039 set read format 3F7.0 60040 set stream read group variable rowid 60041 stream read default statistics elliottr.dat red rowid colid 60042 . 60043 let redmean = red 60044 retain redmean subset tagstat = 6 60045 let redsd = red 60046 retain redsd subset tagstat = 7 60047 let redmin = red 60048 retain redmin subset tagstat = 4 60049 let redmax = red 60050 retain redmax subset tagstat = 5 60051 . 60052 . Step 2: Plot some of the statistics 60053 . 60054 multiplot corner coordinates 5 5 95 95 60055 multiplot scale factor 2 60056 multiplot 2 2 60057 . 60058 label case asis 60059 title case asis 60060 case asis 60061 title offset 2 60062 . 60063 title Mean of Columns 60064 plot redmean 60065 . 60066 title SD of Columns 60067 plot redsd 60068 . 60069 title Minimum of Columns 60070 plot redmin 60071 . 60072 title Maximum of Columns 60073 plot redmax 60074 . 60075 end of multiplot 60076 . 60077 justification center 60078 move 50 97 60079 text Statistics for Columns of Red Pixels in ELLIOTTR.DAT 60080 . 60081 . Step 2: Reset read settings 60082 . 60083 skip 0 60084 set read format 60085 60086Program 3: 60087 . Step 1: Demonstrate the default statistic option of stream read 60088 . 60089 skip 25 60090 set read format 3F7.0 60091 stream read full statistics elliottr.dat red rowid colid 60092 . 60093 . Step 2: Print statistics for red variable 60094 . 60095 feedback off 60096 set write decimals 2 60097 print "Statistics for variable RED:" 60098 print " " 60099 print " " 60100 let aval = red(1) 60101 print "Size: ^aval" 60102 let aval = red(2) 60103 print "Minimum: ^aval" 60104 let aval = red(3) 60105 print "Maximum: ^aval" 60106 let aval = red(4) 60107 let aval = round(aval,2) 60108 print "Mean: ^aval" 60109 let aval = red(5) 60110 let aval = round(aval,2) 60111 print "SD: ^aval" 60112 let aval = red(6) 60113 let aval = round(aval,2) 60114 print "Skewness: ^aval" 60115 let aval = red(7) 60116 let aval = round(aval,2) 60117 print "Kurtosis: ^aval" 60118 let aval = red(8) 60119 print "Range: ^aval" 60120 feedback on 60121 . 60122 . Step 3: Reset read settings 60123 . 60124 skip 0 60125 set read format 60126 60127Program 4: 60128 set write decimals 4 60129 set read missing value -999 60130 let itype = data 1 1 1 1 0 60131 set stream read variable type itype 60132 set stream read cross tabulate variable one groupid 60133 . 60134 skip 25 60135 stream read cross tabulate iris.dat y1 y2 y3 y4 groupid 60136 print y1 y2 y3 y4 groupid tagstat 60137 60138Program 5: 60139 set write decimals 4 60140 set read missing value -999 60141 let itype = data 1 1 1 1 0 60142 set stream read variable type itype 60143 skip 25 60144 . 60145 . Options to pick which distance/similarity metric to compute 60146 . let iflag1 = 1 60147 let iflag1 = 2 60148 let iflag2 = 1 60149 . let iflag2 = 2 60150 . let iflag2 = 3 60151 . let iflag2 = 4 60152 . let iflag2 = 5 60153 . let iflag2 = 6 60154 . let iflag2 = 7 60155 . let iflag2 = 8 60156 . let iflag2 = 9 60157 . let iflag2 = 10 60158 . let iflag2 = 11 60159 . 60160 if iflag1 = 1 60161 if iflag2 = 1 60162 stream read covariance iris.dat y1 y2 y3 y4 60163 else if iflag2 = 2 60164 stream read correlation iris.dat y1 y2 y3 y4 60165 end of if 60166 else if iflag1 = 2 60167 if iflag2 = 1 60168 stream read euclidean distance iris.dat y1 y2 y3 y4 60169 else if iflag2 = 2 60170 stream read manhattan distance iris.dat y1 y2 y3 y4 60171 else if iflag2 = 3 60172 stream read chebychev distance iris.dat y1 y2 y3 y4 60173 else if iflag2 = 4 60174 stream read cosine distance iris.dat y1 y2 y3 y4 60175 else if iflag2 = 5 60176 stream read cosine similarity iris.dat y1 y2 y3 y4 60177 else if iflag2 = 6 60178 stream read angular cosine distance iris.dat y1 y2 y3 y4 60179 else if iflag2 = 7 60180 stream read angular cosine similarity iris.dat y1 y2 y3 y4 60181 else if iflag2 = 8 60182 let v = jaccard column similarity x 60183 stream read jaccard similarity iris.dat y1 y2 y3 y4 60184 else if iflag2 = 9 60185 stream read jaccard distance iris.dat y1 y2 y3 y4 60186 else if iflag2 = 10 60187 stream read hamming distance iris.dat y1 y2 y3 y4 60188 else if iflag2 = 11 60189 stream read canberra distance iris.dat y1 y2 y3 y4 60190 end of if 60191 end of if 60192 . 60193 print y1 y2 y3 y4 60194 60195Program 6: 60196 set write decimals 4 60197 set read missing value -999 60198 set stream read cross tabulate variable one groupid 60199 let itype = data 1 1 1 1 0 60200 set stream read variable type itype 60201 skip 25 60202 . 60203 . Options to select which distance metric to use 60204 . 60205 . let iflag1 = 1 60206 let iflag1 = 2 60207 let iflag2 = 1 60208 . let iflag2 = 2 60209 . let iflag2 = 3 60210 . let iflag2 = 4 60211 . let iflag2 = 5 60212 . let iflag2 = 6 60213 . let iflag2 = 7 60214 . let iflag2 = 8 60215 . let iflag2 = 9 60216 . let iflag2 = 10 60217 . let iflag2 = 11 60218 . 60219 if iflag1 = 1 60220 if iflag2 = 1 60221 stream read cross tabulate covariance iris.dat y1 y2 y3 y4 groupid 60222 else if iflag2 = 2 60223 stream read cross tabulate correlation iris.dat y1 y2 y3 y4 groupid 60224 end of if 60225 else if iflag1 = 2 60226 if iflag2 = 1 60227 stream read cross tabulate euclidean distance iris.dat y1 y2 y3 y4 groupid 60228 else if iflag2 = 2 60229 stream read cross tabulate manhattan distance iris.dat y1 y2 y3 y4 groupid 60230 else if iflag2 = 3 60231 stream read cross tabulate chebychev distance iris.dat y1 y2 y3 y4 groupid 60232 else if iflag2 = 4 60233 stream read cross tabulate cosine distance iris.dat y1 y2 y3 y4 groupid 60234 else if iflag2 = 5 60235 stream read cross tabulate cosine similarity iris.dat y1 y2 y3 y4 groupid 60236 else if iflag2 = 6 60237 stream read cross tabulate angular cosine distance iris.dat y1 y2 y3 y4 groupid 60238 else if iflag2 = 7 60239 stream read cross tabulate angular cosine similarity iris.dat y1 y2 y3 y4 groupid 60240 else if iflag2 = 8 60241 stream read cross tabulate jaccard similarity iris.dat y1 y2 y3 y4 groupid 60242 else if iflag2 = 9 60243 stream read cross tabulate jaccard distance iris.dat y1 y2 y3 y4 groupid 60244 else if iflag2 = 10 60245 stream read cross tabulate hamming distance iris.dat y1 y2 y3 y4 groupid 60246 else if iflag2 = 11 60247 stream read cross tabulate canberra distance iris.dat y1 y2 y3 y4 groupid 60248 end of if 60249 end of if 60250 . 60251 print y1 y2 y3 y4 groupid tagstat 60252 60253-----STRING COMBINE------------------------------------------- 60254 60255STRING COMBINE 60256 60257Name: 60258 STRING COMBINE 60259 60260Type: 60261 Let Subcommand 60262 60263Purpose: 60264 Combine strings or create a string from a list of arguments. 60265 60266Description: 60267 The STRING CONCATENATE command is used to concatenate strings. 60268 The STRING COMBINE command is a variant of STRING CONCATENATE 60269 that varies in the following ways: 60270 60271 1. With STRING CONCATENATE, the arguments are previously 60272 defined strings. With STRING COMBINE, Dataplot first 60273 checks to see if the argument is the name of a previously 60274 defined string. If yes, the contents of the string 60275 are added to the contents of the output string (i.e., 60276 the same as STRING CONCATENATE). However if the argument 60277 is of any type other than string or it is not a previously 60278 defined name, the argument is added to the output string 60279 as literal text. 60280 60281 2. The STRING COMBINE inserts a space between the input 60282 strings/arguments. With STRING CONCATENATE, this has 60283 to be done manually (i.e., you need to define a string 60284 that contains a space and use this between the other 60285 arguments). 60286 60287 3. The STRING COMBINE command supports the TO syntax. That 60288 is, entering 60289 60290 LET SOUT = STRING COMBINE X1 TO X8 60291 60292 is equivalent to entering 60293 60294 LET SOUT = STRING COMBINE X1 X2 X3 X4 X5 X6 X7 X8 60295 60296 This command has two primary uses: 60297 60298 1. As an alternative to STRING CONCATENATE when you want to 60299 automatically include a space between the input strings. 60300 60301 2. Most Dataplot analysis and graphics commands now support 60302 the TO syntax. However, there are cases, such as the 60303 LET command, where the TO syntax can be useful. The 60304 STRING COMBINE can be used to easily create a command 60305 string. This is demonstrated in the program example 60306 below. 60307 60308Syntax: 60309 LET <sout> = STRING COMBINE <s1> ... <sk> 60310 where <sout> is the name of the resulting string; 60311 and <s1> ... <sk> is a list of one or more previously defined strings. 60312 60313Examples: 60314 LET STALL = STRING COMBINE X1 X2 X3 60315 LET STALL = STRING COMBINE X1 TO X8 60316 60317Note: 60318 The name of the output string can be the same as one of the 60319 input strings. For example, 60320 60321 LET STRING S1 = One 60322 LET STRING S2 = Two 60323 LET STRING S3 = Three 60324 LET SOUT = STRING COMBINE S1 S2 S3 60325 60326Note: 60327 By default, a space character is used as the separator character. 60328 To specify a different separator command, enter 60329 60330 SET STRING SEPARATOR <char> 60331 60332 where <char> denotes the character to be used as the separator. 60333 60334Note: 60335 The total number of characters that DATAPLOT can use for storing 60336 functions and strings is set when DATAPLOT is built. The current 60337 default (11/2008) is 50,000 characters. Previous versions may set 60338 this limit at 1,000 or 10,000 characters. This limit applies to 60339 the combined number of characters for all functions and strings. 60340 60341Default: 60342 None 60343 60344Synonyms: 60345 None 60346 60347Related Commands: 60348 STRING CONCATENATE = Concatenate two or more strings. 60349 & = Concatenate two strings. 60350 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 60351 LET FUNCTION = Defines a function. 60352 LET STRING = Defines a string. 60353 READ STRING = Reads a string from a file. 60354 SUBTRING = Extract a substring from an existing string. 60355 STRING INDEX = Extract the start/stop positions of a substring 60356 within a string. 60357 STRING EDIT = Edit a string. 60358 STRING LENGTH = Return the length of a string. 60359 STRING MERGE = Insert a string into another string without 60360 overwrite. 60361 STRING REPLACE = Insert a string into another string with 60362 overwrite. 60363 LOWER CASE = Convert a string to lower case. 60364 UPPER CASE = Convert a string to upper case. 60365 CHARACTER = Convert numeric values to strings based on 60366 the ASCII collating sequence. 60367 ICHAR = Convert a string to numeric values based on 60368 the ASCII collating sequence. 60369 GROUP LABEL = Define the text for group labels. 60370 60371Applications: 60372 Data Management 60373 60374Implementation Date: 60375 2018/02 60376 2019/12: Added SET STRING SEPARATOR 60377 60378Program 1: 60379 SKIP 25 60380 READ BOXREACT.DAT Y X1 TO X5 60381 LET STALL = STRING COMBINE X1 TO X5 60382 LET CONFTAG1 CONFTAG2 = DEX CONFOUND ^STALL 60383 60384-----STRING COMPARE----------------------------------------------------- 60385 60386STRING COMPARE 60387 60388Name: 60389 STRING COMPARE 60390 60391Type: 60392 Let Subcommand 60393 60394Purpose: 60395 Compare two strings and return a 1 if they are identical and 60396 return a 0 if they are not. 60397 60398Syntax: 60399 LET <ival> = STRING COMPARE <s1> <s2> 60400 where <ival> is a parameter containing a 1 if the strings are 60401 identical and 0 if they are not; 60402 <s1> is the name of the first string; 60403 and <s2> is the name of the second string. 60404 60405Examples: 60406 LET IVAL = STRING COMPARE S1 S2 60407 60408Default: 60409 None 60410 60411Synonyms: 60412 None 60413 60414Related Commands: 60415 LET FUNCTION = Defines a function. 60416 LET STRING = Defines a string. 60417 READ STRING = Reads a string from a file. 60418 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 60419 & = Concatenate two strings. 60420 SUBTRING = Extract a substring from an existing string. 60421 STRING LENGTH = Return the length of the string. 60422 STRING INDEX = Extract the start/stop positions of a substring 60423 within a string. 60424 STRING CONCATENATE = Concatenate one or more previously defined 60425 strings. 60426 STRING EDIT = Edit a string. 60427 STRING MERGE = Insert a string into another string without 60428 overwrite. 60429 STRING REPLACE = Insert a string into another string with 60430 overwrite. 60431 LOWER CASE = Convert a string to lower case. 60432 UPPER CASE = Convert a string to upper case. 60433 CHARACTER = Convert numeric values to strings based on 60434 the ASCII collating sequence. 60435 ICHAR = Convert a string to numeric values based on 60436 the ASCII collating sequence. 60437 GROUP LABEL = Define the text for group labels. 60438 60439Applications: 60440 Data Management 60441 60442Implementation Date: 60443 1/2011 60444 60445Program: 60446 LET STRING S1 = file23.dat 60447 LET STRING S2 = file13.dat 60448 LET STRING S3 = file23.dat 60449 LET IVAL1 = STRING COMPARE S1 S2 60450 LET IVAL2 = STRING COMPARE S1 S3 60451 60452 The resulting values of IVAL1 and IVAL2 are 0 and 1, respectively. 60453 60454-----STRING COMPARE AND REPLACE-------------------------------------------- 60455 60456STRING COMPARE AND REPLACE 60457 60458Name: 60459 STRING COMPARE AND REPLACE 60460 60461Type: 60462 Let Subcommand 60463 60464Purpose: 60465 Compare a string to a list of strings and if a match is found 60466 define a replacement string. 60467 60468Description: 60469 This is a specialized command that was developed to improve 60470 performance in the EST.DP macro used by the 10-step macros for 60471 the analysis of 2-level full or fractional factorial designs. 60472 60473 The specific code that motivated this command was 60474 60475 loop for j1 = 1 1 numeff 60476 let string stefc^j1 = -999 60477 let string stprobe = ^stmain^j1 60478 loop for j2 = 1 1 numconf 60479 let string starch = ^stt^j2 60480 if stprobe = starch 60481 let string stefc^j1 = ^stc^j2 60482 end if 60483 end loop 60484 end loop 60485 60486 In this code, we are looping over the main factors. For 60487 each main factor, a string is compared to a list of strings. 60488 The numconf parameter defines the number of strings being 60489 compared. This value can grow fairly large. For example, 60490 for a 2**(8-4) design, numconf is 96. If a match is 60491 found, a new string (stefc^j1) is set to a string that 60492 is not in the list being compared (^stc^j2). 60493 60494 The updated code using the STRING AND REPLACE command is 60495 60496 loop for j1 = 1 1 numeff 60497 let string stefc^j1 = -999 60498 let stefc^j1 = string compare and replace stmain^j1 stc ... 60499 stt1 to stt^numconf 60500 end loop 60501 60502 This command eliminates the inner loop. For our 2**(8-4) 60503 example, this reduces the number of loop iterations from 60504 8*96 = 768 to 8. The string stmain^j1 is being compared 60505 to the strings stt1 to stt^numconf. If stt9 matches stmain^j1, 60506 the stefc^j1 is set equal to stc9. That is, the replacement 60507 string defines a base name to which the index of the matching 60508 string is appended to define the replacement string name. 60509 60510 If in our example, the string "stc" is a previously defined 60511 string, then this would be used rather than "stc9". 60512 60513Syntax: 60514 LET <sout> = STRING COMPARE AND REPLACE <sorg> <sold> <srepl> 60515 <sc1> ... <sck> 60516 where <sout> is the name of the resulting string; 60517 <sorg> is a pre-existing string that will be compared 60518 to each of <sc1> ... <sck>; 60519 <srepl> is pre-existing string that will be set to 60520 <sout> if a match is found; 60521 and where <sc1> ... <sck> is a list of pre-existing strings. 60522 60523 If <srepl> does not exist but <srepl1> ... <sreplk> do exist, 60524 the replacement string will be <sreplj> where j denotes the 60525 index of the match. 60526 60527 If no match is found, <sout> will not be created. 60528 60529 The TO syntax can be used for <sc1> ... <sck>. 60530 60531Examples: 60532 LET STRING STNEW = STRING COMPARE AND REPLACE SOLD SREPLACE ... 60533 S1 S2 S3 S4 S5 S6 60534 LET STRING STNEW = STRING COMPARE AND REPLACE SOLD SREPLACE ... 60535 S1 TO S6 60536 60537Default: 60538 None 60539 60540Synonyms: 60541 None 60542 60543Related Commands: 60544 LET FUNCTION = Defines a function. 60545 LET STRING = Defines a string. 60546 READ STRING = Reads a string from a file. 60547 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 60548 & = Concatenate two strings. 60549 SUBTRING = Extract a substring from an existing string. 60550 STRING EDIT = Edit the contents of a string. 60551 STRING INDEX = Extract the start/stop positions of a substring 60552 within a string. 60553 STRING CONCATENATE = Concatenate one or more previously defined 60554 strings. 60555 STRING LENGTH = Return the length of a string. 60556 STRING MERGE = Insert a string into another string without 60557 overwrite. 60558 STRING REPLACE = Insert a string into another string with 60559 overwrite. 60560 LOWER CASE = Convert a string to lower case. 60561 UPPER CASE = Convert a string to upper case. 60562 CHARACTER = Convert numeric values to strings based on 60563 the ASCII collating sequence. 60564 ICHAR = Convert a string to numeric values based on 60565 the ASCII collating sequence. 60566 GROUP LABEL = Define the text for group labels. 60567 60568Applications: 60569 Data Management 60570 60571Implementation Date: 60572 2018/03 60573 60574Program: 60575 LET STRING S1 = One 60576 LET STRING S2 = Two 60577 LET STRING S3 = Three 60578 LET STRING S4 = Four 60579 LET STRING S5 = Five 60580 . 60581 LET STRING SOLD = Four 60582 LET STRING SREPL = String Found 60583 LET STRING SNEW = String Not Found 60584 LET SNEW = STRING COMPARE AND REPLACE SOLD SREPL S1 TO S5 60585 PRINT "SNEW: ^SNEW" 60586 60587-----STRING CONCATENATE------------------------------------------- 60588 60589STRING CONCATENATE 60590 60591Name: 60592 STRING CONCATENATE 60593 60594Type: 60595 Let Subcommand 60596 60597Purpose: 60598 Concatenate one or more strings. 60599 60600Description: 60601 This command allows you to concatenate strings. Although this 60602 can also be done using the "^" and "&" characters, using the 60603 STRING CONCATENATE command may result in Dataplot code that is 60604 somewhat easier to use and read (particularly when many strings 60605 are being concatenated). 60606 60607Syntax: 60608 LET <sout> = STRING CONCATENATE <s1> ... <sk> 60609 where <sout> is the name of the resulting string; 60610 and <s1> ... <sk> is a list of one or more previously defined strings. 60611 60612Examples: 60613 LET STRING S1 = file 60614 LET STRING S2 = 99 60615 LET STRING S3 = .dat 60616 LET SOUT = STRING CONCATENATE S1 S2 S3 60617 60618Note: 60619 The name of the new string can be the same as one of the 60620 previously defined strings. For example, 60621 60622 LET FNAME = FILE 60623 LET SINDEX = ^K 60624 LET SEXT = .DAT 60625 LET FNAME = STRING CONCATENATE FNAME SINDEX SEXT 60626 60627Note: 60628 All strings on the right hand side of the equal sign must be 60629 previously existing strings. That is, expressions are not allowed. 60630 For example, instead of 60631 60632 LET FNAME = STRING CONCATENATE FNAME ".txt" 60633 60634 you need to do 60635 60636 LET STRING SEXT = .txt 60637 LET FNAME = STRING CONCATENATE FNAME SEXT 60638 60639Note: 60640 The total number of characters that DATAPLOT can use for storing 60641 functions and strings is set when DATAPLOT is built. The current 60642 default (11/2008) is 50,000 characters. Previous versions may set 60643 this limit at 1,000 or 10,000 characters. This limit applies to 60644 the combined number of characters for all functions and strings. 60645 60646Default: 60647 None 60648 60649Synonyms: 60650 None 60651 60652Related Commands: 60653 & = Concatenate two strings. 60654 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 60655 LET FUNCTION = Defines a function. 60656 LET STRING = Defines a string. 60657 READ STRING = Reads a string from a file. 60658 SUBTRING = Extract a substring from an existing string. 60659 STRING INDEX = Extract the start/stop positions of a substring 60660 within a string. 60661 STRING EDIT = Edit a string. 60662 STRING LENGTH = Return the length of a string. 60663 STRING MERGE = Insert a string into another string without 60664 overwrite. 60665 STRING REPLACE = Insert a string into another string with 60666 overwrite. 60667 LOWER CASE = Convert a string to lower case. 60668 UPPER CASE = Convert a string to upper case. 60669 CHARACTER = Convert numeric values to strings based on 60670 the ASCII collating sequence. 60671 ICHAR = Convert a string to numeric values based on 60672 the ASCII collating sequence. 60673 GROUP LABEL = Define the text for group labels. 60674 60675Applications: 60676 Data Management 60677 60678Implementation Date: 60679 11/2008 60680 60681Program 1: 60682 LET STRING S1 = file 60683 LET STRING S2 = 23 60684 LET STRING S3 = .txt 60685 LET SOUT = STRING CONCATENATE S1 S2 S3 60686 60687 The resulting string SOUT will contain 60688 60689 file23.txt 60690 60691Program 2: 60692 . Assume we have variables X and Y in the files "file1.dat" to 60693 . "file10.dat" and we want to plot each of these in turn. 60694 . 60695 LET STRING SBASE = file 60696 LET STRING SEXT = xx 60697 TITLE CASE ASIS 60698 LOOP FOR K = 1 1 10 60699 LET STRING SINDEX = ^K 60700 LET FNAME = STRING CONCATENATE SBASE SINDEX SEXT 60701 READ ^FNAME Y X 60702 TITLE Data from File ^SOUT 60703 PLOT Y X 60704 DELETE Y X 60705 END OF LOOP 60706 60707-----STRING CONTAIN---------------------------------------------- 60708 60709STRING CONTAIN 60710 60711Name: 60712 STRING CONTAIN 60713 60714Type: 60715 Let Subcommand 60716 60717Purpose: 60718 Return a 1 if a string contains a specified substring and a 0 if it 60719 does not. 60720 60721Syntax: 60722 LET <iflag> = STRING CONTAIN <s1> <s2> 60723 where <iflag> is a parameter containing a 1 if <s1> contains 60724 the string <s2> and 0 otherwise; 60725 <s1> is the name of a pre-existing string; 60726 and <s2> is the name of a pre-existing string. 60727 60728Examples: 60729 LET IFLAG = STRING CONTAINS SORG SMATCH 60730 60731Note: 60732 The strings on the right hand side of the equal sign must be 60733 previously existing strings. That is, expressions are not allowed. 60734 For example, the following will result in an error message 60735 60736 LET IFLAG = STRING CONTAINS "alan.heckert@nist.gov" "alan" 60737 60738 you need to do 60739 60740 LET STRING SORG = alan.heckert@nist.gov 60741 LET STRING SMATCH = alan 60742 LET SOUT = STRING CONTAINS SORG SMATCH 60743 60744 The name on the left hand side of the equal sign should either be a 60745 previously existing parameter or not previously defined. If it is a 60746 previously existing string, variable, or matrix name, an error will 60747 be reported and the requested parameter will not be created. 60748 60749Note: 60750 The total number of characters that DATAPLOT can use for storing 60751 functions and strings is set when DATAPLOT is built. The current 60752 default (11/2008) is 50,000 characters. Previous versions may set 60753 this limit at 1,000 or 10,000 characters. This limit applies to 60754 the combined number of characters for all functions and strings. 60755 60756Default: 60757 None 60758 60759Synonyms: 60760 None 60761 60762Related Commands: 60763 SUBTRING = Extract a substring from an existing string. 60764 STRING ENDS WITH = Check whether a string starts with a 60765 specified substring. 60766 STRING ENDS WITH = Check whether a string ends with a 60767 specified substring. 60768 LET STRING = Defines a string. 60769 READ STRING = Reads a string from a file. 60770 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 60771 & = Concatenate two strings. 60772 STRING LENGTH = Return the length of the string. 60773 STRING INDEX = Extract the start/stop positions of a substring 60774 within a string. 60775 STRING CONCATENATE = Concatenate one or more previously defined 60776 strings. 60777 STRING EDIT = Edit a string. 60778 STRING MERGE = Insert a string into another string without 60779 overwrite. 60780 STRING REPLACE = Insert a string into another string with 60781 overwrite. 60782 LOWER CASE = Convert a string to lower case. 60783 UPPER CASE = Convert a string to upper case. 60784 CHARACTER = Convert numeric values to strings based on 60785 the ASCII collating sequence. 60786 ICHAR = Convert a string to numeric values based on 60787 the ASCII collating sequence. 60788 GROUP LABEL = Define the text for group labels. 60789 60790Applications: 60791 Data Management 60792 60793Implementation Date: 60794 2019/01 60795 60796Program: 60797 LET STRING S1 = alan.heckert@gmail.com 60798 LET STRING S2 = alan 60799 LET IFLAG = STRING CONTAINS S1 S2 60800 60801-----STRING DELETE------------------------------------------ 60802 60803STRING DELETE 60804 60805Name: 60806 STRING DELETE 60807 60808Type: 60809 Let Subcommand 60810 60811Purpose: 60812 Remove a user specified list of characters from a string. 60813 60814Description: 60815 The STRING REMOVE SPACES, STRING REMOVE WHITESPACE, and STRING 60816 REMOVE PUNCTUATION commands can be used to remove certain pre-defined 60817 sets of characters from a string. However, there may be times when 60818 you need to specifiy a specific list of characters to remove. The 60819 STRING DELETE command can be used to do that. 60820 60821Syntax: 60822 LET <sout> = STRING DELETE <sorg> <slist> 60823 where <sout> is the name of the resulting string; 60824 <sorg> is the name of the original string; 60825 and <slist> is the name of the original string. 60826 60827 You specifiy the characters you want to delete by defining the 60828 <slist> string. That is, <sorg> will be checked against each 60829 character in <slist>. 60830 60831Examples: 60832 LET SOUT = STRING DELETE STIN SLIST 60833 60834Note: 60835 The name of the new string can be the same as the original 60836 string. For example, 60837 60838 LET STR = STRING DELETE STR SDELETE 60839 60840 In this case, STR will now contain the the string with the 60841 characters removed rather than the original string. 60842 60843Note: 60844 The strings on the right hand side of the equal sign must be 60845 previously existing strings. That is, expressions are not allowed. 60846 For example, the following will result in an error message 60847 60848 LET STOUT = STRING DELETE "alan.heckert@nist.gov" "@" 60849 60850 you need to do 60851 60852 LET STRING SORG = alan.heckert@nist.gov 60853 LET STRING SLIST = @ 60854 LET SOUT = STRING DELETE SORG SLIST 60855 60856 The name on the left hand side of the equal sign may be a 60857 previously existing string. However, if it is a previously 60858 existing parameter, variable, or matrix name, an error will 60859 be reported and the requested string will not be created. 60860 60861Note: 60862 The total number of characters that DATAPLOT can use for storing 60863 functions and strings is set when DATAPLOT is built. The current 60864 default (11/2008) is 50,000 characters. Previous versions may set 60865 this limit at 1,000 or 10,000 characters. This limit applies to the 60866 combined number of characters for all functions and strings. 60867 60868Default: 60869 None 60870 60871Synonyms: 60872 None 60873 60874Related Commands: 60875 STRING REMOVE PUNCTUATION = Remove punctuatuin characters from a string. 60876 STRING REMOVE SPACE = Remove spaces from a string. 60877 STRING REMOVE WHITESPACE = Remove white space characters from a string. 60878 NUMBER OF WORDS = Return the number of words in a string. 60879 UPPER CASE = Convert a string to upper case. 60880 LOWER CASE = Convert a string to lower case. 60881 LET FUNCTION = Defines a function. 60882 LET STRING = Defines a string. 60883 READ STRING = Reads a string from a file. 60884 SUBSTITUTE CHARACTER (^) = Substitute the value of a string or 60885 parameter. 60886 CONCATENATE CHARACTER (&) = Concatenate two strings. 60887 SUBTRING = Extract a substring from an existing 60888 string. 60889 STRING INDEX = Extract the start/stop positions of a 60890 substring within a string. 60891 STRING CONCATENATE = Concatenate one or more previously 60892 defined strings. 60893 STRING EDIT = Edit a string. 60894 STRING MERGE = Insert a string into another string 60895 without overwrite. 60896 STRING LENGTH = Return the length of a string. 60897 STRING WORD = Extract a specified word from a string. 60898 CHARACTER = Convert numeric values to strings based 60899 on the ASCII collating sequence. 60900 ICHAR = Convert a string to numeric values based 60901 on the ASCII collating sequence. 60902 GROUP LABEL = Define the text for group labels. 60903 60904Applications: 60905 Data Management 60906 60907Implementation Date: 60908 2018/10 60909 60910Program: 60911 let string stin = abcdefgabcdefg 60912 let string slist = cde 60913 let stout = string delete stin slist 60914 print stin stout 60915 60916-----STRING EDIT----------------------------------------------------- 60917 60918STRING EDIT 60919 60920Name: 60921 STRING EDIT 60922 60923Type: 60924 Let Subcommand 60925 60926Purpose: 60927 Edit the contents of a string. 60928 60929Description: 60930 This command allows you to edit the contents of a previosuly defined 60931 string. 60932 60933 The STRING EDIT command involves three string: 60934 60935 1) The original string which we will call SORG. 60936 60937 2) A substring, which we will call SOLD, that contains the text 60938 to be changed. 60939 60940 3) A substring, which we will call SNEW, which contains the 60941 replacement text. 60942 60943 The STRING EDIT command searches the string SORG for the 60944 substring SOLD. If found, it replaces the SOLD text with 60945 the SNEW text. If no match is found, an error message is 60946 printed and the new string is not created. 60947 60948Syntax 1: 60949 LET <sout> = STRING EDIT <sorg> <sold> <snew> 60950 where <sout> is the name of the resulting string; 60951 <sorg> is the name of the original string to be edited; 60952 <sold> is the name of the match string; 60953 and where <snew> is the name of the replacement string. 60954 60955 This syntax edits the first occurence of <sold> only. 60956 60957Syntax 2: 60958 LET <sout> = STRING GLOBAL EDIT <sorg> <sold> <snew> 60959 where <sout> is the name of the resulting string; 60960 <sorg> is the name of the original string to be edited; 60961 <sold> is the name of the match string; 60962 and where <snew> is the name of the replacement string. 60963 60964 This syntax edits all occurences of <sold>. 60965 60966Examples: 60967 LET STRING S1 = filexx.dat 60968 LET STRING S2 = xx 60969 LET STRING S3 = 23 60970 LET SOUT = STRING EDIT S1 S2 S3 60971 60972 LET SOUT = STRING GLOBAL EDIT SIN SOLD SNEW 60973 60974Note: 60975 The name of the new string can be the same as the original string. 60976 For example, 60977 60978 LET FNAME = STRING EDIT FNAME SOLD SNEW 60979 60980Note: 60981 All three strings on the right hand side of the equal sign must be 60982 previously existing strings. That is, expressions are not allowed. 60983 For example, instead of 60984 60985 LET FNAME = STRING EDIT FNAME ".dat" ".txt" 60986 60987 you need to do 60988 60989 LET STRING SOLD = .dat 60990 LET STRING SNEW = .txt 60991 LET FNAME = STRING EDIT FNAME SOLD SNEW 60992 60993Note: 60994 The total number of characters that DATAPLOT can use for storing 60995 functions and strings is set when DATAPLOT is built. The current 60996 default (11/2008) is 50,000 characters. Previous versions may set 60997 this limit at 1,000 or 10,000 characters. This limit applies to 60998 the combined number of characters for all functions and strings. 60999 61000Note: 61001 Only the first occurrence that is matched is changed. That is, 61002 there is currently no "global" option and no option to specify 61003 that the second or third or last occurence be changed. 61004 61005 Also, there is currently no support for wild cards or regular 61006 expressions. 61007 61008Note: 61009 If you want the replacement string to be null (i.e., you want 61010 to delete the match string), then you can do the following 61011 61012 LET STRING SOUT = NULL() 61013 LET SOUT = STRING EDIT STIN SOLD SNEW 61014 61015 or 61016 61017 LET SOUT = STRING EDIT STIN NULL() SNEW 61018 61019 The use of "NULL()" is currently specific to this command. 61020 61021Default: 61022 None 61023 61024Synonyms: 61025 None 61026 61027Related Commands: 61028 LET FUNCTION = Defines a function. 61029 LET STRING = Defines a string. 61030 READ STRING = Reads a string from a file. 61031 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 61032 & = Concatenate two strings. 61033 SUBTRING = Extract a substring from an existing string. 61034 STRING INDEX = Extract the start/stop positions of a substring 61035 within a string. 61036 STRING CONCATENATE = Concatenate one or more previously defined 61037 strings. 61038 STRING LENGTH = Return the length of a string. 61039 STRING MERGE = Insert a string into another string without 61040 overwrite. 61041 STRING REPLACE = Insert a string into another string with 61042 overwrite. 61043 LOWER CASE = Convert a string to lower case. 61044 UPPER CASE = Convert a string to upper case. 61045 CHARACTER = Convert numeric values to strings based on 61046 the ASCII collating sequence. 61047 ICHAR = Convert a string to numeric values based on 61048 the ASCII collating sequence. 61049 GROUP LABEL = Define the text for group labels. 61050 61051Applications: 61052 Data Management 61053 61054Implementation Date: 61055 2008/11 61056 2015/02: Support for STRING GLOBAL EDIT<BR> 61057 2015/02: Support for "NULL()" for replacement string<BR> 61058 61059Program 1: 61060 LET STRING S1 = file23.dat 61061 LET STRING S2 = dat 61062 LET STRING S3 = txt 61063 LET SOUT = STRING EDIT S1 S2 S3 61064 61065 The resulting string SOUT will contain 61066 61067 file23.txt 61068 61069Program 2: 61070 . Assume we have variables X and Y in the files "file1.dat" to 61071 . "file10.dat" and we want to plot each of these in turn. 61072 . 61073 LET STRING SOLD = filexx.dat 61074 LET STRING S3 = xx 61075 TITLE CASE ASIS 61076 LOOP FOR K = 1 1 10 61077 LET STRING S2 = ^K 61078 LET FNAME = STRING EDIT SOLD S3 S2 61079 READ ^FNAME Y X 61080 TITLE Data from File ^SOUT 61081 PLOT Y X 61082 DELETE Y X 61083 END OF LOOP 61084 61085-----STRING ENDS WITH---------------------------------------------- 61086 61087STRING ENDS WITH 61088 61089Name: 61090 STRING ENDS WITH 61091 61092Type: 61093 Let Subcommand 61094 61095Purpose: 61096 Return a 1 if a string ends with a specified substring 61097 and a 0 if it does not. 61098 61099Syntax: 61100 LET <iflag> = STRING ENDS WITH <s1> <s2> 61101 where <iflag> is a parameter containing a 1 if <s1> ends 61102 with <s2> and 0 otherwise; 61103 <s1> is the name of a pre-existing string; 61104 and <s2> is the name of a pre-existing string. 61105 61106Examples: 61107 LET IFLAG = STRING ENDS WITH S1 S2 61108 61109Note: 61110 The strings on the right hand side of the equal sign must be 61111 previously existing strings. That is, expressions are not allowed. 61112 For example, the following will result in an error message 61113 61114 LET IFLAG = STRING ENDS WITH "alan.heckert@nist.gov" "nist.gov" 61115 61116 you need to do 61117 61118 LET STRING SORG = alan.heckert@nist.gov 61119 LET STRING SMATCH = nist.gov 61120 LET SOUT = STRING ENDS WITH SORG SMATCH 61121 61122 The name on the left hand side of the equal sign should either be a 61123 previously existing parameter or not previously defined. If it is a 61124 previously existing string, variable, or matrix name, an error will 61125 be reported and the requested parameter will not be created. 61126 61127Note: 61128 The total number of characters that DATAPLOT can use for storing 61129 functions and strings is set when DATAPLOT is built. The current 61130 default (11/2008) is 50,000 characters. Previous versions may set 61131 this limit at 1,000 or 10,000 characters. This limit applies to 61132 the combined number of characters for all functions and strings. 61133 61134Default: 61135 None 61136 61137Synonyms: 61138 None 61139 61140Related Commands: 61141 STRING STARTS WITH = Check whether a string starts with a 61142 specified substring. 61143 LET FUNCTION = Defines a function. 61144 LET STRING = Defines a string. 61145 READ STRING = Reads a string from a file. 61146 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 61147 & = Concatenate two strings. 61148 SUBTRING = Extract a substring from an existing string. 61149 STRING LENGTH = Return the length of the string. 61150 STRING INDEX = Extract the start/stop positions of a substring 61151 within a string. 61152 STRING CONCATENATE = Concatenate one or more previously defined 61153 strings. 61154 STRING EDIT = Edit a string. 61155 STRING MERGE = Insert a string into another string without 61156 overwrite. 61157 STRING REPLACE = Insert a string into another string with 61158 overwrite. 61159 LOWER CASE = Convert a string to lower case. 61160 UPPER CASE = Convert a string to upper case. 61161 CHARACTER = Convert numeric values to strings based on 61162 the ASCII collating sequence. 61163 ICHAR = Convert a string to numeric values based on 61164 the ASCII collating sequence. 61165 GROUP LABEL = Define the text for group labels. 61166 61167Applications: 61168 Data Management 61169 61170Implementation Date: 61171 2018/10 61172 61173Program: 61174 LET STRING S1 = alan.heckert@gmail.com 61175 LET STRING S2 = gmail.com 61176 LET IFLAG = STRING ENDS WITH S1 S2 61177 61178-----STRING EXPAND WHITESPACE---------------------------------------- 61179 61180STRING EXPAND WHITESPACE 61181 61182Name: 61183 STRING EXPAND WHITESPACE 61184 61185Type: 61186 Let Subcommand 61187 61188Purpose: 61189 Replace non-printing characters in a string with a single space 61190 character. 61191 61192Description: 61193 When extracting strings from external sources, you may encounter 61194 non-printing characters. The STRING REMOVE WHITESPACE can be used 61195 to simply remove these characters from the string. Alternatively, 61196 the STRING EXPAND WHITESPACE can be used to convert non-printing 61197 characters to a single space character. 61198 61199 The tab character is treated somewhat differently. Specifically, 61200 you can use the command 61201 61202 SET TAB EXPAND <value> 61203 61204 to specify how tab characters are handled. Specifically, if <value> 61205 is 0, then the tab character is retained in the string (no space 61206 is added). If <value> is a positive integer, the tab character 61207 will be replaced with <value> spaces. 61208 61209 The non-printing characters are the ones with codes 0 to 31 and 127 61210 in the ASCII collating sequence. Currently, Dataplot only checks 61211 for characters in the 0 - 127 range of the ASCII collating sequence. 61212 61213Syntax: 61214 LET <sout> = STRING EXPAND WHITESPACE <sorg> 61215 where <sout> is the name of the resulting string; 61216 and <sorg> is the name of the original string. 61217 61218Examples: 61219 LET SOUT = STRING EXPAND WHITESPACE STIN 61220 61221Note: 61222 The name of the new string can be the same as the original 61223 string. For example, 61224 61225 LET STR = STRING EXPAND WHITESPACE STR 61226 61227 In this case, STR will now contain the the string with all white 61228 space characters removed rather than the original string. 61229 61230Note: 61231 The string on the right hand side of the equal sign must be a 61232 previously existing string. That is, expressions are not allowed. 61233 For example, the following will result in an error message 61234 61235 LET STOUT = STRING EXPAND WHITESPACE "a b c d" 61236 61237 you need to do 61238 61239 LET STRING SORG = a b c d 61240 LET SOUT = STRING EXPAND WHITESPACE SORG 61241 61242 The name on the left hand side of the equal sign may be a 61243 previously existing string. However, if it is a previously 61244 existing parameter, variable, or matrix name, an error will 61245 be reported and the requested string will not be created. 61246 61247Note: 61248 The total number of characters that DATAPLOT can use for storing 61249 functions and strings is set when DATAPLOT is built. The current 61250 default (11/2008) is 50,000 characters. Previous versions may set 61251 this limit at 1,000 or 10,000 characters. This limit applies to the 61252 combined number of characters for all functions and strings. 61253 61254Default: 61255 None 61256 61257Synonyms: 61258 None 61259 61260Related Commands: 61261 STRING REMOVE WHITE SPACE = Remove white space and non-printing 61262 characters from a string. 61263 STRING REMOVE SPACE = Remove spaces from a string. 61264 STRING REMOVE PUNCTUATION = Remove punctuation from a string. 61265 STRING DELETE = Remove user specifed characters from a 61266 string. 61267 NUMBER OF WORDS = Return the number of words in a string. 61268 UPPER CASE = Convert a string to upper case. 61269 LOWER CASE = Convert a string to lower case. 61270 LET FUNCTION = Defines a function. 61271 LET STRING = Defines a string. 61272 READ STRING = Reads a string from a file. 61273 SUBSTITUTE CHARACTER (^) = Substitute the value of a string or 61274 parameter. 61275 CONCATENATE CHARACTER (&) = Concatenate two strings. 61276 SUBTRING = Extract a substring from an existing 61277 string. 61278 STRING INDEX = Extract the start/stop positions of a 61279 substring within a string. 61280 STRING CONCATENATE = Concatenate one or more previously 61281 defined strings. 61282 STRING EDIT = Edit a string. 61283 STRING MERGE = Insert a string into another string 61284 without overwrite. 61285 STRING LENGTH = Return the length of a string. 61286 STRING WORD = Extract a specified word from a string. 61287 CHARACTER = Convert numeric values to strings based 61288 on the ASCII collating sequence. 61289 ICHAR = Convert a string to numeric values based 61290 on the ASCII collating sequence. 61291 GROUP LABEL = Define the text for group labels. 61292 61293Applications: 61294 Data Management 61295 61296Implementation Date: 61297 2019/02 61298 61299Program: 61300 set tab expand 3 61301 read string tab.dat t 61302 let tout = string expand whitespace t 61303 print t tout 61304 61305-----STRING HAMMING DISTANCE----------------------------------------- 61306 61307STRING HAMMING DISTANCE 61308 61309Name: 61310 STRING HAMMING DISTANCE 61311 61312Type: 61313 Let Subcommand 61314 61315Purpose: 61316 Given two equal length strings, returns the count of the number 61317 of character positions that match. 61318 61319Syntax: 61320 LET <dist> = STRING HAMMING DISTANCE <s1> <s2> 61321 where <dist> is a parameter containing the Hamming distance; 61322 <s1> is the name of a pre-existing string; 61323 and <s2> is the name of a pre-existing string. 61324 61325 The <s1> and <s2> strings must be the same length. 61326 61327Examples: 61328 LET IFLAG = STRING HAMMING DISTANCE S1 S2 61329 61330Note: 61331 The strings on the right hand side of the equal sign must be 61332 previously existing strings. That is, expressions are not allowed. 61333 For example, the following will result in an error message 61334 61335 LET IFLAG = STRING HAMMING DISTANCE "gmail.com" "gmail.org" 61336 61337 you need to do 61338 61339 LET STRING S1 = gmail.com 61340 LET STRING S2 = gmail.org 61341 LET SOUT = STRING HAMMING DISTANCE S1 S2 61342 61343 The name on the left hand side of the equal sign may be a 61344 previously existing parameter. However, if it is a previously 61345 existing string, variable, or matrix name, an error will 61346 be reported and the requested parameter will not be created. 61347 61348Default: 61349 None 61350 61351Synonyms: 61352 None 61353 61354Related Commands: 61355 HAMMING DISTANCE = Compute the Hamming distance of two 61356 vectors. 61357 EUCLIDEAN DISTANCE = Compute the Euclidean distance. 61358 COSINE DISTANCE = Compute the cosine distance. 61359 MANHATTAN DISTANCE = Compute the Manhattan distance. 61360 LET STRING = Defines a string. 61361 READ STRING = Reads a string from a file. 61362 61363Applications: 61364 Data Management 61365 61366Implementation Date: 61367 2018/10 61368 61369Program: 61370 LET STRING S1 = 1011100111 61371 LET STRING S2 = 1010010110 61372 LET DIST = STRING HAMMING DISTANCE S1 S2 61373 61374-----STRING INDEX----------------------------------------------------- 61375 61376STRING INDEX 61377 61378Name: 61379 STRING INDEX 61380 STRING RIGHT INDEX 61381 61382Type: 61383 Let Subcommand 61384 61385Purpose: 61386 Return the start and stop position of a substring within a 61387 string. 61388 61389Syntax 1: 61390 LET <nstart> <nstop> = STRING INDEX <sorg> <smatch> 61391 where <nstart> is a parameter containing the returned start position; 61392 <nstop> is a parameter containing the returned stop position; 61393 <sorg> is the original string; 61394 and <smatch> is the substring to be matched within <sorg>. 61395 61396 This syntax searches <sorg> from left to right. 61397 61398Syntax 2: 61399 LET <nstart> <nstop> = STRING RIGHT INDEX <sorg> <smatch> 61400 where <nstart> is a parameter containing the returned start position; 61401 <nstop> is a parameter containing the returned stop position; 61402 <sorg> is the original string; 61403 and <smatch> is the substring to be matched within <sorg>. 61404 61405 This syntax searches <sorg> from right to left. 61406 61407Examples: 61408 LET NSTART NSTOP = STRING INDEX S1 S2 61409 LET NSTART NSTOP = STRING RIGHT INDEX SORG SMATCH 61410 61411Note: 61412 Both of the strings on the right hand side of the equal sign 61413 must be previously defined strings. String expressions are 61414 not allowed. So 61415 61416 LET NSTART NSTOP = STRING INDEX SORG ".dat" 61417 61418 should be coded as 61419 61420 LET STRING S2 = .dat 61421 LET NSTART NSTOP = STRING INDEX SORG S2 61422 61423Default: 61424 None 61425 61426Synonyms: 61427 STRING FIND is a synonym for STRING INDEX 61428 STRING RIGHT FIND is a synonym for STRING RIGHT INDEX 61429 61430Related Commands: 61431 LET FUNCTION = Defines a function. 61432 LET STRING = Defines a string. 61433 READ STRING = Reads a string from a file. 61434 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 61435 & = Concatenate two strings. 61436 SUBTRING = Extract a substring from an existing string. 61437 STRING LENGTH = Return the length of a string. 61438 STRING CONCATENATE = Concatenate one or more previously defined 61439 strings. 61440 STRING EDIT = Edit a string. 61441 STRING MERGE = Insert a string into another string without 61442 overwrite. 61443 STRING REPLACE = Insert a string into another string with 61444 overwrite. 61445 LOWER CASE = Convert a string to lower case. 61446 UPPER CASE = Convert a string to upper case. 61447 CHARACTER = Convert numeric values to strings based on 61448 the ASCII collating sequence. 61449 ICHAR = Convert a string to numeric values based on 61450 the ASCII collating sequence. 61451 GROUP LABEL = Define the text for group labels. 61452 61453Applications: 61454 Data Management 61455 61456Implementation Date: 61457 2008/11 61458 2018/10: Added STRING RIGHT INDEX 61459 2018/10: Added STRING FIND as a synonym for STRING INDEX 61460 61461Program: 61462 LET STRING S1 = file23.dat 61463 LET STRING S2 = 23 61464 LET NSTART NSTOP = STRING INDEX S1 S2 61465 61466 The resulting values of NSTART and NSTOP are 5 and 6, 61467 respectively. 61468 61469-----STRING INTERACTION------------------------------------------------- 61470 61471STRING INTERACTION 61472 61473Name: 61474 STRING INTERACTION 61475 61476Type: 61477 Let Subcommand 61478 61479Purpose: 61480 Given a list of parameters, create a string that represents 61481 an interaction term. 61482 61483Description: 61484 This is a specialized command that is used in creating labels 61485 in the context of a 2-level full or fractional factorial design. 61486 61487 As an example, suppose we have the parameters J1, J2, and J3 61488 where J1 = 3, J2 = 1, and J3 = 5, then this command will create a 61489 string containing 61490 61491 X3 * X1 * X5 61492 61493 The parameters identify factors of interest, so they will 61494 typically contain integers in the range 1 to k where k is the 61495 number of factors in the design. If the parameter is negative, 61496 then that parameter will not be included in the output string. 61497 61498Syntax: 61499 LET <sout> = STRING INTERACTION <j1> ... <jk> 61500 where <sout> is the name of the resulting string; 61501 and <j1> ... <jk> is a list of parameters. 61502 61503Examples: 61504 LET SOUT = STRING INTERACTION J1 J2 J3 61505 LET SOUT = STRING INTERACTION J1 J2 J3 J4 J5 61506 61507Note: 61508 The total number of characters that DATAPLOT can use for storing 61509 functions and strings is set when DATAPLOT is built. The current 61510 default (11/2008) is 50,000 characters. Previous versions may set 61511 this limit at 1,000 or 10,000 characters. This limit applies to the 61512 combined number of characters for all functions and strings. 61513 61514Default: 61515 None 61516 61517Synonyms: 61518 None 61519 61520Related Commands: 61521 NUMBER OF WORDS = Return the number of words in a string. 61522 UPPER CASE = Convert a string to upper case. 61523 LOWER CASE = Convert a string to lower case. 61524 LET FUNCTION = Defines a function. 61525 LET STRING = Defines a string. 61526 READ STRING = Reads a string from a file. 61527 SUBSTITUTE CHARACTER (^) = Substitute the value of a string or 61528 parameter. 61529 CONCATENATE CHARACTER (&) = Concatenate two strings. 61530 BLANK STRING = Create a blank string. 61531 SUBTRING = Extract a substring from an existing 61532 string. 61533 STRING INDEX = Extract the start/stop positions of a 61534 substring within a string. 61535 STRING CONCATENATE = Concatenate one or more previously 61536 defined strings. 61537 STRING EDIT = Edit a string. 61538 STRING MERGE = Insert a string into another string 61539 without overwrite. 61540 STRING LENGTH = Return the length of a string. 61541 CHARACTER = Convert numeric values to strings based 61542 on the ASCII collating sequence. 61543 ICHAR = Convert a string to numeric values based 61544 on the ASCII collating sequence. 61545 GROUP LABEL = Define the text for group labels. 61546 61547Applications: 61548 2-Level Full and Fractional Factorial Designs 61549 61550Implementation Date: 61551 2018/04 61552 61553Program: 61554 . Step 1: Define inputs 61555 . 61556 let j1 = 1 61557 let j2 = 2 61558 let j3 = 3 61559 let j4 = 4 61560 let j5 = 5 61561 . 61562 . Step 2: Execute the command 61563 . 61564 let stnew = string interaction j1 j2 j3 j4 j5 61565 . 61566 let j4 = -9999 61567 let j5 = -9999 61568 let stnew2 = string interaction j1 j2 j3 j4 j5 61569 . 61570 print "stnew: ^stnew" 61571 print "stnew2: ^stnew2" 61572 61573-----STRING JUSTIFY------------------------------------------------- 61574 61575STRING JUSTIFY 61576 61577Name: 61578 STRING <LEFT/CENTER/RIGHT> JUSTIFY 61579 61580Type: 61581 Let Subcommand 61582 61583Purpose: 61584 Left, center, or right justify a string. 61585 61586Description: 61587 The STRING REMOVE SPACES command can be used to remove leading or 61588 trailing spaces from a string. This command allows you to add 61589 leading or trailing spaces. 61590 61591 That is, you specify the desired length of the string. If LEFT 61592 justification is requested, trailing spaces will be added to the end 61593 of the string so that the string has the desired length. Likewise, if 61594 RIGHT justification is requested, leading spaces will be added to the 61595 beginning of the string. If CENTER justification is requested, both 61596 leading and trailing spaces will be added. 61597 61598 If the requested string already has a length greater than the 61599 requested length, the output string will be set equal to the input 61600 string. 61601 61602 By default, the added leading and trailing characters are spaces. 61603 You can specify a different character by entering the command 61604 61605 SET STRING JUSTIFICATION CHARACTER <char> 61606 61607 To reset the default of spaces, enter 61608 61609 SET STRING JUSTIFICATION CHARACTER SPACE 61610 61611Syntax 1: 61612 LET <sout> = STRING LEFT JUSTIFY <sorg> <nlen> 61613 where <sout> is the name of the resulting string; 61614 <sorg> is the name of the original string; 61615 and <nlen> is the desired length of the output string. 61616 61617 If n1 is the length of the original string and <nlen> is n2, then 61618 n2 - n1 spaces will be added to the end of <sorg>. If n1 >= n2, 61619 <sout> will be set equal to <sorg>. 61620 61621Syntax 2: 61622 LET <sout> = STRING RIGHT JUSTIFY <sorg> <nlen> 61623 where <sout> is the name of the resulting string; 61624 <sorg> is the name of the original string; 61625 and <nlen> is the desired length of the output string. 61626 61627 If n1 is the length of the original string and <nlen> is n2, then 61628 n2 - n1 spaces will be added to the beginning of <sorg>. If n1 >= n2, 61629 <sout> will be set equal to <sorg>. 61630 61631Syntax 3: 61632 LET <sout> = STRING CENTER JUSTIFY <sorg> <nlen> 61633 where <sout> is the name of the resulting string; 61634 <sorg> is the name of the original string; 61635 and <nlen> is the desired length of the output string. 61636 61637 If n1 is the length of the original string and <nlen> is n2, then 61638 (n2 - n1)/2 spaces will be added to the beginning of <sorg> and 61639 (n2 - n1)/2 spaces will be added to the end of <sorg>. If n2 - n1 61640 is odd, the extra space will be added to the beginning of <sorg>. If 61641 n1 >= n2, <sout> will be set equal to <sorg>. 61642 61643Examples: 61644 LET SOUT = STRING LEFT JUSTIFY S1 NLEN 61645 LET SOUT = STRING RIGHT JUSTIFY S1 20 61646 LET SOUT = STRING CENTER JUSTIFY S1 NLEN 61647 61648Note: 61649 The name of the new string can be the same as the original 61650 string. For example, 61651 61652 LET SORG = STRING RIGHT JUSTIFY SORG NLEN 61653 61654Note: 61655 The string on the right hand side of the equal sign must be a 61656 previously existing string. That is, expressions are not allowed. 61657 For example, instead of 61658 61659 LET SOUT = STRING RIGHT JUSTIFY "XXXXX" 10 61660 61661 you need to do 61662 61663 LET STRING SORG = XXXXX 61664 LET SOUT = STRING RIGHT JUSTIFY SORG 10 61665 61666 The length parameter can be either a parameter or a numeric 61667 value. However, it cannot be a numeric expression. So 61668 61669 LET SOUT = STRING RIGHT JUSTIFY SORG 10 61670 LET SOUT = STRING RIGHT JUSTIFY SORG NLEN 61671 61672 are both allowed but 61673 61674 LET SOUT = STRING RIGHT JUSTIFY SORG NLEN/2 61675 61676 is not allowed. You would need to enter this as 61677 61678 LET NLEN2 = NLEN/2 61679 LET SOUT = STRING RIGHT JUSTIFY SORG NLEN2 61680 61681Note: 61682 The total number of characters that DATAPLOT can use for storing 61683 functions and strings is set when DATAPLOT is built. The current 61684 default (11/2008) is 50,000 characters. Previous versions may set 61685 this limit at 1,000 or 10,000 characters. This limit applies to the 61686 combined number of characters for all functions and strings. 61687 61688Default: 61689 None 61690 61691Synonyms: 61692 None 61693 61694Related Commands: 61695 LET FUNCTION = Defines a function. 61696 LET STRING = Defines a string. 61697 READ STRING = Reads a string from a file. 61698 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 61699 & = Concatenate two strings. 61700 STRING INDEX = Extract the start/stop positions of a substring 61701 within a string. 61702 STRING CONCATENATE = Concatenate one or more previously defined 61703 strings. 61704 STRING LENGTH = Return the length of a string. 61705 STRING EDIT = Edit a string. 61706 STRING MERGE = Insert a string into another string without 61707 overwrite. 61708 STRING REPLACE = Insert a string into another string with 61709 overwrite. 61710 LOWER CASE = Convert a string to lower case. 61711 UPPER CASE = Convert a string to upper case. 61712 CHARACTER = Convert numeric values to strings based on 61713 the ASCII collating sequence. 61714 ICHAR = Convert a string to numeric values based on 61715 the ASCII collating sequence. 61716 GROUP LABEL = Define the text for group labels. 61717 61718Applications: 61719 Data Management 61720 61721Implementation Date: 61722 2019/01 61723 61724Program: 61725 SKIP 25 61726 READ BERGER1.DAT Y X 61727 FIT Y X 61728 LET CC = CORRELATION Y X 61729 . 61730 LET STRING S1 = A0: 61731 LET STRING S2 = A1: 61732 LET STRING S3 = CORR: 61733 LET NLEN = 8 61734 LET S1 = STRING LEFT JUSTIFY S1 NLEN 61735 LET S2 = STRING LEFT JUSTIFY S2 NLEN 61736 LET S3 = STRING LEFT JUSTIFY S3 NLEN 61737 LET A0 = ROUND(A0,2) 61738 LET A1 = ROUND(A1,2) 61739 LET CC = ROUND(CC,2) 61740 LEGEND 1 ^S1 ^A0 61741 LEGEND 2 ^S2 ^A1 61742 LEGEND 3 ^S3 ^CC 61743 . 61744 CHARACTER X BLANK 61745 LINE BLANK SOLID 61746 . 61747 PLOT Y PRED VS X 61748 61749-----STRING LENGTH----------------------------------------------------- 61750 61751STRING LENGTH 61752 61753Name: 61754 STRING LENGTH 61755 61756Type: 61757 Let Subcommand 61758 61759Purpose: 61760 Return the number of characters in a previously defined string. 61761 61762Syntax: 61763 LET <nlen> = STRING LENGTH <sorg> 61764 where <nlen> is a parameter containing the returned length 61765 of the string; 61766 and <sorg> is the name of the string. 61767 61768Examples: 61769 LET NLEN = STRING LENGTH S1 61770 61771Default: 61772 None 61773 61774Synonyms: 61775 None 61776 61777Related Commands: 61778 LET FUNCTION = Defines a function. 61779 LET STRING = Defines a string. 61780 READ STRING = Reads a string from a file. 61781 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 61782 & = Concatenate two strings. 61783 SUBTRING = Extract a substring from an existing string. 61784 STRING INDEX = Extract the start/stop positions of a substring 61785 within a string. 61786 STRING CONCATENATE = Concatenate one or more previously defined 61787 strings. 61788 STRING EDIT = Edit a string. 61789 STRING MERGE = Insert a string into another string without 61790 overwrite. 61791 STRING REPLACE = Insert a string into another string with 61792 overwrite. 61793 LOWER CASE = Convert a string to lower case. 61794 UPPER CASE = Convert a string to upper case. 61795 CHARACTER = Convert numeric values to strings based on 61796 the ASCII collating sequence. 61797 ICHAR = Convert a string to numeric values based on 61798 the ASCII collating sequence. 61799 GROUP LABEL = Define the text for group labels. 61800 61801Applications: 61802 Data Management 61803 61804Implementation Date: 61805 11/2008 61806 61807Program: 61808 LET STRING S1 = file23.dat 61809 LET NLEN = STRING LENGTH S1 61810 61811 The resulting value of NLEN is 10. 61812 61813-----STRING MERGE----------------------------------------------------- 61814 61815STRING MERGE 61816 61817Name: 61818 STRING MERGE 61819 61820Type: 61821 Let Subcommand 61822 61823Purpose: 61824 Insert the contents of one string into another string at a 61825 specified position. 61826 61827Description: 61828 This command is used to insert the contents of one string 61829 into an arbitrary position of another string. For example, 61830 if the original string is 61831 61832 FILE.DAT 61833 61834 and the insertion string is 61835 61836 99 61837 61838 and the merge position is given as 5, then the resulting 61839 merged string would be 61840 61841 FILE99.DAT 61842 61843 Note that if the the merge position is 5, then the 61844 insertion string starts at position 5 (i.e., the position 61845 parameter is the before position rather than the after 61846 position). 61847 61848 The STRING REPLACE command performs a similar function. 61849 However, the original string is not shifted. In the above 61850 example, the resulting string from the STRING REPLACE command 61851 would be 61852 61853 FILE99AT 61854 61855 The STRING EDIT command can be used to perform more 61856 general edits of a string. 61857 61858Syntax: 61859 LET <sout> = STRING MERGE <sorg> <snew> <nstart> 61860 where <sout> is the name of the resulting string; 61861 <sorg> is the name of the original string; 61862 <snew> is the name of the insertion string; 61863 and <nstart> is the merge position. 61864 61865Examples: 61866 LET SOUT = STRING MERGE S1 SNEW NSTART 61867 61868Note: 61869 The name of the new string can be the same as the original 61870 string. For example, 61871 61872 LET FNAME = STRING MERGE FNAME SNEW NSTART 61873 61874Note: 61875 Both strings on the right hand side of the equal sign must be 61876 previously existing strings. That is, expressions are not allowed. 61877 For example, instead of 61878 61879 LET FNAME = STRING MERGE FNAME ".dat" NSTART 61880 61881 you need to do 61882 61883 LET STRING SNEW = .dat 61884 LET FNAME = STRING MERGE FNAME SNEW NSTART 61885 61886 The starting position can be either a parameter or a numeric 61887 value. However, it cannot be a numeric expression. So 61888 61889 LET FNAME = STRING MERGE FNAME SNEW NSTART 61890 LET FNAME = STRING MERGE FNAME SNEW 5 61891 61892 are both allowed but 61893 61894 LET FNAME = STRING MERGE FNAME SNEW NLEN/2 61895 61896 is not allowed. You would need to enter this as 61897 61898 LET NSTART = NLEN/2 61899 LET FNAME = STRING MERGE FNAME SNEW NSTART 61900 61901Note: 61902 The total number of characters that DATAPLOT can use for storing 61903 functions and strings is set when DATAPLOT is built. The current 61904 default (11/2008) is 50,000 characters. Previous versions may set 61905 this limit at 1,000 or 10,000 characters. This limit applies to the 61906 combined number of characters for all functions and strings. 61907 61908Default: 61909 None 61910 61911Synonyms: 61912 None 61913 61914Related Commands: 61915 LET FUNCTION = Defines a function. 61916 LET STRING = Defines a string. 61917 READ STRING = Reads a string from a file. 61918 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 61919 & = Concatenate two strings. 61920 SUBTRING = Extract a substring from an existing string. 61921 STRING INDEX = Extract the start/stop positions of a substring 61922 within a string. 61923 STRING CONCATENATE = Concatenate one or more previously defined 61924 strings. 61925 STRING LENGTH = Return the length of a string. 61926 STRING EDIT = Edit a string. 61927 STRING REPLACE = Insert a string into another string with 61928 overwrite. 61929 LOWER CASE = Convert a string to lower case. 61930 UPPER CASE = Convert a string to upper case. 61931 CHARACTER = Convert numeric values to strings based on 61932 the ASCII collating sequence. 61933 ICHAR = Convert a string to numeric values based on 61934 the ASCII collating sequence. 61935 GROUP LABEL = Define the text for group labels. 61936 61937Applications: 61938 Data Management 61939 61940Implementation Date: 61941 11/2008 61942 61943Program 1: 61944 LET STRING S1 = file.dat 61945 LET STRING S2 = 23 61946 LET NPOS = 5 61947 LET SOUT = STRING MERGE S1 S2 NPOS 61948 61949 The resulting string SOUT will contain 61950 61951 file23.txt 61952 61953Program 2: 61954 . Assume we have variables X and Y in the files "file1.dat" to 61955 . "file10.dat" and we want to plot each of these in turn. 61956 . 61957 LET STRING SOLD = file.dat 61958 LET NPOS = 5 61959 TITLE CASE ASIS 61960 LOOP FOR K = 1 1 10 61961 LET STRING S2 = ^K 61962 LET FNAME = STRING MERGE SOLD S2 NPOS 61963 READ ^FNAME Y X 61964 TITLE Data from File ^SOUT 61965 PLOT Y X 61966 DELETE Y X 61967 END OF LOOP 61968 61969-----STRING REMOVE PUNCTUATION-------------------------------------- 61970 61971STRING REMOVE PUNCTUATION 61972 61973Name: 61974 STRING REMOVE PUNCTUATION 61975 61976Type: 61977 Let Subcommand 61978 61979Purpose: 61980 Remove the punctuation characters from a string. 61981 61982Description: 61983 The following punctuation characters will be removed from the string 61984 61985 !"'#$%&\()*+,-./:;<=>?@[]^_`~{}| 61986 61987 If you would like to define your own list of characters to delete, 61988 you can use the command STRING DELETE. 61989 61990Syntax: 61991 LET <sout> = STRING REMOVE PUNCTUATION <sorg> 61992 where <sout> is the name of the resulting string; 61993 and <sorg> is the name of the original string. 61994 61995Examples: 61996 LET SOUT = STRING REMOVE PUNCTUATION STIN 61997 61998Note: 61999 The name of the new string can be the same as the original 62000 string. For example, 62001 62002 LET STR = STRING REMOVE PUNCTUATION STR 62003 62004 In this case, STR will now contain the the string with punctuation 62005 characters removed rather than the original string. 62006 62007Note: 62008 The string on the right hand side of the equal sign must be a 62009 previously existing string. That is, expressions are not allowed. 62010 For example, the following will result in an error message 62011 62012 LET STOUT = STRING REMOVE PUNCTUATION "alan.heckert@nist.gov" 62013 62014 you need to do 62015 62016 LET STRING SORG = alan.heckert@nist.gov 62017 LET SOUT = STRING REMOVE PUNCTUATION SORG 62018 62019 The name on the left hand side of the equal sign may be a 62020 previously existing string. However, if it is a previously 62021 existing parameter, variable, or matrix name, an error will 62022 be reported and the requested string will not be created. 62023 62024Note: 62025 The total number of characters that DATAPLOT can use for storing 62026 functions and strings is set when DATAPLOT is built. The current 62027 default (11/2008) is 50,000 characters. Previous versions may set 62028 this limit at 1,000 or 10,000 characters. This limit applies to the 62029 combined number of characters for all functions and strings. 62030 62031Default: 62032 None 62033 62034Synonyms: 62035 None 62036 62037Related Commands: 62038 STRING REMOVE SPACE = Remove spaces from a string. 62039 STRING REMOVE WHITESPACE = Remove white space characters from a string. 62040 STRING DELETE = Remove user specifed characters from a 62041 string. 62042 NUMBER OF WORDS = Return the number of words in a string. 62043 UPPER CASE = Convert a string to upper case. 62044 LOWER CASE = Convert a string to lower case. 62045 LET FUNCTION = Defines a function. 62046 LET STRING = Defines a string. 62047 READ STRING = Reads a string from a file. 62048 SUBSTITUTE CHARACTER (^) = Substitute the value of a string or 62049 parameter. 62050 CONCATENATE CHARACTER (&) = Concatenate two strings. 62051 SUBTRING = Extract a substring from an existing 62052 string. 62053 STRING INDEX = Extract the start/stop positions of a 62054 substring within a string. 62055 STRING CONCATENATE = Concatenate one or more previously 62056 defined strings. 62057 STRING EDIT = Edit a string. 62058 STRING MERGE = Insert a string into another string 62059 without overwrite. 62060 STRING LENGTH = Return the length of a string. 62061 STRING WORD = Extract a specified word from a string. 62062 CHARACTER = Convert numeric values to strings based 62063 on the ASCII collating sequence. 62064 ICHAR = Convert a string to numeric values based 62065 on the ASCII collating sequence. 62066 GROUP LABEL = Define the text for group labels. 62067 62068Applications: 62069 Data Management 62070 62071Implementation Date: 62072 2018/10 62073 62074Program: 62075 read string stin 62076 alan.heckert@nist.gov;james.filliben@nist.gov 62077 let stout = string remove punctuation stin 62078 print stin stout 62079 62080-----STRING REMOVE SPACES------------------------------------------ 62081 62082STRING REMOVE SPACES 62083 62084Name: 62085 STRING REMOVE SPACES 62086 62087Type: 62088 Let Subcommand 62089 62090Purpose: 62091 Remove the spaces from a string. 62092 62093Description: 62094 You can optionally remove all spaces, just the leading spaces, or 62095 just the trailing spaces from a string. 62096 62097Syntax 1: 62098 LET <sout> = STRING REMOVE SPACES <sorg> 62099 where <sout> is the name of the resulting string; 62100 and <sorg> is the name of the original string. 62101 62102 This syntax removes all spaces from the string. 62103 62104Syntax 2: 62105 LET <sout> = STRING REMOVE LEADING SPACES <sorg> 62106 where <sout> is the name of the resulting string; 62107 and <sorg> is the name of the original string. 62108 62109 This syntax removes only leading spaces from the string. 62110 62111Syntax 3: 62112 LET <sout> = STRING REMOVE TRAILING SPACES <sorg> 62113 where <sout> is the name of the resulting string; 62114 and <sorg> is the name of the original string. 62115 62116 This syntax removes only trailing spaces from the string. 62117 62118Examples: 62119 LET SOUT = STRING REMOVE SPACES STIN 62120 LET SOUT = STRING REMOVE LEADING SPACES STIN 62121 LET SOUT = STRING REMOVE TRAILING SPACES STIN 62122 62123Note: 62124 The name of the new string can be the same as the original 62125 string. For example, 62126 62127 LET FNAME = STRING REMOVE SPACES FNAME 62128 62129 In this case, FNAME will now contain the the string with all spaces 62130 removed rather than the original string. 62131 62132Note: 62133 The string on the right hand side of the equal sign must be a 62134 previously existing string. That is, expressions are not allowed. 62135 For example, the following will result in an error message 62136 62137 LET STOUT = STRING REMOVE SPACES "a b c d" 62138 62139 you need to do 62140 62141 LET STRING SORG = a b c d 62142 LET SOUT = STRING REMOVE SPACES SORG 62143 62144 The name on the left hand side of the equal sign may be a 62145 previously existing string. However, if it is a previously 62146 existing parameter, variable, or matrix name, an error will 62147 be reported and the requested string will not be created. 62148 62149Note: 62150 The total number of characters that DATAPLOT can use for storing 62151 functions and strings is set when DATAPLOT is built. The current 62152 default (11/2008) is 50,000 characters. Previous versions may set 62153 this limit at 1,000 or 10,000 characters. This limit applies to the 62154 combined number of characters for all functions and strings. 62155 62156Default: 62157 None 62158 62159Synonyms: 62160 None 62161 62162Related Commands: 62163 NUMBER OF WORDS = Return the number of words in a string. 62164 UPPER CASE = Convert a string to upper case. 62165 LOWER CASE = Convert a string to lower case. 62166 LET FUNCTION = Defines a function. 62167 LET STRING = Defines a string. 62168 READ STRING = Reads a string from a file. 62169 SUBSTITUTE CHARACTER (^) = Substitute the value of a string or 62170 parameter. 62171 CONCATENATE CHARACTER (&) = Concatenate two strings. 62172 SUBTRING = Extract a substring from an existing 62173 string. 62174 STRING INDEX = Extract the start/stop positions of a 62175 substring within a string. 62176 STRING CONCATENATE = Concatenate one or more previously 62177 defined strings. 62178 STRING EDIT = Edit a string. 62179 STRING MERGE = Insert a string into another string 62180 without overwrite. 62181 STRING LENGTH = Return the length of a string. 62182 STRING WORD = Extract a specified word from a string. 62183 CHARACTER = Convert numeric values to strings based 62184 on the ASCII collating sequence. 62185 ICHAR = Convert a string to numeric values based 62186 on the ASCII collating sequence. 62187 GROUP LABEL = Define the text for group labels. 62188 62189Applications: 62190 Data Management 62191 62192Implementation Date: 62193 2015/03 62194 62195Program: 62196 let string stin = a b c d 62197 let stout = string remove spaces stin 62198 print stin stout 62199 62200-----STRING REMOVE WHITESPACE------------------------------------------ 62201 62202STRING REMOVE WHITESPACE 62203 62204Name: 62205 STRING REMOVE WHITESPACE 62206 62207Type: 62208 Let Subcommand 62209 62210Purpose: 62211 Remove the white space characters from a string. 62212 62213Description: 62214 The STRING REMOVE SPACES command can be used to remove spaces from a 62215 string. This command will remove, in addition to spaces, the 62216 non-printing characters (i.e., codes 0 to 32 and 127 in the ASCII 62217 collating sequence). Currently, Dataplot only checks for characters 62218 in the 0 - 127 range of the ASCII collating sequence. 62219 62220Syntax: 62221 LET <sout> = STRING REMOVE WHITESPACE <sorg> 62222 where <sout> is the name of the resulting string; 62223 and <sorg> is the name of the original string. 62224 62225Examples: 62226 LET SOUT = STRING REMOVE WHITESPACE STIN 62227 62228Note: 62229 The name of the new string can be the same as the original 62230 string. For example, 62231 62232 LET STR = STRING REMOVE WHITESPACE STR 62233 62234 In this case, STR will now contain the the string with all white 62235 space characters removed rather than the original string. 62236 62237Note: 62238 The string on the right hand side of the equal sign must be a 62239 previously existing string. That is, expressions are not allowed. 62240 For example, the following will result in an error message 62241 62242 LET STOUT = STRING REMOVE WHITESPACE "a b c d" 62243 62244 you need to do 62245 62246 LET STRING SORG = a b c d 62247 LET SOUT = STRING REMOVE SPACES SORG 62248 62249 The name on the left hand side of the equal sign may be a 62250 previously existing string. However, if it is a previously 62251 existing parameter, variable, or matrix name, an error will 62252 be reported and the requested string will not be created. 62253 62254Note: 62255 The total number of characters that DATAPLOT can use for storing 62256 functions and strings is set when DATAPLOT is built. The current 62257 default (11/2008) is 50,000 characters. Previous versions may set 62258 this limit at 1,000 or 10,000 characters. This limit applies to the 62259 combined number of characters for all functions and strings. 62260 62261Default: 62262 None 62263 62264Synonyms: 62265 None 62266 62267Related Commands: 62268 STRING REMOVE SPACE = Remove spaces from a string. 62269 STRING REMOVE PUNCTUATION = Remove punctuation from a string. 62270 STRING DELETE = Remove user specifed characters from a 62271 string. 62272 NUMBER OF WORDS = Return the number of words in a string. 62273 UPPER CASE = Convert a string to upper case. 62274 LOWER CASE = Convert a string to lower case. 62275 LET FUNCTION = Defines a function. 62276 LET STRING = Defines a string. 62277 READ STRING = Reads a string from a file. 62278 SUBSTITUTE CHARACTER (^) = Substitute the value of a string or 62279 parameter. 62280 CONCATENATE CHARACTER (&) = Concatenate two strings. 62281 SUBTRING = Extract a substring from an existing 62282 string. 62283 STRING INDEX = Extract the start/stop positions of a 62284 substring within a string. 62285 STRING CONCATENATE = Concatenate one or more previously 62286 defined strings. 62287 STRING EDIT = Edit a string. 62288 STRING MERGE = Insert a string into another string 62289 without overwrite. 62290 STRING LENGTH = Return the length of a string. 62291 STRING WORD = Extract a specified word from a string. 62292 CHARACTER = Convert numeric values to strings based 62293 on the ASCII collating sequence. 62294 ICHAR = Convert a string to numeric values based 62295 on the ASCII collating sequence. 62296 GROUP LABEL = Define the text for group labels. 62297 62298Applications: 62299 Data Management 62300 62301Implementation Date: 62302 2018/10 62303 62304Program: 62305 let string stin = a b c d 62306 let stout = string remove whitespace stin 62307 print stin stout 62308 62309-----STRING REPLACE----------------------------------------------------- 62310 62311STRING REPLACE 62312 62313Name: 62314 STRING REPLACE 62315 62316Type: 62317 Let Subcommand 62318 62319Purpose: 62320 Insert the contents of one string into another string at a 62321 specified position. 62322 62323Description: 62324 This command is used to insert the contents of one string 62325 into an arbitrary position of another string. For example, 62326 if the original string is 62327 62328 FILExx.DAT 62329 62330 and the insertion string is 62331 62332 99 62333 62334 and the replacement position is given as 5, then the 62335 resulting string would be 62336 62337 FILE99.DAT 62338 62339 Note that the replacement string overwrites the contents 62340 of the original string. Also note that if the the replacement 62341 position is 5, then the replacement string starts at position 5 62342 (i.e., the position parameter is the before position rather than 62343 the after position). 62344 62345 The STRING MERGE command performs a similar function. 62346 However, the original string is shifted to the right at the 62347 replacement position rather than overwritten. In the above 62348 example, the resulting string from the STRING MERGE command 62349 would be 62350 62351 FILE99xx.DAT 62352 62353 The STRING EDIT command can be used to perform more 62354 general edits of a string. 62355 62356Syntax: 62357 LET <sout> = STRING REPLACE <sorg> <snew> <nstart> 62358 where <sout> is the name of the resulting string; 62359 <sorg> is the name of the original string; 62360 <snew> is the name of the replacement string; 62361 and <nstart> is the replacement position. 62362 62363Examples: 62364 LET SOUT = STRING REPLACE S1 SNEW NSTART 62365 62366Note: 62367 The name of the new string can be the same as the original 62368 string. For example, 62369 62370 LET FNAME = STRING REPLACE FNAME SNEW NSTART 62371 62372Note: 62373 Both strings on the right hand side of the equal sign must be 62374 previously existing strings. That is, expressions are not 62375 allowed. For example, instead of 62376 62377 LET FNAME = STRING REPLACE FNAME ".dat" NSTART 62378 62379 you need to do 62380 62381 LET STRING SNEW = .dat 62382 LET FNAME = STRING REPLACE FNAME SNEW NSTART 62383 62384 The starting position can be either a parameter or a numeric 62385 value. However, it cannot be a numeric expression. So 62386 62387 LET FNAME = STRING REPLACE FNAME SNEW NSTART 62388 LET FNAME = STRING REPLACE FNAME SNEW 5 62389 62390 are both allowed but 62391 62392 LET FNAME = STRING REPLACE FNAME SNEW NLEN/2 62393 62394 is not allowed. You would need to enter this as 62395 62396 LET NSTART = NLEN/2 62397 LET FNAME = STRING REPLACE FNAME SNEW NSTART 62398 62399Note: 62400 The total number of characters that DATAPLOT can use for storing 62401 functions and strings is set when DATAPLOT is built. The current 62402 default (11/2008) is 50,000 characters. Previous versions may set 62403 this limit at 1,000 or 10,000 characters. This limit applies to the 62404 combined number of characters for all functions and strings. 62405 62406Default: 62407 None 62408 62409Synonyms: 62410 None 62411 62412Related Commands: 62413 LET FUNCTION = Defines a function. 62414 LET STRING = Defines a string. 62415 READ STRING = Reads a string from a file. 62416 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 62417 & = Concatenate two strings. 62418 SUBTRING = Extract a substring from an existing string. 62419 STRING INDEX = Extract the start/stop positions of a substring 62420 within a string. 62421 STRING CONCATENATE = Concatenate one or more previously defined 62422 strings. 62423 STRING LENGTH = Return the length of a string. 62424 STRING EDIT = Edit a string. 62425 STRING MERGE = Insert a string into another string without 62426 overwrite. 62427 LOWER CASE = Convert a string to lower case. 62428 UPPER CASE = Convert a string to upper case. 62429 CHARACTER = Convert numeric values to strings based on 62430 the ASCII collating sequence. 62431 ICHAR = Convert a string to numeric values based on 62432 the ASCII collating sequence. 62433 GROUP LABEL = Define the text for group labels. 62434 62435Applications: 62436 Data Management 62437 62438Implementation Date: 62439 11/2008 62440 62441Program 1: 62442 LET STRING S1 = filexx.dat 62443 LET STRING S2 = 23 62444 LET NPOS = 5 62445 LET SOUT = STRING REPLACE S1 S2 NPOS 62446 62447 The resulting string SOUT will contain 62448 62449 file23.txt 62450 62451Program 2: 62452 . Assume we have variables X and Y in the files "file1.dat" to 62453 . "file10.dat" and we want to plot each of these in turn. 62454 . 62455 LET STRING SOLD = filex.dat 62456 LET NPOS = 5 62457 TITLE CASE ASIS 62458 LOOP FOR K = 1 1 9 62459 LET STRING S2 = ^K 62460 LET FNAME = STRING REPLACE SOLD S2 NPOS 62461 READ ^FNAME Y X 62462 TITLE Data from File ^SOUT 62463 PLOT Y X 62464 DELETE Y X 62465 END OF LOOP 62466 62467-----STRING SPACE (SET)-------------------------------------------- 62468 62469STRING SPACE 62470 62471Name: 62472 STRING SPACE (SET) 62473 62474Type: 62475 Set Subcommand 62476 62477Purpose: 62478 Specify how a "SP()" is interpreted in a string. 62479 62480Description: 62481 By default, the command 62482 62483 LET STRING S = SP() 62484 62485 will create a string S with a single space character. 62486 62487 However, if you do something like 62488 62489 LET STRING S = SP() 62490 LET STRING T = ^S 62491 62492 you will get an error message and the string T will not be 62493 created. This is due to the fact that the substitution 62494 (i.e., the "^") is performed before the command is 62495 interpreted. That is, the command that Dataplot tries to 62496 interpret is 62497 62498 LET STRING T = 62499 62500 However, if you enter the commands 62501 62502 SET STRING SPACE IGNORE 62503 LET STRING S = SP() 62504 SET STRING SPACE EXPAND 62505 LET STRING T = ^S 62506 62507 then Dataplot sees the command 62508 62509 LET STRING T = SP() 62510 62511 and it creates the string T with a single space character. 62512 62513 Since in most cases you want the SP() to be converted to a 62514 single space, EXPAND is the default. 62515 62516Syntax: 62517 SET STRING SPACE <EXPAND/IGNORE> 62518 62519 Specifying EXPAND means that if SP() is encountered in a 62520 LET STRING command, it will be converted to a single space. 62521 Specifying IGNORE means that if SP() is encountered in a 62522 LET STRING command, it will left as SP(). 62523 62524 Any argument other than PROMPT or TERMINATE will be treated as 62525 equivalent to IGNORE (for example, SET FATAL ERROR DEFAULT). 62526 62527Examples: 62528 SET STRING SPACE IGNORE 62529 SET STRING SPACE EXPAND 62530 62531Default: 62532 EXPAND is the default. 62533 62534Synonyms: 62535 OFF and NO will be interpreted as IGNORE. All other arguments 62536 will be interpreted as EXPAND. 62537 62538Related Commands: 62539 LET STRING = Define a string. 62540 ^ = Substitute the value of a string or parameter. 62541 62542Applications: 62543 String Manipulation 62544 62545Implementation Date: 62546 2009/02 62547 62548Program: 62549 . The following sequence of commands results in an error 62550 . for the string st2. 62551 . 62552 let string st1 = sp() 62553 let string st2 = ^st1 62554 . 62555 . The following successfully creates st2 as a string with 62556 . single blank character. 62557 . 62558 set string space ignore 62559 let string st1 = sp() 62560 set string space expand 62561 let string st2 = ^st1 62562 62563-----STRING SPLIT------------------------------------------- 62564 62565STRING SPLIT 62566 62567Name: 62568 STRING SPLIT 62569 62570Type: 62571 Let Subcommand 62572 62573Purpose: 62574 Extract the individual words from a currently existing string. 62575 62576Description: 62577 This command is used to extract the individual words from a string. 62578 62579 This command is an alternative to using STRING WORD. STRING WORD is 62580 used to extract a specific word in the string while STRING SPLIT will 62581 extract all the words in a string to individual strings. Note that 62582 only the base name will be specified. For example, if you specify 62583 SOUT as the base name and there are three words in the original 62584 string, then string SOUT1 will contain the first word, SOUT2 will 62585 contain the second word, and SOUT3 will contain the third word. 62586 62587 In Dataplot, spaces are used to separate words. 62588 62589Syntax: 62590 LET <sout> = STRING SPLIT <sorg> 62591 where <sorg> is the name of a pre-existing string. 62592 and <sout> is the base name of the resulting strings; 62593 62594 The <sout> defines the base name. An integer index will be appended 62595 to the base name for each string (the index starts at 1). 62596 62597Examples: 62598 LET STBASE = STRING SPLIT SORG 62599 62600Note: 62601 The original string being processed must be a pre-existing string. 62602 If you want to split literal text, you need to do something like 62603 62604 LET STRING SORG = xxxx yyyy zzzz 62605 LET SOUT = STRING SPLIT SORG 62606 62607 Using 62608 62609 LET SOUT = STRING SPLIT xxxx yyyy zzzz 62610 62611 will not work. It will try to see if "xxxx" is the name of currently 62612 defined string. If it is not, no new strings will be created. 62613 Enclosing the literal text in quotes will not make this work. 62614 62615 The name on the left hand side of the equal sign may be a 62616 previously existing string. However, if it is a previously 62617 existing parameter, variable, or matrix name, an error will 62618 be reported and the requested string will not be created. 62619 62620Note: 62621 By default, Dataplot uses a space as the word delimiter. You can 62622 specify an alternative character to be the word delimiter with 62623 the command 62624 62625 SET WORD DELIMITER <char> 62626 62627 with <char> denoting the character to use as the word delimiter. 62628 62629Note: 62630 The total number of characters that DATAPLOT can use for storing 62631 functions and strings is set when DATAPLOT is built. The current 62632 default (11/2008) is 50,000 characters. Previous versions may set 62633 this limit at 1,000 or 10,000 characters. This limit applies to 62634 the combined number of characters for all functions and strings. 62635 62636Default: 62637 None 62638 62639Synonyms: 62640 None 62641 62642Related Commands: 62643 STRING CONCATENATE = Concatenate two or more strings. 62644 & = Concatenate two strings. 62645 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 62646 LET FUNCTION = Defines a function. 62647 LET STRING = Defines a string. 62648 READ STRING = Reads a string from a file. 62649 SUBTRING = Extract a substring from an existing string. 62650 STRING INDEX = Extract the start/stop positions of a substring 62651 within a string. 62652 STRING EDIT = Edit a string. 62653 STRING LENGTH = Return the length of a string. 62654 STRING MERGE = Insert a string into another string without 62655 overwrite. 62656 STRING REPLACE = Insert a string into another string with 62657 overwrite. 62658 LOWER CASE = Convert a string to lower case. 62659 UPPER CASE = Convert a string to upper case. 62660 CHARACTER = Convert numeric values to strings based on 62661 the ASCII collating sequence. 62662 ICHAR = Convert a string to numeric values based on 62663 the ASCII collating sequence. 62664 GROUP LABEL = Define the text for group labels. 62665 62666Applications: 62667 Data Management 62668 62669Implementation Date: 62670 2018/10 62671 62672Program: 62673 LET STRING SORG = X1 X2 X3 X4 X5 62674 LET SNAME = STRING SPLIT SORG 62675 PRINT SNAME1 SNAME2 SNAME3 SNAME4 SNAME5 62676 62677-----STRING STARTS WITH---------------------------------------------- 62678 62679STRING STARTS WITH 62680 62681Name: 62682 STRING STARTS WITH 62683 62684Type: 62685 Let Subcommand 62686 62687Purpose: 62688 Return a 1 if a string starts with a specified substring 62689 and a 0 if it does not. 62690 62691Syntax: 62692 LET <iflag> = STRING STARTS WITH <s1> <s2> 62693 where <iflag> is a parameter containing a 1 if <s1> starts 62694 with <s2> and 0 otherwise; 62695 <s1> is the name of a pre-existing string; 62696 and <s2> is the name of a pre-existing string. 62697 62698Examples: 62699 LET IFLAG = STRING STARTS WITH S1 S2 62700 62701Note: 62702 The strings on the right hand side of the equal sign must be 62703 previously existing strings. That is, expressions are not allowed. 62704 For example, the following will result in an error message 62705 62706 LET IFLAG = STRING STARTS WITH "alan.heckert@nist.gov" "alan" 62707 62708 you need to do 62709 62710 LET STRING SORG = alan.heckert@nist.gov 62711 LET STRING SMATCH = alan 62712 LET SOUT = STRING STARTS WITH SORG SMATCH 62713 62714 The name on the left hand side of the equal sign should either be a 62715 previously existing parameter or not previously defined. If it is a 62716 previously existing string, variable, or matrix name, an error will 62717 be reported and the requested parameter will not be created. 62718 62719Note: 62720 The total number of characters that DATAPLOT can use for storing 62721 functions and strings is set when DATAPLOT is built. The current 62722 default (11/2008) is 50,000 characters. Previous versions may set 62723 this limit at 1,000 or 10,000 characters. This limit applies to 62724 the combined number of characters for all functions and strings. 62725 62726Default: 62727 None 62728 62729Synonyms: 62730 None 62731 62732Related Commands: 62733 STRING ENDS WITH = Check whether a string ends with a 62734 specified substring. 62735 LET FUNCTION = Defines a function. 62736 LET STRING = Defines a string. 62737 READ STRING = Reads a string from a file. 62738 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 62739 & = Concatenate two strings. 62740 SUBTRING = Extract a substring from an existing string. 62741 STRING LENGTH = Return the length of the string. 62742 STRING INDEX = Extract the start/stop positions of a substring 62743 within a string. 62744 STRING CONCATENATE = Concatenate one or more previously defined 62745 strings. 62746 STRING EDIT = Edit a string. 62747 STRING MERGE = Insert a string into another string without 62748 overwrite. 62749 STRING REPLACE = Insert a string into another string with 62750 overwrite. 62751 LOWER CASE = Convert a string to lower case. 62752 UPPER CASE = Convert a string to upper case. 62753 CHARACTER = Convert numeric values to strings based on 62754 the ASCII collating sequence. 62755 ICHAR = Convert a string to numeric values based on 62756 the ASCII collating sequence. 62757 GROUP LABEL = Define the text for group labels. 62758 62759Applications: 62760 Data Management 62761 62762Implementation Date: 62763 2018/10 62764 62765Program: 62766 LET STRING S1 = alan.heckert@gmail.com 62767 LET STRING S2 = alan 62768 LET IFLAG = STRING STARTS WITH S1 S2 62769 62770-----STRING SUBSET COUNT----------------------------------------- 62771 62772STRING SUBSET COUNT 62773 62774Name: 62775 STRING SUBSET COUNT 62776 62777Type: 62778 Let Subcommand 62779 62780Purpose: 62781 Return the number of times a substring occurs within another string. 62782 62783Syntax: 62784 LET <count> = STRING SUBSET COUNT <sorg> <smatch> 62785 where <count> is a parameter containing the number of times <smatch> 62786 is found in <sorg>; 62787 <sorg> is the name of a pre-existing string; 62788 and <smatch> is the name of a pre-existing string. 62789 62790Examples: 62791 LET NC = STRING SUBSET COUNT SORG SMATCH 62792 62793Note: 62794 The strings on the right hand side of the equal sign must be 62795 previously existing strings. That is, expressions are not allowed. 62796 For example, the following will result in an error message 62797 62798 LET NC = STRING SUBSET COUNT "alan.heckert@nist.gov" "@" 62799 62800 you need to do 62801 62802 LET STRING SORG = alan.heckert@nist.gov 62803 LET STRING SMATCH = @ 62804 LET NC = STRING SUBSET COUNT SORG SMATCH 62805 62806 The name on the left hand side of the equal sign should either be a 62807 previously existing parameter or not previously defined. If it is a 62808 previously existing string, variable, or matrix name, an error will 62809 be reported and the requested parameter will not be created. 62810 62811Note: 62812 The total number of characters that Dataplot can use for storing 62813 functions and strings is set when Dataplot is built. The current 62814 default (11/2008) is 50,000 characters. 62815 62816Default: 62817 None 62818 62819Synonyms: 62820 None 62821 62822Related Commands: 62823 SUBTRING = Extract a substring from an existing string. 62824 STRING ENDS WITH = Check whether a string starts with a 62825 specified substring. 62826 STRING ENDS WITH = Check whether a string ends with a 62827 specified substring. 62828 LET STRING = Defines a string. 62829 READ STRING = Reads a string from a file. 62830 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 62831 & = Concatenate two strings. 62832 STRING LENGTH = Return the length of the string. 62833 STRING INDEX = Extract the start/stop positions of a substring 62834 within a string. 62835 STRING CONCATENATE = Concatenate one or more previously defined 62836 strings. 62837 STRING EDIT = Edit a string. 62838 STRING MERGE = Insert a string into another string without 62839 overwrite. 62840 STRING REPLACE = Insert a string into another string with 62841 overwrite. 62842 LOWER CASE = Convert a string to lower case. 62843 UPPER CASE = Convert a string to upper case. 62844 CHARACTER = Convert numeric values to strings based on 62845 the ASCII collating sequence. 62846 ICHAR = Convert a string to numeric values based on 62847 the ASCII collating sequence. 62848 GROUP LABEL = Define the text for group labels. 62849 62850Applications: 62851 Data Management 62852 62853Implementation Date: 62854 2019/02 62855 62856Program: 62857 LET STRING S1 = alan.heckert@nist.gov,james.filliben@nist.gov 62858 LET STRING S2 = @ 62859 LET NNAMES = STRING SUBSET COUNT S1 S2 62860 62861-----STRING VARIABLE (SET)--------------------------------------- 62862 62863SET STRING VARIABLE 62864 62865Name: 62866 STRING VARIABLE (SET) 62867 62868Type: 62869 Set Subcommand 62870 62871Purpose: 62872 Specify whether the READ and STRING VARIABLE commands will overwrite 62873 the contents of the dpzchf.dat file or append the new data to the 62874 current contents of the dpzchf.dat file. 62875 62876Description: 62877 The READ command can optionally read character variables 62878 (HELP SET CONVERT CHARACTER). Dataplot saves the character 62879 variables in the file "dpzchf.dat". In addition, the 62880 LET ... = STRING VARIABLE command can be used to create a character 62881 variable from a list of strings. This variable will be saved in 62882 the "dpzchf.dat" as well. 62883 62884 By default, Dataplot overwrites the current contents of the 62885 "dpzchf.dat" file whenever a READ or STRING VARIABLE command 62886 creates new character variables. To have these commands append 62887 the contents of the new character variables to the current contents 62888 of "dpzchf.dat", enter the command 62889 62890 SET STRING VARIABLE APPEND 62891 62892 To reset the default of overwriting the current contents of 62893 "dpzchf.dat", enter 62894 62895 SET STRING VARIABLE OVERWRITE 62896 62897Syntax: 62898 SET STRING VARIABLE <OVERWRITE/APPEND> 62899 where OVERWRITE replaces the current contents of "dpzchf.dat" 62900 and APPEND appends to the current contents of "dpzchf.dat". 62901 62902Examples: 62903 SET STRING VARIABLE APPEND 62904 SET STRING VARIABLE OVERWRITE 62905 62906Default: 62907 None 62908 62909Synonyms: 62910 None 62911 62912Related Commands: 62913 STRING VARIABLE = Create a character variable from a list of 62914 strings. 62915 READ = Read numeric/character variables from a file. 62916 62917Applications: 62918 Character Data 62919 62920Implementation Date: 62921 2019/09 62922 62923Program: 62924 set string variable overwrite 62925 let string s1 = Group 1 62926 let string s2 = Group 2 62927 let string s3 = Group 3 62928 let ix = string variable s1 s2 s3 62929 list dpzchf.dat 62930 pause 62931 . 62932 set string variable append 62933 let string s4 = Group 4 62934 let string s5 = Group 5 62935 let string s6 = Group 6 62936 let iy = string variable s4 s5 s6 62937 list dpzchf.dat 62938 62939-----STRING VARIABLE------------------------------------------- 62940 62941STRING VARIABLE 62942 62943Name: 62944 STRING VARIABLE 62945 62946Type: 62947 Let Subcommand 62948 62949Purpose: 62950 Create a string variable from a list of strings and save it to 62951 the file dpzchf.dat. 62952 62953Description: 62954 The Dataplot READ command can optionally read character data. The 62955 READ command saves these character variables to the file 62956 "dpzchf.dat". 62957 62958 The STRING VARIABLE command allows you to add character variables 62959 to "dpzchf.dat" from a list of scalar strings. 62960 62961 You can specify whether you want Dataplot to overwrite the current 62962 contents of "dpzchf.dat" or append the new variable to the current 62963 contents of "dpzchf.dat". 62964 62965 To have the STRING VARIABLE command overwrite the current contents 62966 of "dpzchf.dat", enter 62967 62968 SET CHARACTER VARIABLE OVERWRITE 62969 62970 To have the STRING VARIABLE command append the new string variable to 62971 the current contents of "dpzchf.dat", enter 62972 62973 SET CHARACTER VARIABLE APPEND 62974 62975Syntax: 62976 LET <sout> = STRING VARIABLE <s1> ... <sk> 62977 where <sout> is the name of the resulting string variable; 62978 and <s1> ... <sk> is a list of one or more previously defined 62979 strings or literal text strings. 62980 62981 Literal text strings should be enclosed in quotes. If an 62982 argument on the right hand side of the equal sign is not enclosed 62983 in quotes, it will be assumed to be a previously defined string. 62984 If an argument is not enclosed in quotes and is not the name of 62985 a previously defined string, an error message will be returned and 62986 <sout> will not be created. 62987 62988 The TO syntax is supported for the argument list (see the Examples). 62989 62990Examples: 62991 LET IX = STRING VARIABLE S1 S2 S3 62992 LET IX = STRING VARIABLE S1 TO S10 62993 LET IX = STRING VARIABLE "Group 1" "Group 2" "Group 3" 62994 LET IX = STRING VARIABLE "Group 1" S2 "Group 3" S4 62995 62996Default: 62997 None 62998 62999Synonyms: 63000 None 63001 63002Related Commands: 63003 READ = Read variables from the terminal or a file. 63004 READ STRING = Reads a string from a file. 63005 LET STRING = Defines a string. 63006 STRING CONCATENATE = Concatenate two or more strings. 63007 & = Concatenate two strings. 63008 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 63009 LET FUNCTION = Defines a function. 63010 SUBTRING = Extract a substring from an existing string. 63011 STRING INDEX = Extract the start/stop positions of a substring 63012 within a string. 63013 STRING EDIT = Edit a string. 63014 STRING LENGTH = Return the length of a string. 63015 STRING MERGE = Insert a string into another string without 63016 overwrite. 63017 STRING REPLACE = Insert a string into another string with 63018 overwrite. 63019 LOWER CASE = Convert a string to lower case. 63020 UPPER CASE = Convert a string to upper case. 63021 CHARACTER = Convert numeric values to strings based on 63022 the ASCII collating sequence. 63023 ICHAR = Convert a string to numeric values based on 63024 the ASCII collating sequence. 63025 GROUP LABEL = Define the text for group labels. 63026 63027Applications: 63028 Data Management 63029 63030Implementation Date: 63031 2019/10 63032 63033Program 1: 63034 set string variable overwrite 63035 let ix = string variable "Group 1" "Group 2" "Group 3" 63036 list dpzchf.dat 63037 63038Program 2: 63039 set string variable overwrite 63040 let string s1 = Group 1 63041 let string s2 = Group 2 63042 let string s3 = Group 3 63043 let ix = string variable s1 s2 s3 63044 list dpzchf.dat 63045 pause 63046 . 63047 set string variable append 63048 let string s4 = Group 4 63049 let string s5 = Group 5 63050 let string s6 = Group 6 63051 let iy = string variable s4 s5 s6 63052 list dpzchf.dat 63053 63054-----STRING WORD----------------------------------------------------- 63055 63056STRING WORD 63057 63058Name: 63059 STRING WORD 63060 63061Type: 63062 Let Subcommand 63063 63064Purpose: 63065 Extract a specified word from a string. 63066 63067Description: 63068 There may be times when it is useful to extract the individual 63069 words in a string. 63070 63071 Dataplot delineates words in a string by spaces. It will treat 63072 non-printing characters in the string as spaces. That is, 63073 any character in the string with an ASCII collating index less 63074 than or equal to 32 or greater than 127 will be treated as a space. 63075 In particular, tabs will be treated as spaces. However, hyphens 63076 and other special characters such as "&" will not be treated as 63077 word boundaries. 63078 63079Syntax: 63080 LET <sout> = STRING WORD <sorg> <nword> 63081 where <sout> is the name of the resulting string; 63082 <sorg> is the name of the original string; 63083 and <nword> is the index of the word to extract. 63084 63085Examples: 63086 LET SOUT = STRING WORD S1 NWORD 63087 LET SOUT = STRING WORD S1 5 63088 63089Note: 63090 The name of the new string can be the same as the original 63091 string. For example, 63092 63093 LET FNAME = STRING WORD FNAME NWORD 63094 63095 In this case, FNAME will now contain the extracted word rather than 63096 the original string. 63097 63098Note: 63099 The string on the right hand side of the equal sign must be a 63100 previously existing string. That is, expressions are not allowed. 63101 For example, instead of 63102 63103 LET FNAME = STRING WORD "a b c d" 2 63104 63105 you need to do 63106 63107 LET STRING SORG = a b c d 63108 LET FNAME = STRING WORD SORG 2 63109 63110 The word index position can be either a parameter or a numeric 63111 value. However, it cannot be a numeric expression. So 63112 63113 LET FNAME = STRING WORD SORG 5 63114 LET FNAME = STRING WORD SORG NWORD 63115 63116 are both allowed but 63117 63118 LET FNAME = STRING WORD SORG NWORD/2 63119 63120 is not allowed. You would need to enter this as 63121 63122 LET NWORD = NWORD/2 63123 LET FNAME = STRING WORD FNAME NWORD 63124 63125 The name on the left hand side of the equal sign may be a 63126 previously existing string. However, if it is a previously 63127 existing parameter, variable, or matrix name, an error will 63128 be reported and the requested string will not be created. 63129 63130Note: 63131 If the requested word is less than one or is greater than the 63132 number of words in the string, an error is reported and the 63133 requested string will not be created. 63134 63135Note: 63136 The total number of characters that DATAPLOT can use for storing 63137 functions and strings is set when DATAPLOT is built. The current 63138 default (11/2008) is 50,000 characters. Previous versions may set 63139 this limit at 1,000 or 10,000 characters. This limit applies to the 63140 combined number of characters for all functions and strings. 63141 63142Default: 63143 None 63144 63145Synonyms: 63146 None 63147 63148Related Commands: 63149 NUMBER OF WORDS = Return the number of words in a string. 63150 UPPER CASE = Convert a string to upper case. 63151 LOWER CASE = Convert a string to lower case. 63152 LET FUNCTION = Defines a function. 63153 LET STRING = Defines a string. 63154 READ STRING = Reads a string from a file. 63155 SUBSTITUTE CHARACTER (^) = Substitute the value of a string or 63156 parameter. 63157 CONCATENATE CHARACTER (&) = Concatenate two strings. 63158 SUBTRING = Extract a substring from an existing 63159 string. 63160 STRING INDEX = Extract the start/stop positions of a 63161 substring within a string. 63162 STRING CONCATENATE = Concatenate one or more previously 63163 defined strings. 63164 STRING EDIT = Edit a string. 63165 STRING MERGE = Insert a string into another string 63166 without overwrite. 63167 STRING LENGTH = Return the length of a string. 63168 CHARACTER = Convert numeric values to strings based 63169 on the ASCII collating sequence. 63170 ICHAR = Convert a string to numeric values based 63171 on the ASCII collating sequence. 63172 GROUP LABEL = Define the text for group labels. 63173 63174Applications: 63175 Data Management 63176 63177Implementation Date: 63178 10/2010 63179 63180Program: 63181 let string s = funnel ramp cone square 63182 . 63183 feedback off 63184 print "String s = ^s" 63185 let nword = number of words s 63186 loop for k = 1 1 nword 63187 let s^k = string word s k 63188 print "String ^k = ^s^k" 63189 end of loop 63190 feedback on 63191 63192-----STRIP PLOT------------------------------------------------------- 63193 63194STRIP PLOT 63195 63196Name: 63197 ... STRIP PLOT 63198 63199Type: 63200 Graphics Command 63201 63202Purpose: 63203 Generates a strip plot (also known as a dot plot). 63204 63205Description: 63206 A strip plot is a graphical data anlysis technique for 63207 summarizing a univariate data set. The strip plot consists of: 63208 63209 Horizontal axis = the value of the response variable; 63210 Verticalal axis = all values are set to 1. 63211 63212 That is, a strip plot is simply a plot of the sorted response 63213 values along one axis. The strip plot is an alternative 63214 to a histogram or a density plot. It is typically used for 63215 small data sets (histograms and density plots are typically 63216 preferred for larger data sets). 63217 63218 There are a few variations supported for the strip plot. 63219 63220 1) One problem with strip plots is how to display 63221 multiple points with the same value. Dataplot provides 63222 two options to address this. 63223 63224 i) With the jitter option, a small amount of random 63225 noise is added to the vertical coordinate. 63226 63227 ii) With the stack option, repeated values add a 63228 fixed increment to the vertical coordinate. 63229 So if there are 3 points with the same value, 63230 the y coordinates might be 1, 1.1, and 1.2. 63231 This gives the strip plot a histogram-like 63232 appearance. 63233 63234 The value of the fixed increment can be set 63235 with the command 63236 63237 SET STRIP PLOT INCREMENT <value> 63238 63239 The default value is 1, although a value of 63240 on the order of 0.1 is often desirable. This 63241 command can be used with the YLIMITS command and 63242 the CHARACTER SIZE command to generate the desired 63243 appearance for the plot. 63244 63245 You can specify your preference with the command 63246 63247 SET STRIP PLOT STYLE <STACK/JITTER> 63248 63249 The default value is STACK. 63250 63251 2) The strip plot can be generated with a group-id 63252 variable. For this variant, the y coordinate is 63253 is set equal to the corresponding value of the 63254 group-id variable. This results in a set of parallel 63255 strip plots. 63256 63257 63258 3) You can generate a strip plot with binned data. 63259 In this case, the STACK option is automatically 63260 used. This option is essentially an alternative 63261 form for a histogram. Binned data can also be 63262 grouped. 63263 63264 You can bin your data with the command 63265 63266 LET Y2 X2 = BINNED Y 63267 63268 The binning algorithm can be controlled with the 63269 commands 63270 63271 CLASS LOWER <value> 63272 CLASS UPPER <value> 63273 CLASS WIDTH <value> 63274 63275Syntax 1: 63276 STRIP PLOT <y> <SUBSET/EXCEPT/FOR qualification> 63277 where <y> is the response variable; 63278 and where the <SUBSET/EXCEPT/FOR qualification is optional. 63279 63280 This syntax is used when you have raw data with a single group. 63281 63282Syntax 2: 63283 STRIP PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 63284 where <y> is the variable of pre-computed frequencies; 63285 <x> is the variable containing the class mid-points; 63286 and where the <SUBSET/EXCEPT/FOR qualification is optional. 63287 63288 This syntax is used when you have binned data with a single 63289 group. 63290 63291Syntax 3: 63292 BATCH STRIP PLOT <y> <tag> <SUBSET/EXCEPT/FOR qualification> 63293 where <y> is the response variable; 63294 <tag> is a group-id variable; 63295 and where the <SUBSET/EXCEPT/FOR qualification is optional. 63296 63297 This syntax is used when you have raw data with multiple 63298 groups. 63299 63300 The word BATCH is required here to distinguish the 63301 multiple groups case from the binned data case. 63302 63303Syntax 4: 63304 BATCH STRIP PLOT <y> <x> <tag> 63305 <SUBSET/EXCEPT/FOR qualification> 63306 where <y> is the variable of pre-computed frequencies; 63307 <x> is the variable containing the class mid-points; 63308 <tag> is a group-id variable; 63309 and where the <SUBSET/EXCEPT/FOR qualification is optional. 63310 63311 This syntax is used when you have binned data with multiple 63312 groups. 63313 63314 In this case, the word BATCH is optional. 63315 63316Syntax 5: 63317 BATCH MULTIPLE STRIP PLOT <y> <tag1> <tag2> 63318 <SUBSET/EXCEPT/FOR qualification> 63319 where <y> is the response variable; 63320 <tag1> is a group-id variable; 63321 <tag2> is a group-id variable; 63322 and where the <SUBSET/EXCEPT/FOR qualification is optional. 63323 63324 This syntax is used when you have raw data with two group-id 63325 variables. 63326 63327 The first group-id variable works as in Syntax 3. That is, it 63328 defines the position on the y-axis. The second group-id variable 63329 is used to identify multiple curves within the first group-id 63330 variable. Appropriate settings for the the CHARACTER command 63331 and its various attribute setting commands can be used to highlight 63332 the different sub-groups within a group. This option is 63333 demonstrated with the Program 4 example below. 63334 63335Examples: 63336 STRIP PLOT Y 63337 STRIP PLOT Y SUBSET Y > 2 63338 STRIP PLOT Y X 63339 63340Note: 63341 The appearance of the strip plot can be controlled by 63342 appropriate settings for the CHARACTER command (and its 63343 attributes). 63344 63345 This is demonstrated in the sample programs below. 63346 63347Note: 63348 You may want to generate strip plots for the case where there 63349 are multiple group variables. This can done using the 63350 CODE CROSS TABULATE command. For example, if there are two 63351 group id variables, you can do something like 63352 63353 LET ICODE = CODE CROSS TABULATE X1 X2 63354 63355 Then use ICODE as the single group id variable. 63356 63357Default: 63358 None 63359 63360Synonyms: 63361 None 63362 63363Related Commands: 63364 HISTOGRAM = Generates a histogram. 63365 FREQUENCY PLOT = Generates a frequency plot. 63366 CLASS LOWER = Sets the lower class minimum for 63367 histograms, frequency plots, and 63368 pie charts. 63369 CLASS UPPER = Sets the upper class maximum for 63370 histograms, frequency plots, and 63371 pie charts. 63372 CLASS WIDTH = Sets the class width for histograms, 63373 frequency plots, and pie charts. 63374 HISTOGRAM CLASS WIDTH = Specify alternative default class wdith 63375 algorithms for histograms. 63376 LIMITS = Sets the frame limits for all plots. 63377 CHARACTERS = Sets the character symbol for plots. 63378 63379Reference: 63380 "Standard Practice for Statistical Analysis of One-Sample and 63381 Two-Sample Interlaboratory Proficiency Testing Programs", 2006, 63382 ASTM International, 100 Barr Harbor Drive, PO BOX C700, 63383 West Conshohoceken, PA 19428-2959, USA. 63384 63385 Unwin, Theus, and Hofmann (2006), "Graphics of Large 63386 Datasets: Visualizing a Million", Springer, p. 36. 63387 63388Applications: 63389 Data Analysis 63390 63391Implementation Date: 63392 11/2008 63393 10/2009: Added the "BATCH MULTIPLE" option 63394 63395Program 1: 63396 . 63397 . Step 1: Read the data 63398 . 63399 skip 25 63400 read E2489A.DAT labid y 63401 . 63402 title case asis 63403 title offset 2 63404 label 63405 x2frame off 63406 y2frame off 63407 char circle all 63408 char hw 1 0.75 all 63409 char fill on all 63410 line blank all 63411 tic offset units data 63412 tic offset 0 0 63413 xtic offset 0.2 0.2 63414 . 63415 set strip plot increment 0.1 63416 set strip plot style stack 63417 . 63418 multiplot corner coordiantes 5 5 95 95 63419 multiplot scale factor 2 1 63420 multiplot 2 1 63421 . 63422 . Step 2a: Generate the strip plot for unbinned data 63423 . (with one group) Stack Option 63424 . 63425 ylimits 0 2 63426 y1tic marks off 63427 y1tic mark labels off 63428 y1frame off 63429 title Strip Plot - Stacked, Single Group 63430 y1label Number of Occurrences 63431 x1label Data Values 63432 label case asis 63433 strip plot y 63434 . 63435 . Step 2b: Generate the strip plot for unbinned data 63436 . (with one group) Jitter Option 63437 . 63438 set strip plot style jitter 63439 . 63440 title Strip Plot - Jittered, Single Group 63441 x1label Data Values 63442 strip plot y 63443 . 63444 end of multiplot 63445 63446Program 2: 63447 . 63448 . Step 1: Read the data 63449 . 63450 skip 25 63451 read gear.dat y x 63452 . 63453 title case asis 63454 title offset 2 63455 label 63456 x2frame off 63457 y2frame off 63458 char circle all 63459 char hw 1 0.75 all 63460 char fill on all 63461 line blank all 63462 . 63463 set strip plot increment 0.15 63464 set strip plot style stack 63465 . 63466 ylimits 1 10 63467 major ytic mark number 10 63468 minor ytic mark number 0 63469 y1tic mark offset 1 1 63470 tic offset unit data 63471 ygrid on 63472 title Strip Plot - Stacked, Multiple Groups 63473 y1label Batch Number 63474 x1label Data Values 63475 label case asis 63476 xlimits 0.98 1.02 63477 major xtic mark number 5 63478 minor xtic mark number 1 63479 xtic mark offset 0.002 0.002 63480 . 63481 batch strip plot y x 63482 63483Program 3: 63484 . 63485 . Step 1: Read the data 63486 . 63487 skip 25 63488 read E2489A.DAT labid y 63489 . 63490 . Step 2: Bin the data 63491 . 63492 class lower 0.0 63493 class upper 5.0 63494 class width 0.1 63495 let y2 x2 = binned y 63496 . 63497 . Step 3: Define the appearance of the plot 63498 . 63499 title case asis 63500 title offset 2 63501 label 63502 x2frame off 63503 y2frame off 63504 char circle all 63505 char hw 1 0.75 all 63506 char fill on all 63507 line blank all 63508 tic offset units data 63509 tic offset 0 0 63510 xtic offset 0.2 0.2 63511 . 63512 ylimits 0.8 2 63513 y1tic marks off 63514 y1tic mark labels off 63515 y1frame off 63516 title Strip Plot - Single Group with Binned Data 63517 y1label Number of Occurrences 63518 x1label Data Values 63519 label case asis 63520 . 63521 . Step 4: Generate the strip plot 63522 . 63523 frame corner coordinate 15 35 85 70 63524 set strip plot increment 0.1 63525 set strip plot style stack 63526 strip plot y2 x2 63527 63528Program 4: 63529 . 63530 . Step 1: Read the data 63531 . 63532 skip 25 63533 read ripken.dat y x1 x2 63534 . 63535 . Step 2: Set Plot Options 63536 . 63537 title case asis 63538 title offset 2 63539 label 63540 x2frame off 63541 y2frame off 63542 char circle all 63543 char hw 1 0.75 all 63544 char fill on all 63545 char color red blue green red blue green red blue green 63546 line blank all 63547 . 63548 tic offset unit data 63549 ylimits 1 3 63550 major ytic mark number 3 63551 minor ytic mark number 0 63552 y1tic mark label format alpha 63553 y1tic mark label content Inside Middle Outside 63554 y1label Horizontal Location 63555 y1tic mark offset 0.2 0.2 63556 ygrid on 63557 grid pattern dotted 63558 x1label Batting Average 63559 label case asis 63560 tic mark label case asis 63561 xlimits 0 1 63562 major xtic mark number 6 63563 minor xtic mark number 1 63564 xtic mark offset 0.05 0.05 63565 x3label Vertical Location: Red = Low, Blue = Middle, Green = High 63566 . 63567 . Step 3: Generate the Strip Plot 63568 . 63569 set strip plot increment 0.1 63570 . set strip plot style stack 63571 set strip plot style jitter 63572 title Strip Plot - Stacked, Multiple Batch Option 63573 batch multiple strip plot y x1 x2 63574 63575-----STROM (LET)-------------------------------- 63576 63577STROM 63578 63579Name: 63580 STROM (LET) 63581 63582Type: 63583 Library Function 63584 63585Purpose: 63586 Compute the Stromgren integral. 63587 63588Description: 63589 The Stromgren integral is defined as: 63590 63591 f(x) = C*INTEGRAL[t**7*EXP(2*t)/((EXP(t)-1)**3)dt] x >= 0 63592 63593 where C = (15/(4*PI**4)) and the integral is defined from 63594 0 to x. 63595 63596 Dataplot computes this function using ACM Algorithm 757 (see 63597 Reference: below). 63598 63599Syntax: 63600 LET <y> = STROM(<x>) <SUBSET/EXCEPT/FOR qualification> 63601 where <x> is a non-negative number, variable or parameter; 63602 <y> is a variable or a parameter (depending on what <x> 63603 is) where the computed Stromgren integral values are 63604 stored; 63605 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 63606 63607Examples: 63608 LET A = STROM(2) 63609 LET A = STROM(X) 63610 LET X2 = STROM(X) FOR X1 = 0.1 0.1 3.0 63611 63612Note: 63613 Library functions are distinguished from let subcommands 63614 in the following ways. 63615 1) Functions enclose the input value in parenthesis. Let 63616 subcommands use spaces. 63617 2) Functions can accept (and return) either parameters 63618 (i.e., single values) or variables (i.e., an array of 63619 values) while let subcommands are specific in which they 63620 accept as input and what they return as output. 63621 3) Functions can accept expressions while let subcommands 63622 do not. For example, the following is legal: 63623 LET Y2 = ABS(Y1-INT(Y1)) 63624 For let subcommands, you typically have to do something 63625 like the following: 63626 LET YTEMP = Y**2 + 8 63627 LET A = SUM YTEMP 63628 63629Default: 63630 None 63631 63632Synonyms: 63633 None 63634 63635Related Commands: 63636 ABRAM = Compute the Abramowitz integral. 63637 CLAUSN = Compute the Clausen integral. 63638 DEBYE = Compute the Debye function. 63639 EXP3 = Compute the cubic exponential integral. 63640 GOODST = Compute the Goodwin and Stanton integral. 63641 LOBACH = Compute the Lobachevski integral. 63642 SYNCH1 = Compute the synchrotron radiation function. 63643 SYNCH2 = Compute the synchrotron radiation function. 63644 TRAN = Compute the transport integral. 63645 63646Reference: 63647 "ACM Transactions of Mathematical Software", Allan MacLead, 63648 Vol. 22, No. 3, September, 1996, pp. 288-301. 63649 63650Applications: 63651 Special Functions 63652 63653Implementation Date: 63654 1999/6 63655 63656Program: 63657 TITLE AUTOMATIC 63658 PLOT STROM(X) FOR X = 0 0.01 10 63659 63660-----SUBREGION -------------------------------------------------- 63661 63662SUBREGION 63663 63664Name: 63665 SUBREGION 63666 63667Type: 63668 Plot Control Command 63669 63670Purpose: 63671 Specifies whether subregions on subsequent plots are on (active) 63672 or off (inactive). 63673 63674Description: 63675 Dataplot now supports subregions on plots. Subregions are 63676 motivated by the desire to denote "engineering limits" on a 63677 plot. That is, a rectangle, denoting an acceptance region in 63678 both the X and Y directions, is drawn and then the plot is 63679 overlaid on top of this. 63680 63681 Although the subregion capability was motivated for the purpose 63682 of denoting engineering limits, they can in fact be used for 63683 whatever purpose you want. Subregions apply to all subsequent 63684 2-D plots (but not 3-D plots). 63685 63686 Currently, subregions are limited to rectangular regions. This 63687 will be upgraded to polygonal regions in a future implementation. 63688 63689 The SUBREGION command is used to turn subregions on or off and 63690 up to 10 subregions can be specified. In most cases where 63691 subregions are defined, only a single subregion is used. 63692 63693Syntax: 63694 SUBREGION <ON/OFF> <ON/OFF> ... <ON/OFF> 63695 where <ON> specifies that the subregion is active and OFF 63696 specifies that it is inactive. Up to 10 subregion 63697 switches can be set. 63698 63699 In most cases, only a single subregion is specified. 63700 63701Examples: 63702 SUBREGION ON 63703 SUBREGION OFF 63704 SUBREGION ON ON ON 63705 63706Note: 63707 The coordinates for the subregion areas are set with the 63708 SUBREGION LIMITS command. 63709 63710Note: 63711 The subregions are plotted before any of the plot 63712 curves. The significance of this is that a solid filled 63713 subregion will be drawn and then the regular plot points 63714 are drawn on top. The effect of this can be hardware 63715 dependent. On X11 and Postscript devices, a solid character 63716 can be seen on top of a light gray scale box (if the gray 63717 scale gets too dark, the plot points are no longer 63718 distinguishable). However, on some hardware devices, you may 63719 not be able to see points plotted on top of a solid fill 63720 region. In this case, plot the border of the subregion and 63721 leave the interior blank. 63722 63723 It is this order of plotting that distinguishes the 63724 subregion from simply using a BOX <id> command to plot 63725 rectangular regions on the screen. 63726 63727Note: 63728 For the first subregion defined, Dataplot returns the following 63729 internal parameters on subsequent plots: 63730 63731 NACCEPT = number of plot points inside the subregion. 63732 NREJECT = number of plot points outisde the subregion. 63733 NTOTAL = number of plot points (NACCEPT + NREJECT). 63734 63735Note: 63736 You do not need to adjust the settings for the CHARACTER, LINE, 63737 BAR, and SPIKE when using subregions. DATAPLOT automatically 63738 shifts these in the background. The attributes for the subregion 63739 are set with the following commands: 63740 63741 REGION FILL <ON/OFF> 63742 REGION COLOR <COLOR> 63743 REGION BORDER LINE <LINETYPE> 63744 REGION BORDER COLOR <COLOR> 63745 63746 The REGION FILL and REGION COLOR determine the attributes of the 63747 interior of the rectangle. The two most common choices are 63748 to leave it blank or to fill it with some type of light 63749 gray scale color. The attributes of the rectangle border are 63750 set with the REGION BORDER LINE and REGION BORDER COLOR commands. 63751 The standard line types (SOLID, BLANK, DASH, DOTTED) are supported. 63752 If you have more than one subregion defined, you should specify 63753 multiple settings on the above commands. For example, 63754 63755 REGION FILL ON ON ON 63756 REGION COLOR G25 G25 G25 63757 63758Note: 63759 The SUBREGION command with no argument turns off all subregions. 63760 63761Default: 63762 No subregions are drawn. 63763 63764Synonyms: 63765 None 63766 63767Related Commands: 63768 PLOT = Generates a data or function plot. 63769 SUBREGION LIMITS = Specifiy the limits for a subregion. 63770 63771Applications: 63772 Denoting "Engineering Limits" on plots. 63773 63774Implementation Date: 63775 2000/1 63776 63777Program: 63778 dimension 50 varialbes 63779 skip 25 63780 read simon1.dat y1 y2 x1 x2 x3 x4 x5 block runseq 63781 . 63782 char x 63783 line blank 63784 . 63785 subregion on 63786 subregion xlimits 0.35 0.42 63787 subregion ylimits 2000 3000 63788 region fill on 63789 region border line dash 63790 region color g90 63791 . 63792 plot y1 vs x1 63793 . 63794 move 20 80 63795 text n = ^ntotal 63796 move 20 75 63797 text accept = ^naccept 63798 move 20 70 63799 text reject = ^nreject 63800 63801-----SUBREGION LIMITS-------------------------------------------------- 63802 63803SUBREGION LIMITS 63804 63805Name: 63806 ...SUBREGION LIMITS 63807 63808Type: 63809 Plot Control Command 63810 63811Purpose: 63812 Specifies the limits (minimum and maximum) for subregions 63813 of subsequent plots. 63814 63815Description: 63816 Dataplot now supports subregions on plots. Subregions are 63817 motivated by the desire to denote "engineering limits" on a 63818 plot. That is, a rectangle, denoting an acceptance region in 63819 both the X and Y directions, is drawn and then the plot is 63820 overlaid on top of this. 63821 63822 Although the subregion capability was motivated for the purpose 63823 of denoting engineering limits, they can in fact be used for 63824 whatever purpose you want. Subregions apply to all subsequent 63825 2-D plots (but not 3-D plots). 63826 63827 Currently, subregions are limited to rectangular regions. This 63828 will be upgraded to polygonal regions in a future implementation. 63829 63830 The SUBREGION command is used to turn subregions on or off and 63831 up to 10 subregions can be specified. In most cases where 63832 subregions are defined, only a single subregion is used. 63833 63834Syntax 1: 63835 SUBREGION <prefix>LIMITS <n1> <n2> 63836 where <n1> is a number or parameter that specifies the desired 63837 lower limit; 63838 <n2> is a number or parameter that specifies the desired 63839 upper limit; 63840 and <prefix> is one of the following: 63841 X refers to vertical axis 63842 Y refers to horizontal axis 63843 no prefix refers to both axes. 63844 63845 This syntax sets the subregion limits for the first subregion. 63846 63847Syntax 2: 63848 SUBREGION <id> <prefix>LIMITS <n1> <n2> 63849 where <id> is a number or parameter between 1 and 10 that specifies 63850 which of the 10 subregions that these limits apply to; 63851 <n1> is a number or parameter that specifies the desired 63852 lower limit; 63853 <n2> is a number or parameter that specifies the desired 63854 upper limit; 63855 and <prefix> is one of the following: 63856 X refers to vertical axis 63857 Y refers to horizontal axis 63858 no prefix refers to both axes. 63859 63860Examples: 63861 SUBREGION LIMITS 0.5 4.5 63862 SUBREGION XLIMITS 0 100 63863 SUBREGION YLIMITS 0 100 63864 SUBREGION XLIMITS A B 63865 SUBREGION 2 LIMITS 0.5 4.5 63866 63867Note: 63868 You do not need to adjust the settings for the CHARACTER, LINE, 63869 BAR, and SPIKE when using subregions. DATAPLOT automatically 63870 shifts these in the background. The attributes for the subregion 63871 are set with the following commands: 63872 63873 REGION FILL <ON/OFF> 63874 REGION COLOR <COLOR> 63875 REGION BORDER LINE <LINETYPE> 63876 REGION BORDER COLOR <COLOR> 63877 63878 The REGION FILL and REGION COLOR determine the attributes of the 63879 interior of the rectangle. The two most common choices are 63880 to leave it blank or to fill it with some type of light 63881 gray scale color. The attributes of the rectangle border are 63882 set with the REGION BORDER LINE and REGION BORDER COLOR commands. 63883 The standard line types (SOLID, BLANK, DASH, DOTTED) are supported. 63884 If you have more than one subregion defined, you should specify 63885 multiple settings on the above commands. For example, 63886 63887 REGION FILL ON ON ON 63888 REGION COLOR G25 G25 G25 63889 63890Note: 63891 The SUBREGION ...LIMITS command with no argument reverts the limits 63892 to the default. A SUBREGION ...LIMITS command with no prefix refers 63893 to both axes. Thus SUBREGION LIMITS 3 7 sets the limits for both 63894 axes to 3 and 7. 63895 63896Default: 63897 No subregions are drawn. If a subregion is turned on, but no 63898 limits are specified, then the subregion extends to the minimum and 63899 maximum points in both the X and Y axes. 63900 63901Synonyms: 63902 None 63903 63904Related Commands: 63905 PLOT = Generates a data or function plot. 63906 SUBREGION = Specifiy whether a subregion is on or off. 63907 63908Applications: 63909 Denoting "Engineering Limits" on plots. 63910 63911Implementation Date: 63912 2000/1 63913 63914Program: 63915 dimension 50 varialbes 63916 skip 25 63917 read simon1.dat y1 y2 x1 x2 x3 x4 x5 block runseq 63918 . 63919 char x 63920 line blank 63921 . 63922 subregion on 63923 subregion xlimits 0.35 0.42 63924 subregion ylimits 2000 3000 63925 region fill on 63926 region border line dash 63927 region color g90 63928 . 63929 plot y1 vs x1 63930 . 63931 move 20 80 63932 text n = ^ntotal 63933 move 20 75 63934 text accept = ^naccept 63935 move 20 70 63936 text reject = ^nreject 63937 63938-----SUBSAMPLE (LET)-------------------------------- 63939 63940SUBSAMPLE 63941 63942Name: 63943 SUBSAMPLE (LET) 63944 63945Type: 63946 Let Subcommand 63947 63948Purpose: 63949 Compute a subsample for a variable based on another index variable. 63950 63951Description: 63952 The SUBSAMPLE command is similar to the BOOTSTRAP SAMPLE command. 63953 In either case, an index variable is generated (often with the 63954 DISCRETE UNIFORM RANDOM NUMBERS, BOOTSTRAP INDEX or JACKNIFE INDEX 63955 commands). This index variable contains integer entries into the 63956 original variable. For example, an index variable containing the 63957 values 3, 5, 1, and 8 refers to Y(3), Y(5), Y(1), and Y(8) where Y 63958 is the original data variable. 63959 63960 The distinction between SUBSAMPLE and BOOTSTRAP SAMPLE is that 63961 BOOTSTRAP SAMPLE expects the original variable and the index 63962 variable to be the same length while SUBSAMPLE allows the index 63963 variable to be smaller than the original variable. With SUBSAMPLE, 63964 the returned variable is the same length as the index variable. 63965 63966 Both commands allow repeated values (i.e., sampling with 63967 replacement). This is determined by repeat values in the index 63968 variable. 63969 63970Syntax: 63971 LET <resp> = SUBSAMPLE <var> <ind> <SUBSET/EXCEPT/FOR qualification> 63972 where <var> is the variable being sampled; 63973 <ind> is the index variable (size less than or equal to 63974 <var>); 63975 <resp> is a variable (with the same length as <ind>) where the 63976 sampled values are returned; 63977 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 63978 63979Examples: 63980 LET RES3 = SUBSAMPLE RES2 IND 63981 63982Note: 63983 Index values less than 1 or greater than the size of the variable 63984 being sampled are ignored. 63985 63986Default: 63987 None 63988 63989Synonyms: 63990 None 63991 63992Related Commands: 63993 BOOTSTRAP SAMPLE = Generate a bootstrap sample. 63994 BOOTSTRAP INDEX = Generate a bootstrap index. 63995 LOOP = Initiate a loop. 63996 BOOTSTRAP PLOT = Generate a bootstrap plot. 63997 JACKNIFE PLOT = Generate a jacknife plot. 63998 JACKNIFE INDEX = Generate a jacknife index. 63999 64000Applications: 64001 XX 64002 64003Implementation Date: 64004 89/2 64005 64006Program: 64007 . PERFORM A JACKNIFE ANALYSIS 64008 LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 100 64009 LOOP FOR K = 1 1 100 64010 LET IND = SEQUENCE 1 1 100 64011 LET IND(K) = 0 64012 LET JUNK = SUBSAMPLE Y IND 64013 LET YMEAN = MEAN JUNK 64014 LET Y0(K) = YMEAN 64015 END OF LOOP 64016 HISTOGRAM Y0 64017 64018-----SUBSET------------------------------------------------------- 64019 64020SUBSET 64021 64022Name: 64023 SUBSET 64024 64025Type: 64026 Keyword 64027 64028Purpose: 64029 Specifies a subset to be included for any plot, analysis, and 64030 certain support commands. 64031 64032Syntax 1: 64033 <command> SUBSET <var> <qual> <list of values> 64034 where <command> is a DATAPLOT command that allows subsets; 64035 <var> is a variable for which the subset is defined; 64036 <qual> is an optional qualifier (=, <, >, <>, <=, >=); 64037 and <list of values> are the values of <var> to be excluded. 64038 64039 If <qual> is omitted, equality (i.e, =) is assumed. 64040 64041Syntax 2: 64042 <command> SUBSET <var> <min> TO <max> 64043 <command> SUBSET <var> = <min> TO <max> 64044 where <command> is a DATAPLOT command that allows subsets; 64045 <var> is a variable for which the subset is defined; 64046 <min> is the minimum value of <var> to exclude; 64047 and <max> is the maximum value of <var> to exclude. 64048 64049 The "=" qualifier is optional in this syntax. This syntax excludes 64050 all values between (inclusive) <min> and <max>. 64051 64052Examples: 64053 FIT Y=A*EXP(B*X) SUBSET X 101 TO 1000 64054 PLOT Y PRED VERSUS X SUBSET LAB 4 64055 PLOT Y X SUBSET LAB 2 TO 8 SUBSET LAB 4 64056 LET Y1 = Y2 SUBSET TAG = 4 64057 64058Note: 64059 The SUBSET variable does not have to be one of the variables used 64060 in the command (e.g., PLOT X SUBSET TAG > 0). 64061 64062Note: 64063 Using SUBSET TAG 101 1000 means to subset on the specific values 64064 101 and 1000 (you can list more than two values) while using 64065 SUBSET 101 TO 1000 means to subset on the values between 101 and 64066 1000 (inclusive). 64067 64068Note: 64069 Although DATAPLOT does not explicitly support missing values, the 64070 SUBSET command can be used to exclude missing data (pick a value 64071 to mean missing and SUBSET on that value). 64072 64073Note: 64074 More than one SUBSET clause can be used on a single command. 64075 64076Default: 64077 None 64078 64079Synonyms: 64080 None 64081 64082Related Commands: 64083 EXCEPT = Allows exclusion-specification of a subset. 64084 FOR = Allows row-specification of a subset. 64085 < = Allows "less than" subset. 64086 <= = Allows "less than or equal to" subset. 64087 = = Allows "equal to" subset. 64088 >= = Allows "greater than or equal to" subset. 64089 > = Allows "greater than" subset. 64090 <> = Allows "not equal" subset. 64091 64092Applications: 64093 XX 64094 64095Implementation Date: 64096 Pre-1987 64097 64098Program: 64099 XX 64100 64101-----SUBSTITUTE CHARACTER-------------------------------------------- 64102 64103SUBSTITUTE CHARACTER 64104 64105Name: 64106 SUBSTITUTE CHARACTER 64107 64108Type: 64109 Support Command 64110 64111Purpose: 64112 Specify the character to use as the substitution character. 64113 64114Description: 64115 The substitute character signifies that the parameter name 64116 following it should be replaced with the value of that parameter. 64117 64118 The following name types can be substituted. 64119 64120 1. If the name is a parameter, the value of the parameter 64121 will be substituted. 64122 64123 2. If the name is a string, the value of the string will 64124 be substituted. 64125 64126 3. If the name is a variable, Dataplot will check to see 64127 if an alias for the variable name has been defined 64128 (via the VARIABLE LABEL command). If so, that alias 64129 will be substituted. If an alias has not been defined, 64130 the substitution may be unpredictable. 64131 64132 If Y is a variable, the following is not currently 64133 supported 64134 64135 LET STRING S = ^Y(2) 64136 64137 For this case, you need to do something like 64138 64139 LET A = Y(2) 64140 LET STRING S = ^A 64141 64142 4. If you have defined row labels (via READ ROW LABEL or 64143 LET ... = ROW LABEL ...), you can do something like 64144 64145 ^ROWLABEL^K 64146 64147 where K in an index to the desired row of the row 64148 labels. 64149 64150 5. Any other name type will result in an error message 64151 with no substitution being performed. 64152 64153Syntax: 64154 SUBSTITUTE CHARACTER <char> 64155 where <char> is the character to use as the substitute character. 64156 64157Examples: 64158 SUBSTITUTE CHARACTER @ 64159 SUBSTITUTE CHARACTER ^ 64160 64161Note: 64162 Generally it is not necessary to change the substitute character. 64163 The one exception is if you want to define strings that contain 64164 the default substitute character. 64165 64166Note: 64167 The substitute character can be used effectively with the LOOP 64168 command. For example, assume that variables Y1 thru YN and 64169 strings S1 and SN have been previously defined: 64170 64171 LOOP FOR K = 1 1 N 64172 TITLE Y^K VS X 64173 LEGEND 1 ^S^K 64174 PLOT Y^K VS X 64175 END OF LOOP 64176 64177 Note the distinction between Y^K in the PLOT command and ^S^K in 64178 the LEGEND command. For the plot command, we want PLOT Y1 VS X 64179 while for the LEGEND command we want to insert the value of the 64180 string S1. This is the reason that the Y^K has no preceding ^ 64181 while the ^S^K does. 64182 64183Note: 64184 The following characters are used to determine the end of the 64185 parameter name: 64186 - a space 64187 ( - a left parenthesis 64188 ) - a right parenthesis 64189 " - a quote character 64190 & - an ampersand character 64191 . - a period 64192 ^ - another substitute character 64193 , - a comma 64194 : - a colon 64195 ; - a semi-colon 64196 ] - a right bracket 64197 + - a plus 64198 - - a minus 64199 * - an asterisk 64200 / - a forward slash 64201 64202Note: 64203 The substitution is performed before the command is interpreted. 64204 64205Note: 64206 If the parameter is undefined, it is replaced with a space 64207 character in the command line. 64208 64209Note: 64210 The VALU() command also performs parameter substitution. However, 64211 it only works for a few commands (specifically LEGEND, TITLE, 64212 LABEL, and TEXT) while the substitute character works on any 64213 command. 64214 64215Note: 64216 The substitute character can also be changed with the command 64217 64218 SET REPLACE <char> 64219 64220Note: 64221 There may be occassions where you want to suppress the 64222 character substitution. For examle, you may want to use 64223 the "^" character in a string. You can suspend character 64224 substitution with the command 64225 64226 SET COMMAND SUBSTITUTION OFF 64227 64228 To resume character substitution, enter 64229 64230 SET COMMAND SUBSTITUTION ON 64231 64232Note: 64233 If you are substituting for a parameter, there are several 64234 ways you can control the appearance. 64235 64236 1. You can use the ROUND command. For example, 64237 64238 LET CC = ROUND(CC,2) 64239 LET STRING S = CORR: ^CC 64240 64241 2. By default, parameters are expanded into numeric 64242 format (e.g., 0.0017). If you would like the parameter 64243 expanded in exponential format, enter the command 64244 64245 SET PARAMETER EXPANSION EXPONENTIAL 64246 64247 To restore the default, enter 64248 64249 SET PARAMETER EXPANSION NUMERIC 64250 64251 3. For the most control, you can specify a Fortran 64252 format by entering the command 64253 64254 SET SUBSTITUTION FORMAT <string> 64255 64256 For example, 64257 64258 SET SUBSTITUTION FORMAT F4.2 64259 SET SUBSTITUTION FORMAT E15.7 64260 64261 To turn this off, enter 64262 64263 SET SUBSTITUTION FORMAT OFF 64264 64265 Dataplot uses the specified format with an internal Fortran 64266 WRITE statement. That is 64267 64268 WRITE(ISTR,IFORMT,ERR=statement)VAL 64269 64270 where IFORMT is the specified format and VAL is the 64271 value of the parameter. Dataplot does no parsing or 64272 error checking on the specified format. Typically, only 64273 F, E, or G formats should be used. If there is an error 64274 using the Fortran format specification, Dataplot will 64275 revert to its default parameter expansion (no error 64276 message will be generated). The format string is limited 64277 to a maximum of 8 characters and the maximum number of 64278 characters for the expanded parameter is 20. 64279 64280Synonyms: 64281 REPLACEMENT CHARACTER 64282 64283Related Commands: 64284 LOOP = Perform a loop. 64285 VALU() = Perform parameter substitution within 64286 certain 64287 commands. 64288 TERMINATOR CHARACTER = Define the character that terminates a 64289 command. 64290 CONTINUE CHARACTER = Define the character that specifies that 64291 a command is continued onto the next line. 64292 64293Applications: 64294 XX 64295 64296Implementation Date: 64297 Pre-1987 64298 2000/01: Support for VARIABLE LABEL substitution 64299 2007/09: Support for ^ROWLABEL^K 64300 2019/01: Support for SET SUBSTITUTION FORMAT 64301 2019/01: Support for SET COMMAND SUBSTITUTION 64302 64303Program: 64304 . Step 1: Read the data 64305 . 64306 skip 25 64307 read weibbury.dat y 64308 skip 0 64309 . 64310 . Step 2: Maximum likelihood estimates 64311 . 64312 set write decimals 5 64313 weibull mle y 64314 let gamma = gammaml 64315 let pploc = 0 64316 let ppscale = alphaml 64317 . 64318 title case asis 64319 label case asis 64320 title Weibull Probability Plot 64321 y1label Sorted Data 64322 x1label Percentiles for Fitted Weibull Distribution 64323 character circle 64324 character hw 1 0.75 64325 character fill on 64326 line blank 64327 . 64328 . Step 3: Generate probability plot 64329 . 64330 weibull probability plot y 64331 . 64332 let gamma = round(gamma,2) 64333 move 20 85 64334 text Gamma = ^gamma 64335 let ppscale = round(ppscale,2) 64336 move 20 82 64337 text Scale = ^ppscale 64338 let ppcc = round(ppcc,3) 64339 move 20 79 64340 text PPCC = ^ppcc 64341 64342-----SUBSTRING----------------------------------------------------- 64343 64344SUBSTRING 64345 64346Name: 64347 SUBSTRING 64348 64349Type: 64350 Let Subcommand 64351 64352Purpose: 64353 Extract a substring of a previously defined string. 64354 specified position. 64355 64356Syntax: 64357 LET <sout> = SUBSTRING <sorg> <nstart> <nstop> 64358 where <sout> is the name of the resulting string; 64359 <sorg> is the name of the original string; 64360 <nstart> is the start position in <sorg>; 64361 and <nstop> is the stop position in <sorg>. 64362 64363Examples: 64364 LET SOUT = SUBSTRING S1 NSTART NSTOP 64365 LET SOUT = SUBSTRING S1 3 8 64366 64367Note: 64368 The name of the new string can be the same as the original 64369 string. For example, 64370 64371 LET FNAME = SUBSTRING FNAME NSTART NSTOP 64372 64373 In this case, FNAME will now contain the substring rather than 64374 the original string. 64375 64376Note: 64377 The string on the right hand side of the equal sign must be a 64378 previously existing string. That is, expressions are not allowed. 64379 For example, instead of 64380 64381 LET FNAME = SUBSTRING "file99.dat" 5 6 64382 64383 you need to do 64384 64385 LET STRING SORG = file99.dat 64386 LET FNAME = SUBSTRING SORG 5 6 64387 64388 The start and stop position can be either a parameter or a numeric 64389 value. However, it cannot be a numeric expression. So 64390 64391 LET FNAME = SUBSTRING SORG 5 6 64392 LET FNAME = SUBSTRING SORG NSTART NSTOP 64393 64394 are both allowed but 64395 64396 LET FNAME = SUBSTRING SORG NSTART NLEN/2 64397 64398 is not allowed. You would need to enter this as 64399 64400 LET NSTOP = NLEN/2 64401 LET FNAME = SUBSTRING FNAME NSTART NSTOP 64402 64403Note: 64404 The total number of characters that DATAPLOT can use for storing 64405 functions and strings is set when DATAPLOT is built. The current 64406 default (11/2008) is 50,000 characters. Previous versions may set 64407 this limit at 1,000 or 10,000 characters. This limit applies to the 64408 combined number of characters for all functions and strings. 64409 64410Default: 64411 None 64412 64413Synonyms: 64414 None 64415 64416Related Commands: 64417 LET FUNCTION = Defines a function. 64418 LET STRING = Defines a string. 64419 READ STRING = Reads a string from a file. 64420 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 64421 & = Concatenate two strings. 64422 STRING INDEX = Extract the start/stop positions of a substring 64423 within a string. 64424 STRING CONCATENATE = Concatenate one or more previously defined 64425 strings. 64426 STRING LENGTH = Return the length of a string. 64427 STRING EDIT = Edit a string. 64428 STRING MERGE = Insert a string into another string without 64429 overwrite. 64430 STRING REPLACE = Insert a string into another string with 64431 overwrite. 64432 LOWER CASE = Convert a string to lower case. 64433 UPPER CASE = Convert a string to upper case. 64434 CHARACTER = Convert numeric values to strings based on 64435 the ASCII collating sequence. 64436 ICHAR = Convert a string to numeric values based on 64437 the ASCII collating sequence. 64438 GROUP LABEL = Define the text for group labels. 64439 64440Applications: 64441 Data Management 64442 64443Implementation Date: 64444 11/2008 64445 64446Program: 64447 LET STRING S1 = file23.dat 64448 LET NSTOP = STRING LENGTH S1 64449 LET NSTART = STRING INDEX S1 SPERIOD 64450 LET SEXT = SUBSTRING S1 NSTART NSTOP 64451 LET NSTOP = NSTART - 1 64452 LET NSTART = 1 64453 LET SBASE = SUBSTRING S1 NSTART NSTOP 64454 64455 The resulting strings SEXT and SBASE will contain 64456 64457 .dat 64458 file23 64459 64460-----SUM (LET)--------------------------------------------------- 64461 64462SUM 64463 64464Name: 64465 SUM (LET) 64466 64467Type: 64468 Let Subcommand 64469 64470Purpose: 64471 Sum the elements of a variable. 64472 64473Syntax: 64474 LET <par> = SUM <x1> <SUBSET/EXCEPT/FOR qualification> 64475 where <x1> is the variable for which the sum is to be computed; 64476 <par> is a parameter where the computed sum is saved; 64477 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 64478 64479Examples: 64480 LET A = SUM Y 64481 LET A = SUM Y SUBSET TAG > 2 64482 64483Default: 64484 None 64485 64486Synonyms: 64487 None 64488 64489Related Commands: 64490 PRODUCT = Compute the product of the elements of a variable. 64491 INTEGRAL = Compute the integral of elements in a variable. 64492 SUM PLOT = Generate a sums (vs subsets) plot. 64493 64494Applications: 64495 XX 64496 64497Implementation Date: 64498 XX 64499 64500Program: 64501 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 64502 LET A = SUM Y1 64503 64504-----SUM OF SQUARES (LET)----------------------------------------- 64505 64506SUM OF SQUARES 64507 64508Name: 64509 SUM OF SQUARES (LET) 64510 64511Type: 64512 Let Subcommand 64513 64514Purpose: 64515 Compute the sum of squares of a variable. 64516 64517Description: 64518 The sum of squares has the formula: 64519 64520 SSQ = SUM[i=1 to N][X(i)**2] 64521 64522Syntax 1: 64523 LET <par> = SUM OF SQUARES <y> <SUBSET/EXCEPT/FOR qualification> 64524 where <y> is the response variable; 64525 <par> is a parameter where the computed sum of squares is saved; 64526 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 64527 64528Syntax 2: 64529 LET <par> = DIFFERENCE OF SUM OF SQUARES <y1> <y2> 64530 <SUBSET/EXCEPT/FOR qualification> 64531 where <y1> is the first response variable; 64532 <y2> is the second response variable; 64533 <par> is a parameter where the computed difference of 64534 the sum of squares is saved; 64535 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 64536 64537 This syntax computes the sum of squares of <y1> and <y2> and then 64538 computes the difference of the two sum of squares values. 64539 64540Examples: 64541 LET A = SUM OF SQUARES Y1 64542 LET A = SUM OF SQUARES Y1 SUBSET TAG > 2 64543 LET A = DIFFERENCE OF SUM OF SQUARES Y1 Y2 64544 64545Note: 64546 In some applications it may be desired to cap the value 64547 of outliers. This is most common when the response variable 64548 is a z-score or some other standardized score. 64549 64550 To specify this value, enter the command 64551 64552 LET CAPVALUE = <value> 64553 64554 where <value> is typically 3 or 4 (if the reponse data are 64555 z-scores or z-score type data). Note that the value represents 64556 an absolute value. For example, if CAPVALUE is 4, values greater 64557 than 4 will be set to 4 and values less than -4 will be set to -4. 64558 64559Note: 64560 Dataplot statistics can be used in a number of commands. For 64561 details, enter 64562 64563 HELP STATISTICS 64564 64565Default: 64566 None 64567 64568Synonyms: 64569 SSQ is a synonym for SUM OF SQUARES 64570 64571Related Commands: 64572 MEAN = Compute the mean of a variable. 64573 STANDARD DEVIATION = Compute the standard deviation of a variable. 64574 ROOT MEAN SQUARE = Compute the root mean square error of a 64575 variable. 64576 64577Applications: 64578 Statistics 64579 64580Implementation Date: 64581 2012/2 64582 2012/6: Added DIFFERENCE OF SUM OF SQUARES 64583 64584Program: 64585 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 64586 LET SSQ = SUM OF SQUARES Y1 64587 64588-----SUM OF SQUARES FROM MEAN (LET)---------------------------------- 64589 64590SUM OF SQUARES FROM MEAN 64591 64592Name: 64593 SUM OF SQUARES FROM MEAN (LET) 64594 64595Type: 64596 Let Subcommand 64597 64598Purpose: 64599 Compute the sum of squares from the mean of a variable. 64600 64601Description: 64602 The sum of squares from the mean has the formula: 64603 64604 SSQ = SUM[i=1 to N][(X(i) - Xbar)**2] 64605 64606 with Xbar denoting the mean of the X(i). 64607 64608Syntax 1: 64609 LET <par> = SUM OF SQUARES FROM MEAN <y> 64610 <SUBSET/EXCEPT/FOR qualification> 64611 where <y> is the response variable; 64612 <par> is a parameter where the computed sum of squares from the 64613 mean is saved; 64614 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 64615 64616Syntax 2: 64617 LET <par> = DIFFERENCE OF SUM OF SQUARES FROM MEAN <y1> <y2> 64618 <SUBSET/EXCEPT/FOR qualification> 64619 where <y1> is the first response variable; 64620 <y2> is the second response variable; 64621 <par> is a parameter where the computed difference of 64622 the sum of squares from the mean is saved; 64623 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 64624 64625 This syntax computes the sum of squares from the mean of <y1> and 64626 <y2> and then computes the difference of the two sum of squares 64627 values. 64628 64629Examples: 64630 LET A = SUM OF SQUARES FROM MEAN Y1 64631 LET A = SUM OF SQUARES FROM MEAN Y1 SUBSET TAG > 2 64632 LET A = DIFFERENCE OF SUM OF SQUARES FROM MEAN Y1 Y2 64633 64634Default: 64635 None 64636 64637Synonyms: 64638 SUMS OF SQUARES FROM MEAN is a synonym for SUM OF SQUARES FROM MEAN 64639 64640Related Commands: 64641 SUM OF SQUARES = Compute the sum of squares for a variable. 64642 MEAN = Compute the mean of a variable. 64643 STANDARD DEVIATION = Compute the standard deviation of a variable. 64644 ROOT MEAN SQUARE = Compute the root mean square error of a 64645 variable. 64646 64647Applications: 64648 Statistics 64649 64650Implementation Date: 64651 2013/2 64652 64653Program: 64654 LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100 64655 LET Y1 = 10 + 5*Y1 64656 LET SSQM = SUM OF SQUARES FROM MEAN Y1 64657 SET WRITE DECIMALS 4 64658 PRINT "Sum of Squares from Mean = ^SSQM" 64659 64660-----SUM PLOT--------------------------------------------------- 64661 64662SUM PLOT 64663 64664Name: 64665 SUM PLOT 64666 64667Type: 64668 Graphics Command 64669 64670Purpose: 64671 Generates a sum plot. 64672 64673Description: 64674 A sum plot is a plot consisting of subsample sums versus 64675 subsample index. The subsample sum is the sum of the data in the 64676 subsample. The sum plot is used to answer the question-- "Does 64677 the subsample sum-of-counts change over different subsamples?". 64678 It consists of: 64679 Vertical axis = subsample sum; 64680 Horizontal axis = subsample index. 64681 The sum plot yields 2 traces: 64682 1. a subsample sum trace; and 64683 2. a full-sample sum reference line. 64684 Like usual, the appearance of these 2 traces is 64685 controlled by the first 2 settings of the LINES, 64686 CHARACTERS, SPIKES, BARS, and similar attributes. 64687 64688Syntax: 64689 SUM PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification> 64690 where <y> is the response (= dependent) variable; 64691 <x> is the subsample identifier variable (this variable 64692 will appear on the horizontal axis); 64693 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 64694 64695Examples: 64696 SUM PLOT Y X 64697 SUM PLOT Y X1 64698 64699Default: 64700 None 64701 64702Synonyms: 64703 None 64704 64705Related Commands: 64706 CHARACTERS = Sets the type for plot characters. 64707 LINES = Sets the type for plot lines. 64708 FREQUENCY (LET) = Compute subsample frequencies. 64709 HISTOGRAM = Generates a histogram. 64710 PRODUCT PLOT = Generates a product plot. 64711 MEAN PLOT = Generates a mean plot. 64712 BOX PLOT = Generates a box plot. 64713 PLOT = Generates a data or function plot. 64714 64715Applications: 64716 Exploratory Data Analysis 64717 64718Implementation Date: 64719 88/9 64720 64721Program: 64722 LET Y = DATA 2 4 5 10 10 20 25 30 35 64723 LET X = DATA 1 1 1 2 2 3 3 3 3 64724 LINE BLANK DASH 64725 CHARACTER X BLANK 64726 XLIMITS 0.5 3.5 64727 Y1LABEL SUM 64728 X1LABEL GROUP ID 64729 SUM PLOT Y X 64730 64731-----SUMMARY------------------------------------------------------- 64732 64733SUMMARY 64734 64735Name: 64736 SUMMARY 64737 64738Type: 64739 Analysis Command 64740 64741Purpose: 64742 Carries out a summary analysis. 64743 64744Description: 64745 A summary analysis is a data analysis technique for computing and 64746 tabulating a variety of summary statistics for a data set. This 64747 includes measures of location (e.g., the mean), of dispersion 64748 (e.g., the standard deviation), of randomness (the 64749 autocorrelation), and of the distribution (e.g., the skewness). 64750 64751Syntax: 64752 SUMMARY <y1> <SUBSET/EXCEPT/FOR qualification> 64753 where <y1> is a response variable; 64754 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 64755 64756Examples: 64757 SUMMARY Y 64758 SUMMARY Y2 64759 64760Note: 64761 Most of the statistics computed by SUMMARY can also be computed 64762 individually as LET subcommands. 64763 64764Default: 64765 None 64766 64767Synonyms: 64768 None 64769 64770Related Commands: 64771 LET = Compute various statistics and transformations. 64772 64773Applications: 64774 XX 64775 64776Implementation Date: 64777 XX 64778 64779Program: 64780 LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 100 64781 SUMMARY Y 64782 64783-----SUPERSCRIPT SCALE (SET)--------------------------------------- 64784 64785SUPERSCRIPT SCALE 64786 64787Name: 64788 SUPERSCRIPT SCALE (SET) 64789 64790Type: 64791 Set Subcommand 64792 64793Purpose: 64794 Specify the horizontal and vertical scale factors for the size 64795 of superscript and subscript characters. 64796 64797Description: 64798 By default, Dataplot sets the height and width of characters 64799 drawn in superscripts and subscripts to 0.5 of the current 64800 character height and width. 64801 64802 This command allows you to specify a different size factor. 64803 Note that the value is entered as a fraction of the current 64804 character size. For example, a size of 1.0 leaves the 64805 character size unchanged and the default size is 0.5. 64806 64807Syntax 1: 64808 SET SUPERSCRIPT HORIZONTAL SCALE <value> 64809 where <value> is positive number between 0 and 20. 64810 64811 This syntax sets the width of the superscript/subscript 64812 characters relative to the current character width. 64813 64814Syntax 2: 64815 SET SUPERSCRIPT VERTICAL SCALE <value> 64816 where <value> is positive number between 0 and 20. 64817 64818 This syntax sets the height of the superscript/subscript 64819 characters relative to the current character height. 64820 64821Examples: 64822 SET SUPERSCRIPT VERTICAL SCALE 1.0 64823 SET SUPERSCRIPT HORIZONTAL SCALE 1.0 64824 64825 SET SUPERSCRIPT VERTICAL SCALE 0.75 64826 SET SUPERSCRIPT HORIZONTAL SCALE 0.5 64827 64828 SET SUPERSCRIPT VERTICAL SCALE 0.25 64829 SET SUPERSCRIPT HORIZONTAL SCALE 0.5 64830 64831Default: 64832 The default is to set both the character height and width to 64833 0.5 of their current value. 64834 64835Synonyms: 64836 SET SUBSCRIPT VERTICAL SCALE is a synonym for SET SUPERSCRIPT 64837 VERTICAL SCALE and SET SUBSCRIPT HORIZONTAL SCALE is a synonym for 64838 SET SUPERSCRIPT HORIZONTAL SCALE. 64839 64840Related Commands: 64841 SUP() = Initiate a superscript in a text string. 64842 UNSP() = Terminate a superscript in a text string. 64843 SUB() = Initiate a subscript in a text string. 64844 UNSB() = Terminate a subscript in a text string. 64845 TEXT = Generate a text string on a graph. 64846 64847Applications: 64848 Presentation Graphics 64849 64850Implementation Date: 64851 2001/3 64852 64853Program: 64854 erase 64855 font triplex italic 64856 crlf off 64857 hw 4 3 64858 . 64859 move 20 95 64860 text default size: 64861 move 20 90 64862 text sub()tunsb()nsup()()13unsp() 64863 hw .5 1 64864 arrow 36 91 44 91 64865 hw 4 3 64866 text sub()6unsb()csup()13unsp() + lc()beta()sup()+unsp() + nu() 64867 . 64868 move 20 75 64869 text size 1: 64870 move 20 70 64871 set superscript horizontal scale 1 64872 set superscript vertical scale 1 64873 text sub()tunsb()nsup()()13unsp() 64874 hw .5 1 64875 arrow 36 71 44 71 64876 hw 4 3 64877 text sub()6unsb()csup()13unsp() + lc()beta()sup()+unsp() + nu() 64878 . 64879 move 20 55 64880 text size 0.5, 0.75: 64881 move 20 50 64882 set superscript horizontal scale 0.5 64883 set superscript vertical scale 0.75 64884 text sub()tunsb()nsup()()13unsp() 64885 hw .5 1 64886 arrow 36 51 44 51 64887 hw 4 3 64888 text sub()6unsb()csup()13unsp() + lc()beta()sup()+unsp() + nu() 64889 64890-----SYMBOL PLOT-------------------------------------- 64891 64892SYMBOL PLOT 64893 64894Name: 64895 SYMBOL PLOT 64896 64897Type: 64898 Graphics Command 64899 64900Purpose: 64901 Generates a symbol plot. 64902 64903Description: 64904 A symbol plot is a scatter plot for which the attributes of the 64905 plot symbols are controlled by the values of other variables. 64906 This plot allows the size, type, color, and fill attribute to be 64907 controlled. 64908 64909Syntax 1: 64910 SYMBOL PLOT <y> <x> <size> <SUBSET/EXCEPT/FOR qualification> 64911 where <y> is the vertical axis variable; 64912 <x> is the horizontal axis variable; 64913 <size> is a variable that controls the size of the plot 64914 symbol; 64915 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 64916 64917Syntax 2: 64918 SYMBOL PLOT <y> <x> <size> <symbol> 64919 <SUBSET/EXCEPT/FOR qualification> 64920 where <y> is the vertical axis variable; 64921 <x> is the horizontal axis variable; 64922 <size> is a variable that controls the size of the plot 64923 symbol; 64924 <symbol> is a variable that controls the type of symbol 64925 plotted; 64926 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 64927 64928Syntax 3: 64929 SYMBOL PLOT <y> <x> <size> <symbol> <color> 64930 <SUBSET/EXCEPT/FOR qualification> 64931 where <y> is the vertical axis variable; 64932 <x> is the horizontal axis variable; 64933 <size> is a variable that controls the size of the plot 64934 symbol; 64935 <symbol> is a variable that controls the type of symbol 64936 plotted; 64937 <color> is a variable that controls the color of the symbol; 64938 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 64939 64940Syntax 4: 64941 SYMBOL PLOT <y> <x> <size> <symbol> <color> <fill> 64942 <SUBSET/EXCEPT/FOR qualification> 64943 where <y> is the vertical axis variable; 64944 <x> is the horizontal axis variable; 64945 <size> is a variable that controls the size of the plot 64946 symbol; 64947 <symbol> is a variable that controls the type of symbol 64948 plotted; 64949 <color> is a variable that controls the color of the symbol; 64950 <fill> is an optional variable that controls whether the 64951 symbol is filled or not; 64952 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 64953 64954Examples: 64955 SYMBOL PLOT Y X PRESSURE 64956 SYMBOL PLOT Y X PRESSURE TYPE 64957 SYMBOL PLOT Y X PRESSURE TYPE ICOL 64958 SYMBOL PLOT Y X PRESSURE TYPE ICOL IFILL 64959 64960Note: 64961 SYMBOL PLOT Y and SYMBOL PLOT Y X are equivalent to PLOT Y and 64962 PLOT Y X respectively. The only difference is that the line 64963 pattern is automatically set to blank. 64964 64965Note: 64966 The <size>, <symbol>, <color>, and <fill> variables are optional, 64967 but must be entered in that order. To skip one, set all the 64968 elements of the skipped variable to 1. For example, 64969 LET N = SIZE Y 64970 LET SYMBOL = 1 FOR I = 1 1 N 64971 SYMBOL PLOT Y X SIZE SYMBOL COLOR 64972 64973Note: 64974 The size for Y(i) is scaled to: Y(i)/MAXIMUM(ABS(Y)). The maximum 64975 value of Y is set to the size given in the CHARACTER SIZE (or 64976 CHARACTER HW) command while the others multiply this size by the 64977 scale factor. The minimum scale factor is truncated at 5%. 64978 64979Note: 64980 The <symbol> and <color> variables define indices to the CHARACTER 64981 and CHARACTER COLOR commands respectively. That is, they contain 64982 values between 1 and 100 (e.g., a value of 3 would go to the third 64983 setting of these commands). 64984 64985Note: 64986 Zero values for the <fill> variable indicate non-filled characters 64987 while non-zero values indicate filled characters. In addition, to 64988 generate filled characters a fillable symbol must be used (e.g., 64989 CIRCLE or SQUARE). 64990 64991Default: 64992 None 64993 64994Synonyms: 64995 None 64996 64997Related Commands: 64998 CHARACTER = Sets the type for plot characters. 64999 CHARACTER COLOR = Sets the color for plot characters. 65000 CHARACTER FILL = Sets the fill for plot characters. 65001 ANDREWS PLOT = Generates an Andrews plot. 65002 PROFILE PLOT = Generates a profile plot. 65003 STAR PLOT = Generates a star plot. 65004 PLOT = Generates a data or function plot. 65005 65006Reference: 65007 "Graphical Methods of Data Analysis", Chambers, Cleveland, Kleiner, 65008 and Tukey. Wadsworth, 1983. 65009 65010Applications: 65011 Multivariate Analysis 65012 65013Implementation Date: 65014 92/12 65015 65016Program: 65017 DIMENSION 20 COLUMNS 65018 MULTIPLOT 2 2; MULTIPLOT CORNER COORDINATES 0 0 100 100 65019 SKIP 25 65020 READ CURRIE.DAT ID1 ID2 FRWC CTOTAL POT LEAD IRON 65021 LET TYPE = ID1 65022 LET TYPE = 1 SUBSET ID1 < 10 65023 LET TYPE = 2 SUBSET ID1 = 11 TO 19 65024 LET TYPE = 3 SUBSET ID1 > 19 65025 LET N = SIZE ID1 65026 LET DUMMY = 1 FOR I = 1 1 N 65027 TITLE AUTOMATIC 65028 Y1LABEL POTASSIUM 65029 X1LABEL LEAD 65030 LEGEND SIZE 1.2 65031 CHARACTER SIZE 6.0 ALL 65032 . 65033 CHARACTER CIRCLE SQUARE DIAMOND TRIANGLE 65034 LEGEND 1 IRON DETERMINES SYMBOL SIZE 65035 SYMBOL PLOT POT LEAD IRON 65036 . 65037 CHARACTER SIZE 2.0 ALL 65038 LEGEND 1 ID1 DETERMINES SYMBOL TYPE 65039 SYMBOL PLOT POT LEAD DUMMY TYPE 65040 . 65041 CHARACTER SIZE 6.0 ALL 65042 LEGEND 1 IRON DETERMINES SYMBOL SIZE 65043 LEGEND 2 ID1 DETERMINES SYMBOL TYPE 65044 SYMBOL PLOT POT LEAD IRON TYPE 65045 . 65046 LET AFILL = 0 FOR I = 1 1 N 65047 LET AFILL = 1 SUBSET ID2 = 1 65048 LEGEND 3 ID2 DETERMINES FILL 65049 SYMBOL PLOT POT LEAD IRON TYPE DUMMY AFILL 65050 END OF MULTIPLOT 65051 65052-----SYMMETRY PLOT-------------------------------------- 65053 65054SYMMETRY PLOT 65055 65056Name: 65057 SYMMETRY PLOT 65058 65059Type: 65060 Graphics Command 65061 65062Purpose: 65063 Generates a symmetry plot. 65064 65065Description: 65066 A symmetry plot is a graphical data analysis technique for 65067 assessing if a data set is symmetric about the mean. It consists 65068 of: 65069 Vertical axis = Y(n-i+1) - median; 65070 Horizontal axis = median - Y(i); 65071 where median is the sample median, Y is sample variable, and i goes 65072 from 1 to the index of the median point. This plot graphs the 65073 distance from the median of points above the median against the 65074 corresponding points below the median. The interpretation of this 65075 plot is that the closer these points lie to the 45% line, the 65076 more symmetric the data is. The symmetry plot can be generated 65077 for either raw data of for pre-computed frequencies (i.e., grouped 65078 data). 65079 65080Syntax 1: 65081 SYMMETRY PLOT <y> <SUBSET/EXCEPT/FOR qualification> 65082 where <y> is the variable of raw data values; 65083 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 65084 65085 This syntax is used when you have raw data. 65086 65087Syntax 2: 65088 SYMMETRY PLOT <y> <X> <SUBSET/EXCEPT/FOR qualification> 65089 where <y> is the variable of pre-computed frequencies; 65090 <x> is the variable of group identifiers; 65091 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 65092 65093 This syntax is used when you have raw data. 65094 65095Examples: 65096 SYMMETRY PLOT Y1 65097 SYMMETRY PLOT Y1 GROUP 65098 SYMMETRY PLOT Y1 SUBSET Y1 > -3.0 65099 65100Default: 65101 None 65102 65103Synonyms: 65104 None 65105 65106Related Commands: 65107 LINES = Sets the type for plot lines. 65108 CHARACTERS = Sets the type for plot characters. 65109 PLOT = Generates a data or function plot. 65110 PROBABILITY PLOT = Generate a probability plot. 65111 PERCENT POINT PLOT = Generates a percent point plot. 65112 65113Reference: 65114 "Graphical Methods for Data Analysis", Chambers, Cleveland, 65115 Kleiner, and Tukey. Wadsworth, 1983. 65116 65117Applications: 65118 Exploratory Data Analysis 65119 65120Implementation Date: 65121 88/9 65122 65123Program: 65124 SKIP 25 65125 READ MARSHAK.DAT Y 65126 CHARACTER CIRCLE 65127 CHARACTER HW 2.0 1.5 65128 LINE BLANK 65129 Y1LABEL POINTS ABOVE MEDIAN 65130 X1LABEL POINTS BELOW MEDIAN 65131 TITLE AUTOMATIC 65132 SYMMETRY PLOT Y 65133 65134-----SYNTAX------------------------------------------------------- 65135 65136 65137Syntax: 65138 65139Name: 65140 SYNTAX 65141 65142Type: 65143 Keyword 65144 65145Purpose: 65146 Symbolic name for DATAPLOT's syntax file. It is used with the 65147 SEARCH and LIST commands. 65148 65149Description: 65150 DATAPLOT's syntax file contains an example of the syntax for each 65151 DATAPLOT command sorted alphabetically. 65152 65153Syntax: 65154 None 65155 65156Examples: 65157 SEARCH SYNTAX FIT 65158 LIST SYNTAX FOR I = 1 1 35 65159 65160Note: 65161 The SYNTAX file is stored in the DATAPLOT directory. It has the 65162 name SYNTAX (or syntax for Unix systems). The exact file name and 65163 the directory where it is stored can vary depending on the 65164 installation (see your local DATAPLOT implementor to find the 65165 exact name on your system). 65166 65167Note: 65168 If DATAPLOT is unable to open the syntax file, it is most likely 65169 because the directory name is not specified correctly in the local 65170 DATAPLOT code. See your local DATAPLOT implementor to have this 65171 corrected. 65172 65173Default: 65174 None 65175 65176Synonyms: 65177 None 65178 65179Related Commands: 65180 SEARCH = Search a file for a string. 65181 LIST = Lists the contents of a file. 65182 DIRECTORY = Symbolic name for DATAPLOT's directory file. 65183 DICTIONARY = Symbolic name for DATAPLOT's dictionary file. 65184 DATASETS = Symbolic name for DATAPLOT's data sets file. 65185 DESIGNS = Symbolic name for DATAPLOT's design of experiments 65186 file. 65187 COMMANDS = Symbolic name for DATAPLOT's command file. 65188 MACROS = Symbolic name for DATAPLOT's macros file. 65189 PROGRAMS = Symbolic name for DATAPLOT's programs file. 65190 DISTRIBU = Symbolic name for DATAPLOT's distributions file. 65191 FUNCTION = Symbolic name for DATAPLOT's function file. 65192 65193Applications: 65194 XX 65195 65196Implementation Date: 65197 93/12 65198 65199Program: 65200 XX 65201 65202-----SYNCH (LET)-------------------------------- 65203 65204SYNCH 65205 65206Name: 65207 SYNCH (LET) 65208 65209Type: 65210 Library Function 65211 65212Purpose: 65213 Compute the synchrotron radiation function. 65214 65215Description: 65216 The synchrotron radiation function of order 1 is 65217 defined as: 65218 65219 f(x,1) = x*INTEGRAL[K(5/3)(t)dt], x >= 0 65220 65221 where the integral is defined from x to positive 65222 infinity and K(n) is the modified Bessel function of 65223 order n. 65224 65225 The synchrotron radiation function of order 2 is 65226 defined as: 65227 65228 f(x,2) = x*K(2/3)(x) x >= 0 65229 65230 where K(n) is the modified Bessel function of order n. 65231 65232 Dataplot computes this function using ACM Algorithm 757 (see 65233 Reference: below). 65234 65235Syntax 1: 65236 LET <y> = SYNCH1(<x>) <SUBSET/EXCEPT/FOR qualification> 65237 where <x> is a non-negative number, variable or parameter; 65238 <y> is a variable or a parameter (depending on what <x> 65239 is) where the computed synchrotron radiation 65240 function values are stored; 65241 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 65242 65243 This syntax computes the order 1 synchrotron radiation 65244 function. 65245 65246Syntax 2: 65247 LET <y> = SYNCH2(<x>) <SUBSET/EXCEPT/FOR qualification> 65248 where <x> is a non-negative number, variable or parameter; 65249 <y> is a variable or a parameter (depending on what <x> 65250 is) where the computed synchrotron radiation 65251 function values are stored; 65252 and where the <SUBSET/EXCEPT/FOR qualification> is optional. 65253 65254 This syntax computes the order 2 synchrotron radiation 65255 function. 65256 65257Examples: 65258 LET A = SYNCH1(2) 65259 LET A = SYNCH2(X) 65260 LET X2 = SYNCH1(X) FOR X1 = 0.1 0.1 3.0 65261 65262Note: 65263 Library functions are distinguished from let subcommands 65264 in the following ways. 65265 1) Functions enclose the input value in parenthesis. Let 65266 subcommands use spaces. 65267 2) Functions can accept (and return) either parameters 65268 (i.e., single values) or variables (i.e., an array of 65269 values) while let subcommands are specific in which they 65270 accept as input and what they return as output. 65271 3) Functions can accept expressions while let subcommands 65272 do not. For example, the following is legal: 65273 LET Y2 = ABS(Y1-INT(Y1)) 65274 For let subcommands, you typically have to do something 65275 like the following: 65276 LET YTEMP = Y**2 + 8 65277 LET A = SUM YTEMP 65278 65279Default: 65280 None 65281 65282Synonyms: 65283 None 65284 65285Related Commands: 65286 ABRAM = Compute the Abramowitz integral. 65287 CLAUSN = Compute the Clausen integral. 65288 DEBYE = Compute the Debye function. 65289 EXP3 = Compute the cubic exponential integral. 65290 GOODST = Compute the Goodwin and Stanton integral. 65291 LOBACH = Compute the Lobachevski integral. 65292 STROM = Compute the Stromgren integral. 65293 TRAN = Compute the transport integral. 65294 65295Reference: 65296 "ACM Transactions of Mathematical Software", Allan MacLead, 65297 Vol. 22, No. 3, September, 1996, pp. 288-301. 65298 65299Applications: 65300 Special Functions 65301 65302Implementation Date: 65303 1999/6 65304 65305Program: 65306 LINE SOLID DOTTED 65307 PLOT SYNCH1(X) FOR X = 0 0.01 10 AND 65308 PLOT SYNCH2(X) FOR X = 0 0.01 10 65309 65310-----SYSTEM------------------------------------------------------- 65311 65312SYSTEM 65313 65314Name: 65315 SYSTEM 65316 65317Type: 65318 Support Command 65319 65320Purpose: 65321 This command allows DATAPLOT to issue an operating system command 65322 on the host computer. 65323 65324Description: 65325 The Fortran 77/90 standard do not explicitly support a SYSTEM 65326 library function, so this command is compiler dependent. However, 65327 most Fortran compilers do provide a library function that supports 65328 this capability. 65329 65330 This command should be available on most currently suppported 65331 platforms. However, it is possible that the command is not 65332 available on your local platform. 65333 65334Syntax: 65335 SYSTEM <string> 65336 where <string> contains a command to be executed on the local 65337 operating system. 65338 65339Examples: 65340 SYSTEM DIR (on an IBM/PC system) 65341 SYSTEM ls (on a Unix system) 65342 65343Note: 65344 This command is host dependent. It is operational on the 65345 following systems: 65346 65347 UNIX/Linux (except Cray UNICOS) 65348 Microsoft Windows (based on Intel compiler) 65349 CYBER NOS/VE 65350 65351 It has been coded, but not tested, on the VAX/VMS system. 65352 65353Note: 65354 DATAPLOT does no error checking on the requested command. It is 65355 the users responsibility to enter the correct operating system 65356 command. 65357 65358Note: 65359 Systems may vary somewhat in how sophisticated a command can be 65360 executed. Also be aware that on most systems, a separate process 65361 is spawned and the environment is not passed back to the calling 65362 system. Specifically, on a Unix system, the following does not 65363 work: 65364 65365 SYSTEM cd ~/datasets 65366 65367 since the current environment is restored after the command 65368 completes execution. 65369 65370Note: 65371 The following updates were made to the SYSTEM command 03/2019. 65372 65373 For the Windows 7/8/10 platforms, the SYSTEM command works 65374 as follows: 65375 65376 1) A new terminal window is opened. 65377 2) The requested command is executed. 65378 3) When the requested command is completed, the new window is 65379 closed and control returns to the Dataplot session. 65380 65381 Several SET commands have been added to control this behavior. 65382 Specifically, 65383 65384 1) In some cases, it is desirable to leave the new Window up. 65385 For example, you may need to view the results from the 65386 SYSTEM command. To specify that the new command window 65387 should remain, enter the command 65388 65389 SET SYSTEM PERSIST ON 65390 65391 To reset the default, enter 65392 65393 SET SYSTEM PERSIST OFF 65394 65395 Note that control does not return to the Dataplot session 65396 until the new terminal window is closed. 65397 65398 This command has no effect on Unix/Linux and MacOS platforms. 65399 65400 2) In some cases, you may want the SYSTEM command to operate in 65401 the background and not open a new terminal window. To specify 65402 this, enter the command 65403 65404 SET SYSTEM HIDDEN ON 65405 65406 For Windows, Dataplot normally executes the SYSTEM command with 65407 the SYSTEMQQ system call in the Intel Fortran library. If 65408 HIDDEN is set to ON, Dataplot will use the EXECUTE_COMMAND_LINE 65409 routine that was added in the Fortran 2008 standard. If you 65410 compile Dataplot for Windows using an older version of the Intel 65411 compiler or a non-Intel compiler, the EXECUTE_COMMAND_LINE 65412 subroutine may or may not be available. If not, Dataplot will 65413 revert to using SYSTEMQQ (and HIDDEN ON will have no effect). 65414 65415 To reset the default, enter 65416 65417 SET SYSTEM HIDDEN OFF 65418 65419 This command has no effect on Unix/Linux and MacOS platforms. 65420 65421 3) By default, Dataplot uses "CALL SYSTEM" for Linux/Unix and 65422 MacOS platforms and "CALL SYSTEMQQ" for Windows platforms. 65423 65424 You can request that Dataplot use the EXECUTE_COMMAND_LINE 65425 subroutine instead by entering the command 65426 65427 SET QWIN SYSTEM EXECUTE COMMAND LINE 65428 65429 Be aware that this is relatively new addition to the Fortran 65430 standard and may not be available in all Fortran compilers (or 65431 in older versions of compilers). Specifically, it is not 65432 supported in gfortran (Linux, MacOS) until version 5.x and 65433 version 16 of the Intel compiler. So this option may not be 65434 available on all platforms. The Windows executable for 2019/03 65435 that can be downloaded from the Dataplot web site uses version 17 65436 of the Intel compiler, so this feature is available. If you are 65437 running Dataplot on a platform where EXECUTE_COMMAND_LINE is not 65438 available, Dataplot will revert to "CALL SYSTEM" or 65439 "CALL SYSTEMQQ". 65440 65441 One advantage of using EXECUTE_COMMAND_LINE is that it supports 65442 either synchronous or asynchronous execution. By synchronous, we 65443 mean that control does not return to the Dataplot session until 65444 the SYSTEM command completes execution. By asynchronous, we 65445 mean that control returns to the Dataplot session after the 65446 SYSTEM command is initated (but not neccessarily completed). 65447 65448 To specify asynchronous, enter 65449 65450 SET COMMAND LINE EXECUTE WAIT ON 65451 65452 To restore the default of synchronous, enter 65453 65454 SET COMMAND LINE EXECUTE WAIT OFF 65455 65456 Note that this command only applies if EXECUTE_COMMAND_LINE is 65457 used to implement the SYSTEM command. 65458 65459Note: 65460 This command preserves the case as entered. This is 65461 important for the Unix implementation since Unix commands are 65462 case sensitive. DATAPLOT does not try to guess what case 65463 should be passed to the local host. 65464 65465Default: 65466 None 65467 65468Synonyms: 65469 DOS 65470 UNIX 65471 65472Related Commands: 65473 SLEEP = Pause for <n> seconds. 65474 CD = Change the current directory 65475 PWD = Retrieve the current working directory. 65476 65477Applications: 65478 Interact with the local operating system 65479 65480Implementation Date: 65481 1989/02: Original implementation 65482 2019/03: Support for SET SYSTEM PERSIST 65483 2019/03: Support for SET SYSTEM HIDDEN 65484 2019/03: Support for SET QWIN SYSTEM EXECUTE COMMAND LINE 65485 2019/03: Support for SET COMMAND LINE EXECUTE WAIT 65486 65487Program: 65488 DEVICE 2 POSTSCRIPT 65489 PLOT X**2 FOR X = 1 1 9 65490 DEVICE 2 CLOSE 65491 SYSTEM lpr dppl1f.dat 65492 65493-----SYSTEM SWITCHES (SET)-------------------------------------------- 65494 65495SYSTEM SWITCHES 65496 65497Name: 65498 SYSTEM SWITCHES (SET) 65499 65500Type: 65501 Set Subcommand 65502 65503Purpose: 65504 Probe for values pertaining to certain operating system values. 65505 65506Description: 65507 Dataplot extracts the values of several operating system 65508 environment variables. These values can be obtained by the user 65509 using the PROBE command. Note that these settings cannot be 65510 modified with the SET command. 65511 65512 The list of available environment variable switches is 65513 65514 HOME - Returns the user's home directory. 65515 65516 On Windows platforms, this is the value of 65517 the USERPROFILE environment variable. 65518 65519 On Linux platforms, this is the value of the 65520 HOME environment variable. 65521 65522 USER - Returns the user name. 65523 65524 On Windows platforms, this is the value of the 65525 USERPNAME environment variable. 65526 65527 On Linux platforms, this is the value of the 65528 USER environment variable. 65529 65530 HOST - Returns the computer name. 65531 65532 On Windows platforms, this is the value of the 65533 COMPUTERNAME environment variable. 65534 65535 On Linux platforms, this is the value of the 65536 HOST environment variable for the c-shell or 65537 t-shell and the HOSTNAME variable for the 65538 bash shell. 65539 65540 DEFAULT PRINTER - Returns the default printer. 65541 65542 On Linux platforms, this is the value of the 65543 PRINTER environment variable. 65544 65545 This is not supported on Windows platforms. 65546 65547 SHELL - Returns the current shell. 65548 65549 On Linux platforms, this is the value of the 65550 SHELL environment variable. 65551 65552 This is not supported on Windows platforms. 65553 65554 WINDOWS BITS - Returns "64" if the machine is a 64-bit 65555 machine and "32" if the machine is a 65556 32-bit machine. 65557 65558 On Windows platforms, this is determined 65559 from the PROCESSOR_ARCHITECTURE environment 65560 variable. 65561 65562 This is not supported on Linux platforms. 65563 65564 PROGRAM FILES - On Windows platforms, this is the value of 65565 the PROGRAMFILES environment variable. 65566 65567 This is not supported on Linux platforms. 65568 65569 PROGRAM FILES X86 - On Windows platforms, this is the value 65570 of the PROGRAMFILES(X86) environment 65571 variable. 65572 65573 This is not supported on Linux platforms. 65574 65575Syntax: 65576 PROBE <SYSTEM SWITCH> 65577 where <SYSTEM SWITCH> is one of the names listed above. 65578 65579Examples: 65580 PROBE HOME 65581 PROBE USER 65582 PROBE HOST 65583 PROBE DEFAULT PRINTER 65584 PROBE SHELL 65585 PROBE PROGRAM FILES X86 65586 PROBE PROGRAM FILES 65587 PROBE WINDOW BITS 65588 65589Note: 65590 The value is saved in the string PROBESTR. You can save the 65591 value to your own string as follows 65592 65593 PROBE USER 65594 LET STRING USERNAME = ^PROBESTR 65595 65596Default: 65597 Dataplot queries the values of these settings when Dataplot 65598 is first initialized. 65599 65600Synonyms: 65601 USER PROFILE is a synonym for HOME 65602 USER NAME is a synonym for USER 65603 HOST NAME is a synonym for HOST 65604 COMPUTER NAME is a synonym for HOST 65605 65606Related Commands: 65607 WORKSPACE SWITCHES = Probe for values pertaining to the Dataplot 65608 workspace. 65609 HOUSEKEEPING SWITCHES = Probe for values pertaining to certain 65610 Dataplot housekeeping settings. 65611 SYSTEM LIMITS = Parameters defining certain Dataplot limits. 65612 MACHINE CONSTANTS = Return the values for certain machine 65613 constants. 65614 65615Applications: 65616 Debugging 65617 65618Implementation Date: 65619 2020/01 65620 65621Program: 65622 PROBE USER 65623 LET STRING USERNAME = ^PROBESTR 65624 PROBE HOST 65625 LET STRING COMPNAME = ^PROBESTR 65626 PROBE HOME 65627 LET STRING USERHOME = ^PROBESTR 65628 . 65629 PRINT "Computer Name: ^COMPNAME" 65630 PRINT "User Name: ^USERNAME" 65631 PRINT "Home Directory: ^USERHOME" 65632 65633-----SUN------------------------------------------------------- 65634 65635SUN 65636 65637Name: 65638 SUN 65639 65640Type: 65641 Output Device Command 65642 65643Purpose: 65644 The SUN command is used to direct graphical output to a SUN 65645 workstation running in SunWindows (either in a gfxtool or a Sun 65646 View window). 65647 65648Description: 65649 As gfxtool and Sun View are no longer supported, this is an obsolete 65650 device. 65651 65652Syntax 1: 65653 SUN 65654 65655 This form designates device 1 as a Sun device. 65656 65657Syntax 2: 65658 DEVICE <1/2/3> SUN 65659 65660 This form designates one of DATAPLOT's 3 devices (typically device 65661 1) as a Sun device. 65662 65663Examples: 65664 SUN 65665 DEVICE 1 SUN 65666 65667Note: 65668 The SUN driver only works if DATAPLOT is running on the SUN using 65669 the Sun View window system. The SUN driver uses SUN specific 65670 libraries. This means the local DATAPLOT installers must uncomment 65671 some source code before this driver is operational. If the SUN is 65672 running DATAPLOT from another host machine, or if the SUN driver 65673 has not been activated at your site, then run DATAPLOT in a 65674 TEKTOOLS window (and specify a Tektronix 4014 device). 65675 65676Note: 65677 The SUN driver can automatically determine whether you are running 65678 on a color or a black and white device. 65679 65680Note: 65681 This driver is becoming obsolete since Sun is switching to OpenLook 65682 and Motif based window systems. Use the X11 driver (HELP X11 for 65683 details) with OpenLook, Motif, or a plain vanilla X11 window 65684 system. 65685 65686Default: 65687 Off 65688 65689Synonyms: 65690 None 65691DEVICE NOTES 65692 1) HARDWARE TEXT - Hardware characters are scalable. No special 65693 fonts are supported. Vertical strings are not rotated. 65694 2) COLOR - The colors WHITE, BLACK, RED, GREEN, BLUE, MAGENTA, and 65695 YELLOW are supported. All other colors are mapped to one of 65696 these colors (enter SHOW COLORS SUN for the list). 65697 3) HARDWARE FILL - Solid area fills are generated in hardware. 65698 4) DASH PATTERNS - Unique dash patterns are generated for DASH, 65699 DOT, DASH2, and DASH3. DASH4 and DASH5 generate whatever the 65700 most recently set pattern was. 65701 5) LINE WIDTH - Thick lines are generated in hardware. 65702 6) GRAPHICS INPUT - The CROSS-HAIR command is supported for this 65703 device. 65704 65705Related Commands: 65706 TEKTRONIX = Direct graphical output to a Tektronix device. 65707 X11 = Direct graphical output to an X11 device. 65708 HP = Direct graphical output to an HP device. 65709 POSTSCRIPT = Direct graphical output to a Postscript device. 65710 DEVICE = Specify certain actions for the graphics output. 65711 65712Applications: 65713 Device Specification 65714 65715Implementation Date: 65716 1989/02 65717 65718Program: 65719 XX 65720 65721-----SWAP CASE----------------------------------------------------- 65722 65723SWAP CASE 65724 65725Name: 65726 SWAP CASE 65727 65728Type: 65729 Let Subcommand 65730 65731Purpose: 65732 Given a string, convert all upper case characters to lower case and 65733 convert all lower case characters to upper case. 65734 65735Syntax: 65736 LET <sout> = SWAP CASE <sorg> 65737 where <sout> is the resulting string; 65738 and <sorg> is the name of the original string. 65739 65740Examples: 65741 LET SOUT = SWAP CASE S1 65742 65743Default: 65744 None 65745 65746Synonyms: 65747 None 65748 65749Related Commands: 65750 LOWER CASE = Convert a string to lower case. 65751 UPPER CASE = Convert a string to upper case. 65752 LET FUNCTION = Defines a function. 65753 LET STRING = Defines a string. 65754 READ STRING = Reads a string from a file. 65755 SUBSTITUTE CHARACTE = Substitute the value of a string or parameter. 65756 & = Concatenate two strings. 65757 SUBTRING = Extract a substring from an existing string. 65758 STRING INDEX = Extract the start/stop positions of a substring 65759 within a string. 65760 STRING CONCATENATE = Concatenate one or more previously defined 65761 strings. 65762 STRING EDIT = Edit a string. 65763 STRING MERGE = Insert a string into another string without 65764 overwrite. 65765 STRING REPLACE = Insert a string into another string with 65766 overwrite. 65767 STRING LENGTH = Return the length of a string. 65768 CHARACTER = Convert numeric values to strings based on 65769 the ASCII collating sequence. 65770 ICHAR = Convert a string to numeric values based on 65771 the ASCII collating sequence. 65772 GROUP LABEL = Define the text for group labels. 65773 65774Applications: 65775 Data Management 65776 65777Implementation Date: 65778 2019/02 65779 65780Program: 65781 LET STRING S1 = XXXXyyyyZZZZwwww 65782 LET SOUT = UPPER CASE S1 65783 65784 The resulting string is xxxxYYYYzzzzWWWW. 65785 65786-----SVG--------------------------------------------------------- 65787 65788SVG 65789 65790Name: 65791 SVG 65792 65793Type: 65794 Output Device Command 65795 65796Purpose: 65797 Create SVG (Scalable Vector Graphics) format graphics files. 65798 65799Description: 65800 The ability to generate graphics for web based applications is 65801 increasingly important. The three most common formats for 65802 web applications are: 65803 65804 1) GIF 65805 2) JPEG 65806 3) PNG (Portable Network Graphics) 65807 65808 Note that these are all bit mapped formats. 65809 65810 SVG (Scalable Vector Graphics) is an XML based graphics format 65811 for web applications. Note that XML is a meta markup language, 65812 that is it is a langauge for defining languages. SVG is one 65813 specific implementation of an XML language. This is analogous 65814 to HTML being a specific implementation of a SGML (Standard 65815 Generalized Markup Language) language. 65816 65817 As of 9/2010, most major browsers provide native support for 65818 SVG files. The one exception is Internet Explorer. However, 65819 version 9 of Internet Explorer is expected to provide native 65820 support and various SVG plugins are available for earlier 65821 versions. 65822 65823 In addition to web browsers, a number of image viewers and 65824 graphics editing programs now support SVG files. For example, 65825 the open source GIMP program can view SVG files. Having a 65826 non web-based viewer can be helpful when debugging web applications 65827 in addition to providing another alternative for graphics output. 65828 65829 SVG is a vector based rather than a bitmap based protocol. 65830 Also, SVG is an ASCII file that contains a textual 65831 description of the graph. One of the primary advantages 65832 of this approach is that web graphics can be easily edited 65833 much the way the HTML files can be edited. This can make 65834 the maintenance of the graphics on a web site easier. 65835 65836 This driver was substantially overhauled 10/2010. If you 65837 are interested in using this driver, it is strongly recommended 65838 that you upgrade to a version of Dataplot that is at least as 65839 new as 10/2010. 65840 65841Syntax 1: 65842 SVG 65843 65844 This form designates device 1 as an SVG graphics device, 65845 which results in the SVG output being written to the 65846 screen. This syntax is not partiucularly useful since the 65847 SVG needs to be saved in a file so that an external SVG viewer 65848 or web browser can read it. 65849 65850Syntax 2: 65851 DEVICE <1/2/3> SVG 65852 65853 This form designates one of DATAPLOT's 3 devices (typically 65854 device 2) as an SVG device. 65855 65856Syntax 3: 65857 DEVICE <1/2/3> SVG <hor> <vert> 65858 where <hor> specifies the width (in pixels) of the graph; 65859 and where <vert> specifies the height (in pixels) of the graph. 65860 65861 By default, Dataplot generates the SVG graph at 600x465 65862 pixels. Since the dimensions of the SVG graph are defined when 65863 the device is intialized (i.e., when the DEVICE 2 SVG command is 65864 entered), the typical method for specifying the pixel dimensions 65865 65866 DEVICE 2 PICTURE POINTS 800 600 65867 65868 cannot be used. This syntax provides a method for overriding 65869 the default dimensions. Note that the minimum dimension is 200 65870 pixels and the maximum dimension is 1200 pixels. 65871 65872Examples: 65873 SET IPL1NA plot1.svg 65874 DEVICE 2 SVG 65875 65876 DEVICE 2 SVG 800 600 65877 65878Note: 65879 For SVG, it is typically desirable to put each plot in a 65880 separate file with a unique name. This can be accomplished 65881 with a sequence of commands like the following: 65882 65883 SET IPL1NA plot1.svg 65884 DEVICE 2 SVG 65885 generate first plot 65886 DEVICE 2 CLOSE 65887 SET IPL1NA plot2.svg 65888 DEVICE 2 SVG 65889 generate second plot 65890 DEVICE 2 CLOSE 65891 65892 The SET IPL1NA command must come before the DEVICE 2 SVG command 65893 in order for the name to be used. 65894 65895Note: 65896 SVG was designed primarily as a graphics format for web pages. 65897 In Dataplot, you can generate an HTML page with embedded SVG 65898 graphics by using the CAPTURE HTML command. This is 65899 demonstrated in the Program example below. Note that 65900 when the CAPTURE HTML is in effect, a DEVICE 2 CLOSE will 65901 cause the following lines are inserted into the HTML output: 65902 65903 <OBJECT data="plot.svg" 65904 width=" 600" height=" 465" 65905 type="image/svg+xml"> 65906 </OBJECT> 65907 65908 The "plot.svg" will actually be the name specified on the 65909 SET IPL1NA command. 65910 65911 Note that in some cases, you may want to specify a URL for 65912 the file name. This can be specified with the command 65913 65914 SET SVG URL <url> 65915 65916 In this case, the path will be removed from the file name 65917 and replaced with the specified URL. To turn this off, enter 65918 65919 SET SVG URL NULL 65920 65921Note: 65922 Style sheets allow easier maintenance/editing by specifying 65923 default attributes in an external style sheet file. The 65924 default Dataplot style sheet is "dataplot.css" and it is 65925 stored in the Dataplot "HELP" sub-directory. 65926 65927 Currently, Dataplot supports the following class for 65928 the background (this only sets the color, not the size): 65929 65930 rect.background 65931 65932 Currently, Dataplot supports the following classes for 65933 lines: 65934 65935 polyline.narrow-solid 65936 polyline.medium-solid 65937 polyline.wide-solid 65938 polyline.extrawide-solid 65939 polyline.narrow-dotted 65940 polyline.medium-dotted 65941 polyline.wide-dotted 65942 polyline.extrawide-dotted 65943 polyline.narrow-dash 65944 polyline.medium-dash 65945 polyline.wide-dash 65946 polyline.extrawide-dash 65947 polyline.narrow-dash2 65948 polyline.medium-dash2 65949 polyline.wide-dash2 65950 polyline.extrawide-dash2 65951 polyline.narrow-dash3 65952 polyline.medium-dash3 65953 polyline.wide-dash3 65954 polyline.extrawide-dash3 65955 polyline.narrow-dash4 65956 polyline.medium-dash4 65957 polyline.wide-dash4 65958 polyline.extrawide-dash4 65959 polyline.narrow-dash5 65960 polyline.medium-dash5 65961 polyline.wide-dash5 65962 polyline.extrawide-dash5 65963 65964 Currently, Dataplot supports the following classes for 65965 text: 65966 65967 text.left-horizontal 65968 text.center-horizontal 65969 text.right-horizontal 65970 65971 Currently, no classes are supported for region fills. 65972 65973 As we develop more experience with SVG graphics, we may 65974 expand the supported classes. 65975 65976 When using external style sheets, you modify the attributes 65977 of the clases. However, you do not edit which classes are 65978 available (Dataplot generates the SVG file based on the above 65979 classes. 65980 65981 Dataplot will check the value of certain attributes 65982 (color for lines, color and size for text) when generating 65983 the SVG file. If these are not the default values, then 65984 a local "style" option will be added for that element 65985 to override the value in the style sheet. 65986 65987 To make your own style sheets, simply copy the default 65988 file "dataplot.css" to a new file name and then edit that 65989 file. Use the SET SVG STYLE SHEET NAME command (see below) 65990 to specify the location of the style sheet you wish to use 65991 (this should be the location of the style sheet relative to 65992 the location of the SVG file on your web pages). 65993 65994Note: 65995 The following SET commands apply to the SVG output. 65996 65997 SET SVG COORDINATE SYSTEM <PIXEL/PERCENT> 65998 - specify whether coordinates are specified in 65999 pixel units or percent untis. Currently, only 66000 pixel units are supported. The PERCENT option is 66001 reserved for possible future implementation. 66002 66003 SET SVG FONT NAME <SERIF/SANS/MONOSPACE> 66004 - specify the font name for hardware characters. 66005 Generic names (i.e., supported on all SVG viewers) 66006 are: serif, sans-serif, and monospace. Specific 66007 font names (e.g., Arial) depend on what fonts are 66008 installed on your local system. Currently, only 66009 the generic fonts are supported. For specific 66010 fonts, use style sheets and set the name in the 66011 style sheet. The default is sans-serif. 66012 SET SVG FONT WEIGHT <NORMAL/BOLD> 66013 - specify whether text is drawn as bold or normal. 66014 The default is bold. 66015 SET SVG FONT STYLE <NORMAL/ITALIC> 66016 - specify whether text is drawn in an italic style 66017 or a normal style. The default is normal. 66018 66019 SET SVG CAP STYLE <BUTT/ROUND/SQUARE/NONE> 66020 - specify the cap style for line drawing. The default 66021 is butt. 66022 SET SVG JOIN STYLE <MITER/ROUND/BEVEL/NONE> 66023 - specify the join style for line draweing. The default 66024 is miter. 66025 66026 SET SVG HARDWARE FILL SWITCH <NONZERO/EVENODD/SOFTWARE> 66027 - by default, region fills are performed in hardware 66028 using a "non-zero" rule. You can also specify 66029 that an "evenodd" rule be used. In general, using 66030 hardware region fill will have better performance. 66031 However, hardware fills can occassionally have 66032 unpredictable results. In this case, you can 66033 have Dataplot perform region fills in software 66034 by specifing SOFTWARE. 66035 66036 SET SVG STYLE SHEET <INTERNAL/EXTERNAL/NONE> 66037 - specify whether the SVG graphics are generated 66038 using style sheets (EXTERNAL) or not (NONE). In 66039 general, style sheets are most beneficial when 66040 multiple graphics are being used on a web site. 66041 SVG supports both external style sheets (i.e., 66042 stored in a separate file) or internal to the 66043 SVG file. Currently, Dataplot only supports 66044 external style sheets. The INTERNAL switch is 66045 reserved for possible future implementation. 66046 There is also an EXTERNAL USE and an EXTERNAL 66047 CREATE option. This is reserved for future use, 66048 but it currently has no effect. 66049 SET SVG STYLE SHEET NAME <file name> 66050 - specify the name of the external file sheet 66051 (up to 80 characters). The default name is 66052 "dataplot.css". 66053 SET SVG FOREGROUND COLOR <color> 66054 - specify the default foreground color when style 66055 sheets are being used. If a line or text color 66056 does not match this foreground color, then Dataplot 66057 inserts a "style" option that overrides the style 66058 sheet value. Note that the default color is 66059 set independently in the style sheet file. So 66060 you may need to edit the style sheet as well. 66061 66062Note: 66063 Each "page" is assigned an ID using the "<g>" element. 66064 You can add your own translate, scale, and rotate options 66065 to the SVG file to transform the full plot (this is an element 66066 of the "Scalable" part of Scalable Vector Graphics). 66067 66068Note: 66069 Currently, Dataplot generates static plots in SVG format. 66070 SVG supports advanced capabilities such as animation, 66071 gradients, and Javascript scripting. Support for at least 66072 some of these capabilities may be added in future 66073 implementations. However, you can edit the SVG file 66074 (either via an ASCII text editor or a graphics editing 66075 program) to add such capabilities. 66076 66077Note: 66078 Graphic elements are now assigned "layers". This may be 66079 useful if you import the SVG graphic into a graphics editing 66080 program (i.e., it may allow individual elements of the graph 66081 to be edited). 66082 66083Default: 66084 None 66085 66086Synonyms: 66087 None 66088 66089Device Notes: 66090 HARDWARE TEXT - The SVG device currently supports 66091 hardware characters. Available fonts may 66092 depend on what fonts you have supported on 66093 your system. 66094 COLOR - SVG supports the full range of 88 colors supported 66095 by Dataplot. 66096 HARDWARE FILL - Solid area fills are performed in hardware. You 66097 can override this to generate them in software. 66098 DASH PATTERNS - The following dash patterns are available: 66099 66100 DASH - 3 pixels on, 3 pixels off; 66101 DOT - 1 pixel on, 1 pixels off; 66102 DASH2 - 9 pixels on, 5 pixels off 66103 DASH3 - 5 pixels on, 3 pixels off, 66104 9 pixel on, 2 pixel off; 66105 DASH4 - 9 pixels on, 3 pixels off, 66106 5 pixel on, 9 pixel off, 66107 3 pixel on, 5 pixel off; 66108 DASH5 - 5 pixels on, 2 pixels off; 66109 66110 If you want to modify these patterns, it is 66111 recommended that you use external style sheets. 66112 LINE WIDTH - Thick lines are generated in hardware. 66113 GRAPHICS INPUT - The CROSS-HAIR command is not supported 66114 for this device. 66115 The CHARACTER PIXEL option is supported on this device. 66116 66117Related Commands: 66118 GD PNG/JPEG = Direct graphical output to a file in PNG/JPEG 66119 format. 66120 POSTSCRIPT = Direct graphical output to a Postscript device. 66121 LATEX = Direct graphical output to a file in Latex format. 66122 HPGL = Direct graphical output to an HPGL device. 66123 DEVICE = Specify certain actions for the graphics output. 66124 66125Applications: 66126 Web Applications, Graphics Import Into Graphics Editing 66127 Programs 66128 66129Reference: 66130 David Eisenberg (2002), "SVG Essentials", O'Reilly. 66131 66132 Andrew Watt (2002), "Designing SVG Web Graphics", New Riders. 66133 66134Implementation Date: 66135 2002/3 66136 2008/3 - Added support for layers 66137 2010/9 - Substantially overhauled this driver 66138 66139Program 1: 66140 SET IPL1NA PLOT1.SVG 66141 DEVICE 2 SVG 66142 DEVICE 2 PICTURE POINTS 400 300 66143 TITLE SAMPLE SVG PLOT 66144 PLOT X**2 FOR X = 1 1 9 66145 DEVICE 2 CLOSE 66146 SET IPL1NA PLOT2.SVG 66147 DEVICE 2 SVG 66148 DEVICE 2 PICTURE POINTS 500 400 66149 TITLE SECOND SAMPLE SVG PLOT 66150 PLOT X**3 FOR X = 1 1 9 66151 DEVICE 2 CLOSE 66152 66153Program 2: 66154 . svg.dp - Sample SVG program 66155 . 66156 . Demonstrate how to generate SVG within an 66157 . HTML page 66158 . 66159 background color yellow 66160 . 66161 set ipl1na plot.svg 66162 device 2 svg 800 600 66163 . 66164 title size 3 66165 title offset 2 66166 title case asis 66167 label case asis 66168 title Sample SVG Plot 66169 title offset 2 66170 y1label Y Axis 66171 x1label X Axis 66172 label size 1.5 66173 char size 1 66174 . 66175 char x circle box 66176 char hw 1 0.5 0.5 0.375 0.5 0.375 66177 char fill off on on 66178 line solid dash dotted 66179 . 66180 feedback off 66181 capture html svg.htm 66182 plot x for x = 1 1 9 and 66183 plot x**1.5 for x = 1 1 9 and 66184 plot x**2 for x = 1 1 9 66185 device 2 close 66186 end of capture 66187 feedback on 66188 66189--------------------------------------------------------- 66190 66191 66192 66193 66194 66195 66196 66197 66198 66199 66200 66201 66202 66203 66204 66205 66206 66207 66208 66209 66210 66211 66212 66213 66214 66215 66216 66217 66218 66219 66220 66221 66222 66223 66224 66225 66226 66227 66228 66229 66230 66231 66232 66233 66234 66235 66236 66237 66238 66239 66240 66241 66242 66243 66244 66245 66246 66247 66248 66249 66250 66251 66252 66253 66254 66255 66256 66257 66258 66259 66260 66261 66262 66263 66264 66265 66266 66267 66268 66269 66270 66271 66272 66273 66274 66275 66276 66277 66278 66279 66280 66281 66282 66283 66284 66285 66286 66287 66288 66289 66290 66291 66292 66293 66294 66295 66296 66297 66298 66299 66300-END -----*----- ----------------ZZZZZ------ 66301
