1%% Copyright (C) 1995, 1996, 1997  Kurt Hornik
2%%
3%% This file is part of Octave.
4%%
5%% Octave is free software; you can redistribute it and/or modify it
6%% under the terms of the GNU General Public License as published by
7%% the Free Software Foundation; either version 2, or (at your option)
8%% any later version.
9%%
10%% Octave is distributed in the hope that it will be useful, but
11%% WITHOUT ANY WARRANTY; without even the implied warranty of
12%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
13%% General Public License for more details.
14%%
15%% You should have received a copy of the GNU General Public License
16%% along with Octave; see the file COPYING.  If not, write to the Free
17%% Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
18%% 02110-1301, USA.
19
20%% -*- texinfo -*-
21%% @deftypefn {Function File} {[@var{pval}, @var{z}] =} u_test (@var{x}, @var{y}, @var{alt})
22%% For two samples @var{x} and @var{y}, perform a Mann-Whitney U-test of
23%% the null hypothesis PROB (@var{x} > @var{y}) == 1/2 == PROB (@var{x}
24%% < @var{y}).  Under the null, the test statistic @var{z} approximately
25%% follows a standard normal distribution.  Note that this test is
26%% equivalent to the Wilcoxon rank-sum test.
27%%
28%% With the optional argument string @var{alt}, the alternative of
29%% interest can be selected.  If @var{alt} is @code{'~='} or
30%% @code{'<>'}, the null is tested against the two-sided alternative
31%% PROB (@var{x} > @var{y}) ~= 1/2.  If @var{alt} is @code{'>'}, the
32%% one-sided alternative PROB (@var{x} > @var{y}) > 1/2 is considered.
33%% Similarly for @code{'<'}, the one-sided alternative PROB (@var{x} >
34%% @var{y}) < 1/2 is considered,  The default is the two-sided case.
35%%
36%% The p-value of the test is returned in @var{pval}.
37%%
38%% If no output argument is given, the p-value of the test is displayed.
39%% @end deftypefn
40
41%% This implementation is still incomplete---for small sample sizes,
42%% the normal approximation is rather bad ...
43
44%% Author: KH <Kurt.Hornik@wu-wien.ac.at>
45%% Description: Mann-Whitney U-test
46%% Adapted for the use with M*tlab by AS <alois.schloegl@gmail.com> Dec 2006
47
48function [pval, z] = u_test (x, y, alt)
49
50  if ((nargin < 2) || (nargin > 3))
51    print_usage ();
52  end
53
54  if (~ (isvector (x) && isvector (y)))
55    error ('u_test: both x and y must be vectors');
56  end
57
58  n_x  = length (x);
59  n_y  = length (y);
60  r    = ranks ([(reshape (x, 1, n_x)), (reshape (y, 1, n_y))]);
61  z    = (sum (r(1 : n_x)) - n_x * (n_x + n_y + 1) / 2) ...
62           / sqrt (n_x * n_y * (n_x + n_y + 1) / 12);
63
64  cdf  = normcdf (z);
65
66  if (nargin == 2)
67    alt  = '~=';
68  end
69
70  if (~ ischar (alt))
71    error('u_test: alt must be a string');
72  end
73  if (strcmp (alt, '~=') || strcmp (alt, '<>'))
74    pval = 2 * min (cdf, 1 - cdf);
75  elseif (strcmp (alt, '>'))
76    pval = cdf;
77  elseif (strcmp (alt, '<'))
78    pval = 1 - cdf;
79  else
80    error ('u_test: option %s not recognized', alt);
81  end
82
83  if (nargout == 0)
84    printf ('  pval: %g\n', pval);
85  end
86
87end
88