1\name{sf.test} 2\alias{sf.test} 3\title{Shapiro-Francia test for normality} 4\description{ 5 Performs the Shapiro-Francia test for the composite hypothesis of normality, 6 see e.g. Thode (2002, Sec. 2.3.2). 7} 8\usage{ 9sf.test(x) 10} 11 12\arguments{ 13 \item{x}{a numeric vector of data values, the number of 14 which must be between 5 and 5000. Missing values are allowed.} 15} 16\details{The test statistic of the Shapiro-Francia test is simply the 17squared correlation between the ordered sample values and the (approximated) 18expected ordered quantiles from the standard normal 19distribution. The p-value is computed from the formula given by Royston (1993). 20} 21\value{ 22 A list with class \dQuote{htest} containing the following components: 23 \item{statistic}{the value of the Shapiro-Francia statistic.} 24 \item{p.value }{the p-value for the test.} 25 \item{method}{the character string \dQuote{Shapiro-Francia normality test}.} 26 \item{data.name}{a character string giving the name(s) of the data.} 27} 28\references{Royston, P. (1993): A pocket-calculator algorithm for the 29Shapiro-Francia test for non-normality: an application to medicine. 30Statistics in Medicine, 12, 181--184. 31 32Thode Jr., H.C. (2002): Testing for Normality. Marcel Dekker, New York.} 33 34\author{Juergen Gross} 35 36\note{The Shapiro-Francia test is known to perform well, 37see also the comments by Royston (1993). The expected ordered quantiles 38from the standard normal distribution are approximated by 39\code{qnorm(ppoints(x, a = 3/8))}, being slightly different from the approximation 40\code{qnorm(ppoints(x, a = 1/2))} used for the normal quantile-quantile plot by 41\code{\link{qqnorm}} for sample sizes greater than 10.} 42 43\seealso{\code{\link{shapiro.test}} for performing the Shapiro-Wilk test for normality. 44\code{\link{ad.test}}, \code{\link{cvm.test}}, 45\code{\link{lillie.test}}, \code{\link{pearson.test}} for performing further tests for normality. 46\code{\link{qqnorm}} for producing a normal quantile-quantile plot.} 47 48\examples{ 49sf.test(rnorm(100, mean = 5, sd = 3)) 50sf.test(runif(100, min = 2, max = 4)) 51 52} 53\keyword{htest} 54