X-Git-Url: https://pintos-os.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=doc%2Fstatistics.texi;h=63c97b06078e564dcc0e94cb55cef35b05ee641a;hb=df291f0446ae11b5a3c788a06ee73eb9ac877ca5;hp=c475f306b3644431b9e248e629b6e04b8b550b3b;hpb=38b40b6e700680ede4e2f6203e1200ad4197b4b4;p=pspp-builds.git diff --git a/doc/statistics.texi b/doc/statistics.texi index c475f306..63c97b06 100644 --- a/doc/statistics.texi +++ b/doc/statistics.texi @@ -681,8 +681,14 @@ is used. @menu * BINOMIAL:: Binomial Test * CHISQUARE:: Chisquare Test -* WILCOXON:: Wilcoxon Signed Ranks Test +* COCHRAN:: Cochran Q Test +* FRIEDMAN:: Friedman Test +* KENDALL:: Kendall's W Test +* KRUSKAL-WALLIS:: Kruskal-Wallis Test +* MANN-WHITNEY:: Mann Whitney U Test +* RUNS:: Runs Test * SIGN:: The Sign Test +* WILCOXON:: Wilcoxon Signed Ranks Test @end menu @@ -762,20 +768,131 @@ sum of the frequencies need not be 1. If no /EXPECTED subcommand is given, then then equal frequencies are expected. -@node WILCOXON -@subsection Wilcoxon Matched Pairs Signed Ranks Test -@comment node-name, next, previous, up -@vindex WILCOXON -@cindex wilcoxon matched pairs signed ranks test + +@node COCHRAN +@subsection Cochran Q Test +@vindex Cochran +@cindex Cochran Q test +@cindex Q, Cochran Q @display - [ /WILCOXON varlist [ WITH varlist [ (PAIRED) ]]] + [ /COCHRAN = varlist ] @end display -The /WILCOXON subcommand tests for differences between medians of the +The Cochran Q test is used to test for differences between three or more groups. +The data for @var{varlist} in all cases must assume exactly two distinct values (other than missing values). + +The value of Q will be displayed and its Asymptotic significance based on a chi-square distribution. + +@node FRIEDMAN +@subsection Friedman Test +@vindex FRIEDMAN +@cindex Friedman test + +@display + [ /FRIEDMAN = varlist ] +@end display + +The Friedman test is used to test for differences between repeated measures when there is no indication that the distributions are normally distributed. + +A list of variables which contain the measured data must be given. The procedure prints the sum of ranks for each variable, the test statistic and its significance. + +@node KENDALL +@subsection Kendall's W Test +@vindex KENDALL +@cindex Kendall's W test +@cindex coefficient of concordance + +@display + [ /KENDALL = varlist ] +@end display + +The Kendall test investigates whether an arbitrary number of related samples come from the +same population. +It is identical to the Friedman test except that the additional statistic W, Kendall's Coefficient of Concordance is printed. +It has the range [0,1] --- a value of zero indicates no agreement between the samples whereas a value of +unity indicates complete agreement. + + +@node KRUSKAL-WALLIS +@subsection Kruskal-Wallis Test +@vindex KRUSKAL-WALLIS +@vindex K-W +@cindex Kruskal-Wallis test + +@display + [ /KRUSKAL-WALLIS = varlist BY var (lower, upper) ] +@end display + +The Kruskal-Wallis test is used to compare data from an +arbitrary number of populations. It does not assume normality. +The data to be compared are specified by @var{varlist}. +The categorical variable determining the groups to which the +data belongs is given by @var{var}. The limits @var{lower} and +@var{upper} specify the valid range of @var{var}. Any cases for +which @var{var} falls outside [@var{lower}, @var{upper}] will be +ignored. + +The mean rank of each group as well as the chi-squared value and significance +of the test will be printed. +The abbreviated subcommand K-W may be used in place of KRUSKAL-WALLIS. + + +@node MANN-WHITNEY +@subsection Mann-Whitney U Test +@vindex MANN-WHITNEY +@vindex M-W +@cindex Mann-Whitney U test +@cindex U, Mann-Whitney U + +@display + [ /MANN-WHITNEY = varlist BY var (group1, group2) ] +@end display + +The Mann-Whitney subcommand is used to test whether two groups of data come from different populations. +The variables to be tested should be specified in @var{varlist} and the grouping variable, that determines to which group the test variables belong, in @var{var}. +@var{Var} may be either a string or an alpha variable. +@var{Group1} and @var{group2} specify the +two values of @var{var} which determine the groups of the test data. +Cases for which the @var{var} value is neither @var{group1} or @var{group2} will be ignored. + +The value of the Mann-Whitney U statistic, the Wilcoxon W, and the significance will be printed. +The abbreviated subcommand M-W may be used in place of MANN-WHITNEY. + + +@node RUNS +@subsection Runs Test +@vindex RUNS +@cindex runs test + +@display + [ /RUNS (@{MEAN, MEDIAN, MODE, value@}) varlist ] +@end display + +The /RUNS subcommand tests whether a data sequence is randomly ordered. + +It works by examining the number of times a variable's value crosses a given threshold. +The desired threshold must be specified within parentheses. +It may either be specified as a number or as one of MEAN, MEDIAN or MODE. +Following the threshold specification comes the list of variables whose values are to be +tested. + +The subcommand shows the number of runs, the asymptotic significance based on the +length of the data. + +@node SIGN +@subsection Sign Test +@vindex SIGN +@cindex sign test + +@display + [ /SIGN varlist [ WITH varlist [ (PAIRED) ]]] +@end display + +The /SIGN subcommand tests for differences between medians of the variables listed. -The test does not make any assumptions about the variances of the samples. -It does however assume that the distribution is symetrical. +The test does not make any assumptions about the +distribution of the data. If the @code{WITH} keyword is omitted, then tests for all combinations of the listed variables are performed. @@ -789,20 +906,20 @@ If the @code{WITH} keyword is given, but the of variable preceding @code{WITH} against variable following @code{WITH} are performed. - -@node SIGN -@subsection Sign Test -@vindex SIGN -@cindex sign test +@node WILCOXON +@subsection Wilcoxon Matched Pairs Signed Ranks Test +@comment node-name, next, previous, up +@vindex WILCOXON +@cindex wilcoxon matched pairs signed ranks test @display - [ /SIGN varlist [ WITH varlist [ (PAIRED) ]]] + [ /WILCOXON varlist [ WITH varlist [ (PAIRED) ]]] @end display -The /SIGN subcommand tests for differences between medians of the +The /WILCOXON subcommand tests for differences between medians of the variables listed. -The test does not make any assumptions about the -distribution of the data. +The test does not make any assumptions about the variances of the samples. +It does however assume that the distribution is symetrical. If the @code{WITH} keyword is omitted, then tests for all combinations of the listed variables are performed.