A S A S R Macro for the Multivariate Extension of the Kruskal - Wallis Test Including Multiple Comparisons : Randomization and Z 2 Criteria 1 Warren

In a multi-group experimental design where interest is in a univariate response, the nonparametric Kruskal-Wallis test [Kniskal and Wallis (1952)] provides a potentially more powerful alternative to the parametric one-way analysis of variance when the assumptions of normality are in question. For multivariate response, Puri and Sen (1966) proposed a generalization of the KmskalWallis test that is a nonparametric analog of the one-way multivariate analysis of variance and can be used when multivariate response data are measured on at least an ordinal scale. Large sample theory suggests that the multivariate Knlskal-Wallis statistic is approximately distributed as chi-square, but in small samples the behavior of the statistic warrants conditioning on the observed data and using randomization theory to tabulate the exact distribution. We have written a SAS [SAS Institute, Inc. (1985)] macro that computes the probability values and tabulates the exact distribution for the univariate and multivariate Kruskal-Wallis test that will be useful to applied statisticians. (SSNinCSDA 26, 239-250 (December 1997))