Nonparametric Decision Research Articles

Some Rank Sum Multiple Comparisons Tests

A number of nonparametric tests based on ranks have been proposed for the comparison of treatments in a completely random design. For example, we have the Wilcoxon-Mann-Whitney test [21, 10], basically a two-sample test with a per-comparison error rate. Also, Kruskal and Wallis [9] have proposed a rank test which is an analogue of Snedecor's F-test. This test provides evidence concerning the presence of real differences but is of limited use in locating them. Steel [16, 17] has presented rank tests for comparing treatments against control and for all pairwise comparisons. Both of these tests use experiment-wise error rates. Pfanzagl [13], as part of a more general theory, has discussed a two-step nonparametric decision process based on ranks, for testing the null hypothesis that lk samples come from the same population and, if this is rejected, for deciding which one of the samples comes from a different population. No tables are given but it is suggested that they might be obtained by random sampling. It is also shown that the limiting distribution of the multivariate criterion is multinormal. The per-comparison error rate test is sometimes criticized, particularly when all possible paired comparisons are made, because it will almost certainly lead to false declarations of significance when the experiment includes many treatments and if customary significance levels are used. It is also deemed inappropriate when the experiment is considered to be the conceptual unit. The experimentwise error rate test is sometimes criticized because it