Markus Neuhäuser (Byk Gulden Pharmaceuticals, Germany),

Frank Bretz (University of Hannover, Germany)

Nonparametric all-pairs multiple comparisons

Nonparametric all-pairs multiple comparisons based on pairwise rankings can be per-formed in the one-way design with the Steel-Dwass procedure. To apply this test, Wilcoxon's rank sum statistic is calculated for all pairs of groups; the maximum of the rank sums is the test statistic. For large sample sizes we introduce a generalization of the Steel-Dwass procedure for unbalanced designs and provide exact calculations of the asymptotic critical values. It should be noted that the method proposed by Critchlow and Fligner (1991, Commun. Statist. - Theory Meth. 20, 127-139) gives approximate critical values only in case of unbalanced sample sizes. For small sample sizes we recommend to use the new statistic according to Baum-gartner, Weiß, and Schindler (1998, Biometrics, 54, 1129-1135) instead of Wilcoxon's rank sum for the multiple comparisons. We show that the resultant proce-dure can be less conservative and, according to simulation results, more powerful than the original Steel-Dwass procedure. We also investigate the behaviour of the procedure in case of heteroscedasticity. We illustrate the methods with example data.