Nonparametric All-Pairs Multiple Comparisons

Abstract

Nonparametric all-pairs multiple comparisons based on pairwise rankings can be performed 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. We provide exact calculations of the asymptotic critical values (and P-values, respectively) even for unbalanced designs. We recommend this asymptotic method whenever large sample sizes are present. For small sample sizes we recommend the use of the new statistic according to Baumgartner, Weiss, and Schindler (1998, Biometrics 54, 1129–1135) instead of Wilcoxon's rank sum for the multiple comparisons. We show that the resultant procedure can be less conservative and, according to simulation results, more powerful than the original Steel-Dwass procedure. We illustrate the methods with a practical data set.