On distribution-free multiple comparisons in the one-way analysis of variance

Two methods are described for conducting distribution-free multiple comparisons of k > 2 populations. The Steel-Dwass method, based on pairwise rankings, possesses several desirable properties that are investigated. New large sample approximations are given, that are less conservative than those of the Bonferroni type suggested by Dunn (1964), and small sample tables for k = 3 populations are provided. Simultaneous confidence intervals are derived for all the pairwise location differences. Finally, an example illustrates the methodology.