6.5 Distribution-Free Two-Sided All-Treatments Multiple Comparisons Based on Pairwise Rankings—General Configuration (Dwass, Steel, and Critchlow–Fligner)
In this section we present a multiple comparison procedure based on pairwise two-sample rankings that is designed to make decisions about individual differences between pairs of treatment effects (), for , in a setting where general alternatives (6.3) are of interest. Thus, the multiple comparison procedure of this section would generally be applied to one-way layout data after rejection of (6.2) with the Kruskal–Wallis procedure from Section 6.1. In this setting, it is important to reach conclusions about all pairs of treatment effects, and these conclusions are naturally two-sided in nature.
For each pair of treatments (), let
where are the ranks of , respectively, among the combined th and th samples; that is, ...