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Nonparametric Statistical Methods, 3rd Edition by Eric Chicken, Douglas A. Wolfe, Myles Hollander

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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 (images), for images, in a setting where general alternatives images (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 images (6.2) with the Kruskal–Wallis procedure from Section 6.1. In this setting, it is important to reach conclusions about all images pairs of treatment effects, and these conclusions are naturally two-sided in nature.

Procedure

For each pair of treatments (images), let

6.60

where are the ranks of , respectively, among the combined th and th samples; that is, ...

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