Multiple rank tests for pairwise comparisons

Abstract

Consider a balanced one way layout without a normality assumption. That is, assume each population has an unknown translation parameter and has a continuous distribution. We wish to test the C^k₂ pairwise differences in translation parameters assuming there are k populations.We propose a multiple testing method based on ranks that is analogous to the method developed for testing pairwise contrasts among means by Cohen, Sackrowitz and Chen (2010) [3] (CSC). This latter method has an intuitive and important practical property not shared by most multiple testing methods. Namely, for each individual pairwise hypothesis relevant acceptance sections are intervals. Furthermore, the CSC method is shown to do well in terms of power compared to competitive methods. In the nonparametric setting the analogous procedure has the desirable interval property and also stacks up well in a comparative simulation study.