Nonparametric Closed Testing Procedures for All Pairwise Comparisons in a Randomized Block Design

Abstract

We consider multiple comparison test procedures among treatment effects in a randomized block design. We propose closed testing procedures based on signed rank statistics and Friedman test statistics for all pairwise comparisons of treatment effects. Although anyone has been failed to discuss a distribution-free method except Bonferroni procedures as a multiple comparison test, the proposed procedures are exactly distribution-free. Next we consider the randomized block design under simple ordered restrictions of treatment effects. We propose distribution-free closed testing procedures based on one-sided signed rank statistics and rank statistics of Chacko (1963) for all pairwise comparisons. Simulation studies are performed under the null hypothesis and some alternative hypotheses. In this studies, the proposed procedures show a good performance. We also illustrate an application to death rates by using proposed procedures.