NOTE ON CLOSED TESTING PROCEDURE AND SEQUENTIALLY REJECTIVE STEP DOWN PROCEDURE

摘要

Among various types of stepwise multiple comparison procedures for normal means we focus on the closed testing procedure and the sequentially rejective step down procedure and discuss the relation between them. First, we consider the multiple comparison with a control. Specifically, we indicate that the power of the sequentially rejective step down procedure is not higher than that of the closed testing procedure and two procedures are equivalent when we use same critical values for them. Next, we consider the all-pairwise multiple comparison. Ryan-Einot-Gabriel-Welsch's procedure using Tukey-Welsh's allocation of the significance level is the well known closed testing procedure. When we test an intersection of mutually disjoint plural hypotheses by it, we should test each hypothesis allocating an specified significance level to it. It is accompanied with computational complications when the number of populations is large. Here, we propose a method of testing the intersection of mutually disjoint plural hypotheses at a time in the closed testing procedure. Next, among several types of sequentially rejective step down procedures for the all-pairwise multiple comparison we focus on Holland-Copenhaver's procedure and indicate that the power of Holland-Copenhaver's procedure is not higher than that of the proposed closed testing procedure specifying the total number of populations. We give simulation results regarding the power of the test intended to compare the procedures.