Multiple Comparison Test Procedures Based on X̅²-Statistics for Comparing Several Treatments with a Control under a Simple Ordered Restriction

Abstract

Under the assumptions of continuous distribution and homogeneous variance, we consider multiple comparison tests for comparing several treatments with a control in k sample models under a simple ordered restriction．Williams (1971) proposed a closed testing procedure based on t-tests similar to two-sample t-tests under assuming normality. We propose closed testing procedures based on tests of Batholomew (1959). The powers of the proposed tests are superior to Williams (1971). Furthermore nonparametric closed testing procedures are discussed based on ranks. The procedures proposed in this paper are also applicable for the models with unequal sample sizes.