Multiple Comparison Test Procedures for Comparing Several Treatments With a Control Under Simple Ordered Restrictions in a Randomized Block Design

Abstract

We consider multiple comparison tests for comparing several treatments with a control in a randomized block design under simple ordered restrictions. Williams (1971) proposed a closed testing procedure based on similar to two-sample t-tests under assuming normality in multi-sample models. We propose closed testing procedures based on similar to Shiraishi and Matsuda (2015), the maximal component of the cumulative chi-squared statistic, and linear statistic. The powers of the proposed tests are investigated in Monte-Carlo simulation studies. As a result, closed testing procedures based on and the maximal component of the cumulative chi-squared statistic are superior to the similar to Williams (1971).