Appropriate Critical Values for Pairwise Comparisons of Multiple Comparison Procedures for Normal Variances When Sample Sizes Are Unbalanced

In this study we discuss the determination of appropriate critical values for pairwise comparisons of the multiple comparison with a control and the all-pairwise multiple comparison for normal variances when sample sizes are unbalanced. Although Imada (2018A, 2018B) used a common critical value for all hypotheses, the probability that the true hypothesis is rejected is not uniform. Here, we construct the critical value for each hypothesis so that the probability that it is rejected when it is true may be as uniform as possible. Finally, we give some numerical results regarding critical values and power of the test.