Tukey's multiple comparisons procedure in imbalanced one-way ANOVA : Evaluation of Tukey-Kramer's approximate method based on the exact calculation

Abstract

In an imbalanced one-way ANOVA model with homogeneous variance, we examine the performances of Tukey's multiple comparisons procedure. The efficiency of Tukey-Kramer's approximate method to the exact method is evaluated based on some numerical results, which are focused on both of the critical value and the p-value. When the sample size is severely imbalanced, we recommend to use the exact calculation since Tukey-Kramer's method is too conservative in such a case. We conclude that Tukey-Kramer's method is a good approximation for moderately imbalanced cases that are frequently encountered in many practical applications.