Using the Tukey-Kramer omnibus test in the Hayter-Fisher procedure

Using Tukey-Kramer versus the ANOVA F-test as the omnibus test of the Hayter-Fisher procedure for comparing all pairs of normally distributed means, when sample sizes are unequal, is investigated. Simulation results suggest that using Tukey-Kramer leads to as much or more any-pairs power compared to using the F-test for certain patterns of mean differences, and equivalent per-pair and all-pairs power for all cases. Furthermore, using Tukey-Kramer results in a consonant test procedure, where there cannot be disagreement between the results of the omnibus test and the subsequent pairwise tests. The results suggest that when sample sizes are unequal, Tukey-Kramer may be preferred over the F-test as the omnibus test for the Hayter-Fisher procedure.