Choosing the best pairwise comparisons of means from non-normal populations, with unequal variances, but equal sample sizes

A Monte Carlo simulation evaluated five pairwise multiple comparison procedures for controlling Type I error rates, any-pair power, and all-pairs power. Realistic conditions of non-normality were based on a previous survey. Variance ratios were varied from 1:1 to 64:1. Procedures evaluated included Tukey's honestly significant difference (HSD) preceded by an F test, the Hayter-Fisher, the Games-Howell preceded by an F test, the Pertiz with F tests, and the Peritz with Alexander-Govern tests. Tukey's procedure shows the greatest robustness in Type I error control. Any-pair power is generally best with one of the Peritz procedures. All-pairs power is best with the Pertiz F test procedure. However, Tukey's HSD preceded by the Alexander-Govern F test may provide the best combination for controlling Type I and power rates in a variety of conditions of non-normality and variance heterogeneity.