Alternatives for correcting the Tukey's statistics for unbalanced experiments

Unbalanced experiments are those in which treatments do not have the same number of replications. Some multiple comparison tests need to be correct to behave well in unbalanced situations. For the Tukey test is suggested the use of the harmonic mean of the numbers of replications. The aim of this paper is to verify the performance of the harmonic, arithmetic, weighted, quadratic, and geometric means, the minimum, maximum and median number of repetitions as a correction for the Tukey test, and propose a correction that improves the performance of harmonic mean. We measured the type I error rate and power via Monte Carlo simulation, at 5\% of significance. The harmonic mean performs best but could be improved. The proposal made in this work was capable of controlling the type I error in all cases studied.