Comparisons of ten corrections methods for t-test in multiple comparisons via Monte Carlo study

Multiple comparisons of treatments means are common in several fields of knowledge. The Student's t-test is one of the first procedures to be used in multiple comparisons, however the \emph{p}-values associated with it are inaccurate, since there is no control on the family-wise Type I error. To solve this problem several corrections were developed. In this work, based on Monte Carlo simulations, we evaluated the t-test and the following corrections: Bonferroni, Holm, Hochberg, Hommel, Holland, Rom, Finner, Benjamini–Hochberg, Benjamini–Yekutieli and Li with respect to their power and Type I error rate. The study was lead varying the sample size, the sample distribution and the degree of variability. For all instances we regarded three balanced treatments and the probability distributions considered were: Gumbel, Logistic and Normal. Although the corrections were approaching when the sample size increased, our study reveals that the BH correction provides the best family-wise Type I error rate and the second overall most powerful correction.