Power evaluation of various modified Bonferroni procedures by a Monte Carlo study.

Various modified Bonferroni procedures (MBPs) have been proposed in order to improve the power of the classical Bonferroni procedure (CBP). In the present paper, powers of these MBPs are investigated by a Monte Carlo study for pairwise comparisons. It is shown that they can be remarkably more powerful than the CBP and Tukey's procedure with respect to all-pairs power, whereas all these procedures with respect to any-pair power are almost the same. Therefore, we recommend the use of MBPs rather than the CBP or Tukey's procedure. Shaffer's procedure sometimes shows higher power than other MBPs and would be the best choice for pairwise comparisons.