A note on the conservative multivariate Tukey-Kramer multiple comparison procedure

In this article, the conservative simultaneous confidence intervals for pairwise multiple comparisons among correlated mean vectors including the case of unequal sample sizes are considered. One of the important problems is to evaluate the bound of simultaneous confidence levels for approximate multiple comparisons procedures. For all pairwise comparisons as a particular case, the multivariate Tukey-Kramer procedure proposed by Seo, Mano and Fujikoshi is discussed, and its bound for conservativeness is given by the reduction of the coverage probability. The numerical results by Monte Carlo simulations are presented for the selected parameters.