A method of unconstrained multiple comparisons with the best

Abstract

There are three types of multiple comparisons: all-pairwise multiple comparisons (MCA), multiple comparisons with the best (MCB), and multiple comparisons with a control (MCC). There are also three levels of multiple comparisons inference: confidence sets, subset comparisons, test of homogeneity. In current practice, MCA procedures dominate. In correct attempts at more efficient comparisons, in the form of employing lower level MCA procedures for higher level inference, account for the most frequent abuses in multiple comparisons. A better strategy is to choose the correct type of inference at the level of inference desired. In particular, very often the simulataneous comparisons of each treatment with the best of the other treatments (MCB) suffice. Hsu (1984b) gave simultaneous confidence intervals for θi − maxj≠iθj having the simple form [− (Yi −maxj≠i Yj − C) (Yi−maxj≠i Yj + C)+]. Those intervals were constrained, sothat even if a treatment is inferred to be the best, no positive bound on how much it i...