Minimum Bayes Risk t-Intervals for Multiple Comparisons

Abstract

The purpose is to develop interval estimates for differences between treatment means which, when used for testing, would be equivalent to the Waller-Duncan k-ratio rule for multiple comparisons. First the intervals are derived from a family of extended k-ratio Bayes testing rules (exchangeable priors and additive linear losses). Then the intervals are shown to be Bayes also (same priors and squared-error losses). Particularly striking is the dependence of width and location on the between-treatments F-ratio rather than the number of treatments. As F decreases the new k-ratio t-intervals shrink in width and shift toward zero.