t Tests and Intervals for Comparisons Suggested by the Data

SUMMARY The problem of testing a comparison c stuggested by the data is first identified with the mtultiple comparisons problem for the class C of a priori equally plauisible comparisonis. A multiple comparisons dilemma is then illustrated by a simple example E emphasizing the impossibility of developing an acceptable a-level Neyman-Peaison test for c. A recent empirical Bayes additive losses and exchangeable priors (EBALEP) approach is discussed and illutstrated in getting a simple solution for E. A brief review is giveii of the use of the same approach by Waller, Dixon and Dunican in getting the k-ratio t test and interval for the all-pairwise differences problem. These rules are showii to apply to the all contrasts problem as well and several worked examples are given for their application. The k-ratio rtules are seen to have considerably increased power and low type-i error probabilities in dealiing with heterogeneous and near honmogeneous treatments, respectively.