To Pool or Not to Pool in Hypothesis Testing.

Necessary and sufficient conditions for admissibility are given for test procedures based on a preliminary test of significance. Three types of problems are studied-testing the normal mean, fixed effects models of the analysis of variance and random effects models. Admissibility in this instance is equivalent to the intuitive and practical condition that acceptance regions of the procedures have convex sections in certain variables, while other variables are fixed, It is easy to check when the conditions hold. A discussion of optimality properties of these and other types of pooling procedures is given. [ABSTRACT FROM AUTHOR]