Abstract
The problem of controlling the probability (EW) that at least one Type I Error occur in a family of N statistical tests, has received much attention in recent psychological literature. However, the related problem of assessing the loss of Power in the collection of N tests, resulting from keeping EW at a tolerably low level, has received relatively little attention. The present paper addresses itself to this problem in the case of a family of tests of N planned orthogonal contrasts. A method is described which allows the determination of the probability that, given the existence of any pre-specified number of Small, Medium, and Large Effect Sizes (as defined by Cohen, 1969), exactly x out of m true alternative hypotheses (where 0 ≤ x ≤ m) concerning pairwise contrasts will be accepted when the EW is controlled using a method advocated by Games (1971) and Schafer and Macready (1975). The method is then generalized to handle other Effect Sizes and to handle contrasts involving more than two means.
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