Issues of Power: Rejoinder

Abstract

I am sorry that Brewer (1974) chose not to comment on the many points raised in my paper (Meyer, 1974) regarding surveys of power and decision theoretic methods for these issues deserve discussion. Since the major thrust of the arguments was made within a classical statistics framework, and indeed, two-thirds of the paper was written in this manner, it is distressing that Brewer sees this as part of a Bayesian, non-Bayesian issue.It appears from point (5) in Brewer's clarification (1974) that I did correctly "pigeonhole" him as one who tests hypotheses in a decisiontheoretic way. The burden is on him to be consistent with his own methods. If he doesn't use minimax rules, what does he use? What kind of loss functions does he use, and why does he persist in ascribing his to everyone else? His points (4) and (6) are only value judgments to which he is entitled, but he should respect other opinions (loss functions) made by researchers in the diverse fields who publish in AERJ. The word "dismal" causes no semantic problems. It is just inappropriate since it ignores the practical realities such as sampling cost and the fact that many researchers may be uninterested in Brewer's loss function.To repeat the statement (Brewer, 1974, p. 163) that "I refuse to take seriously a test (or the researcher who conducts it)" (if power is .46 for Brewer's ES) is amazing to me and is just plain unacceptable, even if he were knowledgeable in the particular fields of application.Relative to points (1) and (2) of Brewer's clarification, I, at least, was misled because I thought these sentences had some informational content. If the statement in (1) was not intended to apply after results are known, then it only defines power and reads like "a rose is a rose." However, the sentence immediately preceding it in the original article (Brewer, 1972, p. 391) is: "The computation is essential to the interpretation of negative results, that is, failures to reject the null hypothesis." This statement, besides being objectionable for the same reasons given by Dayton et al (1973), provides the mental set that Brewer thought power was useful for something beyond its calculation a priori.The statement in point (2) regarding coin-flipping is said by Brewer to be