Testing the hypothesis that treatments have negligible effects: Minimum-effect tests in the general linear model.

Researchers are often interested in testing the hypothesis that the effects of treatments, interventions, and so on are negligibly small rather than testing the hypothesis that treatments have no effect whatsoever. A number of procedures for conducting such tests have been suggested but have yet to be widely adopted. In this article, simple methods of testing such minimum-effect hypotheses are illustrated in a variety of applications of the general linear model. Tables and computational routines that can be used in conjunction with the familiar F test to evaluate the hypothesis that the effects of treatments or interventions exceed some minimum level are also provided. One of the most common statistical procedures in the be-havioral and social sciences is to test the hypothesis that treatments or interventions have no effect, or that the correla-tion between two variables is equal to zero, and so on. Cohen (1994) referred to these procedures as nil hypothesis tests, a label that differentiates them from the more general category of null hypothesis tests (which allow researchers to test the hy-pothesis that the difference between two treatments is equal to any specific figure, including but not limited to zero) and that makes it explicit that this particular class of tests is used to evaluate the plausibility of the hypothesis that treatments or interventions have no true effect whatsoever. Although nil hypothesis tests are extremely common, there is a substantial controversy about their value and meaning (Chow, 1988; Co-