Significance testing to establish equivalence between treatments, with special reference to data in the form of 2X2 tables

Abstract

In this paper, the role of significance testing in establishing equivalence between treatments is described. In place of the more customary null hypothesis of no difference between treatments, the hypothesis that the true difference is equal to a specified delta is tested. The particular case of comparing two binomial samples is described in detail. Results using a method due to Gart and approximations based on the chi2 and normal distributions are compared. It is found that the test based upon chi2 with continuity correction agrees best overall with Gart's (1971) test and is therefore recommended for use when computational facilities needed for carrying out the latter are not available.