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When it is required to establish a materially significant difference between two treatments, or, alternatively, to show that two treatments are equivalent, standard test statistics and sample size formulae based on a null hypothesis of no difference no longer apply. This paper reviews some of the test statistics and sample size formulae proposed for comparative binomial trials when the null hypothesis is of a specified non‐zero difference or non‐unity relative risk. Methods based on restricted maximum likelihood estimation are recommended and applied to studies of pertussis vaccine.