When designing a clinical trial to show whether a new or experimental therapy is as effective as a standard therapy (but not necessarily more effective), the usual null hypothesis of equality is inappropriate and leads to logical difficulties. Since therapies cannot be shown to be literally equivalent, the appropriate null hypothesis is that the standard therapy is more effective than the experimental therapy by at least some specified amount. The problem is presented in terms of a trial in which the outcome of interest is dichotomous; test statistics, confidence intervals, and sample size calculations are discussed. The required sample size may be larger for either null hypothesis formulation than for the other, depending on the specific assumptions made. Reporting results in terms of confidence intervals is especially useful for this type of trial.