The problem of establishing the equivalence of an experimental treatment to a control with respect to a binary ("success" or "failure") response variable may be solved using an approximate (1-alpha) 100% confidence interval for the difference in the response rates (i.e., success probabilities). If the goal is to show that the experimental treatment is not sufficiently worse than the control, then a decision rule based on the magnitude of one confidence limit can be used. A procedure suggested by the Food and Drug Administration allows the value to which the confidence limit is to be compared to depend on the data. The consequences of determining the sample size assuming that the aforementioned value is fixed are examined. The probability of declaring equivalence and exact sample sizes are also presented for the procedure.