Equivalence testing for binomial random variables: Which test to use?

The hypothesis of "no difference" between two populations is the appropriate null hypothesis in studies intended to show that populations differ. In studies intended to show that two populations are practically equivalent, the null hypothesis that a substantial difference between the populations exists is more appropriate. We consider eight tests of the null hypothesis that the absolute difference of two binomial random variables' success probabilities is at least a prespecified Delta > 0 versus the alternative that the difference is less than Delta. The tests considered are: six forms of the two one-sided test, a modified form of the Patel-Gupta test, and the likelihood ratio rest. The applicability of each test in a given setting depends on how well the test maintains its nominal size, the power of the test, and the ease with which it is implemented. Based on these criteria, we make recommendations for choosing, among these tests.