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

The hypothesis of "no difference" between two populations is the appropriat e null hypothesis in studies intended to show that populations differ. In s tudies intended to show that two populations are practically equivalent, th e null hypothesis that a substantial difference between the populations exi sts is more appropriate. We consider eight tests of the null hypothesis tha t the absolute difference of two binomial random variables' success probabi lities 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 likeli hood 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 re commendations for choosing, among these tests.