On the efficiency of matched pairs in Bernoulli trials

Two methods for testing hypotheses concerning the equality of two proportions are compared. The first method is the large sample test for proportions considered in most elementary texts. The other method is applicable under more general assumptions than the first and requires a pairing of the observations from the two populations. The two procedures are compared, using three different measures of asymptotic efficiency, under conditions where both are applicable. At least for the measures of efficiency considered, the matched pairs procedure is shown to do almost as well as the usual large sample test.