Combining One-Sided Binomial Tests
Abstract Six methods of combining k independent binomial test statistics are compared with respect to their median significance levels, asymptotic relative efficiencies, and accuracy of null distribution approximations. The test statistics considered are the minimum significance level, Fisher's omnibus test, the likelihood ratio, an approximate likelihood ratio, the Mantel-Haenszel statistic, and the sum of chis. Fisher's test and the likelihood ratio perform relatively well for all alternative hypotheses. The Mantel—Haenszel procedure performs well when departures from the null hypotheses are similar for all tests. The minimum is sensitive to the situation in which most of the parameters assume the null value. The sum-of-chis procedure tends to assign too much weight to individual binomial statistics with large standard errors, whereas the approximate likelihood ratio assigns too much weight to statistics with small standard errors.