| Abstract: | The Mantel-Haenszel test is optimal when the odds ratio is constant. This paper investigates the effects of departures from the assumption of a constant odds ratio on the behavior of the Mantel-Haenzel test. A simple approximation is proposed for the non-null distribution of the test statistic. Based on this approximation, the asymptotic relative efficiency of the Mantel-Haenszel test, compared to the overall χ2 test for no partial association, is calculated. For the case of 2 strata, it is shown that the Mantel-Haenszel test is efficient as long as the logarithms of the odds ratios are of the same sign and their absolute values exceed 1. |
