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On the Asymptotic Relative Efficiency of the Mantel‐Haenszel Test
Author(s) -
Haber M.
Publication year - 1987
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710290120
Subject(s) - mathematics , statistics , sign test , mantel test , logarithm , test statistic , constant (computer programming) , likelihood ratio test , asymptotic distribution , sign (mathematics) , odds , odds ratio , test (biology) , statistic , null distribution , econometrics , statistical hypothesis testing , demography , population , wilcoxon signed rank test , logistic regression , mathematical analysis , mann–whitney u test , computer science , estimator , paleontology , sociology , genetic diversity , biology , programming language
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 χ 2 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.