# An evaluation of the Mantel-Fleiss validity criterion for the Mantel-Haenszel statistic

• Younghae Chung (Dept of Computer Science and Statistics, Dongshin University) ;
• Charles S. Davis (Dept of Preventive Medicine and Environmental Health, University of Iowa)
• Published : 1998.04.01

#### Abstract

In testing the partial association between two variables after controlling for the S levels of a third factor, the Mantel and Haenszel (1959) statistic is often used. Since the statistic is based on the asymptotic distribution of the sum X of S hypergeometric variates, a guideline for the minimum requirements for the application of the statistic is useful. Mantel and Fleiss (1980) developed a criterion based on the guideline for the Pearson's $X^2$ statistic. The criterion requires the distance from the expected value to the closer bound of X to be at least five. The Mantel-Fleiss (MF) criterion was studied through a simulation using the hypergeometric sampling scheme. The criterion is not satisfactory. The size of statistic exceeded nominal 0.05 level nearly 1/5 of the cases even when the criteion is met. However, the results show that the statistic is much more unstable and conservative when the criterion is not met.

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