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Biometrika 1987 74(3):661-663; doi:10.1093/biomet/74.3.661
© 1987 by Biometrika Trust
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MISCELLANEA

The equivalence of two corrections to the approximate mean of an entry in a contingency table

JOHN J. GART

Mathematical Statistics and Applied Mathematics Section, Biostatistics Branch, National Cancer Institute Bethesda, Maryland 20892, U.S.A.

Stevens (1951) gives approximate expressions for the conditional mean and variance of an entry in a contingency table with fixed marginals. Cornfield (1956) shows these to be the moments of the asymptotic normal approximation to the noncentral hypergeometric distribution. McCullagh (1984) and Levin (1984) suggest corrections to the expression for the mean. We show that the bias correction preferred by Levin for the conditional case is virtually identical to that derived by Gart (1985a) for the unconditional case. This correction is based on Bartlett's (1955) general results for score statistics. Related theory (Bartlett, 1953) yields Stevens's approximate variance formula and an expression for the third central moment.

Key Words: Contingency table • Noncentral hypergeometric distribution • Odds ratio • Score statistic


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