The Equivalence of Two Corrections to the Approximate Mean of an Entry in a Contingency Table
本文证明了Levin和Gart分别针对条件与非条件情形提出的列联表单元格均值修正公式实质等价，并基于Bartlett的理论推导了Stevens的近似方差公式和三阶中心矩表达式。
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.