The Moments of the Pearson Chi-Squared Statistic and the Minimum Expected Value in Two-Way Tables
推导了二维列联表皮尔逊卡方统计量的前三阶矩，评估卡方近似的准确性，发现最小期望值准则过于保守，并基于矩提出修正方法。
Explicit expressions for the first three moments of Pearson's X2 statistic for a two-way contingency table are used to investigate the accuracy of the χ2 approximation to its distribution. The usual ’minimum expected value' criterion is shown to give a global bound on the accuracy of the moments, but to be too conservative. This is illustrated by examples. It is shown that the adequacy of the approximation depends on the significance level that is to be used as well as the accuracy of the moments. When the χ22 approximation is inadequate, corrections based on the moments can be used. Numerical studies of the usefulness of these corrections are presented.