Cellwise residual analysis in two-way contingency tables

MacDonald and Gardner reported the results of a comparative study of two post hoc cellwise tests in 3 x 4 contingency tables under the independence and homogeneity models. Based on their results, they advised against the use of standardized residuals and in favor of adjusted residuals. Here the authors show that the comparison was biased in favor of adjusted residuals because of a failure to consider the nonunit variance of standardized residuals. The authors define a moment-corrected standardized residual that overcomes this bias and present the results of a thorough study including two-way tables of all dimensions between 2 x 2 and 8 x 12 that aimed at comparing moment-corrected standardized residuals with adjusted residuals. Across the entire set of table dimensions included in this study, the results reveal that both residuals yield essentially the same pattern of cell-by-cell and experimentwise Type I error rates when the data come from variables with uniform marginal distributions. When the data come from variables with peaked marginal distributions, adjusted residuals behave minimally better than moment-corrected residuals.