The Identification of Outliers in Two‐Way Contingency Tables Using 2 Times 2 Subtables

A significant interaction in a two‐way contingency table can often be described parsimoniously as an additive model with a few deviating “outlier” cells. Methods for location of these cells include residual‐based methods and the sequential identification of cells whose deletion leads to the maximum reduction in the statistic for independence. Such procedures, however, tend to suffer from the deficiencies of masking and swamping. The method we propose is an extension of an earlier one by Fienberg and is based on all 2 times 2 subtables containing the cell whose outlying tendency is to be tested. The essential elements of the procedure are the robust estimation of the non‐additivity of each cell; a half‐normal plot of these estimates to give a visual assessment of model fit; and a simultaneous bound to separate outlying from additive cells. The procedure is shown not to be susceptible to masking or swamping and hence identifies multiple outliers reliably in a single pass.