Interactions in Multi-Factor Contingency Tables

Abstract

SUMMARY Interactions in contingency tables are compared with interactions in the analysis of variance. The comparison leads to a new formulation of the hypothesis of no second-order interaction in three-way contingency tables, to an explanation of the paradoxes associated with this hypothesis and to a comparatively simple method of constructing its likelihood-ratio test statistic. The extensions to higher-order interactions are merely outlined as they are not likely to be of practical interest.