Contrast Tests of Interaction Hypotheses

This article argues for the use of contrasts to test a priori interaction hypotheses in 2-way analysis of variance designs. It focuses on 3 underused types of interaction contrast tests: a "matching" pattern for cognate levels of row and column factors; the "qualitative quadratic," for monotonic profiles of means in the same direction but with opposed concavities; and a "differential curvilinearity" test for differences in the curvature of two profiles with the same direction of concavity. The circumstances that best capitalize on the potential advantages of a priori contrast tests are indicated, and an effect size measure for contrasts is presented. Investigators are urged to examine residuals after accounting for the variation attributable to the chosen contrast for patterns that may provide hints for more textured hypotheses in further research. If a posteriori contrasts are used, their effect sizes should be noted.