Exact Tests for Negligible Interaction in Two-way Analysis of Variance/covariance

Statistical analysis of the interaction effect in a two-way analysis of a variance/covariance model (typically unbalanced) is often performed to provide some additional support for the assessment of the main effect of interest. For example, an analysis of treatment-by-center interaction, in addition to the assessment of treatment effect, is required by the International Conference on Harmonization Guidance in multicenter clinical studies. For this purpose, the usual test for interaction with zero interaction as the null hypothesis is not useful: rejecting such a null hypothesis does not tell us whether the interaction is large enough to affect the assessment of the main effect of interest; not rejecting such a null hypothesis does not provide any statistical assurance for ignoring interaction. We define a measure of interaction relative to the error variance, and derive some exact tests for testing negligible interaction (i.e., the relative interaction measure is smaller than a given margin) as the alternative hypothesis. If we conclude that interaction is negligible at a given significance level, we can then go on to assess the main effect. An example is presented for illustration.