Coherent Analysis-of-Variance Hypothesis-Testing Strategies: A General Model

Abstract

Logically consistent (“coherent”) hypothesis-testing strategies for factorial analysis-of-variance (ANOVA) designs are proposed in the context of a hierarchical model. It is shown that all of the hypotheses associated with the “traditional” factorial ANOVA model (i.e., main effects and interactions) are conceptually independent and occupy the lowest levels of the hierarchy. A research example is presented to illustrate the kind of conclusions that legitimately follow from testing the traditional hypotheses on the one hand, versus a variety of alternative hypotheses on the other.