Checking for Proportional n's in Factorial Anova's

Abstract

If the cell frequencies (i.e., the n's) in a factorial ANOVA are not equal to one another, the researcher must determine whether or not the condition of proportionality is satisfied. Although the authors of several texts demonstrate how to test for proportionality, their discussions (a) give the impression that every cell must be tested and (b) are restricted to the case of a simple two-factor ANOVA. The present authors point out that only some of the cells need to be tested, and two rules are provided which will allow the researcher to determine how many and which cells should be tested. More importantly, the authors demonstrate how to test for proportionality in a three-way ANOVA, with comments offered concerning how the test can be generalized to higher-order factorial designs.