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“Some Things You Learn Aren't So”: Cohen's Paradox, Asch's Paradigm, and the Interpretation of Interaction

When interpreting an interaction in the analysis of variance (ANOVA), many active researchers (and, in turn, students) often ignore the residuals defining the interaction Although this problem has been noted previously, it appears that many users of ANOVA remain uncertain about the proper understanding of interaction effects To clear up this problem, we review the way in which the ANOVA model enables us to take apart a table of group means or the individual measurements contributing to the means to reveal the underlying components We also show how (using only published data) to compute a contrast on the question that may be of primary interest and illustrate strategies for interpreting tables of residuals We conclude with an exercise to check on students' understanding of ANOVA and to encourage increased precision in the specification of research results