Misinterpretation of interaction effects: A reply to Rosnow and Rosenthal.
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TL;DR
The structural model of analysis of variance for multiway tables, with main effects and interaction parameters, is overspecified and only the set of estimable functions of the cell means is useful.
Abstract
The structural model of analysis of variance for multiway tables, with main effects and interaction parameters, is overspecified. Only the set of estimable functions of the cell means is useful. The individual estimates of the parameters are artificial as regards the underlying scientific process. Rosnow and Rosenthal (1989a) stated that it is "absolutely necessary" (pg 146) that interactions should be interpreted by examining the usual estimates of the interaction parameters. This is incorrect.