A little learning is a dang'rous thing; Drink deep, or taste not the Pierian spring: There shallow draughts intoxicate the brain, And drinking largely sobers us again.
Interaction is a fundamental issue in psychology; it goes beyond the separate effects of two variables to consider their joint action. Historically, concern with interaction preceded analysis of variance and continues independently in a variety of ways.
Anova, however, seemed to promise unique assistance for studying interaction processes. Anova provides statistical interactions, called residuals in previous chapters. The face meaning of a two-way residual—that the effect of variable A depends on the level of variable B—was thought to be a direct reflection of interactive process. The term interaction presumably originated from this face meaning.
But interaction carries surplus meaning from English language connotations, meaning that is inappropriate and misleading with Anova. Often, perhaps mostly, statistical interaction means very little.
For this reason, the term residual is used to denote Anova “interactions” in this book. In this chapter, however, the customary term will be employed.
Why statistical interactions often lack meaning is essential to their understanding. Current texts are near-unanimous in misunderstanding interactions. They fail to recognize two pitfalls. First, an interaction may be an illusion of a nonlinear response scale, devoid of substantive reality (pages 193 ff). Second, an interaction may be an artifact of the Anova model—not a property of the data, but a distortion by a model that misrepresents the data (pages 196 ff).