The term “interaction” in Anova carries illegitimate surplus meaning that has inflicted needless mystification and confusion on generations of graduate students, who have searched for meaning in the word “interaction, ” meaning that is not there. Contrary to prevailing opinion in current texts, Anova interactions are often artifacts or illusions. Even when real, they are often unimportant. Understanding interactions depends on understanding two problems— model and measurement.
The model problem is that the Anova model is arbitrary, not substantive. Anova interactions are defined as discrepancies from the arbitrary row-plus-column model of Anova. But this addition model does not usually represent psychological process. Even more must discrepancies from this arbitrary model lack substantive meaning.
For process analysis, interaction seems properly defined as nonconstancy of parameters of some substantive model. Models with constant parameters, however, may show Anova interactions (e.g., Figure 7.3). The same data may thus show zero interaction in the substantive model, nonzero interaction in Anova.
The measurement problem is that an observed interaction may be an illusion of the response scale. With a nonlinear response scale, an interaction in the observed data may disappear or even reverse direction in terms of the true linear response scale (Table 7.1). Few response scales in psychology are known to be linear; interactions should therefore be interpreted cautiously in studies oriented at process analysis.
Main effects, as shown in the text, are largely untroubled by these two problems, at least with randomized experiments.
Interactions can be useful, most notably when some theory predicts an interaction of specified shape. Crossover interactions, in which variable A has opposite effects at different levels of variable B, are always interesting. And in general, any interaction between major variables deserves scrutiny. The fact remains, however, that much ado about interactions is nothing.