The meaning and interpretation of interaction.

In many scientific endeavors, it is common to examine the effects of more than a single explanatory variable on the response or outcome variable of interest. For example, in a placebo-controlled clinical trial examining the effects of a new cholesterol-lowering drug, the investigators may also classify participants in the study according to their obesity status (obese versus non-obese). When two or more explanatory variables are considered simultaneously, one could ask whether their joint effect on the response variable is simply the “sum of the parts” (or individual effects). When their joint effect is discernibly larger or smaller than the “sum of the parts,” we say that there is an “interaction” among the explanatory variables. Although the concept of interaction is relatively easy to explain,1 scientific journals abound with articles in which there is apparent confusion about the precise meaning and interpretation of the term interaction. In this column, I discuss the definition and meaning of the term interaction as used in statistics and consider how to appropriately interpret an interaction.