Definition and interpretation of interaction effects.

When interaction is claimed in a factorial arrangement, the results almost always require more detailed analysis than is typically reported in our primary journals. In reporting interactions, research psychologists have gotten into the habit of examining only the differences between the original cell means (the simple effects) instead of more properly examining the residuals, or leftover effects, after the lower order effects have been removed. The logic of decomposing the original cell or condition means into the main effects and the effects of the interaction is described and illustrated by an algorithm for 2 X 2 interactions. The mathematical meaning of interaction effects is unambiguous, and textbooks of mathematical and psychological statistics routinely include proper definitions of interaction effects. Despite this, a substantial number of research psychologists reporting results in our primary journals interpret interactions incorrectly. This was revealed by a systematic review of 320 articles published in 1985 in the first and last issues of the following American Psychological Association journals: Developmen