Understanding Data When Interactions Are Present or Hypothesized

Abstract

The traditional approach to interpreting data when an interaction is present is to interpret cell means as reflecting a difference between differences An alternative is to interpret any main effects and separately interpret interaction residuals Interpretation of interaction residuals can sometimes lead to nonsensical conclusions Thus in deciding between the approaches, researchers should consider (a) the conceptual nature of the variables involved, (b) relevant theories and (c) the additional data that might be necessary to distinguish among competing plausible representations Issues have also arisen regarding how to best test a hypothesis that involves interaction variance Some researchers have argued that the use of a focused contrast designed to test a specific ordering of cell means (e g, a linear contrast) is often the best strategy We note potential problems with the use of such contrasts and discourage researchers from blanket use of contrasts that combine main effect and interaction variance