Analysis of Covariance (ANCOVA) vs. Moderated Regression (MODREG): Why the Interaction Matters

Analysis of covariance (ANCOVA) is a commonly used statistical method in experimental and quasi-experimental studies. One of the fundamental assumptions underlying ANCOVA is that of no interaction between factor and covariate. Unfortunately, many researchers report the outcomes of ANCOVA but not the outcomes of a check on that non-interaction assumption. Through a comparison of ANCOVA (which assumes non-interaction) and moderated regression (MODREG, which allows for interaction) in a worked example, this article demonstrates that omitting the check of the non-interaction assumption comes at the risk of misestimating a treatment effect or other group difference of interest. If there is substantial interaction between factor and covariate, ANCOVA will result in conclusions of there being a group difference or no group difference whereas MODREG indicates that the magnitude of a group difference depends on the level of the covariate. Therefore, this article advises to first check and report on the interaction, to use that check to decide whether a model without interaction (ANCOVA) or with interaction (MODREG) is to be preferred, and to use ANCOVA only if the criteria outlined in this article indicate a preference towards the model without interaction. Moreover, omitted terms, such as the omitted interaction if one proceeds with ANCOVA, should be reported as well.