Teaching ANCOVA: The Importance of Random Assignment

Abstract

The purpose of this paper is to present a simple approach to teaching the fundamental concepts underlying the Analysis of Covariance (ANCOVA) with particular attention to the assumption of random assignment. The main advantage of using ANCOVA in experimental research is the gain in statistical power due to a reduction in error variance. As a by-product, ANCOVA provides statistically modified group means that compensate for non-systematic group differences on the covariate. A continuing misconception, however, is that ANCOVA "equates" previously unequal groups with respect to a covariate even if these preexisting differences are systematic ones. Teachers of research methodologies are urged to clarify and expand on the sometimes insufficient presentations of ANCOVA to prevent further misapplications.