Interpreting Adjusted Means in Analysis of Covariance

• In Event: Advanced Topics in Multiple Regression Analysis

Abstract

In many data analytical applications involving the comparison of means from several populations, analyses are adjusted by including one or more continuous variables in the model. In this paper, we examine the effect of such an adjustment on the precision of inferences regarding the adjusted means and their interpretation. We show that the variance is minimized when the mean of the covariate is the same in both groups. However, when the covariate means differ across groups, the additional term in the model can dominate the variance of the comparison. We investigate the break-even point for this comparison and under what condition that occurs. Finally, we demonstrate with simulation studies, how these results may be manifested in practice.

Authors

• Daniel J. Mundfrom, Eastern Kentucky University

• Dennis L. Clason, New Mexico State University