Adjusted Means in Analysis of Covariance: Are They Meaningful?

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. Such an analysis is often called an Analysis of Covariance. In this study, we examine the effect of such an adjustment on the precision of inferences regarding the adjusted means and the interpretation of those means. We consider the variance of the difference between a pair of adjusted means and 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 several data sets, how these results may be manifested in practice.