The Difference Between ANOVA of Residuals and ANCOVA.

The conceptualization of analysis of covariance (ANCOVA), as an analysis of variance (ANOVA) on the residual scores that are obtained when the dependent variable is regressed on the covariate, is mathematically incorrect. If residuals are obtained from the pooled within-groups regression coefficient, ANOVA on the residuals results in an inflated alpha-level. If the regression coefficient for the total sample combined into one group is used, ANOVA on the residuals yields an inappropriately conservative test. In either case, ANOVA of residuals fails to provide a correct test, because the significance test in ANCOVA requires consideration of both the pooled within-groups regression coefficient and the regression coefficient for the total sample combined into one group. It is recommended that the significance test of treatment effects in ANCOVA be conceptualized as a comparison of models whose parameters are estimated by the principle of least squares. (Author/RL)