FAQ/ANORES - CBU statistics Wiki

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ANORES versus ANCOVA

Maxwell SE (1985) illustrates that an Analysis of Variance on the residuals of the outcome variable with the predictor variable removed (ANORES) is more conservative that an Analysis of Covariance (ANCOVA). Since Maxwell argues this difference depends on how different the group pooled regression coefficient of the continuous predictor on the outcome is to the regression coefficient of the predictor on the outcome assuming all observations are in one group this difference, as in Maxwell's example, will be small since ANCOVA assumes the two regression coefficients of the predictor on outcome are similar in the two groups thus the group pooled estimate of the continuous predictor would be expected to be similar to that of the continuous predictor assuming all the observations came from the same group.

Reference

Maxwell SE (1985) ANOVA of residuals and ANCOVA: Correcting an illusion by using model comparisons and graphs. Journal of Educational Statistics 10(3) 197-209.