Textbook Analysis of Covariance -- Is It Correct?

Abstract : For unbalanced Model I ANOVA data there is a controversy in the literature -- should the partial SS's be computed hierarchically or should they be computed after fitting all other model terms including higher-order interactions? A similar problem exists in the Model I analysis of covariance (ANCOVA), yet the usual prescription given in textbooks uses only the non-hierarchical approach. Using two classic examples of ANCOVA, this paper examines the two approaches to ANCOVA calculations. (Author)