Analysis of Covariance: A Proposed Algorithm

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Abstract
Many researchers erroneously think that analysis of covariance (ANCOVA) should be performed only when there are pre-existing significant differences between the groups on the potential covariate. It has been shown however that, when correctly applied, ANCOVA offers two major advantages over simple analysis of variance (ANOVA): (a) greater statistical power due to a reduction in error variance; and (b) a reduction in bias in experiments where differences between groups exist at the beginning of an experiment. An algorithm has been proposed where the use of ANCOVA is conditional upon (a) a test of homogeneity of within-group regression slopes; (b) a Pearson correlation coefficient 2 0.3 between the covariate (X) and the dependent variable (1) in the case of a randomized study; in a non-randomized study (e.g. intact groups), the use of ANCOVA is not conditional on r5? 0.3 because, in this case, critical adjustments can be obtained with correlation lower than 0.3; and (c) a linear relationship between X and Y