ANCOVA adjusts for differences in the covariate by removing variability accounted for by a linear regression on the covariate. If there is a nonlinear component to the relationship between X and Y, the ANCOVA tests will be biased. Moreover, it is assumed that the same regression adjustment is appropriate for each treatment group. Unless the slopes of the regression equations of Y on X are the same for each treatment group, ANCOVAshould not be used. If there are different slopes, the interesting question is not what would happen if all the participants had the same score on the covariate, but rather, what would happen at different values of the covariate. Atest for homogeneity of regression slopes should be conducted before an ANCOVAis performed.
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