Power Considerations
While the inclusion of a covariate into an ANOVA generally increases statistical power by accounting for some of the variance in the dependent variable and thus increasing the ratio of variance explained by the independent variables, adding a covariate into ANOVA also reduces the degrees of freedom. Accordingly, adding a covariate which accounts for very little variance in the dependent variable might actually reduce power.
Read more about this topic: Analysis Of Covariance
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“For the most part, punishment makes men harder and colder; it concentrates; it sharpens the sense of estrangement; it strengthens the power of resistance.”
—Friedrich Nietzsche (1844–1900)