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I am doing a repeated measures analysis with covariates. I tested the significance of association between the dependent variables and covariates, and also the homogeneity of regression hyperplanes for the covariates. I believe that I have appropriate covariates to work with, but the problem is that the significance level (both MANOVA Wilks and univariate) is decreased by the covariates. Is this possible?
Including a covariate in a model moves one degree of freedom from the error term to the model term. If the covariate does not increase the model sum of squares enough to compensate, then the F-ratio will decrease, and so will the p-value (significance level).
You may have an example of the case where the model sum of squares is not increased by a covariate because the covariate and the other predictor variables share the variance that predicts the dependent variable.
If you have further questions, send E-mail to stats@ssc.utexas.edu.