Effect size as defined elsewhere for Cohen's d for continuous variables is generally the ratio of the observed difference in means to the pooled standard deviation. Once you hit mixed models, the concept of pooled standard deviation becomes murky. And, unfortunately, it can carry over to the difference in means, as can be seen by looking at various covariance structures and random effects models, especially if there is imbalance. This is because the estimates are obtained by maximizing the likelihood (or integrating the likelihood numerically) over both fixed and random effects. As a result, several of the assumptions for the standard measures of effect size are not met. Differences are conditional on the random (or repeated) effects.
This article shows how to extract Cohen's f^2 from PROC MIXED, which may be more appropriate here.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3328081/
Steve Denham
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