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I have the following dilemma:

Design: 1 (Group: Patient vs. Control_1 vs. Control_2) between-factors design arrayed as a 1-way ANOVA

Analysis: Following a main effect of group perform I perform all pairwise comparisons using Tukey tests.

Question: Cohen's d for paired comparisons is the mean difference divided by the pooled standard deviation. This information is not available for Tukey tests. Is there a way to compute Cohen's d or a standardized effect size from these data?

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You can easily compute Cohen's $d$ using the three means and ANOVA output. The square-root of the MS-error (or MS-residual depending on which program you used) is the pooled within-groups standard deviation. Thus, simply divide each mean difference by this value.

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