I have a pre-post study, three groups, and one covariate. I have conducted two contrasts (1st group vs. 2nd+3rd; 2nd vs 3rd). The independent group is multicategorical, the dependent variable (outcome) and the covariate (baseline value) are continuous.
I have calculated partial eta square and I would like to convert it into Cohen's d.
What is the most appropriate approach?
Effect Size: Relationship between partial Eta-squared, Cohen's f, and Cohen's d (ibm.com)
You can also interpret partial eta squared like this:
The following rules of thumb are used to interpret values for Partial eta squared:
- .01: Small effect size
- .06: Medium effect size
- .14 or higher: Large effect size
Why do you always study psychology in statistical ways? The statistical conclusion is about groups. How do you use it to individuals? How to study individuals?
You have the raw data ? If so, you can calculate the Cohen's d -like statistics directly. When using a more complex model ---- rather than just two groups, for which Cohen's d was developed ---- a Cohen's d -like statistic for comparing two groups is the difference in the predicted means for the groups divided by the RMSE for the model.
In general, partial eta-squared is calculated for the variable in the anova table, not for just two groups in that variable. Did you calculate the partial eta-squared for each contrast ?
What software are you using ? In R, for example, the eff_size() function in the emmeans package makes short work of this problem.
You will see some formulae for conversion of partial eta-squared to Cohen's d like this one: https://www.ibm.com/support/pages/effect-size-relationship-between-partial-eta-squared-cohens-f-and-cohens-d . But pay attention to the cases in which these conversions work. I don't think a general procedure for conversion makes sense.
@Béatrice Marianne Ewalds-Kvist, thank you so much.
I had found that article but the resulting effect sizes did not correspond to the interpretation of the partial eta squared that you have also reported (e.g., a partial eta squared of 0.06 should indicate a medium effect size, but it corresponds to a very low Cohen's s when converted with the formula provided on that page).
@Salvatore S. Mangiafico, thank you. I used SPSS, which gives partial eta square as the only option to calculate effect sizes in ANCOVAs. I did calculate partial eta squared for the omnibus test and for the two contrasts as well.
I agree with being cautious about applying a standard formula - I am trying to find what best fits my specific case. Thank you!
If you have the partial eta-squares for the contrasts, then perhaps you could use a formula like at the link I included above. Though I'm not sure about this approach.
The unsophisticated approach is just to calculate Cohen's d. That is, calculate the difference in means and the pooled standard deviation.
But I think the better approach is to get the EMMEANS for each group of interest, and use these for the calculation of Cohen's d for each pair of means. For the pooled standard deviation use the RMSE from the model. (This is just the residual sum of squares divided by the residual degrees of freedom).
I'll offer to calculate these with R, so you can compare what you're getting, if you want to share your actual data, or some hypothetical toy data that has a similar form.
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