Cohen's d from regression coefficient?

Question

Is it appropriate to calculate Cohen's d (effect size) from the regression coefficient of an independent categorical variable?

My coefficient represents participation in an intervention (treatment group = 1; comparison group = 0). My inclination is to simply divide the coefficient by the standard deviation of the dependent variable. This approach makes conceptual sense to me since this coefficient represents the average predicted difference in the dependent variable between subjects in the treatment and comparison groups (while all other independent variables are held constant).

I'm wondering whether the application of Cohen's D does extends to multiple regression.

Thanks!

Answer 1

Cohen's d is the mean difference divided by the (pooled) standard deviation of the data within the groups. Indeed, the coefficient for the dummy variable gives you the mean difference, but instead of dividing by the standard deviation of the dependent variable, you should divide by the (pooled) within-group standard deviation. In fact, the residual standard error will give you exactly what you need.

If there are other covariates in the model, then the coefficient for the dummy variable represents an adjusted mean difference and the residual standard error will be reduced to some extent, depending on how much those other covariates account for the within-group variability. So, keeping that in mind, yes, dividing the coefficient for the dummy by the residual standard error will then give you something analogous to Cohen's d.