# Cohen's d for 2x2 interaction

I have a significant 2x2 interaction in a between-subjects design. I would normally report omega-squared as my effect-size measure, but I've been asked to provide Cohen's d instead? Can Cohen's d be computed for an interaction? If so, how?

In your particular case though you can get a numerator for cohen's d as (a1 - b1) - (a2 - b2). That's the simple effect of a 2x2 interaction with, a and b as the variables (e.g. sex and handedness) and the numbers are levels of the variables (e.g. male / female and left / right). Your denominator is just the square root of the MSE from the ANOVA*.
• I think that a more appropriate effect size is $d=((a1-b1)-(a2-b2))/2\sigma$, where $\sigma$ is the RMSE, as I explain in my answer here: stats.stackexchange.com/questions/179098/… – Jake Westfall Nov 4 '15 at 5:27
• It was never about the variance of d. You might want to vet this argument a different way than the comments on an answer. Perhaps construct your own question about it. That seems the best idea. – John Nov 4 '15 at 18:37