Are d prime (d') in signal detection theory and Cohen's d (mainly reported in the context of the general linear model) measures for the same thing (i.e., the difference of the means in SD-units), and just termed differently? Or is there any difference between those two measures?
Solved – Are Cohen’s d (effect size) and d prime from the signal detection theory measuring the same thing
cohens-dd-primeeffect-sizesignal detection
Best Answer
They are essentially the same thing: differences between means measured in units of standard deviations, as you say. There are some theoretical differences in the substance from which they arise. Cohen's d (and the closely related Hedges' g) are calculated on real observations, whereas the distributions underlying observed responses--and used to compute d'--are latent. In the signal detection world, there has been a good deal of work on the possibility that these latent distributions may not be Gaussian in some cases, with most researchers arguing that in that case d' is not an appropriate metric. Other measures, such as the area under the ROC curve, are advocated in that case. As far as I'm aware, in meta-analysis people are fine with using a scaled mean difference even if the distributions are not Gaussian. Nonetheless, they are fundamentally the same idea. You should realize that statistics is loaded with things that are the same, but have different names and historically developed in isolation from each other.