Dear colleagues working with effect sizes or Pearson correlation,

Have you (ever) though that the traditional descriptions for "small", "medium", and "large" effect size related to Pearson correlation (i.e., .10 - .30 - .50), are, factually, based on assumption that the numbers of observations in the categories of the shorter of the variables are identical (see Cohen, 1988, p. 82). In the case that the observations are condenced in come categories and some are sparcely populated, the effect size is always higher than the traditional thresholds indicate. So, it seems that in some (or many?) cases, we may have under-evaluated the magnitude of the correlation. In the binary settings, we know that a correlation of r = 0.25 is traditionally labelled as "medium" sized association. However, if either of groups has only 5% of the cases, this size of correlation is, factually, "very large". Unfortunately - as far as I understand, you may rectify me - we have had no formula in the polytomous settings for the transformation. BUT. Happy news for you!

No problem. I created a formula which produces the exact transformation between r and d in both dichotomous and polytomous settings. I just mention it briefly in this preprint I just added to my profile (Eq. 29). The preprint is a renewed version of the previous one which seemed to interest collegues. It derives the general formula for using Cohen's d in the polytomous settings. As a side result, I created a corresponding formula for the point-polyserial correlation. The point-biserial case already has a traditional transformation formula. Any comments and recommendations are welcomed. Enjoy!Preprint Generalized Cohen d for polytomous settings