General formulae for transforming Pearson's r to the scale of Cohen's d

The traditional thresholds for product-moment correlation (r) usually condensed in terms of "very small," "small," "medium," "large," "very large," and "huge" are derived on the scale of d. Properly transforming an estimate of r to the scale of Cohen's d is important for qualitatively evaluating the magnitude of the r effect size. A proper formula exists for a transformation between r and d in the binary and dichotomous settings, but not in polytomous or continuous settings. The traditional formula for polytomous settings assumes an equal number of cases in the subpopulations and can lead to a radically misleading transformation if the group sizes are severely imbalanced. Two general formulae are derived for transformations applicable to dichotomous, polytomous, and continuous cases, regardless of the imbalance in the group sizes. Real-life examples are given which illustrate the use of the general forms and difference between the general and the traditional forms.