Dear collegues!
Many of us know that the traditional product-moment coefficient of correlation (PMC, "Pearson correlation") gives radically deflated (or attenuated) estimates of association when the scales of two variables of interest differ from each other. And, the deflation may #really# radical approximating 100% with unbalanced number of cases in the subpopulation denoted by the variable with the shorter scale. In practice, with point-biserial correlation, the scale of PMC may be radically reduced from -1 - +1 to, e.g., -.30 - +.30. This article proposes a new way of correcting this attenuation: attenuation-corrected R (RAC). It elongates the reduced scale back to the limits of correlation. Consequently, RAC can be used in obtaining deflation-corrected t-test statistics (DCt), deflation-corrected Cohen d effect size (DCd), and deflation-corrected explaining power R^2 (RAC^2). See: Article Attenuation-Corrected Estimators of Reliability