Transforming the Area under the Normal Curve (AUC) into Cohen’s d, Pearson’s rpb, Odds-Ratio, and Natural Log Odds-Ratio: Two Conversion Tables

Abstract

The importance of the area under the normal curve (AUC) as a measure of the effect size (ES) in applied and forensic research has been highlighted in several articles and Tables for functioning the AUC curve into Pearson’s rpband Cohen’s d have been published. No Tables have been published for functioning AUC into other frequently used effect size indexes, such as OR and Ln(OR). In this article, two Tables for 500 AUC three-digit values provide the equivalent values for functioning AUC into four ESs, including Cohen’s d values, Pearson’s rpb, odds-ratio (OR), and Ln(OR). In the case of rpb, the values are given for four base rates (.5, .3, .2, and .1). In addition, the formulas for transforming AUC into these effect sizes are provided, so researchers can calculate other values which have not been d in the Tables.