The Receiver Operating Characteristic Area Under the Curve (or Mean Ridit) as an Effect Size

Several authors have recommended adopting the receiver operator characteristic (ROC) area under the curve (AUC) ormean ridit as an effect size, arguing that it measures an important and interpretable type of effect that conventional effect-size measures do not. It is base-rate insensitive, robust to outliers, and invariant under order-preserving transformations. However, applications have been limited to group comparisons, and usually just two groups, in linewith the popular interpretation of the AUCas measuring the probability that a randomly chosen case from one group will score higher on the dependent variable than a randomly chosen case from another group. This tutorial article shows that the AUC can be used as an effect size for both categorical and continuous predictors in a wide variety of general linear models, whose dependent variables may be ordinal, interval, or ratio level. Thus, the AUC is a general effect-size measure. Demonstrations in this article include linear regression, ordinal logistic regression, gamma regression, and beta regression. The online supplemental materials to this tutorial provide a survey of currently available software resources in R for the AUC and ridits, along with the code and access to the data used in the examples.