The ROC area under the curve (or mean ridit) as an effect-size

Several authors have recommended adopting the ROC Area Under the Curve (AUC) as an effect-size for group comparisons, arguing that it measures a type of effect that conventional effect-size measures do not. Likewise, the mean ridit technique has been rediscovered (and renamed) several times, and recommended as an effect-size measure for comparing groups on an ordinal dependent variable. Both the AUC and mean ridit measure the probability that a randomly chosen case from one group will score higher on the dependent variable than a randomly chosen case from the other group. Moreover, as the number of ordinal categories approaches infinity the mean ridit equals the AUC in the limit. Both are base-rate insensitive, robust to outliers, and invariant under order-preserving transformations. However, applications of both AUC and mean ridit have been limited to group comparisons, and usually just two groups. I will show that the AUC and mean ridit 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/mean ridit is a very general effect-size measure and it measures an important and interpretable effect not captured by conventional effect-sizes.