The area above the ordinal dominance graph and the area below the receiver operating characteristic graph

Receiver operating characteristic graphs are shown to be a variant form of ordinal dominance graphs. The area above the latter graph and the area below the former graph are useful measures of both the size or importance of a difference between two populations and/or the accuracy of discrimination performance. The usual estimator for this area is closely related to the Mann-Whitney U statistic. Statistical literature on this area estimator is reviewed. For large sample sizes, the area estimator is approximately normally distributed. Formulas for the variance and the maximum variance of the area estimator are given. Several different methods of constructing confidence intervals for the area measure are presented and the strengths and weaknesses of each of these methods are discussed. Finally, the Appendix presents the derivation of a new mathematical result, the maximum variance of the area estimator over convex ordinal dominance graphs.