A representation and interpretation of the area under a receiver operating characteristic
(ROC) curve obtained by the "rating" method, or by mathematical predictions based
on patient characteristics, is presented. It is shown that in such a setting the area
represents the probability that a randomly chosen diseased subject is (correctly)
rated or ranked with greater suspicion than a randomly chosen non-diseased subject.
Moreover, this probability of a correct ranking is the same quantity that is estimated
by the already well-studied nonparametric Wilcoxon statistic. These two relationships
are exploited to (a) provide rapid closed-form expressions for the approximate magnitude
of the sampling variability, i.e., standard error that one uses to accompany the area
under a smoothed ROC curve, (b) guide in determining the size of the sample required
to provide a sufficiently reliable estimate of this area, and (c) determine how large
sample sizes should be to ensure that one can statistically detect differences in
the accuracy of diagnostic techniques.