The area under normal ROC curves

In this paper a few identities connecting the area under a ROC curve with the expected values of sensitivity and specificity are derived. In the second part, an analytic expression for the area is given in the case of normal distributions of test values for the classes discriminated against as well as a criterion which permits to decide among two (or more) tests which one has the greatest area under its ROC curve. Some numerical examples are given as well as an application to real data.