Predictive Validities of Aptitude Tests
Applications require that the predictor variable be continuously or quasi con tinuously distributed and that the criterion be a dichotomy or convertible to a dichotomy. The ratio of signal to noise changes monotonically with the level of the continuous predictor, and a prediction or decision is made concerning the presence or absence of the signal at each of multiple levels of the predictor. The accuracy of the predictions or decisions at each level of the predictor determines the ROC curve. The A z statistic is defined by the area under the curve and describes the degree of accuracy in detecting the signal. The zero point of the Az scale is .50, which is the chance level of the yes/no decision, and the maximum value is 1.00.