COMPARISON OF PREDICTIVE VALIDITIES MEASURED WITH BISERIAL CORRELATIONS AND ROCS OF SIGNAL-DETECTION-THEORY

Continuous biserial correlations were compared with relative operating characteristics (ROCs) of signal detection theory for three classes in primary pilot training during World War II. The large samples provide a severe test of the applicability of the ROCs to traditional psychometric data. The signal detection model fitted the psychometric data well. Both statistics were influenced by restriction of range, but the measure of area under the ROC (Az) shrank less rapidly toward its null value than did the biserial correlation (rbis). The relation of (rbis), to (Az) is linear as the range of talent is modified by successive truncations in a given distribution, but the two statistics are drawn apart when the distributions differ. (Az) is independent of the shape of the continuous distribution. Implications for use by personnel psychologists are discussed.