Comparison of predictive validities measured with biserial correlations and ROCs of signal detection theory

Abstract

Continuous biserial correlations were compared with relative operating characteristics (ROCs) of signal detection theory for 3 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 ( A z ) shrank less rapidly toward its null value than did the biserial correlation ( r bis ). The relation of r bis to A z is linear as the range of talent is modified by successive truncations in a given distribution, but the 2 statistics are drawn apart when the distributions differ. A z is independent of the shape of the continuous distribution. Implications for use by personnel psychologists are discussed. (PsycInfo Database Record (c) 2025 APA, all rights reserved)