Exploring the shape of signal-detection distributions in individual recognition ROC data

Abstract

Abstract The question of whether recognition performance should be analyzed assuming continuous memory strength or discrete memory states has been bothering researchers for decades. Continuous-strength models (signal-detection theory) assume that memory strength varies according to Gaussian distributions, leading to graded memory-strength values. In contrast, discrete-state models (threshold theory) are formally equivalent to continuous-strength models with rectangular distributions, giving rise to detection and guessing states. Despite these different core properties, the models fits to empirical data are often highly positively correlated, and the form of empirical receiver-operating characteristics (ROCs) supports neither of the rival models conclusively. In an attempt to reconcile opposing model properties and inconclusive empirical findings, we propose that memory distributions may be Gaussian but sometimes deviate more or less in the direction of rectangular distributions. In a series of three experiments, the shape of memory distributions in individual recognition data is explored using a signal-detection model with Tukey-lambda distributions. This family of distributions contains Gaussian and rectangular shapes as special cases, and the Tukey-lambda model—as a formal measurement tool without a psychological interpretation—allows pitting the special cases against each other. The results show that empirical memory distributions are predominantly bell-shaped or rectangular, though hybrid shapes exist. Implications for the continuous–discrete modeling debate and for the future of ROC research are discussed.