Extreme-Value Signal Detection Theory for Recognition Memory: The Parametric Road Not Taken

Signal Detection Theory has long served as a cornerstone of psychological research,particularly in recognition memory. Yet its conventional application hinges almostexclusively on the Gaussian assumption—an adherence rooted more in historicalconvenience than theoretical necessity that comes with a number of well-documenteddrawbacks. In this work, we critically examine these limitations and introduce aprincipled parametric alternative: the Gumbel_min model, based on extreme-valuedistributions of event minima. A key feature of this model is its grounding in abehavioral principle of invariance under uniform choice-set expansions—a predictionwe empirically validate in a novel recognition-memory experiment. We furtherbenchmark the Gumbel_min model against its Gaussian counterpart across multiplerecognition-memory tasks, including confidence-rating, ranking, forced-choice, anddetection-plus-identification paradigms. Our findings highlight the model'sparsimonious yet successful characterization of recognition-memory judgments, aswell as the utility of its associated discriminability index, g', which can be directlycomputed from a single pair of hit and false-alarm rates.