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 almost exclusively on the Gaussian assumption—an adherence rooted more in historical convenience than theoretical necessity that comes with a number of well-documented drawbacks. In this work, we critically examine these limitations and pursue a principled parametric alternative: SDT modeling based on extreme-value distributions of event minima. A key feature of this family of models is its grounding in a behavioral principle of invariance under uniform choice-set expansions, a prediction we empirically validate in a novel recognition-memory experiment. Based on this empirical success, we turn our attention to one particular member of this family, the Gumbel_min model, which has the convenient feature of representing discriminability as a shift in distribution. We benchmark the Gumbel_min model against its Gaussian counterpart across multiple recognition-memory tasks, including confidence-rating, ranking, forced-choice, and detection-plus-identification paradigms. Our findings highlight the model's parsimonious yet successful characterization of recognition-memory judgments, as well as the utility of its associated discriminability index, g', which can be directly computed from a single pair of hit and false-alarm rates.