Correcting for unequal variance in signal detection models using response time

This study examines signal detection theory (SDT) analysis of perceptual detection performance using response time (RT) data. A defining feature of detection tasks is the asymmetry between trials with stimulus presence and absence, often reflected in asymmetric type-1 ROC curves. This asymmetry indicates greater signal variability in stimulus-present trials, which contradicts canonical assumptions in equal-variance SDT models. Across multiple datasets, we implemented an unequal-variance SDT model using RT data and compared it with the traditional confidence-based method. RT-based estimates of SDT parameters-<i>SD</i> ratio (σ) and mean difference (μ)-aligned closely with confidence-based estimates. The resulting sensitivity measure, <i>d</i> _<i>a</i> -an unequal-variance extension of <i>d'</i>-derived from RT and confidence, showed strong consistency. Notably, conventional <i>d'</i> systematically overestimated detection performance compared to the <i>d</i> _<i>a</i> measures, highlighting the importance of accounting for unequal variance. RT-based SDT analysis offers a cost-effective alternative for robustly quantifying detection performance, particularly when confidence ratings are impractical.