Correcting for Unequal Variance in Signal Detection Models Using Response Time

This study examines performance evaluation in perceptual detection tasks using response-time-based signal detection theory (SDT) analysis. 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 ROC 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 response time (RT) data, and compared its estimates with those obtained from the traditional confidence-based method. RT-based estimates of SDT parameters, the SD ratio (σ) and mean difference (μ), aligned closely with confidence-based estimates. The resulting sensitivity measure dₐ—an unequal-variance extension of d′—derived from RT and confidence showed strong consistency across all datasets. Notably, the conventional d′ measure consistently overestimated detection performance compared to the dₐ measures, highlighting the importance of accounting for the degree of unequal variance. Our findings demonstrate that RT-based SDT analysis offers a reliable, cost-effective alternative for the precise evaluation of perceptual detection performance, particularly when confidence ratings are impractical or unavailable.