# Correcting for unequal variance in signal detection models using response time

## TL;DR

This paper introduces a new method using response time data to improve signal detection analysis by accounting for unequal variance, offering a more accurate measure of detection performance.

## Contribution

The study proposes an RT-based unequal-variance SDT model that provides more accurate detection performance estimates than traditional methods.

## Key findings

- RT-based and confidence-based SDT models produced similar estimates of SD ratio and mean difference.
- The new sensitivity measure da showed strong consistency between RT and confidence methods.
- Conventional d′ overestimates detection performance compared to da.

## Abstract

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—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. Notably, conventional d′ systematically overestimated detection performance compared to the da 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.

•RT and confidence data were used for unequal-variance signal detection analysis•Both measures produced similar SD ratio and mean difference estimates•They yielded highly consistent estimates of da (unequal-variance extension of d′)•Conventional d′ systematically overestimated detection performance relative to da

RT and confidence data were used for unequal-variance signal detection analysis

Both measures produced similar SD ratio and mean difference estimates

They yielded highly consistent estimates of da (unequal-variance extension of d′)

Conventional d′ systematically overestimated detection performance relative to da

Neuroscience; Behavioral neuroscience; Psychology