A threshold theory account of psychometric functions with response confidence under the balance condition

Are you sure? The relationship between response certainty and performance in visual detection using a perimetry-style task

Conventional psychophysical methods ignore the degree of confidence associated with each response. We compared the psychometric function for detection with that for "absolute certainty" in a perimetry-style task, to explore how knowledge of response certainty might aid the estimation of detection thresholds. Five healthy subjects performed a temporal 2-AFC detection task, indicating on each trial whether they were "absolutely certain." The method of constant stimuli was used to characterize the shape of the two psychometric functions. Four eccentricities spanning central and peripheral vision were tested. Where possible, conditions approximated those of the Humphrey Field Analyzer (spot size, duration, background luminance, test locations). Based on the empirical data, adaptive runs (ZEST) were simulated to predict the likely improvement in efficiency obtained by collecting certainty information. Compared to detection, threshold for certainty was 0.5 to 1.0 dB worse, and slope was indistinguishable across all eccentricities tested. A simple two-stage model explained the threshold difference; under this model, psychometric functions for detection and for certainty-given-detection are the same. Exploiting this equivalence is predicted to reduce the number of trials required to achieve a given level of accuracy by approximately 30% to 40%. The chances of detecting a spot and the chances of certainty-given-detection were approximately the same in young, healthy subjects. This means, for example, that a spot detected at threshold was labeled as "certainly" detected approximately half the time. The collection of certainty information could be used to improve the efficiency of estimation of detection thresholds.

A quantitative confidence signal detection model: 1. Fitting psychometric functions

Perceptual thresholds are commonly assayed in the laboratory and clinic. When precision and accuracy are required, thresholds are quantified by fitting a psychometric function to forced-choice data. The primary shortcoming of this approach is that it typically requires 100 trials or more to yield accurate (i.e., small bias) and precise (i.e., small variance) psychometric parameter estimates. We show that confidence probability judgments combined with a model of confidence can yield psychometric parameter estimates that are markedly more precise and/or markedly more efficient than conventional methods. Specifically, both human data and simulations show that including confidence probability judgments for just 20 trials can yield psychometric parameter estimates that match the precision of those obtained from 100 trials using conventional analyses. Such an efficiency advantage would be especially beneficial for tasks (e.g., taste, smell, and vestibular assays) that require more than a few seconds for each trial, but this potential benefit could accrue for many other tasks.