Authors: García-Pérez, Miguel A.¹; Alcalá-Quintana, Rocío¹

Source: British Journal of Mathematical and Statistical Psychology, Volume 60, Number 1, May 2007 , pp. 147-174(28)

Abstract:

Bayesian adaptive methods have been extensively used in psychophysics to estimate the point at which performance on a task attains arbitrary percentage levels, although the statistical properties of these estimators have never been assessed. We used simulation techniques to determine the small-sample properties of Bayesian estimators of arbitrary performance points, specifically addressing the issues of bias and precision as a function of the target percentage level. The study covered three major types of psychophysical task (yes-no detection, 2AFC discrimination and 2AFC detection) and explored the entire range of target performance levels allowed for by each task. Other factors included in the study were the form and parameters of the actual psychometric function Ψ, the form and parameters of the model function M assumed in the Bayesian method, and the location of Ψ within the parameter space. Our results indicate that Bayesian adaptive methods render unbiased estimators of any arbitrary point on ψ only when M=Ψ, and otherwise they yield bias whose magnitude can be considerable as the target level moves away from the midpoint of the range of Ψ. The standard error of the estimator also increases as the target level approaches extreme values whether or not M=Ψ. Contrary to widespread belief, neither the performance level at which bias is null nor that at which standard error is minimal can be predicted by the sweat factor. A closed-form expression nevertheless gives a reasonable fit to data describing the dependence of standard error on number of trials and target level, which allows determination of the number of trials that must be administered to obtain estimates with prescribed precision.

Document Type: Research article

DOI: 10.1348/000711006X104596

Affiliations: 1: Departamento de Metodología, Facultad de Psicología, Universidad Complutense, Madrid, Spain