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Efficient estimation of stereo thresholds: What slope should be assumed for the psychometric function?

Lookup NU author(s): Dr Ignacio Serrano-PedrazaORCiD, Dr Kathleen Vancleef, Professor Jenny ReadORCiD



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


© 2020 Serrano-Pedraza et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Bayesian staircases are widely used in psychophysics to estimate detection thresholds. Simulations have revealed the importance of the parameters selected for the assumed subject’s psychometric function in enabling thresholds to be estimated with small bias and high precision. One important parameter is the slope of the psychometric function, or equivalently its spread. This is often held fixed, rather than estimated for individual subjects, because much larger numbers of trials are required to estimate the spread as well as the threshold. However, if this fixed value is wrong, the threshold estimate can be biased. Here we determine the optimal slope to minimize bias and maximize precision when measuring stereoacuity with Bayesian staircases. We performed 2- and 4AFC disparity detection stereo experiments in order to measure the spread of the disparity psychometric function in human observers assuming a Logistic function. We found a wide range, between 0.03 and 3.5 log10 arcsec, with little change with age. We then ran simulations to examine the optimal spread using the empirical data. From our simulations and for three different experiments, we recommend selecting assumed spread values between the percentiles 60–80% of the population distribution of spreads (these percentiles can be extended to other type of thresholds). For stereo thresholds, we recommend a spread around the value σ = 1.7 log10 arcsec for 2AFC (slope β = 4.3 /log10 arcsec), and around σ = 1.5 log10 arcsec for 4AFC (β = 4.9 /log10 arcsec). Finally, we compared a Bayesian procedure (ZEST using the optimal σ) with five Bayesian procedures that are versions of ZEST-2D, Psi, and Psi-marginal. In general, for the conditions tested, ZEST optimal σ showed the lowest threshold bias and highest precision.

Publication metadata

Author(s): Serrano-Pedraza I, Vancleef K, Herbert W, Goodship N, Woodhouse M, Read JCA

Publication type: Article

Publication status: Published

Journal: PLoS ONE

Year: 2020

Volume: 15

Issue: 1

Online publication date: 02/01/2020

Acceptance date: 04/12/2019

Date deposited: 13/01/2020

ISSN (electronic): 1932-6203

Publisher: Public Library of Science


DOI: 10.1371/journal.pone.0226822


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