Abstract
Probit analysis was applied to the problem of threshold estimation from psychometric functions derived from the two-alternative forced-choice (2AFC) method of constant stimuli. Threshold estimates from 2AFC experiments are surprisingly poor: They are about twice as variable as corresponding estimates based on the traditional yes-no method of constant stimuli, and their asymmetrical confidence limits are not readily predicted from conventional standard error formulas. All of these faults are exacerbated in small samples. Computer simulations demonstrated that, for small samples, the probit analysis equations do not give a valid estimate of threshold variability. The variability of staircase estimates of threshold cannot be less than the variability of threshold estimates derived from the method of constant stimuli given an optimum placement of trials. Hence our findings also define the minimum variability of all staircase estimators under the assumptions of probit analysis.
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This work was supported by NIH Grants 5 P-30-EY0GT86, R01-EY03976, R01-EY04776, and R01-EY02920 and by the Smith-Kettlewell Eye research Foundation.
Gerald Westheimer wrote the original probit program for the yes-no case. This program served as a model for subsequent programs that employed different strategies to handle the 2AFC case and the simulations. We also want to acknowledge considerable assistance from Martha Teghtsoonian and an anonymous reviewer in the editing of the final version. A computer program for 2AFC probit analysis is available from the first author on written request. Another program, available from the second author, works with several shapes of the psychometric function; it has several options for estimating confidence limits and an option for estimating the upper asymptote.
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McKee, S.P., Klein, S.A. & Teller, D.Y. Statistical properties of forced-choice psychometric functions: Implications of probit analysis. Perception & Psychophysics 37, 286–298 (1985). https://doi.org/10.3758/BF03211350
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DOI: https://doi.org/10.3758/BF03211350