Abstract
Several investigators have fit psychometric functions to data from adaptive procedures for threshold estimation. Although the threshold estimates are in general quite correct, one encounters a slope bias that has not been explained up to now. The present paper demonstrates slope bias for parametric and nonparametric maximum-likelihood fits and for Spearman-Kärber analysis of adaptive data. The examples include staircase and stochastic approximation procedures. The paper then presents an explanation of slope bias based on serial data dependency in adaptive procedures. Data dependency is first illustrated with simple two-trial examples and then extended to realistic adaptive procedures. Finally, the paper presents an adaptive staircase procedure designed to measure threshold and slope directly. In contrast to classical adaptive threshold-only procedures, this procedure varies both a threshold and a spread parameter in response to double trials.
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References
Barlow, R. E., Bartholomew, D. J., Bremner, J. M., & Brunk, H. D. (1972).Statistical inference under order restrictions. Chichester, U.K.: Wiley.
Green, D. M., Richards, V. M., & Forrest, T. G. (1989). Stimulus step size and heterogeneous stimulus conditions in adaptive psychophysics.Journal of the Acoustical Society of America,86, 629–636.
Kaernbach, C. (1991). Simple adaptive testing with the weighted up-down method.Perception & Psychophysics,49, 227–229.
King-Smith, P. E., & Rose, D. (1997). Principles of an adaptive method for measuring the slope of the psychometric function.Vision Research,37, 1595–1604.
Kontsevich, L. L., & Tyler, C. W. (1999). Bayesian adaptive estimation of psychometric slope and threshold.Vision Research,39, 2729–2737.
Leek, M. R., Hanna, T. E., & Marshall, L. (1992). Estimation of psychometric functions from adaptive tracking procedures.Perception & Psychophysics,51, 247–256.
Levitt, H. (1971). Transformed up-down methods in psychophysics.Journal of the Acoustical Society of America,49, 467–477.
Miller, J., & Ulrich, R. (2001). On the analysis of psychometric functions: The Spearman-Kärber method.Perception & Psychophysics,63, 1399–1420.
Pflug, G. C. (1990). Non-asymptotic confidence bounds for stochastic approximation algorithms with constant step size.Monatshefte für Mathematik,110, 297–314.
Robbins, H., & Monro, S. (1951). A stochastic approximation method.Annals of Mathematical Statistics,22, 400–407.
Strasburger, H. (2001a). Converting between measures of slope of the psychometric function.Perception & Psychophysics,63, 1348–1355.
Strasburger, H. (2001b). Invariance of the psychometric function for character recognition across the visual field.Perception & Psychophysics,63, 1356–1376.
Treutwein, B., & Strasburger, H. (1999). Fitting the psychometric function.Perception & Psychophysics,61, 87–106.
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Kaernbach, C. Slope bias of psychometric functions derived from adaptive data. Perception & Psychophysics 63, 1389–1398 (2001). https://doi.org/10.3758/BF03194550
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DOI: https://doi.org/10.3758/BF03194550