Abstract
There are many ways in which to estimate thresholds from psychometric functions. However, almost nothing is known about the relationships between these estimates. In the present experiment, Monte Carlo techniques were used to compare psychometric thresholds obtained using six methods. Three psychometric functions were simulated using Naka-Rushton and Weibull functions and a probit/logit function combination. Thresholds were estimated using probit, logit, and normit analyses and least-squares regressions of untransformed orz-score and logit-transformed probabilities versus stimulus strength. Histograms were derived from 100 thresholds using each of the six methods for various sampling strategies of each psychometric function. Thresholds from probit, logit, and normit analyses were remarkably similar. Thresholds fromz-score- and logit-transformed regressions were more variable, and linear regression produced biased threshold estimates under some circumstances. Considering the similarity of thresholds, the speed of computation, and the ease of implementation, logit and normit analyses provide effective alternatives to the current “gold standard”—probit analysis—for the estimation of psychometric thresholds.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abromawitz, M., &Stegun, I. A. (1964).Handbook of mathematical functions. Washington, DC: U.S. Government Printing Office.
Berkson, J. (1944). Application of logistic function to bio-assay.Journal of the American Statistical Association,39, 357–365.
Berkson, J. (1953). A statistically precise and relatively simple method of estimating the bio-assay with quantal response, based on the logistic function.Journal of the American Statistical Association,48, 565–599.
Berkson, J. (1955). Estimate of the integrated normal curve by minimum normit chi-square with particular reference to bio-assay.Journal of the American Statistical Association,50, 529–549.
Bliss, C. I. (1935). The calculation of the dosage mortality curve.Annals of Applied Biology,22, 134–167.
Collett, D. (1991).The modelling of binary data. London: Chapman & Hall.
Finney, D. J. (1971).Probit analysis (3rd ed.). Cambridge: Cambridge University Press.
Flom, M. C. (1966, July). New concepts on visual acuity.Optometric Weekly,57, 63–68.
Gescheider, G. A. (1985).Psychophysics: Method, theory, and application. Hillsdale, NJ: Erlbaum.
Harvey, L. O., Jr. (1986). Efficient estimation of sensory thresholds.Behavior Research Methods, Instruments, & Computers,18, 623–632.
Kleinbaum, D. G., Kupper, L. L., &Muller, K. E. (1988).Applied regression analysis and other multivariable methods. Boston: PWSKent Publishing.
Lieberman, H. R. (1983). Computation of psychophysical thresholds using the probit technique.Behavior Research Methods & Instrumentation,15, 446–448.
Naka, K.-I., &Rushton, W. A. H. (1966). S-potentials from colour units in the retina of fish (Cyprinidae).Journal of Physiology,185, 587–599.
Quick, R. F. (1974). A vector magnitude model of contrast detection.Kybernetic,16, 65–67.
Stevens, S. S. (1972, September). A neural quantum in sensory discrimination.Science,177, 749–762.
Weibull, W. (1951). A statistical distribution function of wide applicability.Journal of Applied Mechanics,18, 293–297.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was conducted while the author was a postdoctoral researcher at Toronto Hospital (Western Division), supported by MRC and NEI grants to D. Regan. I would like to thank David Regan, Alex Vincent, Stan Hamstra, and Merton Flom for their help with early versions of this manuscript.
Rights and permissions
About this article
Cite this article
Simpson, T.L. A comparison of six methods to estimate thresholds from psychometric functions. Behavior Research Methods, Instruments, & Computers 27, 459–469 (1995). https://doi.org/10.3758/BF03200444
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03200444