Hostname: page-component-7857688df4-6b9td Total loading time: 0 Render date: 2025-11-14T10:52:31.485Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Psychophysical Law and Estimation Procedures in Psychophysical Scaling

Published online by Cambridge University Press:  01 January 2025

Robert F. Fagot
Robert F. Fagot*
Affiliation:
University of Oregon
Get access Rights & Permissions [Opens in a new window]

Abstract

A general formulation of the power law is presented which has two special features: (1) negative exponents are admissible; and (2) the log law is a special limiting case. Estimation procedures, which provide joint estimates of the exponent and the absolute threshold, are derived for the direct ratio scaling methods. A solution is provided for the averaging problem for ratio production and bisection scaling, two methods generating observations on the physical scale, and Monte Carlo methods are used to evaluate the resulting estimators.

Information

Type
Original Paper
Information
Psychometrika , Volume 28 , Issue 2 , June 1963 , pp. 145 - 160
Copyright
Copyright © 1963 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

*

This research was supported by National Science Foundation grant G19210. Preparation of the manuscript was supported in part by a Public Health Service Fellowship (No. MSP-15800), from the National Institutes of Health, Public Health Service.

†

The author has benefited greatly from consultations with Ernest W. Adams who gave generously of his time and made valuable suggestions which have been incorporated into this work. Indebtedness is also acknowledged to Manard Stewart, especially for his collaboration in the evaluation of the estimation procedures reported in the last section; and to Raymond Hohle, who was helpful in the early stages of the research.

References

Churchman, C. W., Ackoff, R. L., and Arnoff, E. L. Introduction to operations research, New York: Wiley, 1961.Google Scholar
Ekman, G. Two generalized ratio scaling methods. J. Psychol., 1958, 45, 287–295.CrossRefGoogle Scholar
Fagot, R. F. A model for equisection scaling. Behavioral Science, 1961, 6, 127–133.CrossRefGoogle Scholar
Galanter, E. and Messick, S. The relation between category and magnitude scales of loudness. Psychol. Rev., 1961, 68, 363–372.CrossRefGoogle ScholarPubMed
Lewis, D. Quantitative methods in psychology, New York: McGraw-Hill, 1960.CrossRefGoogle Scholar
Luce, R. D. On the possible psychophysical laws. Psychol. Rev., 1959, 66, 81–95.CrossRefGoogle ScholarPubMed
McGill, W. A. The slope of the loudness function: A puzzle. In Gulliksen, H. and Messick, S. (Eds.), Psychological scaling: theory and applications, New York: Wiley, 1960.Google Scholar
Stevens, S. S. On the averaging of data. Science, 1955, 121, 113–116.CrossRefGoogle ScholarPubMed
Stevens, S. S. On the psychophysical law. Psychol. Rev., 1957, 64, 153–181.CrossRefGoogle ScholarPubMed
Stevens, S. S. and Galanter, E. H. Ratio scales and category scales for a dozen perceptual continua. J. exp. Psychol., 1957, 54, 377–411.CrossRefGoogle ScholarPubMed
Stevens, S. S. Tactile vibration: Dynamics of sensory intensity. J. exp. Psychol., 1959, 59, 210–218.CrossRefGoogle Scholar
Torgerson, W. S. Theory and methods of scaling, New York: Wiley, 1958.Google Scholar
Tukey, J. W. On the comparative anatomy of transformations. Ann. math. Statist., 1957, 28, 602–632.CrossRefGoogle Scholar