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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
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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.

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

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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.

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