Hostname: page-component-5f745c7db-rgzdr Total loading time: 0 Render date: 2025-01-06T21:39:59.984Z Has data issue: true hasContentIssue false
  • English
  • Français

Stevens’ Direct Scaling Methods and the Uniqueness Problem

Published online by Cambridge University Press:  01 January 2025

Thomas Augustin
Thomas Augustin*
Affiliation:
University of Graz
*
Requests for reprints should be sent to thomas.augustin@uni-graz.at
Get access Rights & Permissions [Opens in a new window]

Abstract

Stevens postulated that we can use the responses of a participant in a ratio scaling experiment directly to construct a psychophysical function representing the participant’s sensations. Although Stevens’ methods of constructing measurement scales are widely used in the behavioral sciences, the problem of which scale type is appropriate to describe ratio scaling data is still unresolved. To deal with this problem, we develop a theoretical framework to specify the scale type attained by Stevens’ direct scaling methods. It is shown, under fairly mild background assumptions, that the behavioral axioms presented in this paper are necessary and sufficient for the psychophysical functions to be ordinal-, interval-, log-interval-, or ratio-scales. Furthermore, suggestions on how to test these behavioral axioms are provided.

Keywords

Direct scaling methodsratio estimationratio productionuniqueness problemscale typesaxiomatic measurement theory
Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 3 , September 2006 , pp. 469 - 481
Copyright
Copyright © 2006 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.)

References

Anderson, N.H. (1970). Functional measurement and psychophysical judgment. Psychological Review, 77, 153–170.CrossRefGoogle ScholarPubMed
Anderson, N.H. (1976). Integration theory, functional measurement and the psychophysical law. In Geissler, H.G., Zabrodin, Y.M. (Eds.), Advances in psychophysics (pp. 93–129). Berlin: VEB Deutscher Verlag der Wissenschaften.Google Scholar
Ellermeier, W., Faulhammer, G. (2000). Empirical evaluation of axioms fundamental to Stevens’s ratio-scaling approach: I. Loudness production. Perception & Psychophysics, 62, 1505–1511.CrossRefGoogle ScholarPubMed
Ellermeier, W., Narens, L., & Dielmann, B. (2003). Perceptual ratios, differences, and the underlying scale. In Berglund, B., & Borg, E. (Eds.), Fechner Day 2003. Proceedings of the 19th annual meeting of the international society for psychophysics (pp. 71–76). Stockholm: International Society for Psychophysics.Google Scholar
Falmagne, J.-Cl. (1985). Elements of psychophysical theory, Oxford: Oxford University Press.Google Scholar
Gescheider, G.A. (1985). Psychophysics. Method, theory, and application, Hillsdale, NJ: Erlbaum.Google Scholar
Graham, C.H. (1958). Sensation and perception in an objective psychology. Psychological Review, 65, 65–76.CrossRefGoogle Scholar
Luce, R.D. (2000). Utility of gains and losses: Measurement-theoretical and experimental approaches, Mahwah, NJ: Erlbaum.Google Scholar
Luce, R.D. (2002). A psychophysical theory of intensity proportions, joint presentations, and matches. Psychological Review, 109, 520–532.CrossRefGoogle Scholar
Luce, R.D. (2004). Symmetric and asymmetric matching of joint presentations. Psychological Review, 111, 446–454.CrossRefGoogle ScholarPubMed
McKenna, F.P. (1985). Another look at the “New psychophysics. British Journal of Psychology, 76, 97–109.CrossRefGoogle Scholar
Narens, L. (1996). A theory of ratio magnitude estimation. Journal of Mathematical Psychology, 40, 109–129.CrossRefGoogle Scholar
Narens, L. (1997). On subjective intensity and its measurement. In Marley, A.A.J. (Eds.), Choice, decision, and measurement: Essays in honor of R. Duncan Luce (pp. 189–205). Mahwah, NJ: Erlbaum.Google Scholar
Narens, L. (2002). The irony of measurement by subjective estimations. Journal of Mathematical Psychology, 46, 769–788.CrossRefGoogle Scholar
Peißner, M. (1999). Experimente zur direkten Skalierbarkeit von gesehenen Helligkeiten [Experiments on the direct scalability of perceived brightness]. Unpublished master’s thesis, Universität Regensburg.Google Scholar
Shepard, R.N. (1978). On the status of “Direct” psychological measurement. In Savage, C.W. (Eds.), Minnesota studies in the philosophy of science. Vol. 9 (pp. 441–490). Minneapolis: University of Minnesota Press.Google Scholar
Shepard, R.N. (1981). Psychological relations and psychophysical scles: On the status of “Direct” psychological measurement. Journal of Mathematical Psychology, 24, 21–57.CrossRefGoogle Scholar
Steingrimsson, R., & Luce, R.D. (in press (a)). Evaluating a model of global psychophysical judgments—I: Behavioral properties of summations and productions. Journal of Mathematical Psychology.Google Scholar
Steingrimsson, R., & Luce, R.D. (in press (b)). Evaluating a model of global psychophysical judgments—II: Behavioral properties linking summations and productions. Journal of Mathematical Psychology.Google Scholar
Stevens, S.S. (1946). On the theory of scales of measurement. Science, 103, 677–680.CrossRefGoogle ScholarPubMed
Stevens, S.S. (1951). Mathematics, measurement and psychophysics. In Stevens, S.S. (Eds.), Handbook of experimental psychology (pp. 1–49). Dordrecht: Wiley.Google Scholar
Stevens, S.S. (1971). Issues in psychophysical measurement. Psychological review, 78, 426–450.CrossRefGoogle Scholar
Torgerson, W.S. (1961). Distances and ratios in psychological scaling. Acta Psychologica, 19, 201–205.CrossRefGoogle Scholar
Zimmer, K. (2005). Examining the validity of numerical ratios in loudness fractionation. Perception & Psychophysics, 67, 569–579.CrossRefGoogle ScholarPubMed