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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
*
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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

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