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Science 19 June 1987:
Vol. 236. no. 4808, pp. 1527 - 1532
DOI: 10.1126/science.236.4808.1527
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Articles

Measurement Scales on the Continuum

R. DUNCAN LUCE 1 and LOUIS NARENS 2

1 Victor S. Thomas professor of psychology at Harvard University, Cambridge, MA 02138
2 Professor of social science at the University of California at Irvine, CA 92717.

In a seminal article in 1946, S. S. Stevens noted that the numerical measures then in common use exhibited three admissible groups of transformations: similarity, affine, and monotonic. Until recently, it was unclear what other scale types are possible. For situations on the continuum that are homogeneous (that is, objects are not distinguishable by their properties), the possibilities are essentially these three plus another type lying between the first two. These types lead to clearly described classes of structures that can, in principle, be incorporated into the classical structure of physical units. Such results, along with characterizations of important special cases, are potentially useful in the behavioral and social sciences.


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