What Is a Ratio in Ratio Scaling?
R. Duncan Luce Irvine Research Unit in Mathematical Behavioral Science University of California, Irvine
The terms ratio scale, apparently first introduced by Stevens ( 1946, 1951), and ratio scaling, apparently first introduced by Krantz ( 1972) but closely related to previous phrasing, denote different but interrelated things. Although Krantz was very clear on the matter,1 the similarity of the terms seems to invite confusion and confounding. My goal here is to explicate some aspects of the differences and relations.
A ratio scale concerns one aspect of numerical measurement representations2 for a certain class of one-dimensional, empirical structures. In particular, it refers to those cases where the numerical representation of a qualitative structure of stimuli is uniquely specified up to multiplication by a positive constant. The most familiar physical examples of ratio scales are length, mass, and time intervals. They are all examples of what are called extensive structures, and they have in common two primitives. The first is a binary ordering relation ≳ that reflects the ordering induced on____________________