Critique of S. S. Stevens' Theory of Measurement Scale Classification

Abstract

Numerous observations are incongruous with Stevens-tradition theory of scale classification: (a) ratio scales, when available, are not necessarily preferred to interval scales; (b) the same scale changes classification depending on the use to which it is put; (c) a scale considered in isolation cannot be classified; (d) performing an inadmissible transformation on a scale entails no loss of information; and (e) the ratio scales of psychophysics do not qualify as interval scales. These incongruities result from such theorists': (a) belief that they classify scales when they really classify functions between scales; (b) belief that scientists seek new rules for assigning numbers to familiar events when, in fact, they seek new events to assign numbers to using familiar rules; and (c) confusion of function type with judgment type, leading to the erroneous claim that the ratio scales of psychophysics are distinct from other behavioral scales. Implications of the above interpretation of Stevens-tradition theory are that: (a) ranking of scales according to desirability is situation-specific—a situation-free ranking clashes with scientists' frequent preference for “inferior” scales and (b) proscriptions against mathematical manipulations or tests of statistical significance apply not to a single scale but to inferences from one scale to another.