Scaling and Measurement Theory

Abstract

DURING THE past few years, quantitative psychology has developed from its earlier concerns with psychophysics and mental testing into what amounts to the general application of mathematics to the solution of psychological problems (Gulliksen, 1959). Several new areas have come under the purview of mathematical psychology-for example, statistical inference theories of signal detection, scaling models incorporating mathematical descriptions of individual differences, and computer simulations of cognitive processes. Disparate fields of psychology have been coalesced through the maturation of mathematical theories, with a strong trend toward axiomatics appearing among the theoreticians in the field (Luce, Bush, and Galanter, 1963a, b). These theories extract the invariances of structure and form from domains which apparently differ on the surface. Thus, for example, one can see concepts of information theory permeating both theoretical and empirical considerations within psychophysics and scaling. One finds game theory being incorporated into signal detection models, and both of these approaches have their impact on mathematical learning theory. These advances in theory, however, have not usually been matched by equally extensive empirical research, in either experimentation or validation. The theoretical aspects of psychometrics thus appear to have outdistanced by far the verification of empirical consequences of these theories. Considerable theoretical emphasis, for example, has been placed on the metric properties of the numbers generated by a theory-an emphasis making explicit the level of measurement (ordinal, interval, or ratio) consistent with the model. However, this survey of research indicates that neither the numbers themselves nor the transformations allowable on them are put to much further use. Finally, it must be recognized that, unlike physics in which the measuring instruments are special cases of more general laws, measurement techniques in psychology usually have coordinate status. They frequently imply psychological theories of the same order as the hypotheses they are used to evaluate. Therefore, when these measurement techniques are interposed between a hypothesis and the raw data, their filtering action may only allow information conformable with the axioms of the measuring device to become visible to the experimenter (Messick and Ross, 1962).