Empirical Tests of Scale Type for Individual Ratings

Abstract

This article describes eight studies that tested em pirically the hypothesis that rating procedures lead to interval-scale measurements for each single subject. In order to enhance the probability of obtaining interval scales, subjects made numerical ratings and were de liberately instructed to choose their responses so that the algebraic differences between numbers represented the subjective differences between the corresponding objects with respect to the attribute under study. This approach is based on axiomatic measurement theory. It is exemplified by a study from clinical psychologi cal research pertaining to the subjective fear aroused by each of 160 objects or situations. Any subject's ratings are regarded as interval-scale measurements of his or her individual degree of fear if the testable ax ioms of a finite, equally-spaced difference structure are satisfied empirically. These axioms pertain to ordi nal judgments on differences, and they are tested em pirically by deriving statistical hypotheses and using a refined significance-test method as an error theory. For the eight studies criteria were chosen primarily to avoid accepting false interval-scale hypotheses at the expense of relative high risks for false rejections. Nevertheless, empirical data allow acceptance of the hypothesis for 54 of the 114 subjects. As a conse quence, for at least half of the subjects, this rating procedure seems to result in interval scales.