Scaling

Discriminability Scaling

One early schematic approach to scaling, following on Fechner's interest in discriminability, stems largely from the work of Louis Leon Thurstone and explicitly utilizes some statistical ideas. It relies on the fact that there are comparisons that people make with less than perfect reliability. For example, when repeatedly presented with two objects that differ only a little in physical weight and asked which of the two is the heavier, a person will not always make the same selection. Thus we can theorize that although each object's physical weight is constant, its psychological heaviness undergoes some variation from encounter to encounter. That variation in heaviness is presumed to be the source of the unreliability in a person's selections. The variation takes place in the psychological dimension of heaviness, and it can be presumed to follow a normal distribution. In the simplest version of his work (Case V of the Law of Comparative Judgment), Thurstone added some assumptions that entailed the plausible idea that if stimulus A is judged heavier than stimulus B 80% of the time and stimulus X is judged heavier than stimulus Y 67% of the time, then the heavinesses of A and B differ by more than do the heavinesses of X and Y. A final assumption was that the variation in heaviness had as its form the normal distribution, allowing the translation of the probability with which one stimulus was judged heavier than another into the difference between their heavinesses measured as z scores in a normal distribution. Thus a person's performance in an elaborate experiment involving the comparative judgments of many weights can give rise to a scale of heavinesses in which the difference between two weights' scale values accurately predicts the likelihood that one will be judged heavier than the other. Applications of this approach might include having students who had experience with a group of teachers indicate their[Page 863] favorite in every possible pair of teachers; this could produce scale values for the teachers' “goodnesses.” Notice that these scales say nothing about the “absolute” heaviness or goodness of any particular things; they inform us only about the separations among the things being judged.

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