Scaling Stimuli verses Scaling People

Although psychometric methods can be used to scale people, stimuli, or both different methods are often are often used when the focus is on scaling people than when the focus is on scaling objects. As Cronbach (1957) pointed out in a classical article, clinical, counseling, and school psychologists are more inclined to think in terms of individual differences among people, e.g. in measuring such attributes as intelligence and level of adjustment. These individual differences are a nuisance to experimental psychologists and market research who largely ignore individual differences, though both may be interested in group differences. Their problems typically involve scaling stimuli, e.g. measuring which words or advertisements are most readily recalled. Regardless of the focus of the research, the basic data are representable as a two - dimensional array, perhaps extended into other dimensions because of additional considerations.

     Unidimensional scaling of people is probably the easiest situation to describe. For example, a spelling test contains words as stimuli and students as subjects. The data are simply 1 = correct and 0 = incorrect. The simplest model for scaling subjects collapses the stimulus dimension of words by adding the number of 1 s for each person. Although additional analysis are usually conducted to determine the interrelations among responses to different words, these simple sums of correct responses scale students on their spelling ability. Consequently, Dina may obtain a score of 48 and Ralph may obtain a score of 45 out of 50 words. It is quite possible that a simple ranking of the students will suffice so that an ordinal scale may be all that is necessary for such purposes as grading. The major requirement is scaling people is that alternative scaling be monotonically related to one another, i.e. that they rank order people in the same way. Thus if two different methods for scaling anxiety have a strong monotonic relationship, research results will be much the same regardless of which scale is employed.

     The roles of people and stimuli are often reversed to scale objects. Specifically, sums over students for each word describe differences in the difficulty of the words, e.g. if 50 students spell “ abacus ” correctly but only 35 spell “ mnemonic ”  correctly, “ mnemonic ” is considered more difficult than “ abacus. ” In fact, these data are usually a standard part of a test analysis, even when interest is directed toward scaling people. However, studies directed toward scaling stimuli are also more likely to be concerned with establishing functional relationships to various attributes, in which case ordinal scales are quite likely to be insufficient. Assume, for example, that the stimuli are tones of different intensity which subjects rate for loudness. Everyone knows that more intense tones will be rated louder; the key to the study is whether the relationship is logarithmic, linear or some other form. A unidimensional scale of stimuli should also fit a typical (model) individual. Such a scale should be typical of a group even if it imperfectly represents the data from any one individual.