Thurstone's Case Research Articles

Interval Scaling Using Pair Comparisons or Pair Comparison Treatment of Complete Ranks Under Case III Assumptions

Two of the better approaches to the scaling of stimuli are the methods of pair comparison and pair comparison treatment of complete ranks under the assumptions of Thurstone's Case III. This paper outlines a computer program with four data input options which scales up to 40 stimuli using these methods. The program will also compute an absolute scale zero point if the user employs the Horst method of balanced values (acceptance or rejection of pairs) in addition to the pair comparison procedure. Output of the program is detailed and includes, in addition to scale values and standard deviations, several matrices which allow Case IV or V scaling by hand with minimal effort.

On the Assessment of Trip Makers' Preference by Paired Comparison Scaling

Thurstone's Case V has been applied to the study of travellers' attitudes toward various modes of transportation. This paper discusses the validity of this application by examining three assumptions of the Case V as well as the problem of dimensionality. Assumptions are violated tentatively one at a time. The results suggest that the problem of dimensionality and the assumption of equal variances have to be verified before the Case V can be applied successfully to studies of transportation.

Development and Empirical Verification of New Response Categories to Increase the Validity of Multiple Response Alternative Questionnaires

A number of scales, including the Ohio State leadership scales, use the response categories Always, Often, Occasionally, Seldom, and Never, and researchers administering these scales usually assume that the resultant data are interval in nature. Recently, however, the interval properties of such data have been questioned. This paper presents an attempt at clarifying the level of measurement provided by this particular set of response categories. Drawing on previous research concerning the frequency meanings of these adverbs, a study using two samples of 200 students was performed to determine whether the distances between the adverbs become reasonably equal when they are presented as a group ordered according to median frequency values. The results indicate that equal intervals between the adverbs are approached, but not achieved when they are ordered in this manner. A second study, designed to corroborate the first, employed Thurstone Case III pair-comparison of complete ranks. The results, which parallel those obtained from the earlier study, also indicate that the response category set of Always, Very often, About as often as not, Seldom, and Never provides reasonably interval measurement. Data obtained from a third study (using again the frequency estimation procedure of the first study) generally supported the results of the Thurstone Case III method for the new category set.

Similarity between stimuli: An experimental test of the Luce and Restle choice models

A set of choice alternatives was constructed to test Restle's (1961) hypothesis about the role of similarity between alternatives in choice behavior. The set contained names of three political figures, three actresses, and three athletes, with the intention of producing considerable similarity within subsets and minimal similarity between subsets. Subjects were asked to select the individual with whom they would prefer to spend an hour of conversation. Paired-comparison choice data from 234 college subjects were consistent with expectations based on Restle's model, and disconfirmed Luce's (1959) stronger model which does not take similarity into account. Measurements of response strength for choosing the individual alternatives, and of perceived similarity between pairs of alternatives can be obtained using Restle's model, and the present test provides evidence for the validity of such measurements. Finally, Restle's model is shown to be indistinguishable from a modification of Thurstone's (1927) Case V, where the assumption of zero correlation is relaxed to permit nonnegative correlations between pairs of discriminal dispersions.

Perception of grade intervals.

Stone and Sinnett (1968) presented pairs of grade intervals to college professors to be judged using a paired-comparison technique. The question asked of them was which member of each pair was phenomenally larger. Twelve intervals between A and F were judged, including intervals such as C+ to B-. They found the log of the phenomenal scale values best fit the physical A, B, C, D, F scale. These scale values fitted Thurstone's Case 111 rather rhan his Case V. Since pluses and minuses are not given in many colleges, would the same results be obtained using the conventional four-interval scale: AB, BC, CD, DF? The intent of this study was to investigate the relationship of the phenomenal to the physical grade scale in graduate students of educational psychology. Thirty-five graduate students in educational psychology were asked to judge which of each pair of grade intervals appeared larger. A = 4; B = 3; C = 2; D = 1; F = 0 anchors were given. All possible pairs were presented in such a manner as to minimize position effects. An alternate form of the task was presented 1 wk. later. Coefficients of consistence were computed for each S? The median coefficient was 1.00. Circular triads were infrequently noted. Analyses of variance of the frequencies of selecting each interval revealed an effect beyond the 5 per cent level (F = 19.21) of the physical grade (X) on the phenomenal ( Y ) . The trend was s~gniflcantly linear (F = 68.62). Tests for quadratic and cubic trends were also made. I: ratios were nonsignificant, 0.19 and 1.11, respectively. Adjusted z scale values were found to be AB = .000; BC = ,018; CD = .186; DF = .665. The Mosteller test was made to determine goodness of fit to Thurstone Case V. The nonsignificant x 2 was 0.02. The hypothesis of fit to Case V was accepted, there being equal discriminal dispersions for each interval. The absolute average discrepancy among the judges was .004, satisfactory for paired-comparison data. After 1 wk. Ss received an alternate form of the rask. The stability coefficient was 34 . Since both Ss and grade intervals differed from those in Stone and Sinnea's study, the data are not comparable. The present study indicates that higher marks have smaller phenomenal distances between them. As the intervals increase from high ro low grades the phenomenal distances increase. The most frequently occurring pattern of choices was: ALSmal l e s t , BC-Larger, CD-Larger rhan BC, DF-Largest. Perhaps to graduate students failure marks are the apogee of the academic universe but the orbits associated with A, B, C are less distinguishable and close to the perigee. On the other hand, the size of DF may be artifactual. It is the only interval in which a letter (E) next in alphabetical position is missing.

Comparative scaling of unidimensional discrimination and similarity data

Scales constructed from paired-comparison designs under Thurstone's Case V model are discussed in relation to those derived from similarity data by means of the Unilateral Law of Comparative Judgment [3]. Factors inherent in the triadic similarity task are then considered with respect to scale invariance across experimental designs. Illustrative data, although revealing the influence of these factors upon similarity response consistency, indicate the similarity scale to be somewhat robust to their biasing effects.

Testable conditions for triads of paired comparison choices

Forty-two choice models, each representing stimuli by one-dimensional probability distributions, are obtained by relaxing the assumptions of Thurstone's Case V Law of Comparative Judgment. The models which imply or fail to imply each of nine testable probabilistic conditions are determined. Stochastic transitivity is vulnerable in most of these models. The results suggest discarding weak stochastic transitivity, and in its place using the conjunction of weak stochastic transitivity and the triangular condition. However, unless it is possible to predict which stimuli will produce violations of the conditions, none of the conditions can be rejected on the basis of too frequent intransitive triads of choices.

Measurement of moral judgment: a comparison of scaling methods.

Abstract : Scales of moral judgment were obtained by (1) the indirect method of pair comparisons on the assumption of Thurstone's Case 5, and (2) the direct method of ratio estimation. The logarithmic relationship found in previous studies was verified also for this subjective continuum. (Author)

MEASUREMENT OF AESTHETIC VALUE BY ‘DIRECT’ AND ‘INDIRECT’ METHODS

Ekman, G. & Künnapas, T. Measurement of aesthetic value by ‘direct’ and ‘indirect’ methods. Scand. J. Psychol., 1962, 3, 33–39.—The main features of ‘direct’ and ‘indirect’ methods for psychophysical measurement are briefly reviewed. An experiment is described, where the aesthetic value of 18 specimens of handwriting was measured by the direct method of ratio estimation and the indirect method of pair comparisons on the assumption of Thurstone's Case V. The scale constructed by the indirect method was a theoretically expected logarithmic function of the ratio scale obtained by the direct method. If the ratio scale is accepted as a criterion, the results show that a true interval scale may be constructed by the indirect method, in this experiment, provided that the assumption of constant variability is replaced by an assumption of proportional variability.