A program to determine the optimal rank order of pairwise similarities from incomplete triads data: Profit

Abstract

Description. Nonmetric scaling techniques (Kruskal, 1964; Shepard, 1962a, b; Shepard, 1966) as embodied in the TORSCA (Young & Torgerson, 1967) or PARSCAL (Johnson, 1973) programs produce multidimensional scaling solutions from rank orders of pairwise similarities between N points. The present program produces a rank order for (~) pairs of stimuli for data gathered by Torgerson's method of triadic combinations (Torgerson, 1958) or, more· commonly, the method of incomplete triads. Coombs (1964, pp. 352-359) suggests a method of triangular analysis to arrange these triad judgments inte a single rank order. We have supplemented Coombs' basic algorithm with a set of routines to transform triangular matrices to poduce the best rank orders in terms of the fewest number of inconsistencies. With sophisticated subjects, the rank orders needed for the nonmetric scaling programs can be obtained directly by asking the subject to rank order all pairs of stimuli in order of similarity. The method of incomplete triads is particularly appropriate for subjects who cannot consider a large number of relationships simultaneously but who can decide which two of three stimuli are most similar and which two are least similar. Children as young as 5 years of age can make such judgments. Seitz (1971) demonstrated the usefulness of this type of data, using metric scaling techniques suggested by Torgerson (1958). Metric techniques, however, require repeated measurement on each triad since distance is estimated from frequency of choice. For more than five stimuli, many trials for a single subject or the data from several subjects must be combined to obtain the necessary measures. There is a major advantage in not combining the data from more than one subject since one is usually interested in a description of the perceived similarity among stimuli for individuals. The nonmetric procedures used in the present program can be employed without repeated measurements on each triad and can be applied to individual subjects. Thus, for six stimuli, only 20 trials are necessary; for nine stimuli, 84 trials are necessary. Input. Input consists of the data gathered from all possible triads, given N stimuli. The data from each triadic stimulus array forms a data input unit consisting of the designation numbers of the two stimuli judged as most similar and the two stimuli judged as least similar. The data input units can be read into the program in any order as long as the data within each unit follows the sequence: most similar pair, least similar pair.