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A Theoretical and Empirical Investigation of Multidimensional Scaling

Torgerson, Warren S.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Rockefeller Foundation, Color, Multidimensional Scaling, Paired Comparisons, Psychophysics, Visual Discrimination, Visual Measures


Multidimensional scaling involves three basic steps. In the first, a scale of comparative distances between all pairs of stimuli is attained. The second involves estimating an additive constant and using this estimate to convert the comparative distances into absolute distances. In the third, the dimensionality of the psychological space necessary to account for these absolute distances is determined, and the projections of the stimuli on axes of this space are attained. Results of previous experiments are given. The present status of multidimensional scaling is discussed. The purpose of this study is to develop analytical procedures for multidimensional psychophysics, including routine procedures for attaining comparative distances, for estimating the additive constant, and for attaining projections of stimuli on axes when fallible absolute distances are given. Second, the purpose is also to evaluate the method in particular and the euclidean approach in general by empirical investigations of areas of known psychological dimensionality. The method of triads is considered for obtaining distances between the stimuli. Mathematical formulas are given. The purpose of the present experiments is to empirically evaluate the method of multidimensional scaling through the investigation of areas of known dimensionality, and through comparison in a one-dimensional case of the method with the method of paired comparisons. Experimental procedures are described. In the one-dimensional area, a highly consistent scale was attained by the methods of multidimension. In the two-dimensional case, the two dimensions agreed very well with the Munsell scales. Three appendices contain the matrices involved in the computation of comparative distances, from the original proportion matrices up to but not including the matrix of comparative distances. (SGK).

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