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A Technique for the Nonmetric Analysis of Paired Comparisons of Psychological Intervals

Published online by Cambridge University Press:  01 January 2025

Bruce Schneider
Bruce Schneider*
Affiliation:
University of Toronto
*
Requests for reprints should be sent to Bruce Schneider, Department of Psychology, Erindale College, University of Toronto, Mississauga, Ontario, Canada L5L 1C6.
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Abstract

A nonmetric coordinate adjustment technique is developed which determines scale values for objects whose interobject intervals (differences in subjective value) have been directly compared. In Monte Carlo simulations, the degree of metric determinancy of the scale values is shown to be quite high even when the amount of error is relatively high. This robustness under high-error conditions permitted the analysis of individual subject data in experiments on the direct comparison of loudness differences and loudness ratios where only one judgment per interval comparison was obtained per subject.

Keywords

nonmetric scalingpaired comparisonsloudness intervals
Type
Original Paper
Information
Psychometrika , Volume 45 , Issue 3 , September 1980 , pp. 357 - 372
Copyright
Copyright © 1980 The Psychometric Society

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Footnotes

This research was supported by a grant from the National Research Council of Canada.

References

Abelson, R. P. & Tukey, J. W. Efficient utilization of non-numerical information in quantitative analysis: General theory and the case of simple order. Annals of Mathematical Statistics, 1963, 34, 1347–1369.CrossRefGoogle Scholar
Best, A. M., Young, F. W. & Hall, R. G. On the precision of a euclidean structure. Psychometrika, 1979, 44, 395–408.CrossRefGoogle Scholar
Fagot, R. F. A model of ordered metric scaling by comparison of intervals. Psychometrika, 1959, 24, 157–168.CrossRefGoogle Scholar
Johnson, R. M. Pairwise nonmetric multidimensional scaling. Psychometrika, 1973, 38, 11–18.CrossRefGoogle Scholar
Krantz, D. H., Luce, R. D., Suppes, P. & Tversky, A. Foundations of measurement. Vol. I. Additive and polynomial representations, 1971, New York: Academic Press.Google Scholar
Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a non-metric hypothesis. Psychometrika, 1964, 29, 1–27.CrossRefGoogle Scholar
McClelland, G. H. & Coombs, C. H. ORDMET: A general algorithm for constructing all numerical solutions to ordered metric structures. Psychometrika, 1975, 40, 269–290.CrossRefGoogle Scholar
Schneider, B., Parker, S., Farrell, G. & Kanow, G. The perceptual basis of loudness ratio judgments. Perception & Psychophysics, 1976, 19, 309–320.CrossRefGoogle Scholar
Schneider, B., Parker, S. & Stein, D. The measurement of loudness using direct comparisons of sensory intervals. Journal of Mathematical Psychology, 1974, 11, 259–273.CrossRefGoogle Scholar
Torgerson, W. S. Distances and ratios in psychophysical scaling. Acta Psychologica, 1961, 19, 201–205.CrossRefGoogle Scholar
Young, F. W. TORSCA-9, A FORTRAN IV program for nonmetric multidimensional scaling. Behavioral Science, 1968, 13, 343–344.CrossRefGoogle Scholar
Young, F. W. Nonmetric multidimensional scaling: Recovery of metric information. Psychometrika, 1970, 35, 455–473.CrossRefGoogle Scholar
Young, F. W. & Torgerson, W. S. TORSCA, A FORTRAN IV program for Shepard-Kruskal multidimensional scaling analysis. Behavioral Science, 1967, 12, 498–498.Google Scholar