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A Monte Carlo Investigation of the Statistical Significance of Kruskal's Nonmetric Scaling Procedure

Published online by Cambridge University Press:  01 January 2025

David Klahr
David Klahr*
Affiliation:
University of Chicago
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Abstract

Recent advances in computer based psychometric techniques have yielded a collection of powerful tools for analyzing nonmetric data. These tools, although particularly well suited to the behavioral sciences, have several potential pitfalls. Among other things, there is no statistical test for evaluating the significance of the results. This paper provides estimates of the statistical significance of results yielded by Kruskal's nonmetric multidimensional scaling. The estimates, obtained from attempts to scale many randomly generated sets of data, reveal the relative frequency with which apparent structure is erroneously found in unstructured data. For a small number of points (i.e., six or seven) it is very likely that a good fit will be obtained in two or more dimensions when in fact the data are generated by a random process. The estimates presented here can be used as a bench mark against which to evaluate the significance of the results obtained from empirically based nonmetric multidimensional scaling.

Type
Original Paper
Information
Psychometrika , Volume 34 , Issue 3 , September 1969 , pp. 319 - 330
Copyright
Copyright © 1969 The Psychometric Society

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Footnotes

*

A preliminary version of this paper was presented at the International Federation for Information Processing Congress 68 in Edinburgh, Scotland, August 5–10, 1968.

References

Green, B. F. The computer revolution in psychometries. Psychometrika, 1966, 31, 437–445.CrossRefGoogle Scholar
Green, P. E., Carmone, F. J., & Robinson, P. S. Nonmetric scaling: An exposition and overview. Wharton Quarterly, 1968, 3.Google Scholar
Klahr, D. Decision making in a complex environment. Management Science, 1969 (forthcoming).CrossRefGoogle Scholar
Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 1964, 29, 1–27.CrossRefGoogle Scholar
Kruskal, J. B. Nonmetric multidimensional scaling: A numerical method. Psychometrika, 1964, 29, 28–42.CrossRefGoogle Scholar
Lingoes, J. C. An IBM 7090 program for Guttman-Lingoes smallest space analysis—I. Behavioral Science, 1965, 10, 183–184.Google Scholar
Russell, P. N., & Gregson, R. A. A comparison of intermodal and intramodal methods in multidimensional scaling of three-component taste mixtures. Australian Journal of Psychology, 1967, 18, 244–254.CrossRefGoogle Scholar
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function, I. Psychometrika, 1962, 27, 125–140.CrossRefGoogle Scholar
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function, II. Psychometrika, 1962, 27, 219–264.CrossRefGoogle Scholar
Shepard, R. N. Analysis of proximities as a technique for the study of information processing in man. Human Factors, 1963, 5, 33–48.CrossRefGoogle Scholar
Shepard, R. N. Metric structures in ordinal data. Journal of Mathematical Psychology, 1966, 3, 287–315.CrossRefGoogle Scholar
Stenson, H. H., & Knoll, R. L. Goodness of fit for random rankings in Kruskal's nonmetric scaling procedure. Psychological Bulletin, 1969, 71, 122–126.CrossRefGoogle Scholar
Torgerson, W. S. Multidimensional scaling of similarity. Psychometrika, 1965, 30, 379–393.CrossRefGoogle ScholarPubMed