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Evaluating the Conformity of Sociometric Measurements

Published online by Cambridge University Press:  01 January 2025

Lawrence J. Hubert  and
Frank B. Baker
Lawrence J. Hubert*
Affiliation:
University of California, Santa Barbara
Frank B. Baker
Affiliation:
University of Wisconsin, Madison
*
Requests for reprints should be sent to Lawrence Hubert, Department of Educational Psychology, The University of Wisconsin, 1025 West Johnson Street, Madison, Wisconsin, 53706.
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Abstract

The problem of comparing two sociometric matrices, as originally discussed by Katz and Powell in the early 1950’s, is reconsidered and generalized using a different inference model. In particular, the proposed indices of conformity are justified by a regression argument similar to the one used by Somers in presenting his well-known measures of asymmetric ordinal association. A permutation distribution and an associated significance test are developed for the specific hypothesis of “no conformity” reinterpreted as a random matching of the rows and (simultaneously) the columns of one sociometric matrix to the rows and columns of a second. The approximate significance tests that are presented and illustrated with a simple numerical example are based on the first two moments of the permutation distribution, or alternatively, on a random sample from the complete distribution.

Keywords

sociometric measurementpermutation testsociometrynonparametric test
Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 1 , March 1978 , pp. 31 - 41
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

Partial support for the research of the first author was provided by the National Science Foundation through SOC 75-07860. Equal authorship is implied, The work was done when the first author was at the University of Wisconsin.

References

Bradley, J. V. Distribution-free statistical tests, 1968, Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
Conover, W. J. Practical nonparametric statistics, 1971, New York: Wiley.Google Scholar
Glanzer, M. & Glaser, R. Techniques for the study of group structure and behavior: I. Analysis of structure. Psychological Bulletin, 1959, 56, 317–32.CrossRefGoogle Scholar
Hawkes, R. K. The multivariate analysis of ordinal measures. American Journal of Sociology, 1971, 76, 908–26.CrossRefGoogle Scholar
Hubert, L. J. & Levin, J. R. Evaluating object set partitions: Free-sort analysis and some generalizations. Journal of Verbal Learning and Verbal Behavior, 1976, 15, 459–70.CrossRefGoogle Scholar
Hubert, L. J. & Levin, J. R. A general statistical framework for assessing categorical clustering in free recall. Psychological Bulletin, 1976, 83, 1072–80.CrossRefGoogle Scholar
Hubert, L. J. & Schultz, J. V. Quadratic assignment as a general data analysis strategy. British Journal of Mathematical and Statistical Psychology, 1976, 29, 190–241.CrossRefGoogle Scholar
Katz, L. & Powell, J. H. A proposed index of the conformity of one sociometric measurement to another. Psychometrika, 1953, 18, 249–56.CrossRefGoogle Scholar
Mantel, N. The detection of disease clustering and a generalized regression approach. Cancer Research, 1967, 27, 209–20.Google Scholar
Puri, M. L. & Sen, P. K. Nonparametric methods in multivariate analysis, 1971, New York: Wiley.Google Scholar
Schultz, J. V. & Hubert, L. J. A nonparametric test for the correspondence between two proximity matrices. Journal of Educational Statistics, 1976, 1, 59–67.CrossRefGoogle Scholar
Somers, R. H. A new asymmetric measure of association for ordinal variables. American Sociological Review, 1962, 27, 799–811.CrossRefGoogle Scholar