Hostname: page-component-76d6cb85b7-kcxw8 Total loading time: 0 Render date: 2026-07-14T04:36:55.591Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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, 908–26.10.1086/225005CrossRefGoogle 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, 459–70.10.1016/S0022-5371(76)90041-4CrossRefGoogle Scholar
Hubert, L. J. & Levin, J. R. A general statistical framework for assessing categorical clustering in free recall. Psychological Bulletin, 1976, 83, 1072–80.10.1037/0033-2909.83.6.1072CrossRefGoogle Scholar
Hubert, L. J. & Schultz, J. V. Quadratic assignment as a general data analysis strategy. British Journal of Mathematical and Statistical Psychology, 1976, 29, 190–241.10.1111/j.2044-8317.1976.tb00714.xCrossRefGoogle Scholar
Katz, L. & Powell, J. H. A proposed index of the conformity of one sociometric measurement to another. Psychometrika, 1953, 18, 249–56.10.1007/BF02289063CrossRefGoogle 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, 59–67.10.3102/10769986001001059CrossRefGoogle Scholar
Somers, R. H. A new asymmetric measure of association for ordinal variables. American Sociological Review, 1962, 27, 799–811.CrossRefGoogle Scholar