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Simple Statistical Methods for Scalogram Analysis

Published online by Cambridge University Press:  01 January 2025

Leo A. Goodman†
Leo A. Goodman†*
Affiliation:
University of Chicago
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Abstract

Simple statistical methods are developed to test whether coefficients of reproducibility, of homogeneity, or of consistency differ significantly from what can be expected if responses to different items are statistically independent. Simple methods are also developed for estimating the variance of coefficients of reproducibility when it is not assumed that responses to different items are independent. These estimates are used to test whether a coefficient differs significantly from any prescribed value, and also to obtain confidence intervals for these coefficients. The rationale for the measurement of reproducibility is also discussed.

Type
Original Paper
Information
Psychometrika , Volume 24 , Issue 1 , March 1959 , pp. 29 - 43
Copyright
Copyright © 1959 The Psychometric Society

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Footnotes

*

This research was carried out at the Statistical Research Center, University of Chicago, under sponsorship of the Statistics Branch, Office of Naval Research, and of the Social Science Research Committee, University of Chicago. Reproduction in whole or in part is permitted for any purpose of the United States Government. The author is indebted to Jacob Gewirtz for some very helpful comments.

†

This paper is dedicated to Professor Jacob Marschak on the occasion of his sixtieth birthday, July 23, 1958.

References

Anderson, T. W. and Goodman, L. A. Statistical inference about Markov chains. Ann. math. Statist., 1957, 28, 89–110.CrossRefGoogle Scholar
Cochran, W. G. The x2 test of goodness of fit. Ann. math. Statist., 1952, 23, 315–345.CrossRefGoogle Scholar
Cramer, H. Mathematical statistics, Princeton: Princeton Univ. Press, 1946.Google Scholar
Festinger, L. The treatment of qualitative data by scale analysis. Psychol. Bull., 1947, 44, 149–161.CrossRefGoogle ScholarPubMed
Goodman, L. A. and Kruskal, W. H. Measures of association for cross classifications. J. Amer. statist. Ass., 1954, 49, 732–764.Google Scholar
Green, B. F. A method of scalogram analysis using summary statistics. Psychometrika, 1956, 21, 179–188.CrossRefGoogle Scholar
Guttman, L. et al. The basis for scalogram analysis. In Stouffer, S. A. et al (Eds.), Measurement and prediction. Princeton: Princeton Univ. Press, 1950, 60–90.Google Scholar
Guttman, L. On Festinger's evaluation of scale analysis. Psychol. Bull., 1947, 44, 451–465.CrossRefGoogle ScholarPubMed
Jardine, R. Ranking methods and the measurement of attitudes. J. Amer. statist. Ass., 1958, 53, 720–728.CrossRefGoogle Scholar
Loevinger, J. A systematic approach to the construction and evaluation of tests of ability. Psychol. Monogr., 1947, 61, 4.CrossRefGoogle Scholar
Loevinger, J. The technic of homogeneous tests compared with some aspects of “scale analysis.”. Psychol. Bull., 1948, 45, 507–529.CrossRefGoogle ScholarPubMed
Pearson, E. S. and Hartley, H. O. Biometrika tables for statisticians, Vol. 1, Cambridge: Cambridge Univ. Press, 1954.Google Scholar
Sagi, P. C. A statistical test for the significance of the coefficient of reproducibility. Psychometrika, 1959, 24, 19–27.CrossRefGoogle Scholar
Walker, H. M. and Lev, J. Statistical inference, New York: Holt, 1953.CrossRefGoogle Scholar
White, B. W. and Saltz, E. Measurement of reproducibility. Psychol. Bull., 1957, 54, 81–99.CrossRefGoogle ScholarPubMed