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Range Restrictions for Product-Moment Correlation Matrices

Published online by Cambridge University Press:  01 January 2025

Ingram Olkin
Ingram Olkin*
Affiliation:
Stanford University
*
Reprint requests should be addressed to Ingrain Olkin, Sequoia Hall, Department of Statistics, Stanford University, Stanford, California 94305.
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Abstract

It is well-known that for a trivariate distribution if two correlations are fixed the remaining one is constrained. Indeed, if one correlation is fixed, then the remaining two are constrained. Both results are extended to the case of a multivariate distribution. The results are applied to some special patterned matrices.

Keywords

constrained correlationsmultiple correlationpartial correlationpatterned correlation matrices

Information

Type
Notes And Comments
Information
Psychometrika , Volume 46 , Issue 4 , December 1981 , pp. 469 - 472
Copyright
Copyright © 1981 The Psychometric Society

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References

Glass, G. V. & Collins, J. R. Geometric proof of the restriction of possible value of r xy when r xz and r yz are fixed. Educational and Psychological Measurement, 1970, 30, 37–39.CrossRefGoogle Scholar
Gleser, L. J. On bounds for the average correlation between subtest scores in ipsatively scored tests. Educational and Psychological Measurement, 1972, 32, 759–765.CrossRefGoogle Scholar
Hubert, L. J. A note on the restriction of range for Pearson product-moment correlation coefficients. Educational and Psychological Measurement, 1972, 32, 767–770.CrossRefGoogle Scholar
Leung, C.-K. & Lam, K. A note on the geometric representation of the correlation coefficients. The American Statistician, 1975, 29, 128–130.CrossRefGoogle Scholar
McCornack, R. L. A criticism of studies comparing item-weighting methods. The Journal of Applied Psychology, 1956, 40, 343–344.CrossRefGoogle Scholar
Priest, H. F. Range of correlation coefficients. Psychological Reports, 1968, 22, 168–170.CrossRefGoogle ScholarPubMed
Radcliffe, J. A. Some properties of ipsative score matrices and their relevance for some current interest tests. Australian Journal of Psychology, 1963, 15, 1–11.CrossRefGoogle Scholar
Stanley, J. C. & Wang, M. D. Restrictions on the possible values of r 12 given r 13 and r 23. Educational and Psychological Measurement, 1969, 29, 579–581.CrossRefGoogle Scholar