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Linear Correlations between Sets of Variables

Published online by Cambridge University Press:  01 January 2025

William W. Rozeboom
William W. Rozeboom*
Affiliation:
University of Alberta
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Abstract

While the traditional multiple correlation coefficient appears to be inherently an asymmetrical statistic, it is actually a special case of a more general measure of linear relationship between two sets of variables. Another symmetric generalization of linear correlation is to the total relatedness within a set of variables. Both of these developments rest upon the generalized variance of a multivariate distribution, which is seen to be the fundamental concept of linear correlational theory.

Type
Original Paper
Information
Psychometrika , Volume 30 , Issue 1 , March 1965 , pp. 57 - 71
Copyright
Copyright © 1965 Psychometric Society

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References

Anderson, T. W. Introduction to multivariate statistical analysis, New York: Wiley, 1958.Google Scholar
Garner, W. R. Uncertainty and structure as psychological concepts, New York: Wiley, 1962.Google Scholar
Rozeboom, W. W. The theory of abstract partials: An introduction (unpublished manuscript).Google Scholar
Watanabe, S. Information theoretical analysis of multivariate correlation. IBM J. Res. Dev., 1960, 4, 66–82.CrossRefGoogle Scholar