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A Note on the Unbiased Estimation of the Intraclass Correlation

Published online by Cambridge University Press:  01 January 2025

John R. Donoghue  and
Linda M. Collins
John R. Donoghue*
Affiliation:
J. P. Guilford Laboratory of Quantitative Psychology, University of Southern California
Linda M. Collins
Affiliation:
J. P. Guilford Laboratory of Quantitative Psychology, University of Southern California
*
Requests for reprints may be sent to John R. Donoghue, J. P. Guilford Laboratory of Quantitative Psychology, MC 1061, University of Southern California, Los Angeles, CA 90089.
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Abstract

The intraclass correlation, ρ, is a parameter featured in much psychological research. Two commonly used estimators of ρ, the maximum likelihood and least squares estimators, are known to be negatively biased. Olkin and Pratt (1958) derived the minimum variance unbiased estimator of the intraclass correlation, but use of this estimator has apparently been impeded by the lack of a closed form solution. This note briefly reviews the unbiased estimator and gives a FORTRAN 77 subroutine to calculate it.

Keywords

hierarchical linear modelsintraclass correlationunbiased estimationFORTRANalgorithm
Type
Computational Psychometrics
Information
Psychometrika , Volume 55 , Issue 1 , March 1990 , pp. 159 - 164
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

The first author was supported by an All-University Fellowship from the University of Southern California.

References

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Erdelyi, A. (1953). Bateman Manuscript Project, California Institute of Technology: Higher transcendental functions (Vol. 1), New York: McGraw-Hill.Google Scholar
Olkin, I., Pratt, J. W. (1958). Unbiased estimation of certain correlation coefficients. Annals of Mathematical Statistics, 29, 202–211.CrossRefGoogle Scholar
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