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Inferential Theory for Partially Disattenuated Correlation Coefficients

Published online by Cambridge University Press:  01 January 2025

A. Ralph Hakstian ,
Marsha L. Schroeder  and
W. Todd Rogers
A. Ralph Hakstian*
Affiliation:
University of British Columbia
Marsha L. Schroeder
Affiliation:
University of British Columbia
W. Todd Rogers
Affiliation:
University of British Columbia
*
Requests for reprints should be sent to A. Ralph Hakstian, Department of Psychology, University of British Columbia, Vancouver, B. C., CANADA V6T lW5.
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Abstract

Four measurement designs are presented for use with correlation coefficients corrected, in one variable, for attenuation due to unreliability—coefficients that we term partially disattenuated correlation coefficients. Asymptotic expressions are derived for the variances and covariances of the estimates accompanying each design. Empirical simulation results that bear on the preceding mathematical developments are then presented. In addition to providing insights into the distributions of the estimates, the empirical results demonstrate satisfactory Type I error control for typical inferential applications. Power is shown to be equal to or greater than that of corresponding product-moment correlations in three of the four designs. Implications for practice are discussed.

Keywords

correction for attenuationunreliabilitysampling variance and covariancedelta methodhypothesis-testing
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 3 , September 1989 , pp. 397 - 407
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

Support for the research reported in this article was provided by the Natural Sciences and Engineering Research Council of Canada. The authors acknowledge with thanks the contributions of Nancy E. Heckman to some of the theoretical aspects of the study.

References

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