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Inferential Procedures for Correlation Coefficients Corrected for Attenuation

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 Psychdlogy, University of British Columbia, Vancouver, B. C., CANADA V6T lW5.
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Abstract

A model and computational procedure based on classical test score theory are presented for determination of a correlation coefficient corrected for attenuation due to unreliability. Next, variance-covariance expressions for the sample estimates defined earlier are derived, based on application of the delta method. Results of a Monte Carlo study are presented in which the adequacy of the derived expressions was assessed for a large number of data forms and potential hypotheses encountered in the behavioral sciences. It is shown that, based on the proposed procedures, confidence intervals for single coefficients are reasonably precise. Two-sample hypothesis tests, for both independent and dependent samples, are also accurate. However, for hypothesis tests involving a larger number of coefficients than two—both independent and dependent—the proposed procedures require largens for adequate precision. Results of a preliminary power analysis reveal no serious loss in efficiency resulting from correction for attenuation. Implications for practice are discussed.

Keywords

correction for attenuationunreliabilitysampling variance and covariancedelta methodhypothesis-testing

Information

Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 1 , March 1988 , pp. 27 - 43
Copyright
Copyright © 1988 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 constructive comments of the editor and three anonymous reviewers.

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