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Cronbach’s α, Revelle’s β, and Mcdonald’s ωH: their Relations with Each Other and Two Alternative Conceptualizations of Reliability

Published online by Cambridge University Press:  01 January 2025

Richard E. Zinbarg ,
William Revelle ,
Iftah Yovel  and
Wen Li
Richard E. Zinbarg*
Affiliation:
Northwestern University, The Family Institute at Northwestern University
William Revelle
Affiliation:
Northwestern University
Iftah Yovel
Affiliation:
Northwestern University
Wen Li
Affiliation:
Northwestern University
*
Requests for reprints should be sent to Richard Zinbarg, 102 Swift Hall, 2029 Sheridan Rd., Northwestern University, Evanston, IL 60208-2710, USA. E-mail: [email protected]
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Abstract

We make theoretical comparisons among five coefficients—Cronbach’s α, Revelle’s β, McDonald’s ωh, and two alternative conceptualizations of reliability. Though many end users and psychometricians alike may not distinguish among these five coefficients, we demonstrate formally their nonequivalence. Specifically, whereas there are conditions under which α, β, and ωh are equivalent to each other and to one of the two conceptualizations of reliability considered here, we show that equality with this conceptualization of reliability and between α and ωh holds only under a highly restrictive set of conditions and that the conditions under which β equals ωh are only somewhat more general. The nonequivalence of α, β, and ωh suggests that important information about the psychometric properties of a scale may be missing when scale developers and users only report α as is almost always the case.

Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 1 , March 2005 , pp. 123 - 133
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

Preparation of this article was supported by the Patricia M Nielsen Research Chair of the Family Institute at Northwestern University

We thank Lewis R. Goldberg, Win Hill, Dan McAdams, Tony Z. Tang and especially Roderick P. McDonald for their comments on earlier drafts of portions of this article

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