Cronbach’s α, Revelle’s β, and Mcdonald’s ω_{ H }: their relations with each other and two alternative conceptualizations of reliability
 Richard E. Zinbarg,
 William Revelle,
 Iftah Yovel,
 Wen Li
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We make theoretical comparisons among five coefficients—Cronbach’s α, Revelle’s β, McDonald’s ω_{ h }, 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 ω_{ h } 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 ω_{ h } holds only under a highly restrictive set of conditions and that the conditions under which β equals ω_{ h } are only somewhat more general. The nonequivalence of α, β, and ω_{ h } 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
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 Title
 Cronbach’s α, Revelle’s β, and Mcdonald’s ω_{ H }: their relations with each other and two alternative conceptualizations of reliability
 Journal

Psychometrika
Volume 70, Issue 1 , pp 123133
 Cover Date
 20050301
 DOI
 10.1007/s1133600309747
 Print ISSN
 00333123
 Online ISSN
 18600980
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 Richard E. Zinbarg ^{(1)} ^{(5)}
 William Revelle ^{(2)}
 Iftah Yovel ^{(3)}
 Wen Li ^{(4)}
 Author Affiliations

 1. Northwestern University, the Family Institute at Northwestern University, USA
 5. Northwestern University, 102 Swift Hall, 2029 Sheridan Rd., Evanston, IL, 602082710, USA
 2. Northwestern University, USA
 3. Northwestern University, USA
 4. Northwestern University, USA