Cronbach’s α, Revelle’s β, and Mcdonald’s ωH: their Relations with Each Other and Two Alternative Conceptualizations of Reliability
2005/03/01 by Richard E. Zinbarg, William Revelle, Iftah Yovel +2 · 1,438 citations
Decision Sciences · Mathematics · Psychology · #Artificial intelligence #Classical test theory #Computer science #Conceptualization #Cronbach's alpha #Geography #Item response theory #Mathematics #Multi-Criteria Decision Making #Psychology #Psychometric Methodologies and Testing #Psychometrics #Reliability (semiconductor) #Scale (ratio) #Set (abstract data type) #Statistical Distribution Estimation and Applications #Statistics
paper · doi:10.1007/s11336-003-0974-7
published in Psychometrika 70(1), 123-133 (Springer Science+Business Media)
openalex publication_date 2005/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Abstract
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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