The Relationship Between Unstandardized and Standardized Alpha, True Reliability, and the Underlying Measurement Model

Abstract

Popular computer programs print 2 versions of Cronbach’s alpha: unstandardized alpha, αΣ, based on the covariance matrix, and standardized alpha, α R , based on the correlation matrix. Sources that accurately describe the theoretical distinction between the 2 coefficients are lacking, which can lead to the misconception that the differences between α R and αΣ are unimportant and to the temptation to report the larger coefficient. We explore the relationship between α R and αΣ and the reliability of the standardized and unstandardized composite under 3 popular measurement models; we clarify the theoretical meaning of each coefficient and conclude that researchers should choose an appropriate reliability coefficient based on theoretical considerations. We also illustrate that α R and αΣ estimate the reliability of different composite scores, and in most cases cannot be substituted for one another.

Publication
Journal of Personality Assessment