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Structural Equation Modeling: Applications Using Mplus by Xiaoqian Wang, Jichuan Wang

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Appendix 2.C Cronbach's Alpha Coefficient

Cronbach' s alpha coefficient (Cronbach, 1951) is a very popular measure of scale reliability in social science studies. For a set of indicators, y1, y2, . . . , yp that measure the same latent variable img, the sum of the ys, that is, img, is often used as a composite measure of the underlying latent variable. Cronbach' s alpha is the squared correlation between img and img, which can be estimated as (Bollen, 1989a, p. 216):

(2.14) equation

where p is the number of indicators. This estimate of reliability is not for a single indicator, but for a composite measure (i.e., unweighted sum of a set of indicators) under the assumption that the measures are either parallel or tau- equivalent. It would underestimate the reliability for congeneric measures.

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