Coefficient alpha: A basic introduction from the perspectives of classical test theory and structural equation modeling

TLDR

Classical test reliability is explained. The article pedagogically explains coefficient alpha, its uses, and highlights how violations of model assumptions and failure to meet basic homogeneity criteria affect reliability estimation. The authors derive equations for test‑retest, alternative‑forms, and internal‑consistency methods, show α as a lower‑bound approximation to reliability, and represent the classical models as structural equation models with path diagrams.

Abstract

This article is a pedagogical piece on coefficient alpha (α) and its uses. The classical approach to test reliability is explained. Test‐retest, alternative‐forms, and internal‐consistency methods of approximating test reliability are described, equations are derived for each method, and α is shown to be a lower‐bound internal‐consistency approximation to test reliability. Emphasis is placed on the effects of violations of model assumptions on reliability estimation. The classical models are conceptualized as structural equation models and are displayed in path diagrams. Special emphasis is placed on the failure of α to meet certain basic criteria as an index of test homogeneity.