Statistical inference for coefficient alpha

Abstract

Rigorous comparison of the reliability coefficients of several tests or measurement procedures requires a sampling theory for the coefficients. This paper summarizes the important aspects of the sampling theory for Cronbach’s (1951) coefficient alpha, a widely used internal consistency coefficient. This theory enables researchers to test a specific numerical hypothesis about the population alpha and to obtain confidence intervals for the population coefficient. It also permits researchers to test the hypothesis of equality among several coefficients, either under the condition of independent samples or when the same sample has been used for all measurements. The procedures are illustrated numerically, and the assumptions and derivations underlying the theory are discussed.