1 Alpha’s Standard Error (ASE): An Accurate and Precise Confidence Interval Estimate

In this research, we present the inferential statistics for Cronbach’s Coefficient Alpha based on the standard statistical assumption of multivariate normality. The estimation of alpha’s standard error (ASE) and confidence interval for alpha is described, and we conduct an analytical demonstration to illustrate the effects on these estimates of the components of the equations, including the number of items, the item intercorrelations, and sample size. We then empirically examine the consistency and efficiency of alpha and its standard error in a Monte Carlo simulation modeling the effects of alpha’s components, sample size, and compound symmetry. We then demonstrate the superiority of this estimate compared to previous derivations of alpha’s standard error in a separate Monte Carlo simulation. For the researcher interested in assessing the difference between alphas obtained in two independent samples, we present a sampling error and test statistic for such a comparison. We conclude with a prescription that includes the recommendation that all alpha coefficients be reported in conjunction with a standard error or confidence interval estimate. We offer SAS and SPSS programming codes for easy implementation