Cronbach's alpha reliability: Interval estimation, hypothesis testing, and sample size planning

TLDR

Cronbach's alpha is a widely used reliability metric in social and organizational sciences, yet conventional confidence intervals assume equal variances and covariances, an assumption that is often unrealistic. The authors propose a confidence interval for Cronbach's alpha that does not require equal variances or covariances. They develop a new interval estimator, provide sample‑size formulas for desired power or precision, and supply R functions to implement both the interval and the sample‑size calculations. Simulation studies show the new interval outperforms existing alternatives. © 2014 John Wiley & Sons, Ltd.

Abstract

Summary Cronbach's alpha is one of the most widely used measures of reliability in the social and organizational sciences. Current practice is to report the sample value of Cronbach's alpha reliability, but a confidence interval for the population reliability value also should be reported. The traditional confidence interval for the population value of Cronbach's alpha makes an unnecessarily restrictive assumption that the multiple measurements have equal variances and equal covariances. We propose a confidence interval that does not require equal variances or equal covariances. The results of a simulation study demonstrated that the proposed method performed better than alternative methods. We also present some sample size formulas that approximate the sample size requirements for desired power or desired confidence interval precision. R functions are provided that can be used to implement the proposed confidence interval and sample size methods. Copyright © 2014 John Wiley & Sons, Ltd.