Title: A new confindence interval for Cronbachs coefficient alpha
Authors: Laura Trinchera - NEOMA Business School (France) [presenting]
Nicolas Marie - Universite Paris Nanterre (France)
George Marcoulides - University of California Santa Barbara (United States)
Abstract: Reliability is commonly examined in order to assess the measurement quality of scales. To date, Cronbachs coefficient alpha is the most commonly used index for assessing the reliability of a scale. We present an asymptotic distribution of the natural estimator of Cronbachs alpha coefficient and propose a new CI that does not require assumptions of equal variances and covariances, and neither does it require the data to be approximated by a multivariate normal distribution. We also present a test on the sample estimate of coefficient alpha for testing the null hypothesis that the coefficient is higher than 0.7. The proposed approach is compared to four popular methods commonly used to compute confidence intervals (CI) for alpha using a Monte Carlo simulation study under a variety of sample size and number of items in a scale conditions. We compare results for each method in terms of the level of coverage and confidence interval length (CIL). The results of this simulation study indicated that the newly proposed interval estimate was the most accurate of the examined approaches, especially for small sample sizes.