Simultaneous estimation of Cronbach’s alpha coefficients

Abstract

The simultaneous estimation of Cronbachs alpha coefficients from q populations under the compound symmetry assumption is considered. In a multi-sample scenario, it is suspected that all the Cronbachs alpha coefficients are identical. Consequently, the inclusion of non-sample information (NSI) on the homogeneity of Cronbachs alpha coefficients in the estimation process may improve precision. We propose improved estimators based on the linear shrinkage, preliminary test, and the Steins type shrinkage strategies, to incorporate available NSI into the estimation. Their asymptotic properties are derived and discussed using the concepts of bias and risk. Extensive Monte-Carlo simulations were conducted to investigate the performance of the estimators.

Keywords:

• Asymptotic properties
• Cronbach’s alpha
• linear shrinkage
• Monte-Carlo
• preliminary test
• Stein-type shrinkage

Additional information

Funding

The research work of Professor S. Ejaz Ahmed was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. Supranee Lisawadi gratefully acknowledges the financial support provided by Faculty of Science and Technology, Thammasat University Research Scholar, Contract No. 10/2559.