Simultaneous estimation of Cronbach’s alpha coefficients |
| |
Authors: | Supranee Lisawadi S Ejaz Ahmed Orawan Reangsephet Muhammad Kashif Ali Shah |
| |
Institution: | 1. Faculty of Science and Technology, Department of Mathematics and Statistics, Thammasat University, Khlong Luang, Thailand;2. Department of Mathematics and Statistics, Brock University, St. Catharines, Ontario, Canada |
| |
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 |
|
|