Hypothesis testing for two or more independent Cronbach’s $$\alpha $$ coefficients with interval-valued data

Abstract A rigorous methodology is developed for comparing the population value of the extended Cronbach $$\alpha $$ α coefficient, used as an internal consistency reliability measure for interval-valued scale-based items assessing a certain latent variable in a questionnaire, across two or more independent groups. In particular, the limit distribution of the asymptotic and bootstrap test statistics considered is theoretically derived in order to ensure the asymptotic correctness and consistency of the suggested one- and two-tailed two-sample-based hypothesis tests and the multi-sample-based procedures proposed for testing the equality of the population values of several independent extended Cronbach’s $$\alpha $$ α coefficients. In addition, extensive simulation studies are conducted to empirically analyse and compare the performance of these testing methods. Finally, the applicability of the suggested techniques is illustrated by means of a real-life example, which also includes some post hoc multiple pairwise comparisons.