Date of Award

Fall 2023

Document Type


Degree Name

Doctor of Philosophy (PhD)




Health Psychology

Committee Director

Miguel A. Padilla

Committee Member

James M. Henson

Committee Member

Lucia M. Tabacu


There is a focus within the behavioral/social sciences on non-physical, psychological constructs (i.e., constructs). These constructs are indirectly measured using measurement instruments that consist of questions that capture the manifestations of these constructs. The indirect nature of measuring constructs results in a need of ensuring that measurement instruments are reliable. The most popular statistic used to estimate reliability is coefficient alpha as it is easy to compute and has properties that make it desirable to use. Coefficient alpha’s popularity has resulted in a wide breadth of research into its qualities. Notably, research about coefficient alpha’s distribution has led to developments about its confidence intervals (CIs) and implementation through Bayesian methods with corresponding credible intervals (CrIs).

Here, a new method to implement a Bayesian coefficient alpha is proposed. This new method is built on coefficient alpha having a posterior normal distribution based on a posterior mean and variance. To assess the effectiveness of this new method, a simulation was conducted that compared it to previously established methods used to obtain coefficient alpha CI/CrIs. These include bootstrap CIs and Bayesian CrIs that are based on indirectly generating a coefficient alpha posterior though the posterior of the item covariance matrix. All CI/CrIs were assessed for 95% coverage probability. Ultimately, the new method to implement Bayesian coefficient alpha was found to be effective as it tended to have CrIs that were closer and tighter around the target of .95.


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