Estimating Internal Consistency Using Bayesian Methods

Bayesian internal consistency and its Bayesian credible interval (BCI) are developed and Bayesian internal consistency and its percentile and normal theory based BCIs were investigated in a simulation study. Results indicate that the Bayesian internal consistency is relatively unbiased under all investigated conditions and the percentile based BCIs yielded better coverage performance. Introduction Psychological constructs are the building blocks of psychological/behavioral research. Indeed, one can easily argue that constructs are the foundation of these two sciences. A typical way of measuring a construct is through a questionnaire containing items that are purported to indirectly measure the construct of interest; thus, it becomes important that the items be consistent or reliable so that the questionnaire itself is consistent or reliable. Although there are several methods of measuring or estimating the reliability of a questionnaire, by far the most commonly used is coefficient alpha. Coefficient alpha has remained popular since its introduction in Cronbach's (1951) article based on the work of Guttman and others in the 1940s (Guttman, 1945). Coefficient alpha is a measure of internal consistency for a group of items (i.e., questions) that are related in that they measure the same psychological/behavioral construct (Cortina, 1993). There are three main reasons for coefficient alpha's popularity. First,