Bayesian Meta-analysis of Coefficient Alpha

The current paper describes and illustrates a Bayesian approach to the meta‐analysis of coefficient alpha. Alpha is the most commonly used estimate of the reliability or consistency (freedom from measurement error) for educational and psychological measures. The conventional approach to meta‐analysis uses inverse variance weights to combine information from independent studies to provide an overall estimate. The Bayesian approach provides similar estimates to the conventional approach if a diffuse prior is used. However, the Bayesian approach also provides ‘shrunken’ local estimates of reliability in each context. The amount of shrinkage depends upon both the variability in the underlying populations and the sampling variance of the local estimates. Advantages of the approach are the estimation of individual studies adjusted for sampling error and the application of meta‐analytic results to new local studies in which the local study ‘borrows strength’ from the meta‐analysis. The ability to borrow strength for the new local studies is particularly useful in applied work in which the estimate of the local parameter is of primary interest. The approach is illustrated by the analysis of studies of the reliability of the General Ethnicity Questionnaire – Abridged, a measure of identification with the culture of one\u27s heritage and the culture of one\u27s host country