Coefficient alpha is a simple and very useful index of test reliability that is widely used in educational and psychological measurement. Classical statistical inference for coefficient alpha is well developed. This paper presents two methods for Bayesian statistical inference for a single sample alpha coefficient. An approximate analytic method based on conjugate distributions is derived. This method is easy to compute. A second method uses Markov Chain Monte Carlo (MCMC) methodology as implemented by the computer program WinBUGS. WinBUGS may be downloaded for free from the Internet, and this paper includes WinBUGS code for making Bayesian inferences about coefficient alpha. Pseudo-randomly generated data are used to compare the two Bayesian methods to each other and both of these methods to the classical method. The results indicate that the two Bayesian methods work well as long as the number of items and examinees are not too small. Appendixes discuss the derivation of the marginal likelihood, contain WinBUGS code, and present the figures. (Contains 1 table, 9 figures, and 11 references.) (Author/SLD)