For these reasons, we solely focus on Dallal’s model in this paper.

Bayesian methods have gained incredible popularity in recent years both in the theory and practice of statistics. Under non-informative priors, Bayesian inferences yield results similar to that obtained under the frequentist paradigm. As we will show in an example presented in Section \[sub2sec6\], Bayesian inference for Dallal’s model yields similar findings to the corresponding frequentist analysis. Bayesian methods, however, do not rely on the normal approximation to carry out statistical inferences, which is an advantage over the frequentist methods. It is not unusual to encounter $3\times2$ bilateral data where one or more cells have sparse data, thereby preventing the use of the usual normal approximation that underlies frequentist inferences developed in Appendix 1 of the Supplementary Web Materials. Also, in some sparse $3\times2$ bilateral data, frequentist estimates lie on the boundary of the parameter space, which are not permitted by design. In such situations, one cannot compute the confidence intervals for some parameters or carry out tests of hypotheses about some of the parameters. We provide one such example in Section \[sub1sec6\]. Bayesian methods provide a simpler way to analyze such sparse bilateral data. Another benefit of Bayesian 