Meta-analysis can be presented in the Frequentist or Bayesian framework. Based on the model of DuMouchel, a simulation study is conducted which fixes the overall mean and variance-covariance matrix to generate estimates of the true mean effect. These estimates will be compared to the true effect to assess bias. A sensitivity analysis, to measure the robustness of results to the selection of prior distributions, is conducted by employing Uniform and Pareto distributions for the variance components, the t-distribution for the overall mean component and a combination of priors for both variance and mean components respectively. Results were more sensitive when the prior was changed only on the overall mean component.