The last three decades have seen a proliferation of research and use of meta-analytic methods in many areas of scientific inquiry. Despite the publication of many narratives and actual meta-analyses concerning specific research questions, relatively less has been published on comprehensive methodology. Rigorous work by statistical methodologists is currently going on with a view of establishing a concrete body of knowledge on methods for meta-analysis. This book is a contribution towards this goal. The book starts by presenting tests for the overall treatment effect in the one-way fixed effects model that attain significance levels closer to a nominal level. Convexity arguments of composite functions are utilized to derive improved test procedures on the overall treatment effect. The general method of moments estimator of the heterogeneity variance and the DerSimonian-Laird estimator are derived. Alternative positive estimators of the heterogeneity variance are presented. The derivation of the estimators of the heterogeneity variance gives way to the correction of type I error rates in a one-way random-effects model for meta-analysis.