In statistical meta-analysis paradigm dealing with the techniques of pooling of evidence across several studies, the notion of effect size is fundamental and it is necessary to perform appropriate tests for the equality of population effect sizes arising out of these studies before performing any meta-analysis. A well known test for homogeneity in this context is based on Cochran's chi-square statistic. However Cochran's test might be inaccurate in testing homogeneity for some effect sizes in the sense of not maintaining the stipulated Type I errors. In this dissertation, three such scenarios are identified: 1) testing homogeneity of standardized mean difference, 2) testing homogeneity of correlations and correlation matrices, and 3) testing homogeneity of proportions with low event rates, and in each case the severe inadequacy of Cochran's homogeneity test is demonstrated. Apppropriate bootstrap procedures for testing homogeneity hypotheses are suggested, and applications in each problem are indicated. Two additional problems are also dealt with in the dissertation: Mantel-Haenszel and Peto weights in random effects meta-analysis, and extraction methods in statistical meta-analysis
