Variances in meta-analysis

Meta-analysis is a statistical method of combining many individual analyses. This thesis reviews the need for meta-analysis; the many statistical consideration facing the meta-analyst; and some of Hedges' results concerning the combined estimate of effect size with unequal weights from his 1981 and 1982 papers. Unequal weights used to combine estimates of effect size in meta-analysis are derived using the variances given by the large sample, normal approximation of the distribution of Hedges' unbiased estimates of effect sizes. These variances depend on the effect size and the sample sizes of both experimental and control groups. This creates circular definitions and calls for further estimates. This thesis analyzes the limiting normal approximation to derive a variance which is not dependent on effect size, and it provides guidelines for its use.