Examination of outliers in meta-analysis and comparison of methods used in outliers

In this thesis, it is aimed to determine outliers in meta-analysis, and if there is an outlier, it is aimed to find out which method is more efficient in predicting effect size and variance among studies and better to predict the correct effect size. The findings (effect sizes) obtained from scientific studies on the same research subject are combined by meta-analysis. The diversity of the effect sizes obtained from the studies is defined as heterogeneity. One reasons of the heterogeneity in meta-analysis is that the effect sizes obtained from the studies are different from each other. In meta-analysis studies, it should be determined statistically whether the effect sizes of the studies highly differing from the effect sizes of the rest studies are outlier. In this thesis, the traditional effect size combining methods and the novel methods are compared by using simulation methods in terms of bias, mean square error and coverage ratio to determine which method is the most efficient and the least biased in a meta-analysis. As a result of the simulation study, the least affected methods from an outlier are the mixture method and t distribution method in terms of bias and mean square error. According to between-study variance (T²), Hunter Schmidt method and maximum likelihood method produce more efficient estimations when the number of studies is small. In terms of coverage ratio, mixture method and t distribution method have the best results. The t distribution method provides more accurate results for the data generated under high heterogeneity or large effect sizes. As the number of studies increases, almost all methods produce similar results and difference among the methods decreases.