Robust Estimation of Effect Sizes Using Influence Functions
James H. Yen
The estimation of effect sizes is crucial part of meta-analysis. This papers uses influence functions as a fundamental tool in the analysis of estimates of effect size. The generalization to several variables of the influence function provides heuristic information about the robustness of the estimators and a way to calculate their large sample variances, including for non-normal situations. Some commonly used parametric estimators are organized into one of two classes of estimators that we call first order quotient estimators and second order quotient estimators. We provide the influence functions and large sample variance estimates for quotient estimators in general and for certain specific cases. In addition, influence functions are used to analyze several nonparametric estimates and to provide variance estimates where none existed previously. The performance of the various estimators along with their proposed variance estimates and confidence intervals are tested in Monte Carlo experiments.