Estimation of a Single Effect Size: Parametric and Nonparametric Methods

Abstract

This chapter focuses on the study of parametric and nonparametric methods for estimating the effect size (standardized mean difference) from a single experiment. It is important to recognize that estimating and interpreting a common effect size is based on the belief that the population effect size is actually the same across studies. Otherwise, estimating a mean effect may obscure important differences between the studies. The chapter discusses several alternative point estimators of the effect size δ from a single two-group experiment. These estimators are based on the sample standardized mean difference but differ by multiplicative constants that depend on the sample sizes involved. Although the estimates have identical large sample properties, they generally differ in terms of small sample properties. The statistical properties of estimators of effect size depend on the model for the observations in the experiment. A convenient and often realistic model is to assume that the observations are independently normally distributed within groups of the experiment.