An Effect Size for Regression Predictors in Meta-Analysis

Abstract

A new effect size representing the predictive power of an independent variable from a multiple regression model is presented. The index, denoted as rsp, is the semipartial correlation of the predictor with the outcome of interest. This effect size can be computed when multiple predictor variables are included in the regression model and represents a partial effect size in the correlation family. The derivations presented in this article provide the effect size and its variance. Standard errors and confidence intervals can be computed for individual rsp values. Also, meta-analysis of the semipartial correlations can proceed in a similar fashion to typical meta-analyses, where weighted analyses can be used to explore heterogeneity and to estimate central tendency and variation in the effects. The authors provide an example from a meta-analysis of studies of the relationship of teacher verbal ability to school outcomes.