Standardized Regression Coefficients as Indices of Effect Sizes in Meta-Analysis

When conducting a meta-analysis, it is common to find many collected studies that report regression analyses, because multiple regression analysis is widely used in many fields. Meta-analysis uses effect sizes drawn from individual studies as a means of synthesizing a collection of results. However, indices of effect size from regression analyses have not been studied extensively. Standardized regression coefficients from multiple regression analysis are scale free estimates of the effect of a predictor on a single outcome. Thus these coefficients can be used as effect–size indices for combining studies of the effect of a focal predictor on a target outcome. I begin with a discussion of the statistical properties of standardized regression coefficients when used as measures of effect size in meta-analysis. The main purpose of this dissertation is the presentation of methods for obtaining standardized regression coefficients and their standard errors from reported regression results. An example of this method is demonstrated using selected studies from a published meta-analysis on teacher verbal ability and school outcomes (Aloe & Becker, 2009). Last, a simulation is conducted to examine the effect of multicollinearity (intercorrelation among predictors), as well as the number of predictors on the distributions of the estimated standardized regression slopes and their variance estimates. This is followed by an examination of the empirical distribution of estimated standardized regression slopes and their variances from simulated data for different conditions. The estimated standardized regression slopes have larger variance and get close to zero when predictors are highly correlated via the simulation study.