Four Methods for Combining Dependent Effects from Studies Reporting Regression Analysis

Over the years a variety of indices have been proposed to summarize regression analyses. Unfortunately the proposed indices are only appropriate when meta-analysts want to understand the role of a single predictor variable in predicting the outcome variable. However, sometimes meta-analysts want to understand the effect of a set of variables on an outcome variable. In this paper, four methods are presented for obtaining a composite effect for two focal predictor variables from a single regression model. The indices are the average of the standardized regression coefficients (ASC), the average of the standardized regression coefficients using Hedges and Olkin's (1985) approach (AHO), the sheaf coefficient (SC), and the squared multiple semi-partial correlation coefficient (MSP). A simulation study was conducted to examine the behavior of the indices and their variance when the number of predictor variables in the model, the sample size, the correlations between the focal predictor variables in the model, and the correlations between the focal and non-focal predictor variables in the model were manipulated. The results of the study show that the average bias values of the ASC and AHO estimates are small even when the sample size is small. Furthermore, the ASC and AHO estimates and their estimated variances are more precise than the other indices under all conditions examined. Therefore, when meta-analysts are interested in estimating the effect of a set of predictor variables on an outcome variable from a single regression model, the ASC or AHO procedures are preferred.