Illustrating Discrepancies Between the Bivariate Correlation and Effect-Size Indices Estimated from Regression Results

• Activity Number: 518
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Education
• Author(s): Ariel Aloe*+ and Betsy Becker
• Companies: University of Northern Iowa and Florida State University
• Keywords: meta-analysis ; research synthesis ; effect sizes ; graphics ; regresion ; partial effect sizes

Abstract

Meta-analyses of studies of relationships between variables typically use the bivariate correlation as an effect size, However, bivariate correlations may not be reported in observational studies, especially when more sophisticated analytic approaches are used. Consequently, meta-analysts have used a variety of different indices when the bivariate correlation is not reported. These include more complex partial correlations that are difficult to explain to applied researchers. Also indices that are not correlations at all have been computed by some meta-analysts. We show techniques for illustrating the discrepancies between the bivariate correlation and several other indices of association encountered in published meta-analyses. The other indices are ones we have seen estimated from regression results typically reported in primary studies. We illustrate the differences among transformations of regression indices, partial effect sizes for the r-family, and the bivariate correlation. We show these discrepancies with graphical displays. We demonstrate that transformation-based indices are more similar to partial effect sizes than bivariate effects.