Synthesizer 1.0: A varying-coefficient meta-analytic tool

Abstract

Meta-analysis has become an indispensable tool for reaching accurate and representative conclusions about phenomena of interest within a research literature. However, in order for meta-analytic computations to provide accurate estimates of population parameters (e.g., a population correlation), underlying statistical models need to be both efficient and unbiased. Current fixed-effect (i.e., constant-coefficient) models that assume a common effect for all research results perform poorly under conditions of effect size heterogeneity, whereas current random-effects (i.e., random-coefficient) models require unrealistic assumptions about random sampling of observed effect sizes from a normally distributed super population. This article describes a free statistical software tool that employs a varying-coefficient model recently proposed by Bonett (2008, 2009). The software (Synthesizer 1.0) employs procedures that do not require effect homogeneity or random sampling of effect sizes from a normal distribution. It may be used to meta-analyze correlations, alpha reliabilities, and standardized mean differences. The Synthesizer tool for Microsoft Excel 2007 may be downloaded from the author at www.psychology.iastate.edu/~zkrizan/Synthesizer.htm or as a supplement to the article at http://brm.psychonomic-journals.org/content/supplemental. © 2010 The Psychonomic Society, Inc.