The Synthesis of Partial Effect Sizes

Abstract

In this article we focus on three partial effect sizes for the correlation ( family of effects: the standardized slope , the partial correlation , and the semi-partial correlation . These partial effect sizes are useful for meta-analyses in two common situations: when primary studies reporting regression models do not report bivariate correlations, and when it is of specific interest to partial out the effects of other variables. We clarify the use of these three indices in the context of meta-analysis and describe how the indices can be estimated and analyzed. We provide examples of syntheses of these partial effect sizes using a published social work meta-analysis. Finally, we share practical recommendations for meta-analysts wanting to use such indices. Key words: meta-analysis, research synthesis, partial effect sizes, regression analysisMeta-analysis is the statistical analysis of empirical results of a series of studies (Glass, 1977). Quantitative procedures in meta-analysis typically begin by transforming study results to a common metric, which often represents results as effect sizes. An effect size is a scale-free index that assesses the magnitude and direction of some relationship between variables. Almost two decades ago researchers argued that results from regression models can be treated as effect-size indices (e.g., Becker & Schram, 1994;Cooper & Hedges, 1994;Greenwald, Hedges, & Laine, 1996;Valentine, DuBois, & Cooper, 2004). More recently, different approaches have been proposed to synthesize regression models (Aloe & Becker, 2012;Becker & Wu, 2007;Peterson & Brown, 2005;Wu & Becker, 2013). These approaches can be organized into three methodological groups. The first group focuses on methods that combine full regression models (e.g., Wu & Becker, 2013), the second group focuses on attempting to approximate the bivariate correlation when it is not directly reported (e.g., Peterson & Brown, 2005), and the third group focuses on methods that combine partial effect sizes that have been extracted from regression models (e.g., Aloe & Becker, 2012;Keef & Roberts, 2004).This article focuses on the estimation and use of the partial effect sizes for the family of effects, which can be computed when multiple predictor variables are included in a primary study. A partial effect size is an index that describes the magnitude of an effect after controlling for the influence of other variables in a model. Part of our rationale for focusing on partial effect sizes is that they are quantities that researchers typically find familiar. Furthermore, partial effect sizes are often directly reported or easily estimated from results found in primary studies. Finally, typical meta-analysis techniques can be used once partial effects are extracted or computed from primary studies.We begin by briefly introducing the meta-analysis of correlational data. Next we introduce required notation for effects and meta-analytic models, including three partial effect sizes (partial correlation, semi-partial correlation, and standardiz...

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“…The partial correlation has an absolute value of 1. When it is <0.2, which is the case for all papers considered here, the partial correlation is roughly equal to the standard deviation of the change in the health outcome associated with a one standard deviation change in the education variable controlling for, or ‘partialling out’, the other variables in the model . Drawing on Cohen's conventions for interpreting effect sizes, correlation effect sizes less than or equal to 0.10 are considered small, values of 0.25 are considered medium, and values greater than or equal to 0.40 are considered large .…”

Some reflections on combining meta‐analysis and structural equation modeling

“…However, it may occasionally not be feasible to extract correlation matrices from published studies. Some researchers, eg, Aloe and his colleagues, , , , have proposed using the partial effect size when summarizing research findings in regression models. Although the information provided by the partial effect size is not as rich as that in MASEM, it provides a viable alternative when MASEM cannot be used.…”

“…On the other hand, parameter‐based MASEM treats the estimated parameters in SEM as the effect sizes for the meta‐analysis. Only a few studies use this approach , , , , , , . Correlation‐based MASEM conceptualizes the heterogeneity at the correlation level, because there is only 1 structural equation model.…”

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“…One approach focuses on attempting to approximate the bivariate correlation from regression results (Peterson & Brown, 2005). Another synthesizes partial effect sizes that are extracted from regression models (Aloe & Becker, 2012;Aloe & Thompson, 2013;Keef & Roberts, 2004). A third approach focuses on combining full regression models (Wu & Becker, 2013).…”