Equating r-based and d-based Effect Size Indices: Problems with a Commonly Recommended Formula.Report as inadecuate




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Two general categories comprise the various effect size indices that have been proposed for use in meta-analysis: (1) the d-type estimator (based on magnitude of mean difference); and (2) the r-type estimator (based on magnitude of correlation). In meta-analyses, researchers often must convert these effect size indices to a common metric to aggregate and synthesize results from various studies empirically. A commonly recommended formula for equating mean-difference effect sizes and correlational effect sizes was found to lead to inaccurate results, particularly with small sample sizes. A correct formula for converting d-based and r-based effect size indices is presented. Results of applying the common and corrected formulas are illustrated for a variety of data conditions at various sample sizes and effect sizes, suggesting that bias as large as 20 percent results from the common formula, something that can be avoided by applying the alternative equation. (Author/SLD)

Descriptors: Correlation, Effect Size, Estimation (Mathematics), Meta Analysis, Sample Size











Author: Aaron, Bruce; Kromrey, Jeffrey D.; Ferron, John

Source: https://eric.ed.gov/?q=a&ft=on&ff1=dtySince_1992&pg=7839&id=ED433353







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