The Overestimation of Effect Sizes from F Values in Meta-Analysis: The Cause and a Solution
Because estimates of effect sizes are often either misreported or not reported at all, meta-analysts must use conversion formulas that allow them to estimate effect sizes from the information available in a research report. The focus of this paper is on formulas that convert F in ANOVA to eta-squared, d, or the correlation coefficient. This paper demonstrates that the traditional F to r formula can differentially, and in some cases radically, inflate estimates of effect size when extracting the results from studies with varying numbers of factors. Specifically, commonly used conversion formulas for converting F values to r actually yield a partial r statistic that can be substantially larger than the desired zero-order r depending upon the number and relevance of additional factors in ANOVA. An alternative method to calculate nonpartialled effect sizes according to the common formula (SSeffect/SStotal) is provided.
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Document Type: Research Article
Publication date: 2003-03-01