What is it about?

In the realm of meta-analysis, the necessity often arises to harmonize effect sizes into a standardized metric. Various conversion formulas have been devised for this purpose, encompassing both precise mathematical expressions and approximations whose accuracy remains unexplored. In our study, we conducted extensive Monte Carlo simulations, generating samples with predetermined population correlations between the x and y-variables from a normally distributed population. Within each sample, we computed a range of widely utilized effect size measures and statistical parameters. Employing several established conversion formulas, we transformed these statistics into Pearson r and Cohen's d, subsequently comparing them to the r and d values derived directly from the original data. The outcomes revealed a systematic tendency for the converted values to be slightly lower than their direct counterparts. While conversions to Cohen's d displayed commendable accuracy, it should be noted that some conversions to Pearson r exhibited notable biases. Fortunately, in most instances, these systematic discrepancies can be mitigated by a straightforward multiplication with an appropriate correction factor.

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Why is it important?

The importance of this study lies in its contribution to the field of research and meta-analysis. When scientists conduct studies in various fields, they often measure the strength of relationships or the size of effects using different metrics. These metrics might not be directly comparable, making it challenging to combine and compare results from multiple studies. This study addresses this challenge by investigating methods to convert these different metrics into a common metric. This is crucial because it allows researchers to combine findings from multiple studies.

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This page is a summary of: Accuracy of conversion formula for effect sizes: A Monte Carlo simulation, Research Synthesis Methods, April 2022, Wiley,
DOI: 10.1002/jrsm.1560.
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