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Accuracy of conversion formula for effect sizes: A Monte Carlo simulation.

Leo Poom1, Anders Af Wåhlberg2

  • 1Department of Psychology, Uppsala University, Uppsala, Sweden.

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Effect size conversions in meta-analysis can be inaccurate. This study found some conversion formulas systematically underestimate Pearson r, but a correction factor can improve accuracy for Pearson r and Cohen

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Area of Science:

  • Psychological science
  • Statistical methodology

Background:

  • Meta-analysis requires standardized effect sizes.
  • Existing formulas for converting effect sizes vary in accuracy.

Purpose of the Study:

  • To systematically test the accuracy of commonly used effect size conversion formulas.
  • To identify biases in conversions to Pearson r and Cohen's d.
  • To propose methods for correcting systematic errors in effect size conversions.

Main Methods:

  • Monte Carlo simulations were used to generate samples with known population correlations.
  • Various effect size measures were calculated from simulated samples.
  • Formulas were applied to convert calculated statistics into Pearson r and Cohen's d.
  • Converted values were compared against directly calculated Pearson r and Cohen's d.

Main Results:

  • Converted effect sizes were consistently lower than directly calculated values.
  • Conversions to Cohen's d demonstrated good accuracy.
  • Several formulas converting to Pearson r exhibited significant bias.
  • A correction factor was identified to adjust for systematic errors in conversions.

Conclusions:

  • Some effect size conversion formulas introduce systematic bias, particularly for Pearson r.
  • Conversions to Cohen's d are generally accurate.
  • Applying a correction factor can improve the accuracy of biased Pearson r conversions.
  • Researchers should be cautious when using uncorrected effect size conversion formulas.