Accuracy of conversion formula for effect sizes: A Monte Carlo simulation. (21st April 2022)

• Record Type: Journal Article
• Authors: Poom, Leo; af Wåhlberg, Anders
• Is Part Of: Research synthesis methods. Volume 13:Number 4(2022)
• Page Start: 508
• Page End: 519
• Publication Date: 2022-04-21
• Subjects: effect size conversion -- meta‐analysis -- Monte Carlo simulation; Research -- Methodology -- Periodicals; Research -- Statistical methods -- Periodicals; 507.2
• DOI: 10.1002/jrsm.1560
• Languages: English
• ISSNs: 1759-2879

Abstract

Abstract: In meta‐analysis, effect sizes often need to be converted into a common metric. For this purpose conversion formulas have been constructed; some are exact, others are approximations whose accuracy has not yet been systematically tested. We performed Monte Carlo simulations where samples with pre‐specified population correlations between the x and y ‐variables were drawn from a normally distributed population. A number of commonly used effect size measures and statistics were calculated from each sample. Using several available conversion formula these statistics were converted into Pearson r and Cohen's d and compared to r and d calculated directly from the original data. Converted values were systematically lower than the directly calculated values. While conversions to d were quite accurate, some of the conversions to r resulted in large biases. These systematic errors can in most cases be adjusted for by simply multiplying the converted values with a corresponding correction factor.