A SIMULATION STUDY OF THE CONVERSION OF EFFECT SIZES BETWEEN CORRELATION AND STANDARDIZED MEAN DIFFERENCE IN META-ANALYSIS

Abstract

Meta-analysis is the process of quantitative review of primary studies. It has gained popularity over the past decades in many research fields. However, researchers may need to convert extracted effect sizes into a common metric and combine all the effect sizes across all the selected studies. Our study aims to evaluate the magnitude of percentage biases during the conversion between Pearson correlation (r) and standardized mean difference (d) and the differences in biases if researchers choose to exclude or include the studies that require the conversions. Our study uses simulated data in a meta-analysis to observe the trends in magnitude of biases depending on the conditions that are necessary during a meta-analysis. Results show that converting from d to r will mostly be underestimating population r (?). These biases are smaller with smaller ?. However, there are no obvious trends when they are converting from r to d. It is recommended that researchers should exclude studies when it is needed to convert from d to r for more accurate estimates but include studies when it is needed to convert from r to d to preserve the sample size and statistical power.