A new estimator of between study variance of standardized mean difference in meta-analysis

Meta-analysis is a statistical technique that combines the results of different environmental experiments regarding the populations, location, time, and so on. These results will differ more than the within-study variance, and the true effects being evaluated differ between studies. Thus, heterogeneity is present and should be measured. There are different estimators that were introduced to estimate between-study variance, which has received a lot of criticism from previous researchers. All of the estimators encountered the same problem, which was the correlation. To minimize the potential biases caused by interventions between the three estimators (i.e., overall effect size, within-study variance, and between-study variance), we proposed a new measure of heterogeneity known as the Environmental Effect Ratio (EER), the treatment-by-lab variability relative to the experimental error, under individual participant data (IPD) using the linear mixed model approach. We assume different between-study variances instead of constant between-study variances. The simulation of this study focuses on the performance of meta-analyses with small sample sizes. We compared our proposed estimator under two different expressions (τ ^ 1 E E R 2, and τ ^ 2 E E R 2) with the best estimator nominated from previous studies to determine which one is the best performance. Based on the findings, our estimator (τ ^ 2 E E R 2) was better for estimating between-study variance.