Statistical procedures

Meta-Essentials applies the inverse variance weighting method with, in the random effects model, an additive between-studies variance component based on the DerSimonian-Laird estimator (DerSimonian & Laird, 1986). Note that in Workbook 2 ‘Differences between independent groups - binary data.xlsx’ you can choose between three weighting methods. The confidence intervals are estimated using the weighted variance method for random effects models, see Sánchez-Meca and Marín-Martínez (2008). Therefore, the confidence and prediction intervals of the combined effect size calculated by Meta-Essentials might be different from one calculated by another meta-analysis program. Moreover, we also use the Student’s t-distribution to calculate the confidence interval of the individual study effect sizes (not done by most other meta-analysis tools).

For a discussion of the methods applied in the Publication Bias Analysis sheet, their application and how they should be interpreted, see Sterne, Gavaghanb, and Egger (2000) and Anzures-Cabrera and Higgins (2010). Specifically for the Trim and Fill plot, Meta-Essentials uses an iterative procedure for trimming the set of studies from the right (or left), re-estimate a combined effect size, and finally filling the plot with symmetric results on the other side of the mean. Meta-Essentials runs three iterations of the procedure, which is shown to be sufficient for many real-life cases (Duval & Tweedie, 2000a).