On Constructing Confidence Intervals for a Standardized Mean Difference in Meta-analysis

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Simple heterogeneity variance estimation for meta‐analysis (2005, methodology): “For example, Sidik and Jonkman (2003) found that the coverage probability of a 95% confidence interval from expression (8) for the true overall standardized mean difference, using the DerSimonian and Laird estimator of τ2, is generally lower than the nominal coverage value.”
The Hartung-Knapp-Sidik-Jonkman method for random effects meta-analysis is straightforward and considerably outperforms the standard DerSimonian-Laird method (2014, methodology): “In contrast, the Hartung, Knapp, Sidik and Jonkman method estimates the variance of ŷr by varHKSJ ¼ X wτi yi−ŷrð Þ2 k−1ð Þ X wτi and uses the t-distribution with k-1 degrees of freedom to derive P-values and confidence intervals, with k the number of studies in the meta-analysis.”