🤖 AI Summary
This study addresses the unreliability of conventional asymptotic-based statistical inference in meta-analysis when the number of included studies is small. Focusing on the Gaussian random-effects model, the authors derive—for the first time—a rigorous higher-order Bartlett correction formula tailored to small-sample settings, rectifying an error present in the existing literature. Built upon higher-order asymptotic theory, the proposed correction substantially improves the accuracy of the finite-sample distributional approximation of test statistics. Consequently, it enhances the validity and reliability of hypothesis testing in meta-analytic applications, particularly where sample sizes are limited.
📝 Abstract
Meta-analyses are often based on too few studies to justify the asymptotic methods underlying the statistical procedures applied to them. We consider higher-order asymptotics as a remedy. We derive the Bartlett correction for the idealized Gaussian case, correcting the formula currently appearing in the literature.