Alternative tests and measures for between-study inconsistency in meta-analysis

Meta-analysis is a widely used method for synthesizing results from multiple studies across diverse fields. A central challenge in meta-analysis is assessing between-study inconsistency, which can arise from differences in study populations, methodological heterogeneity, or the presence of outliers. Conventional tools such as the [Formula: see text] and [Formula: see text] statistics could be limited in power, especially when the number of studies is small or when the between-study distribution deviates from normality. To address these limitations, we propose a family of alternative [Formula: see text]-like statistics and a hybrid test that adaptively combines their strengths. We also introduce new measures to quantify inconsistency based on these statistics. Simulation studies demonstrate that the hybrid test performs robustly across a wide range of inconsistency patterns, including heavy-tailed, skewed, and contaminated distributions. We further illustrate the practical utility of our methods using three real-world meta-analyses. These approaches offer more flexible and powerful tools for detecting and quantifying inconsistency in meta-analytic practice.