meta-analysislisted

# Meta-Analysis: Pooling Effect Sizes Across Studies > **TL;DR** — Pool effect sizes from multiple studies using fixed-effects or > random-effects models, quantify heterogeneity (I², Cochran Q, τ²), produce > publication-quality forest plots and funnel plots, test for publication bias > (Egger, trim-and-fill), and run subgroup / moderator analyses. --- ## When to Use This Skill Use this Skill when you have: - A completed systematic review with ≥ 2 quantitative studies on the same outcome - A set of effect sizes (Cohen's d, Hedges' g, OR, RR, correlation r) and their standard errors or sample sizes - A need to communicate pooled estimates with forest or funnel plots - Questions about heterogeneity between studies or subgroup differences | Task | Use case | |---|---| | Fixed-effects pooling | Studies estimate the same true effect; low heterogeneity | | Random-effects pooling | True effects vary across studies; I² > 25% | | Heterogeneity decomposition | Understand sources of between-study variance | | Forest plot | Visualize study-level and pooled estimates | | Funnel plot + Egger test | Detect small-study effects / publication bias | | Subgroup analysis | Test whether effect differs by moderator variable | --- ## Background & Key Concepts ### Effect Size Types | Measure | Formula | Use case | |---|---|---| | Cohen's d | (M₁ − M₂) / SD_pooled | Two-group continuous outcome | | Hedges' g | d × correction factor J(df) | Small samples (n < 20 per group) | | Odds Ratio (