TimelyScholarFree Tools › Multilevel Meta-Analysis Tool
Pool several effect sizes per study without ignoring their dependence. The tool fits a three-level random-effects model and shows how much variance lies within and between studies.
FreeNo account neededYour data stays in your browser
Cluster: district · effect: yi · variance: vi · 56 effect sizes in 11 clusters
| Pooled effect | 0.1847 (95% CI 0.0190 to 0.3504)z = 2.18, p = 0.029 |
|---|---|
| σ² between clusters (level 3) | 0.06506 |
| σ² within clusters (level 2) | 0.03274 |
| Three-level vs two-level model | LRT = 17.77, p < 0.001Tests whether the between-cluster variance is needed |
The variance shares follow Cheung (2014), using the typical within-study sampling variance. Estimates match metafor's rma.mv with random = ~ 1 | cluster/effect.
Copy the columns from Excel or Google Sheets, with names in the first row, or load the example.
Estimates, tests and the figure update instantly in your browser.
Download the figure (SVG or PNG) and copy a results sentence.
Standard meta-analysis assumes each effect size is independent. When a study contributes several effect sizes (for example several outcomes, time points or subgroups), those effects are correlated, and treating them as independent overstates precision.
A three-level model separates three sources of variance: sampling error (level 1), variation between effect sizes within the same study (level 2) and variation between studies (level 3). The likelihood ratio test compares the model with a simpler two-level model.
Usually the study. It can be any unit that groups correlated effect sizes, such as a research lab or a cohort.
Not fully. It models dependence through the random effects; if the sampling errors of effect sizes are known to be correlated (for example, the same participants measured twice), consider robust variance estimation as a sensitivity analysis.