Synthesis · Combining studies
Meta-Analysis Calculator
Pool effect estimates across studies under both fixed-effect and random-effects models, with heterogeneity (Q, I², τ²), a forest plot of the studies and the summary, and a funnel plot — the same picture that doubles as a publication-bias check.
Result
In plain English
Meta-analysis pools the results of many studies into one combined estimate, giving more weight to the more precise (usually larger) studies.
- fixed vs random effects
- Fixed-effect assumes every study is estimating one single shared truth. Random-effects allows the true effect to vary from study to study — the safer choice when studies disagree.
- I² (heterogeneity)
- How much of the variation between studies is genuine disagreement rather than chance. High I² means the studies aren't telling the same story.
- forest plot
- Each study shown as a point with its uncertainty bar; the diamond at the bottom is the pooled answer.
- funnel plot
- A symmetry check for publication bias: if small studies cluster on one side, some null results may simply be missing from the literature.
- the input
- Each study goes in as an effect estimate and its standard error (SE) — the smaller the SE, the more that study counts.
Frequently asked
What's the difference between fixed-effect and random-effects models?
Fixed-effect assumes every study estimates one common true effect; random-effects allows the true effect to vary between studies and gives a wider, usually more honest interval. When heterogeneity is non-trivial, prefer random-effects.
What does I² tell me?
I² is the percentage of the variation across studies due to real heterogeneity rather than chance — roughly 25% low, 50% moderate, 75% high. A high I² means the studies disagree, and a single pooled number may oversimplify.
Can meta-analysis fix publication bias?
No — if positive results were likelier to be published, the pool is built on a skewed sample and the summary is inflated. A funnel plot (included here) is a check, not a cure. See winner's curse & publication bias.
What is a forest plot?
A forest plot shows each study’s effect estimate as a square — sized by the weight the study carries — with a horizontal line for its confidence interval, and the pooled result as a diamond at the bottom. It lets you see at a glance whether the studies agree, which ones dominate the pooled estimate, and whether the overall result excludes “no effect”. It is the standard picture of a meta-analysis.