Home / Science / Health and medicine / Biostatistics / Meta-analysis (forest and funnel plots)Tool #469

Meta-analysis calculator: forest plot, funnel plot, I², random effects and Egger's test (free)

Pool studies from 2×2 counts (odds ratio, risk ratio, risk difference), means and SDs (mean difference, Hedges' g) or an estimate with its SE or CI. Fixed effect and random effects (DerSimonian-Laird, REML, Paule-Mandel), Q, I², tau², prediction interval, Egger's test, forest and funnel plots. Matches statsmodels.

Keep it one tap away for everyday use.

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  1. Studies
  2. Pool
  3. Forest plot
  4. Report
Nothing is uploadedWorks offline once open

For study and teaching, not medical advice. Check with a qualified professional.

Studies

A trial with a zero (or every subject) in a group gets 0.5 added to each cell. Trials with no events in either group say nothing about a ratio and are left out of the odds and risk ratio.

Model

Fixed effect assumes every study measures one true effect. Random effects lets the true effect vary between studies (by tau²) and is the usual choice. DerSimonian-Laird is the classic estimate of tau²; REML and Paule-Mandel are often preferred, especially with few studies.

What it does

A meta-analysis combines the results of several studies of the same question into one overall estimate, weighting each study by how precise it is. This tool works out each study’s effect, pools them with a fixed-effect and a random-effects model, measures how much the studies disagree (Q, I², tau² and the prediction interval), draws a forest plot and a funnel plot, and runs Egger’s test for small-study effects. It all runs in your browser and nothing is uploaded.

How to use it

  1. Choose what each study gives you:
    • Events: events and totals in the treated and control groups. Pick the odds ratio, risk ratio or risk difference.
    • Means: mean, SD and number in each group. Pick the mean difference (same scale in every study) or Hedges’ g (different scales).
    • Effect + SE: any estimate with its standard error, for example a regression coefficient or a log hazard ratio.
    • Effect + CI: an estimate with its confidence interval, as most papers report it. Tick ratios for odds, risk or hazard ratios so they are pooled on the log scale.
  2. Paste the studies (or open a CSV or Excel file), one per row, with the study name first.
  3. Choose the main result (random or fixed), the between-study variance method, the level, and the words either side of the line of no effect.
  4. Download the forest plot, funnel plot and table as an image, PDF or Word file, or the table as CSV.

What the numbers mean

  • Fixed effect: inverse-variance weighted mean, assuming one true effect.
  • Random effects: each study’s true effect may differ; weights are 1 ÷ (variance + tau²). DerSimonian-Laird is the classic method-of-moments estimate of tau²; REML (restricted maximum likelihood) and Paule-Mandel are often preferred.
  • Q tests whether the studies disagree more than chance; I² is the share of the variation that is real disagreement.
  • Prediction interval: where the true effect of a new, similar study would probably lie (t with k − 2 df).
  • Egger’s test: regresses effect ÷ SE on 1 ÷ SE; an intercept far from zero hints at a lopsided funnel.
  • Zero cells: a trial with a zero gets 0.5 added to every cell; a trial with no events in either group is left out of ratio measures.

Worked example

The Events example is 8 made-up trials. With the odds ratio and DerSimonian-Laird random effects the page shows:

  • Random effects: OR 0.648 (95 % CI 0.446 to 0.940), p = 0.022.
  • Fixed effect: OR 0.654 (0.497 to 0.860).
  • Q = 10.991 on 7 df, p = 0.139; I² = 36.3 %; tau² = 0.097 on the log scale.
  • 95 % prediction interval 0.265 to 1.580: a new trial could even show harm.
  • Egger’s intercept −0.691, p = 0.586.

Trial E had no events among the treated, so 0.5 was added to each of its cells.

Tips

  • Pool only studies that ask the same question in similar people.
  • With fewer than about 5 studies, tau² is very uncertain; report the fixed-effect result too.
  • Egger’s test needs about 10 studies to be useful.
  • For hazard ratios from papers, use Effect + CI with the ratio box ticked.

FAQ

Why is my tau² different from statsmodels? statsmodels’ DerSimonian-Laird can return a negative tau²; it is set to zero here, as in the original method and in RevMan and metafor.

Can I use a random-effects interval with t (Hartung-Knapp)? Not yet; intervals use the normal distribution.

Is my data sent anywhere? No. Everything is worked out on your device and the page keeps working offline.

Where the numbers come from

  • Formulas: DerSimonian and Laird (1986) Controlled Clinical Trials 7:177; Paule and Mandel (1982) J Res NBS 87:377; Viechtbauer (2005) J Educ Behav Stat 30:261 (REML); Higgins and Thompson (2002) Stat Med 21:1539 and Higgins et al. (2003) BMJ 327:557 (I²); Higgins, Thompson and Spiegelhalter (2009) JRSS A 172:137 (prediction interval); Egger et al. (1997) BMJ 315:629; Hedges (1981) J Educ Stat 6:107; Cochrane Handbook for Systematic Reviews of Interventions (effect sizes, zero-cell correction).
  • Example data: made up for this page.

Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.

Last updated 2026-11-09.

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