Editverse Free Calculator
Meta-Analysis & Forest Plot Calculator
Pool study effects with inverse-variance weights (fixed-effect or DerSimonian-Laird random-effects), draw a forest plot and read I² and tau², with the R command behind the result. Enter each effect with its 95% CI on an additive scale: mean differences and standardised mean differences as they are, and odds, risk or hazard ratios as natural logs (the log of the estimate and of both limits), then exponentiate the pooled result. A full interpretation guide follows below. Validated against R 4.3.3.
In Simple Words
A meta-analysis combines the results of several studies into one pooled estimate, giving each study a weight based on its precision — larger, more precise studies count for more. The forest plot shows each study as a point with its confidence interval, and the pooled result as a diamond at the bottom.
Because studies are never identical, the analysis also reports heterogeneity: how much the true effects differ between studies beyond chance. The I² statistic expresses this as a percentage of total variation, helping you judge whether a single pooled number is meaningful.
When to Use Meta-Analysis
Use a meta-analysis when several studies address the same question and are clinically and methodologically similar enough to combine — for example, trials of the same intervention reporting the same outcome. Pooling increases precision and can resolve conflicting individual results, but only when the studies are genuinely comparable.
Choose a random-effects model when you expect the true effect to vary across studies, and a fixed-effect model only when you can assume a single common effect. Always report I² alongside the pooled effect size and its confidence interval. Not sure your studies should be combined at all? Our interactive Test Selector can help you decide.
Expected format: Studies: Label, Effect, LowerCI, UpperCI (one per line)
Drop a CSV here or click to choose. Parsed in your browser: nothing is uploaded.
Expected format: Studies: Label, Effect, LowerCI, UpperCI (one per line)
library(meta)
studlab <- c({meta_studlab})
TE <- c({meta_te})
lower <- c({meta_lower})
upper <- c({meta_upper})
seTE <- (upper - lower) / (2 * 1.96) # SE from the 95% CI, as the calculator does
m <- metagen(TE, seTE, studlab = studlab, sm = "SMD",
common = {meta_common}, random = {meta_random}, method.tau = "DL")
summary(m) # pooled effect, Cochran's Q, I2, tau2User guide
When to use. Pool effect sizes across studies and quantify heterogeneity (I-squared).
Assumptions. Studies are clinically and methodologically comparable enough to combine.
Common mistakes. High I-squared (>75%) signals substantial heterogeneity: interpret the pooled estimate cautiously.
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- DerSimonian R, Laird N. Meta-analysis in clinical trials. Control Clin Trials. 1986;7:177-188.
Worked Examples
Example 1 — Pooling four studies
Four studies report standardised mean differences of 0.45, 0.60, 0.32, and 0.55, each with its own confidence interval. A random-effects model weights them by precision and combines them into a pooled estimate near 0.48. On the forest plot each study is a square sized by its weight, and the pooled effect is the diamond whose width is its 95% confidence interval.
Example 2 — Reading heterogeneity
The same analysis returns I² = 17%, and Cochran’s Q (3.62 on 3 df, p = 0.31) is non-significant, so the studies are reasonably consistent and the pooled estimate is trustworthy. Had I² been 80%, the true effects would vary widely between studies and a single pooled number would mean little — you would investigate sources of heterogeneity through subgroups or meta-regression instead.
Assumptions to Check
Comparable studies (clinical and methodological). The studies must address the same question with similar populations, interventions, and outcome definitions. Combining studies that are not comparable produces a pooled estimate that answers no real question.
The right model for the question. A fixed-effect model assumes one common true effect; a random-effects model allows the true effect to vary. Choosing fixed-effect when heterogeneity is real understates uncertainty in the pooled estimate.
Independent, unbiased effect estimates. Each study should contribute one independent effect, and the set should not be distorted by selective publication. Assess publication bias before trusting a pooled result.
Common Mistakes
Pooling clinically dissimilar studies
Combining studies with different populations or outcomes just because they share a topic yields a meaningless average. Comparability comes first; statistics cannot rescue an incoherent set.
Treating a high I² as a result to report and move on
A large I² is a prompt to investigate, not a number to footnote. Explore heterogeneity with subgroup analysis or meta-regression before quoting any pooled effect.
Defaulting to fixed-effect to get a tighter interval
A fixed-effect model gives a narrower confidence interval, but only because it ignores between-study variation. When heterogeneity exists, that narrow interval is falsely reassuring.
Ignoring publication bias
Small negative studies often go unpublished, inflating the pooled effect. Inspect a funnel plot and run a formal test before drawing conclusions.
Frequently Asked Questions
What does I² actually measure?
It is the proportion of total variation across studies that is due to real heterogeneity rather than chance — roughly, 25% is low, 50% moderate, and 75% high.
Fixed-effect or random-effects?
Use random-effects when you believe the true effect varies between studies, which is usual in clinical settings; reserve fixed-effect for the rare case of one assumed common effect.
How many studies do I need?
There is no hard minimum, but with very few studies the between-study variance is poorly estimated and heterogeneity statistics become unstable; interpret small meta-analyses cautiously.
Does the result match R, Stata, and RevMan?
Yes, on the scale you enter. The calculator uses standard inverse-variance weighting with DerSimonian-Laird random effects and derives each standard error from the 95% CI as (upper − lower) / 3.92. The R command shown uses sm = "SMD"; for log ratios set sm to "OR", "RR" or "HR" and pass the log estimates so R back-transforms the pooled value.
Related Calculators
References
- Higgins JPT, Thompson SG. Quantifying heterogeneity in a meta-analysis. Stat Med. 2002;21(11):1539–1558. PMID 12111919.
- Higgins JPT, Thompson SG, Deeks JJ, Altman DG. Measuring inconsistency in meta-analyses. BMJ. 2003;327(7414):557–560. PMID 12958120.
- DerSimonian R, Laird N. Meta-analysis in clinical trials. Control Clin Trials. 1986;7(3):177–188.
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