Eigenstate Labs
Eigenstate Labs
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Meta-Analysis Calculator and Forest Plot Generator

Pool study effects with fixed effect or random effects (DerSimonian-Laird, REML, Paule-Mandel), see heterogeneity stated plainly, and export a publication-quality forest plot as vector.

At a glance

Computes
Pooled effects, heterogeneity statistics, and a forest plot.
You supply
Study estimates, counts, means with SDs, or correlations.
Use when
You have several studies of one effect and want a defensible pooled estimate.
Not for
Meta-regression, network or Bayesian meta-analysis, or converting one effect size. Effect Size Calculator

Runs in your browser. Your extraction sheet is never uploaded.

Paste several studies and this page pools them: Hedges' g, mean difference, log odds and log risk ratios, risk difference, Fisher z, or a generic estimate with its own uncertainty, under a fixed-effect model or one of three random-effects estimators. Heterogeneity is reported four ways at once, as Q, I squared, tau squared and a prediction interval. The forest plot puts every study on one scale with the pooled interval as a diamond, and exports as vector. Every result is reproducible: the page emits the R that produces it, and its test suite reproduces the published results of four primary publications. If what you have is a single effect size to convert into another unit, this is the wrong page, and the effect size converter does that in one step.

Display confidence level

Tab, comma, semicolon or pipe. One study per line. Column order matches the table below.

StudyEstimateSEVarianceLowerUpperSubgroup Actions
Model

Pooled estimate

0.0837

Random effects, REML tau-squared. 95% CI -0.0175 to 0.1849.

Q (18 df)
35.8295
I²
41.85%
τ²
0.0188
Prediction interval
-0.2242 to 0.3916

Standardized mean difference; 95% CI; squares scaled by model weight

−0.500.511.521. Ros…2. Con…3. Jos…4. Pel…5. Pel…6. Eva…7. Fie…8. Cla…9. Kes…10. Ma…11. Ca…12. Fl…13. Ke…14. He…15. Fi…16. Gr…17. Ro…18. Fl…19. Gi…Random…Predic…HeterogeneityTest for Random
Some forest row labels are shortened with an ellipsis; full labels remain in the table below.
Study estimates and selected-model weights
StudyEstimate95% CIWeight
Rosenthal et al. 19740.0300-0.2148 to 0.27487.75%
Conn et al. 19680.1200-0.1681 to 0.40816.60%
Jose & Cody 1971-0.1400-0.4674 to 0.18745.71%
Pellegrini & Hicks 1972a1.18000.4490 to 1.91101.69%
Pellegrini & Hicks 1972b0.2600-0.4633 to 0.98331.72%
Evans & Rosenthal 1969-0.0600-0.2618 to 0.14189.06%
Fielder et al. 1971-0.0200-0.2218 to 0.18189.06%
Claiborn 1969-0.3200-0.7512 to 0.11123.97%
Kester 19690.2700-0.0515 to 0.59155.83%
Maxwell 19700.80000.3081 to 1.29193.26%
Carter 19700.5400-0.0519 to 1.13192.42%
Flowers 19660.1800-0.2569 to 0.61693.89%
Keshock 1970-0.0200-0.5864 to 0.54642.61%
Henrikson 19700.2300-0.3384 to 0.79842.59%
Fine 1972-0.1800-0.4918 to 0.13186.04%
Grieger 1970-0.0600-0.3874 to 0.26745.71%
Rosenthal & Jacobson 19680.30000.0277 to 0.57237.00%
Fleming & Anttonen 19710.0700-0.1139 to 0.25399.66%
Ginsburg 1970-0.0700-0.4112 to 0.27125.43%
Export

How each study is weighted

Every study enters the pool with weight 1 / (vᵢ + τ²), so a study whose estimate carries a large within-study variance vᵢ gets a small square and a long interval line. Both marks report the same fact. That variance comes from the study's own numbers: its sample size together with the spread or the event counts it observed. Sample size is the part a study fixes in advance, and the power and sample size calculator is where that choice is worked out.

Plot and export options

The figure uses a grayscale Cochrane-style layout. Study square area follows selected-model weight; the numerical column remains authoritative.

Funnel plot asymmetry and publication bias

These diagnostics require at least ten studies. Funnel asymmetry may reflect heterogeneity, methods, selection, or chance; it is not a verdict about publication bias.

Standard error (increases downward) against Effect estimate

0.00.10.20.30.00.51.0Pooled estimate

Egger intercept 1.6243, t(17) = 2.0380.

Trim and fill estimates 3 missing studies on the right side. Adjusted estimate 0.0282, 95% CI -0.1170 to 0.1734.

Trim and fill is not a way of yielding a more "valid" estimate of the overall effect, but a way of examining the sensitivity of the results to one particular selection mechanism. Funnel asymmetry has causes other than publication bias: genuine heterogeneity, methodological differences between small and large studies, and chance.

Reproducing this in R

library(metafor)

dat <- data.frame(
  study = c("Rosenthal et al. 1974", "Conn et al. 1968", "Jose & Cody 1971", "Pellegrini & Hicks 1972a", "Pellegrini & Hicks 1972b", "Evans & Rosenthal 1969", "Fielder et al. 1971", "Claiborn 1969", "Kester 1969", "Maxwell 1970", "Carter 1970", "Flowers 1966", "Keshock 1970", "Henrikson 1970", "Fine 1972", "Grieger 1970", "Rosenthal & Jacobson 1968", "Fleming & Anttonen 1971", "Ginsburg 1970"),
  yi = c(0.03, 0.12, -0.14, 1.18, 0.26, -0.06, -0.02, -0.32, 0.27, 0.8, 0.54, 0.18, -0.02, 0.23, -0.18, -0.06, 0.3, 0.07, -0.07),
  vi = c(0.0156, 0.0216, 0.0279, 0.1391, 0.1362, 0.0106, 0.0106, 0.0484, 0.0269, 0.063, 0.0912, 0.0497, 0.0835, 0.0841, 0.0253, 0.0279, 0.0193, 0.0088, 0.0303)
)

res <- rma(yi, vi, data = dat, method = "REML")
summary(res)
predict(res)

The worked example on this page

The example loaded above is Raudenbush and Bryk's 19-study teacher-expectancy dataset. It is published, non-clinical, and every displayed summary is asserted in the test suite. The exact REML root is τ² = 0.0188183, so this page prints I² = 41.85%; metafor's default stopping threshold prints 41.86%.

Fixed effect and random effects

A fixed-effect model assumes one common effect. A random-effects model estimates a distribution of effects. The model is a claim about the studies; this tool never chooses it from Q or I².

Choosing a tau-squared estimator

REML is the default. Paule-Mandel is a robust alternative, especially for dichotomous data. DerSimonian-Laird remains for reproducing older analyses and is not the sole option.

Reading heterogeneity honestly

I² is the proportion of observed variance not attributed to sampling error, not the absolute size of study differences. Read τ on the effect scale and the prediction interval alongside it.

Effect measures and what this page computes

The input layer computes Hedges g with its small-sample correction, mean difference with separate or pooled variances, log odds ratios, log risk ratios, risk differences, Fisher z, and generic inverse variance.

Zero cells in 2x2 tables

The default adds 0.5 to all four cells of a study containing a zero cell. Risk differences use the raw counts because their formula is already defined at zero.

Subgroups

One categorical subgroup variable is supported. Blank values remain visible as Unassigned. Singleton subgroups enter the between-group test while their unavailable within-group heterogeneity is stated.

What this page validates against

Tests reproduce the published summaries of the BCG trials, the teacher-expectancy studies, the Normand stroke-unit example, and the Hine zero-heterogeneity example. Package datasets are numerical cross-checks only; the source of record is each primary publication.

What this page will not do

This instrument does not run meta-regression, network or Bayesian meta-analysis, diagnostic-accuracy models, study screening, or clinical decision support. It pools the numbers supplied and stops.

Assumptions, limits, and privacy

Your rows stay in browser memory and are not placed in a URL or device storage. Pooling cannot decide whether studies measured the same construct, whether the search found every study, or whether the evidence is credible.

FAQ

What is a forest plot?

It places each study estimate and interval on one scale, then shows the pooled interval as a diamond.

Why does a prediction interval need five studies?

Between-study variance is too fragile below that point for this page to present the interval responsibly.

Can I export a figure a journal will accept?

SVG is the primary vector export. PNG is rasterized locally and PDF uses the browser print path.

wᵢ = 1 / (vᵢ + τ²); θ = Σwᵢyᵢ / Σwᵢ How?

How this is calculated

Q is computed in two passes from residuals. REML is solved to its estimating-equation root, Paule-Mandel uses a data-derived bracket, and all p-values use direct upper tails.

Formula: wᵢ = 1 / (vᵢ + τ²); θ = Σwᵢyᵢ / Σwᵢ

See Sources below

Sources

  1. Cochrane Handbook, Chapter 10: Analysing data and undertaking meta-analyses. Cochrane.
  2. Cochrane Handbook, Chapter 13: Assessing risk of bias due to missing results. Cochrane.
  3. Raudenbush and Bryk (1985), Empirical Bayes meta-analysis. Journal of Educational Statistics.
  4. Higgins and Thompson (2002), Quantifying heterogeneity in a meta-analysis. Statistics in Medicine.
  5. Veroniki et al. (2016), Methods to estimate between-study variance. Research Synthesis Methods.
  6. IntHout et al. (2014), The Hartung-Knapp-Sidik-Jonkman method. BMC Medical Research Methodology.

How we choose and check our formulas