A browser-based meta-analysis tool. No installation, no server, no dependencies beyond a modern browser. All computation runs locally in JavaScript — data never leaves the machine.

Effect types

Heterogeneity

• τ² estimators: REML (default), DerSimonian–Laird (DL), Paule–Mandel (PM), Empirical Bayes (EB), Paule–Mandel Median (PMM), Generalised Q Median (GENQM), Maximum Likelihood, Hunter–Schmidt, Hedges, Sidik–Jonkman, Generalised Q (GENQ), Iterated DL (DLIT), Hunter–Schmidt corrected (HSk), Square-root GENQ (SQGENQ), EBLUP (= REML) — 15 options
• Pooling methods: Inverse-variance (default; RE and FE); Mantel–Haenszel (OR, RR, RD) and Peto one-step (OR only) — fixed-effects pooling that operates directly on cell counts and handles single-zero cells without a continuity correction
• Common language effect size (CLES) — displayed alongside the RE pooled estimate for standardised mean difference types (SMD, SMDH, SMD_paired, SMD1, SMD1H, SMCC); CLES = Φ(d / √2), the probability that a randomly drawn score from group 1 exceeds group 2; 95% CI transformed from the RE CI (McGraw & Wong, 1992)
• CI methods: Normal/Wald, Knapp–Hartung, t-distribution, Profile Likelihood (REML or ML)
• Statistics: Cochran's Q, I², H², τ², 95% prediction interval (Higgins 2009)
• Confidence intervals on heterogeneity: Profile-likelihood CIs for τ², I², H²
• Profile likelihood plot for τ²: full likelihood surface with LRT-based 95% CI; available when τ² estimator is ML or REML

Publication bias

• Egger's regression — intercept test for funnel plot asymmetry
• Begg's rank correlation — Kendall's τ_b with tie correction
• FAT-PET / PET-PEESE — funnel asymmetry test and precision-effect test; when FAT detects bias (p < .10) the two-stage PET-PEESE correction is applied and the PEESE intercept is highlighted as the corrected effect estimate; the PEESE regression line is overlaid on the contour-enhanced funnel plot (Stanley & Doucouliagos, 2014)
• Harbord's test — score-based Egger variant for binary OR studies; avoids inflated Type I error when effect size and SE share cell-count information (Harbord et al., 2006)
• Peters' test — WLS regression on 1/N; works with any effect type where total N is available; preferred over Egger for OR/RR (Peters et al., 2006)
• Deeks' test — funnel-asymmetry test for diagnostic accuracy (DOR) studies using effective sample size as the precision surrogate (Deeks et al., 2005)
• Rücker's test — arcsine-transformation Egger variant for binary outcomes with better-controlled Type I error (Rücker et al., 2008)
• Fail-safe N — Rosenthal and Orwin estimators
• Test of Excess Significance (TES) — compares the observed number of significant results (O) against the expected (E = Σ power_i) given per-study power to detect the pooled effect; χ² = (O − E)² / [E(1 − E/k)]; p < .10 flags excess significance (Ioannidis & Trikalinos, 2007)
• WAAP-WLS — Weighted Average of Adequately Powered studies; restricts pooling to studies with ≥ 80% power to detect the fixed-effect estimate; if no study qualifies, falls back to the full WLS estimate; a WAAP near zero with a large RE estimate suggests publication bias is inflating the pooled effect (Stanley & Doucouliagos, 2015)
• Henmi-Copas bias-robust CI — confidence interval robust to publication bias; always uses DL τ² and fixed-effect weights; centred on the FE estimate with half-width u₀ × SE, where u₀ = SDR × t₀ and t₀ is solved by numerical integration over the conditional distribution of Q given R; wider than the standard RE CI when small-study effects are present (Henmi & Copas, 2010)
• Trim-and-fill (L0, R0, Q0 estimators) — imputes missing studies and reports the adjusted pooled estimate; estimator selectable in the UI
• Funnel plot — standard or contour-enhanced (α = .10, .05, .01 regions)
• Selection model (Vevea–Hedges) — ω-weighted likelihood model; MLE mode (k ≥ 8) estimates selection weights jointly with μ and τ²; fixed-ω sensitivity presets (Mild / Moderate / Severe, Vevea & Woods 2005) available from k ≥ 3

P-value analyses

• P-curve — distribution of significant p-values; tests for evidential value and right-skew (Simonsohn et al., 2014)
• P-uniform* — publication-bias-corrected effect size estimate using the p-value distribution (van Assen et al., 2015)

Sensitivity and influence

• Leave-one-out — flags studies whose omission would flip statistical significance
• Influence diagnostics — Cook's distance, DFBETA, DFFITS, covariance ratio, hat values, standardised residuals, Δτ²
• Influence plot — per-study leverage and Cook's distance visualised as a bubble chart
• BLUPs — Empirical Bayes shrunken study estimates with CIs; shows shrinkage toward μ̂ (available when τ² > 0)
• Baujat plot — heterogeneity contribution vs. overall influence; identifies studies that simultaneously inflate Q and shift the pooled estimate
• Normal Q-Q plot — normal probability plot of standardised residuals; assesses the normality assumption of the RE distribution
• Radial (Galbraith) plot — precision (1/seᵢ) vs. standardised effect (yᵢ/seᵢ); regression line through the origin has slope equal to the FE pooled estimate; dashed ±2 band flags outliers; right axis shows the effect-size scale
• Estimator comparison — runs all τ² estimators side-by-side on the current dataset
• Cumulative meta-analysis — adds studies in user-selected order (input order, precision, or effect size)

Meta-regression

Continuous and categorical moderators; multiple moderators may be added simultaneously. Results include coefficients, standard errors, z/t statistics, p-values, R² (proportion of heterogeneity explained), and model-fit indices AIC, BIC, and log-likelihood (ML and REML conventions; matches metafor's AIC.rma() / BIC.rma()). Bubble plots are generated per continuous moderator.

When two or more moderators are present, the per-moderator tests panel shows both a Wald QM statistic and a Likelihood Ratio Test (LRT) for each moderator. LRT = 2·(LL_ML,full − LL_ML,reduced) ~ χ²(df); the reduced model omits that moderator's columns. LRT always uses ML estimation internally regardless of the τ² method selected, since REML log-likelihoods cannot be compared across different fixed-effect structures (Verbeke & Molenberghs 2000).

Non-linear transforms for continuous moderators are available via the transform dropdown when adding a moderator:

• Linear (default) — standard single-column predictor
• Poly ² — adds x² to the design matrix (quadratic curve)
• Poly ³ — adds x² and x³ (cubic curve)
• RCS (3–5 knots) — restricted cubic spline; knots placed at Harrell's recommended percentiles (10/50/90 for 3 knots, etc.). Produces a smooth curve that is linear outside the outermost knots. The per-moderator Wald test covers all spline columns jointly. Equivalent to constructing the basis manually in metafor and passing it via mods (Harrell, 2015).

Multiple comparison correction — when m moderators are tested simultaneously, Bonferroni (p_adj = min(1, m·p)) or Holm (step-down, uniformly more powerful than Bonferroni) correction is applied to the per-moderator omnibus QM p-values. Adjusted p-values appear alongside raw values in the per-moderator tests table. Matches R's p.adjust(method="bonferroni"/"holm").

Custom contrasts — after running a meta-regression, expand the Custom contrasts panel to test any linear combination of coefficients: H₀: L·β = 0, where L is a weight vector you supply. SE = √(L′VL) using the full variance–covariance matrix. Typical use: set +1 and −1 weights on two categorical levels to directly compare them.

Location-scale model — add scale moderators (log τ² = Zγ) to model heterogeneity simultaneously with mean effects. Each study gets its own τ̂²ᵢ = exp(Zᵢγ̂). Estimated by ML via profile likelihood (BFGS optimizer). Output includes separate coefficient tables for location (β) and scale (γ), a Wald test per moderator, and a likelihood ratio test comparing the full scale model against the intercept-only scale model. Equivalent to rma(..., scale = ~ ..., method = "ML") in metafor (Viechtbauer, 2021).

Subgroup analysis

Studies are assigned to named groups via the Group column. Pooled estimates are reported within each subgroup alongside Q_between, degrees of freedom, and the between-group p-value.

Risk of bias

User-defined RoB domains with Low / Some concerns / High / Not reported ratings per study. Visualised as a per-study traffic light grid and a per-domain summary bar chart.

Bayesian meta-analysis

Conjugate normal-normal random-effects model fit via grid approximation (300 points over τ) — no MCMC, no external libraries. Prior on μ: N(μ₀, σ_μ²); prior on τ: HalfNormal(σ_τ). Because the prior on μ is conjugate given τ, the marginal posterior of μ is an analytic mixture of normals. Reports posterior mean and 95% credible interval for μ (overall effect) and τ (heterogeneity SD), plus posterior density plots for both parameters. Diffuse priors recover the REML random-effects estimate.

Bayes Factor BF₁₀ — tests H₁: μ ≠ 0 vs H₀: μ = 0 via the Savage-Dickey density ratio: BF₁₀ = prior density(0) / posterior density(0). Reported with log(BF₁₀) and a Jeffreys (1961) verbal interpretation (Anecdotal / Moderate / Strong / Very strong / Decisive).

Prior sensitivity analysis — loops the Bayesian model over a 3 × 3 grid of (σ_μ, σ_τ) pairs ({0.5, 1, 2} × {0.25, 0.5, 1}, nine combinations) and tabulates the posterior mean, credible interval, and BF₁₀ for each. Triggered by the Prior Sensitivity button. Robust conclusions are stable across the grid; prior-sensitive results indicate the posterior is informed by the prior and should be reported with caution.

Dependent effect sizes

When a primary study contributes multiple effect sizes (different outcomes, subgroups, or time points), assigning a Cluster ID activates three complementary analyses in the results panel:

Not available with M-H or Peto pooling methods. Based on Hedges, Tipton & Johnson (2010) and Van den Noortgate et al. (2013).

Plots

All plots export as SVG, PNG, or TIFF.

Data input

• Manual entry — inline editable table with per-field validation and error highlighting; rows can be reordered by drag-and-drop or Alt+↑ / Alt+↓
• CSV import — auto-detects delimiter and effect type from column headers; preview panel with column-mapping controls before committing
• Session save / load — full application state (data, settings, moderators, RoB ratings) serialised to JSON
• Auto-save — drafts written to localStorage; a recovery banner appears on reload if unsaved changes exist
• Cluster ID column — optional study identifier for dependent effect sizes (e.g. multiple outcomes or subgroups from the same trial); activates cluster-robust SE, RVE, and three-level meta-analysis sections in the results panel

CSV column names match the input fields for each effect type (e.g. m1, sd1, n1, m2, sd2, n2 for MD; a, b, c, d for OR). A label column is optional but recommended. A group column assigns studies to subgroups.

Export

• HTML report — self-contained document with all results tables and plots as inline SVG
• Word (.docx) — exports all results tables and plots to a Word document via OOXML/JSZip; no server required
• PDF — via the browser's print dialog
• SVG / PNG / TIFF — individual plot export from each plot's toolbar
• All tables use APA 7th edition style — no vertical lines, merged CI columns, Note paragraphs

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