Alterlab meta analysis

Meta-Analysis — Pool Honestly, Then Interrogate Heterogeneity and Bias

Skill type: ANALYSIS MODULE. Synthesizes effect sizes across studies. The discipline is not the pooled point estimate — it is the model choice (fixed vs random effects), the heterogeneity you must characterize, and the publication-bias diagnostics that decide whether the pooled estimate is trustworthy at all.

Core Mission

THE POOLED EFFECT IS ONLY AS GOOD AS ITS HETEROGENEITY STORY AND ITS PUBLICATION-BIAS CHECK.

When to Use This Skill

• "Pool these effect sizes / run a meta-analysis across N studies."
• "Compute I² / τ² — how heterogeneous are my studies?"
• "Is there publication bias? Draw a funnel plot / run Egger's test."
• "Convert these means and SDs (or 2×2 tables) into effect sizes and combine them."

Does NOT Trigger

The request is really about…	Route to	Why not this skill
Finding / screening the literature (search, PRISMA flow)	alterlab-deep-research	Discovery & screening, upstream of pooling.
A single study's descriptive/inferential statistics	alterlab-statistical-analysis	One dataset, not cross-study synthesis.
Fitting one regression / GLM	alterlab-statsmodels	Not effect-size pooling.
Whether the review question/design is sound	alterlab-ssci-design-gate	Design routing.

Fixed-effect vs random-effects (the first decision)

• Fixed-effect — assumes one true effect; studies differ only by sampling error. Rarely defensible across heterogeneous social-science studies.
• Random-effects — assumes a distribution of true effects (between-study variance τ²); the default when studies vary in population, measure, or design. Report the model and why.

Verified calls (pinned)

Python — statsmodels:

from statsmodels.stats.meta_analysis import effectsize_smd, combine_effects
eff, var = effectsize_smd(m1, sd1, n1, m2, sd2, n2)          # Hedges' g + variance
res = combine_effects(eff, var, method_re="dl")              # DerSimonian-Laird random effects
res.summary_frame()                                          # fixed + random rows, CIs, weights
res.tau2, res.i2, res.q                                      # heterogeneity
res.plot_forest()
# binary outcomes: effectsize_2proportions(c1, n1, c2, n2, statistic="odds-ratio")  # log OR + var

R — metafor (field standard):

library(metafor)
dat <- escalc(measure = "SMD", m1i=, sd1i=, n1i=, m2i=, sd2i=, n2i=, data = studies)  # or "OR"/"RR"
res <- rma(yi, vi, data = dat, method = "REML")              # random-effects
summary(res)                                                 # I2, tau2, Q
forest(res); funnel(res)
regtest(res)                                                 # Egger's test for funnel asymmetry
trimfill(res)                                                # trim-and-fill sensitivity

Heterogeneity — characterize, don't hide

• Cochran's Q (test of homogeneity; low power with few studies),
• I² (% of variation due to heterogeneity, not chance),
• τ² (between-study variance, on the effect-size scale). High I²/τ² means the pooled mean summarizes a distribution — report a prediction interval, and explore moderators (meta-regression / subgroups) rather than over-interpreting the point estimate.

Publication bias

• Funnel plot — asymmetry suggests small-study effects / missing null results.
• Egger's regression test (regtest) — a formal asymmetry test.
• Trim-and-fill (trimfill) — imputes "missing" studies as a sensitivity analysis. No single test is definitive; report the funnel plot plus at least one test, and treat them as sensitivity analyses, not proof.

Reporting standard (PRISMA)

Report per PRISMA 2020: the search/screening flow (hand off discovery to alterlab-deep-research), inclusion criteria, per-study effect sizes and weights, the pooling model, I²/τ²/Q, the publication-bias diagnostics, and risk-of-bias assessment.

References

• references/pooling_and_bias.md — effect-size formulas, RE estimators, heterogeneity, bias diagnostics, PRISMA.

Part of the AlterLab Academic Skills suite.