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.