GUIDE 5 OF 5
Statistical synthesis: heterogeneity and effect sizes
Pooling is a modelling choice, not a button. Pick the scale, the model, and an honest I² before you treat a diamond as the answer. Free calculators handle one study or a heterogeneity check; the project engine pools the extraction table.
Meta-analysis is where extracted numbers become a claim. The credibility of that claim depends on the scale (log OR vs RD), the model (fixed vs random), and whether between-study variance is acknowledged rather than wished away.
Choosing your model: fixed vs random effects
Fixed-effect methods (Mantel-Haenszel, Peto for rare events) assume one true effect, with sampling error as the only extra noise. Random effects (DerSimonian–Laird in EvidenceFlow) assume studies estimate related but not identical effects and add τ² to the weights.
If populations, doses, or follow-up obviously differ, a fixed-effect diamond is the wrong summary even when I² looks modest. Model choice is clinical as much as statistical.
Understanding heterogeneity (I², Q, and τ²)
Cochran’s Q is a heterogeneity statistic that grows with the number of studies. I² rescales Q into a percentage of variation that is not explained by chance. τ² is the between-study variance used in random-effects weights.
Cochrane Handbook interpretation bands for I² (overlapping on purpose)
| I² value | Interpretation |
|---|---|
| 0% to 40% | Might not be important. |
| 30% to 60% | May represent moderate heterogeneity. |
| 50% to 90% | May represent substantial heterogeneity. |
| 75% to 100% | Considerable heterogeneity; be cautious about pooling. |
Compute Q, I², and τ² from study effects and standard errors in the free I² calculator. Compute a single study’s OR, RR, RD, or Hedges’ g in the effect size calculator.
Visualizing the data: forest and funnel plots
A forest plot shows each study’s effect and the pooled diamond. A funnel plot is a screen for small-study patterns that might suggest publication bias — not a verdict by itself.
EvidenceFlow’s meta-analysis engine (free core) pools extracted rows with fixed or random effects, Mantel-Haenszel, Peto, and the same heterogeneity statistics, and writes forest and funnel plots you can export.
FAQ
Should ratio measures go in on the log scale?
Yes. Enter log OR / log RR (and their SEs) into the I² calculator. The effect-size tool displays exponentiated OR/RR for reading.
Is I² a test of whether I may pool?
No. I² describes inconsistency. High I² means you should explain it (subgroups, bias, scales) — not that a random-effects diamond is automatically valid.
Are the calculators enough for a paper?
They match the usual formulas. A submitted review still needs study-level tracking, a chosen model, and plots from the full set — which the free core meta-analysis engine is for.
Core import, screening, extraction, meta-analysis, and PRISMA reporting are free. AI relevance scoring and extraction auto-fill are the paid upgrade.