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Heterogeneity calculator
Pubrica’s free heterogeneity calculator computes I², τ², Cochran’s Q and the fixed-effect and random-effects (DerSimonian–Laird) pooled estimates from a list of study results. Use it to assess whether the studies in a meta-analysis are similar enough to pool.
The tool runs in your browser. No registration, email address or file upload is required, and the formula, reference or assessment criteria used are shown with the result.
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- Method shown with the answer
- Sources dated
The Tool
Assess Heterogeneity Across Studies in a Meta-Analysis
Calculates I², τ², Cochran’s Q and fixed-effect and random-effects pooled estimates from a list of study results.
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Calculates I², τ², Cochran’s Q and fixed-effect and random-effects pooled estimates from a list of study results.
I² · τ² · Q · DerSimonian–Laird55.2%
I² · variation not due to chance
0.0213
τ² · between-study variance
1.49
H · observed over expected spread
Substantial heterogeneity
At I² = 55.2% these studies disagree enough that the disagreement has to be explained before a pooled estimate means anything. I² is a proportion, not a test: with 5 studies it is imprecise, and a low I² with wide studies can still hide real disagreement. The question a reviewer will ask is what differs between these studies clinically — population, dose, follow-up, outcome definition — and that is answered by subgroup or meta-regression, not by the number above.
Method. wᵢ = 1/SEᵢ²; Q = Σwᵢ(yᵢ − ȳ)²; I² = max(0, (Q−df)/Q); τ² = max(0, (Q−df)/(Σw − Σw²/Σw)) (DerSimonian–Laird); the random-effects weights are 1/(SEᵢ²+τ²). Q is referred to a χ² distribution on k−1 degrees of freedom. Ratio measures are log-transformed before pooling and exponentiated afterwards.
Limitations
What This Tool Does Not Cover
Use the result as a starting point. These are the situations in which it needs specialist review.
The calculators
Limitations of the calculators
The sample size calculator gives the closed-form answer for two independent groups. Cluster randomisation, interim analyses, a non-inferiority margin, repeated measures and competing risks each change the number materially, and none of them can be handled by inflating the answer afterwards. The same applies to the test chooser: it cannot know that your observations are clustered within clinics, and clustering overrides almost everything else it would tell you.
Method
Methods and Sources
The calculation or reference set behind this tool. The result panel also shows the formula or criteria used.
Meta-analysis
DerSimonian–Laird
Inverse-variance weights, Cochran’s Q referred to a χ² distribution on k−1 degrees of freedom, and the DerSimonian–Laird estimator of τ². Ratio measures are pooled on the log scale and exponentiated back.
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