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# Heterogeneity (I²)

- Measure

Heterogeneity is how much study results differ beyond chance; I² expresses it as a percentage.

Updated Nov 5, 2026

## Key points

- I² = (Q − df) / Q × 100, with df = number of studies − 1; if Q is smaller than df, I² is set to 0 %.
- Rough guide (Cochrane): 0–40 % might not be important; 30–60 % moderate; 50–90 % substantial; 75–100 % considerable.
- The ranges overlap on purpose: importance depends on the size and direction of effects and the evidence for heterogeneity.
- The Q test has little power with few studies: a non-significant p value does not rule out heterogeneity.
- Faced with heterogeneity: look for its cause (subgroups, meta-regression), use random effects or do not pool.

## What it is

In a meta-analysis, heterogeneity is the variation between study results. Clinical heterogeneity comes from differences in patients, interventions or outcomes; methodological heterogeneity from differences in design or risk of bias; statistical heterogeneity is observed variation larger than chance would produce. It is tested with the Q (chi-squared) test and quantified with I², the percentage of total variation due to heterogeneity rather than chance.

## Formula and reading

- Q = Σ w × (study effect − pooled effect)², with w = 1 / SE².
- df = k − 1, where k is the number of studies.
- I² = max(0, (Q − df) / Q) × 100 %.
- Reading: I² near 0 %, consistent studies; high I², real differences between studies that need explaining.

## Worked example

- Data (made up): a meta-analysis of 6 trials gives Q = 15.
- Degrees of freedom: 6 − 1 = 5.
- I² = (15 − 5) / 15 = 10 / 15 = 0.667, that is, ≈ 67 %.
- Q test: the chi-squared critical value with 5 df at 0.05 is 11.07; since 15 > 11.07, p
- I²
- Q
- df
- Subgroups

## How to read it

- With high heterogeneity, the pooled effect may apply to no actual patient: look at which subgroup resembles yours.
- In GRADE, important inconsistency between studies lowers the certainty of the evidence.

## Common pitfalls

- Treating the I² thresholds as rigid cut-offs: with few studies I² is very uncertain.
- Concluding there is no heterogeneity because the Q test is not significant with 4 or 5 studies.
- Mixing up statistical and clinical heterogeneity: studies of very different populations should not be pooled even if I² is low.

## Memory aid

I² is the part of the disagreement that is not luck: the higher it is, the more you must ask why the studies differ.

## Test yourself

Think of the answer, then tap the question to see it.

## How is I² computed?

I² = (Q − df) / Q × 100, where Q is the heterogeneity statistic and df the number of studies minus 1; if negative, it is set to 0 %.

## By the rough Cochrane guide, what does an I² of 80 % suggest?

Considerable heterogeneity (75–100 %), which should be explored before trusting a pooled effect.

## Why does a non-significant Q test not rule out heterogeneity?

Because with few studies the test has little statistical power.

## How do clinical and statistical heterogeneity differ?

Clinical heterogeneity comes from differences in patients, interventions or outcomes; statistical heterogeneity is variation in results larger than chance would produce.

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## Connections

## Related 5

- [Meta-analysis](https://durgical.com/en/epidemiology/meta-analysis/)
- [Forest plot](https://durgical.com/en/epidemiology/forest-plot/)
- [Chi-square test](https://durgical.com/en/epidemiology/chi-square-test/)
- [The GRADE system](https://durgical.com/en/epidemiology/the-grade-system/)
- [Effect modification (interaction)](https://durgical.com/en/epidemiology/effect-modification/)

[← All of epidemiology](https://durgical.com/en/epidemiology/)

Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.

Sources: [Chapter 10: Analysing data and undertaking meta-analyses](https://www.cochrane.org/authors/handbooks-and-manuals/handbook/current/chapter-10) (Cochrane, 2026); [Chapter 14: Completing ‘Summary of findings’ tables and grading the certainty of the evidence](https://www.cochrane.org/authors/handbooks-and-manuals/handbook/current/chapter-14) (Cochrane, 2026).

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Representative model, for educational purposes only.

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