Heterogeneity (I²)
- Measure
Heterogeneity is how much study results differ beyond chance; I² expresses it as a percentage.
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 < 0.05.
- By the Cochrane guide, 67 % falls in moderate to substantial heterogeneity.
- Subgroups are explored: the 3 trials in older adults show a smaller effect than the 3 in younger adults.
- Contrast: another meta-analysis of 6 trials with Q = 4 gives (4 − 5) / 4 < 0, so I² = 0 %.
- Reading: two thirds of the variation between the 6 trials is not chance; age might explain it.
Markers
- 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.
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.
Connections
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 (Cochrane, 2026); Chapter 14: Completing ‘Summary of findings’ tables and grading the certainty of the evidence (Cochrane, 2026).
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Representative model, for educational purposes only.