Signature
I2 = max(0, (Q - (k - 1)) / Q) * 100
| Inputs | Definition | Unit |
|---|---|---|
Q | Cochran's heterogeneity statistic computed with common-effect weights | none |
k | Number of studies; k-1 is the degrees of freedom of Q | count |
I2 | Percentage of total variation across studies attributed to heterogeneity rather than chance | percent from 0 to 100 |
|---|
Function
Inverse-variance pooling of aggregate study-level effect estimates
Maps the effect estimate and its variance from each of k studies to one pooled estimate, its standard error and measures of between-study heterogeneity. Each study is weighted by the inverse of the variance of its estimate, so more precise studies count for more. Under a common-effect model the weight uses the within-study variance alone; under a random-effects model it also includes the between-study variance tau2. In health technology assessment the pooled relative effect, usually a log hazard ratio or log odds ratio, is then applied to a baseline from another source in a decision model.
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Implementations
Excel
I-squared percentage in one cell
With Q in a cell named QStat and the number of studies in a cell named NStudies, the formula returns I-squared as a percentage, with 0 when Q does not exceed its degrees of freedom.
=IF(QStat>NStudies-1,(QStat-(NStudies-1))/QStat*100,0)
Assumptions
I-squared inherits the degrees of freedom of Q
The formula uses k-1, the degrees of freedom of Q under the common-effect model, and is undefined when Q is zero; in that case I-squared is reported as 0%. With few studies the value is very uncertain.
Worked examples
I-squared of 70.9% for three illustrative trials
A Q of 6.867 on 2 degrees of freedom gives an I-squared of about 70.9%, as in the article.
Q = 6.867; k = 3; I2 = 70.9
I-squared set to zero when Q is below its degrees of freedom
A Q of 1.5 from three studies is below its 2 degrees of freedom, so the raw ratio is negative and I-squared is set to 0%.
Q = 1.5; k = 3; I2 = 0
Common errors
Reading I-squared as the size of heterogeneity
I-squared is a proportion of variation, not an amount of it. The Cochrane Handbook notes that the importance of a value depends on the magnitude and direction of effects and on the strength of evidence for heterogeneity, and that simple thresholds should be avoided when studies are few. The 70.9% in the three-trial example rests on three estimates.
Sources
Higgins and colleagues' definition of I-squared
Higgins JPT, Thompson SG, Deeks JJ, Altman DG. Measuring inconsistency in meta-analyses. BMJ. 2003;327(7414):557-560. Definition of I-squared as 100% times Q minus its degrees of freedom, divided by Q, with negative values set to zero, and its reading as the percentage of variation due to heterogeneity rather than chance.
Interpretation of I-squared in the Cochrane Handbook
Deeks JJ, Higgins JPT, Altman DG, McKenzie JE, Veroniki AA (editors). Chapter 10: Analysing data and undertaking meta-analyses. In: Cochrane Handbook for Systematic Reviews of Interventions version 6.5. Cochrane; 2024. Section 10.10.2, on the uncertainty of I-squared with few studies and the factors on which the importance of an observed value depends.
Canonical Identity
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