What is heterogeneity in meta-analysis, and what does I² actually mean?
I² is widely reported and widely misread. It does not measure how different the studies are, and it is not a threshold for whether pooling is allowed.
Heterogeneity is variation in the true effect between studies. Some of the variation you observe is sampling error; heterogeneity is what is left over.
Three quantities describe it, and they answer different questions.
Tau-squared: how much the true effects vary
Tau-squared estimates the variance of the true effects across studies, on the scale of the effect measure. It is the quantity a random-effects model actually estimates, and its square root, tau, is interpretable: an effect that varies by roughly tau between typical settings.
It is the most directly meaningful of the three, and the least often reported.
Q and its p-value: could this be chance alone?
Cochran's Q tests whether the observed variation exceeds what sampling error would produce. Its power is low when there are few studies, so a non-significant Q usually means "we could not detect heterogeneity", not "there is none".
Reading a non-significant Q as permission to fit a fixed-effect model is one of the most common errors in published meta-analyses.
I²: what proportion of the variation is not chance
I² is the percentage of total variability attributable to heterogeneity rather than sampling error.
Two consequences follow, and both are routinely missed.
- I² is a proportion, not an amount. Very precise studies make the sampling-error denominator small, so a trivially small tau can produce a high I². A large I² in a set of large trials may describe a difference of no clinical importance.
- I² has a confidence interval, and with few studies it is very wide. Reporting "I² = 62%" from five studies as though it were a measurement is reporting a point estimate whose interval might run from 0 to 85.
The thresholds are not rules
The often-quoted 25 / 50 / 75 percent bands were offered as a tentative description and are repeatedly cited as decision criteria. They are not. Nothing about a study set changes when I² crosses 50.
What to do instead
Report tau or tau-squared alongside I², give the prediction interval, and treat substantial heterogeneity as something to explain rather than to declare.
Where you expected variation, say what you think drives it and examine it with subgroups or meta-regression you specified in advance. Where you did not expect it, say so — an unexplained inconsistency is a genuine finding about the evidence base.
Frequently asked questions
What does I² mean in a meta-analysis?
I-squared is the percentage of total variability attributable to heterogeneity rather than sampling error. It is a proportion, not an amount: very precise studies shrink the sampling-error denominator, so a trivially small true variation can produce a high I-squared.
Is I² above 50% too high?
The 25, 50 and 75 percent bands were offered as a tentative description and are repeatedly cited as decision criteria. Nothing about a set of studies changes when I-squared crosses 50. Report tau or tau-squared and a prediction interval alongside it.
What is the difference between tau-squared and I²?
Tau-squared estimates how much the true effects vary, on the scale of the effect measure, and is the quantity a random-effects model actually estimates. I-squared expresses that variation as a proportion of total variability.