Editverse Free Calculator
Heterogeneity Calculator (I² & tau²)
Enter each study’s effect and 95% confidence interval to get Cochran’s Q with its degrees of freedom and p-value, I² and the DerSimonian-Laird tau², with the pooled estimate, a forest plot and the R command behind the result. The fixed-effect option changes only the pooling weights; Q, I² and tau² are reported under either model. A full interpretation guide follows below. Validated against R 4.3.3.
In Simple Words
When you pool studies in a meta-analysis, their results never line up perfectly. Heterogeneity measures how much of that scatter reflects real differences in the underlying effect rather than chance. Cochran’s Q tests whether any heterogeneity exists; I² expresses it as a percentage of total variation; tau² estimates the actual between-study variance on the effect scale.
These three numbers answer different questions. Q gives a yes/no signal but depends heavily on the number of studies. I² is easy to compare across analyses but says nothing about absolute size. tau² captures the real spread of true effects and feeds directly into a random-effects model. Reading them together is what tells you whether a single pooled estimate is meaningful.
When to Use Heterogeneity Statistics
Report heterogeneity whenever you combine studies. A low I² with a non-significant Q supports a pooled estimate; a high I² warns that the studies may be measuring genuinely different effects, and a single summary number could mislead. tau² is essential when you fit a random-effects model, since it determines how much each study is shrunk toward the mean.
Use these statistics to decide what to do next, not just to describe the data. A high I² should prompt subgroup analysis or meta-regression to find the source of variation. Always pair them with the pooled effect size and its confidence interval. Building the full pooled analysis? Use our meta-analysis calculator.
Expected format: Studies: Label, Effect, LowerCI, UpperCI (one per line)
Drop a CSV here or click to choose. Parsed in your browser: nothing is uploaded.
Expected format: Studies: Label, Effect, LowerCI, UpperCI (one per line)
library(meta)
studlab <- c({meta_studlab})
TE <- c({meta_te})
lower <- c({meta_lower})
upper <- c({meta_upper})
seTE <- (upper - lower) / (2 * 1.96) # SE from the 95% CI, as the calculator does
m <- metagen(TE, seTE, studlab = studlab, sm = "SMD",
common = {meta_common}, random = {meta_random}, method.tau = "DL")
summary(m) # pooled effect, Cochran's Q, I2, tau2User guide
When to use. Pool effect sizes across studies and quantify heterogeneity (I-squared).
Assumptions. Studies are clinically and methodologically comparable enough to combine.
Common mistakes. High I-squared (>75%) signals substantial heterogeneity: interpret the pooled estimate cautiously.
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- DerSimonian R, Laird N. Meta-analysis in clinical trials. Control Clin Trials. 1986;7:177-188.
Worked Examples
Example 1 — Reading I²
Suppose Cochran’s Q = 4.1 on 3 degrees of freedom (non-significant) and I² = 0%. The studies are consistent: almost all variation is sampling error, so a fixed- or random-effects pooled estimate will agree closely and the summary is trustworthy.
Example 2 — High between-study variance
Now suppose Q = 22.5 on 4 degrees of freedom with I² = 82% and a sizeable tau². Most of the scatter is real heterogeneity, not chance. A single pooled number means little here — you would explore subgroups or meta-regression before reporting any summary effect.
Assumptions to Check
The same effect metric across studies. Q, I², and tau² are computed on a single effect scale (for example, log odds ratios or standardised mean differences). Mixing metrics without conversion makes the statistics meaningless.
Reasonable number of studies. With very few studies, tau² is estimated imprecisely and I² has wide uncertainty. Treat heterogeneity values from a handful of studies as rough indicators, not firm conclusions.
Independent study estimates. Each study should contribute one independent effect. Multiple correlated estimates from the same sample inflate apparent precision and distort Q.
Common Mistakes
Reading a non-significant Q as “no heterogeneity”
Q has low power when there are few studies, so a non-significant result does not prove homogeneity. Report I² and tau² alongside it rather than relying on the Q p-value alone.
Treating I² thresholds as hard rules
The 25/50/75% bands for low/moderate/high are rough guides, not cut-offs. A “moderate” I² with a small tau² may be unimportant, while the same I² with a large tau² matters.
Ignoring tau² because I² looks small
I² can appear low simply because studies are large and precise, even when the true effects vary. tau² reports that variation on the effect scale and should not be skipped.
Stopping at the numbers
Heterogeneity statistics describe variation but do not explain it. A high value is a prompt to investigate clinical and methodological differences, not a result to report and move on.
Frequently Asked Questions
What is the difference between I² and tau²?
I² is the proportion of total variation due to heterogeneity, expressed as a percentage; tau² is the estimated variance of the true effects on the original effect scale.
Can I² be 0%?
Yes. An I² of 0% means the observed variation is no more than expected from sampling error alone — the studies are statistically consistent.
Why does I² depend on study size?
Larger studies have smaller sampling error, so a fixed amount of true variation makes up a larger share of the total — raising I² even when tau² is unchanged.
Does the result match R and Stata?
Yes. I² and tau² are derived from Cochran’s Q with the standard DerSimonian-Laird estimator. The calculator displays Cochran’s Q with its degrees of freedom and p-value, I² and tau²; the R command (metagen in the meta package, with method.tau = “DL”) prints the same values.
Related Calculators
References
- Higgins JPT, Thompson SG. Quantifying heterogeneity in a meta-analysis. Stat Med. 2002;21(11):1539–1558. PMID 12111919.
- Higgins JPT, Thompson SG, Deeks JJ, Altman DG. Measuring inconsistency in meta-analyses. BMJ. 2003;327(7414):557–560. PMID 12958120.
- DerSimonian R, Laird N. Meta-analysis in clinical trials. Control Clin Trials. 1986;7(3):177–188.
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