Meta-Analysis Heterogeneity Calculator
Calculate Q, I-squared, and tau-squared online
Events & totals example Means & SDs exampleThis heterogeneity calculator uses your study results to calculate Cochran's Q, degrees of freedom, the Q-test p-value, I-squared (I²), and tau-squared (τ²). Enter at least two independent study estimates addressing a comparable research question. The results appear in the Heterogeneity table, alongside the pooled effect and forest plot.
- Choose the format of your study data and the effect measure.
- Choose the estimator. It sets tau-squared; Q, p and I-squared don't depend on it.
- Check the spread of the studies in the forest plot, then read Q, df, p, I-squared and tau-squared in the Heterogeneity table.
How to calculate heterogeneity for your studies
- Select Effect sizes if you have an estimate with its standard error or 95% confidence interval for each study. Choose the matching effect measure.
- Select Standard error or 95% CI, then enter one study per row. Import or paste your data into the table above, then assign the study-label, estimate, and uncertainty columns.
- Correct any flagged values, or exclude studies with the table filter. Results require at least two valid, included studies.
- Q, df, p, I-squared, and tau-squared appear in the Heterogeneity table below the model comparison.
What inputs are supported?
You can also select Events & totals for two-group binary data, Means & SDs for two-group continuous data, or Correlations for Pearson's r and sample size. The calculator derives each study's effect estimate and sampling variance before computing heterogeneity. Do not mix different effect measures in one analysis.
For precomputed OR, RR, or HR values, enter the natural log ratio with its log-scale standard error or the natural logs of its 95% confidence limits. Limits can only be converted to a standard error if they come from a normal-approximation interval that is symmetric on the analysis scale. If you only have Q and degrees of freedom, this study-data calculator does not accept those as inputs. Q and df alone are insufficient to recover tau-squared without information about study weights.
Which heterogeneity statistics will I get?
| Output | Meaning in this calculator |
|---|---|
| Cochran's Q | Weighted squared deviations from the fixed-effect pooled estimate, using inverse sampling-variance weights. |
| df | Number of included studies minus one. |
| p | Q-test p-value from a chi-squared reference distribution. It tests compatibility with a common true effect, not whether the pooled effect is zero. |
| I-squared (%) | Estimated percentage of variability in observed effects attributable to heterogeneity rather than sampling error. |
| Tau-squared | Estimate of between-study variance from the selected random-effects estimator, REML (default) or DerSimonian-Laird, in squared units of the analysis scale. |
For Q greater than zero, I-squared is max(0, (Q - df) / Q) * 100.
This calculator reports I-squared as zero when Q is zero. Tau-squared is also
constrained to be non-negative. Switching between fixed and random effects does not
change these heterogeneity statistics for the same included studies and effect measure.
Tau-squared depends on the selected estimator; Q, df, p, and I-squared do not.
Change it under Estimator; the setting applies to both models.
The Hartung-Knapp adjustment changes pooled inference,
not Q, I-squared, or tau-squared.
How should I use the results?
I-squared is not the percentage of studies that disagree, nor the size of the differences between true effects. A value of zero or a nonsignificant Q test does not establish identical true effects, especially with few studies. Avoid using fixed I-squared cutoffs as an automatic rule for selecting a model or excluding studies.
Tau-squared is calculated on the log scale for ratios and on the Fisher's z scale for correlations. Its numerical size cannot be compared directly across different effect scales. Consider it alongside the forest plot, study designs, populations, and outcomes. For random effects, the 95% prediction interval in Pooled results shows what the estimated heterogeneity means on the effect scale. It assumes normally distributed true effects on the analysis scale and can be unreliable with few studies. This calculator does not identify the cause of heterogeneity or perform subgroup analysis or meta-regression.
When reporting results, include the number of studies, effect measure, Q with df and p, I-squared as a percentage, and tau-squared with its estimator and analysis scale. Use export / import above the table to save your data as Excel or .numiqo. The full calculator guide documents pooling methods and continuity corrections; the Cochrane Handbook, Chapter 10 provides further guidance on assessing heterogeneity.