Enter Cochran's Q and the number of studies to get I² and H² with their interpretation; with the study table (yi, SEi), τ² and the prediction interval too.
Heterogeneity is the variability between the results of the studies you are combining, over and above what sampling error alone would produce. It decides whether the pooled effect can be read as a single number or has to be read as a range, and whether a fixed-effect or a random-effects model is called for. The calculator returns Cochran’s Q, I², H², tau² and the 95% prediction interval.
Cochran’s Q: tests the null hypothesis that all studies share one population effect. A large value means the observed variability exceeds what chance would give.
Higgins and Thompson’s I²: the percentage of total variability due to real heterogeneity rather than sampling error.
tau² (tau squared): the between-study variance on the effect scale. tau² = 0 implies perfect homogeneity; larger values mean the true effect varies substantially across studies.
Prediction interval: unlike the confidence interval, which expresses uncertainty about the mean, it estimates the likely range of the true effect in a new study. It is especially useful when heterogeneity is high.
| I² | Heterogeneity | What it implies |
|---|---|---|
| < 25% | Low | Between-study variability is small; results are fairly homogeneous. |
| 25–50% | Moderate | Worth exploring possible moderators. |
| 50–75% | High | Substantial heterogeneity: random effects and subgroup analyses are advisable. |
| > 75% | Very high | The weighted mean should be read with caution; moderator analysis is recommended. |
If I² is low (below 25%) and Q is not significant (p > .10), a fixed-effect model is reasonable. Otherwise the random-effects model captures the real variability better and produces more realistic confidence intervals.
Higgins, J. P. T., & Thompson, S. G. (2002). Quantifying heterogeneity in a meta-analysis. Statistics in Medicine, 21(11), 1539–1558. DerSimonian, R., & Laird, N. (1986). Meta-analysis in clinical trials. Controlled Clinical Trials, 7(3), 177–188.