Meta-Analysis Calculator

A meta-analysis is a statistical technique that combines the results of multiple independent studies addressing the same research question. By pooling data, it increases statistical power, resolves conflicts between studies, and produces a more precise overall estimate of the true effect size than any single study could provide.

A fixed-effect model assumes all studies share one true underlying effect and that differences between study results are due only to sampling error. A random-effects model (typically DerSimonian-Laird) assumes the true effect varies across studies and models that between-study variance (τ²). Random-effects is generally preferred when studies come from different populations or settings.

I² quantifies the proportion of total variability in effect estimates due to true between-study heterogeneity rather than chance. Values of 25%, 50%, and 75% are commonly interpreted as low, moderate, and high heterogeneity, respectively. High I² suggests the studies may be measuring different things and a random-effects model is more appropriate.

Cochran's Q is a test statistic for heterogeneity. It is calculated as the weighted sum of squared deviations of each study's effect from the pooled estimate. A statistically significant Q (p < 0.10 is common) indicates that heterogeneity is present beyond what would be expected by chance alone.

This calculator supports standardized mean differences (Cohen's d / Hedges' g), raw mean differences (MD), odds ratios (on the log scale), risk ratios (on the log scale), and correlation coefficients (r). Enter the appropriate pre-computed effect size and its standard error for each study.

The standard error is typically reported in the study's results section or statistical tables. If only a confidence interval is reported, you can back-calculate SE as (upper CI − lower CI) / (2 × z*), where z* is the critical value for your chosen confidence level (e.g., 1.96 for 95%). Some effect-size calculators also compute SE from sample sizes and group statistics.

τ² is the estimated variance of the true effect sizes across studies in a random-effects model. It quantifies how much the true effects differ from study to study. A τ² of 0 indicates no between-study variance (equivalent to a fixed-effect model), while larger values indicate greater heterogeneity.

While there is no strict minimum, meta-analyses with fewer than 3–5 studies may produce unstable estimates, especially for heterogeneity statistics like I² and τ². More studies generally yield more reliable pooled estimates and more meaningful heterogeneity assessments. This calculator supports up to 6 studies; for larger datasets, specialized software such as R (metafor) or RevMan is recommended.