Pooled variance combines the variability from two or more groups into a single, more reliable estimate — the same estimate a two-sample t-test or one-way ANOVA relies on when it assumes the groups share a common population variance. This calculator computes it from summary variances, standard deviations, or raw data.
How pooled variance works
Pooled variance weights each group's sample variance by its degrees of freedom (n − 1) rather than treating every group equally. A group with 30 observations tells you more about the true population variance than a group with 5 observations, so it should — and does — carry more weight in the combined estimate: sp² = Σ((nᵢ − 1)sᵢ²) / Σ(nᵢ − 1).
This is the same variance estimator used inside a pooled two-sample t-test and, generalized to more than two groups, the mean-square-within (MSW) term of a one-way ANOVA.
Inputs and what they mean
Each group needs a sample size (n ≥ 2, since a single observation has no variance) and either its variance, its standard deviation, or its raw data list. The variance and SD are mathematically related (variance = SD²), so switching tabs simply changes which one you enter directly — the calculator converts internally. Labels are optional and only used to identify groups in the summary.
Limits and edge cases
Pooling assumes the groups' true population variances are actually equal (or close to it) — if one group is dramatically more variable than another, an F-test for equality of variances should be run first, since pooling very different variances can distort a downstream t-test's standard error. Pooled variance also does not test whether the group means differ — for that, pair it with a two-sample t-test or ANOVA using the pooled estimate this calculator produces.