Pooled variance

Pooled variance is a weighted average of two sample variances, combined using each sample's degrees of freedom, used when a two-sample t-test assumes both populations share equal variance. It is not a simple average.

ByHoang TruongUpdated July 11, 2026

See it move

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Line A samples 10 shifts with variance 16; Line B samples 8 shifts with variance 25. Pooled variance weights each by degrees of freedom: [(10 − 1) × 16 + (8 − 1) × 25] ÷ (10 + 8 − 2) = (144 + 175) ÷ 16 = 319 ÷ 16 = 19.9375, not the plain average of 16 and 25.

Where it fits

SubjectData Analysis & StatisticsAdvancedTopicCommon Significance TestsAdvanced

The formula

LaTeX

s_p^2 = \dfrac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}

Variables

$n_{1}$: Size of sample 1 (count)
$s_{1}^{2}$: Variance of sample 1
$n_{2}$: Size of sample 2 (count)
$s_{2}^{2}$: Variance of sample 2

Combines two sample variances into one pooled estimate, weighted by each sample's degrees of freedom, for use in a two-sample t-test that assumes equal population variances.