How to use this pooled variance calculator
Enter both groups' data above and press Calculate. The pooled result appears with each group's own standard deviation, so you can see how the combination weighted them.
Why pool at all?
Two groups, two sample standard deviations, but a two-sample t-test needs one estimate of the common spread, assuming both groups share a population variance. Pooling builds it: a weighted average of the two variances, weighted by degrees of freedom, so the bigger group's estimate counts for more.
Two classes' test scores. Class A (n = 5): 78, 82, 85, 90, 88, SD ≈ 4.77. Class B (n = 4): 72, 75, 80, 77, SD ≈ 3.37. Pooled variance = [(4 × 22.8) + (3 × 11.33)] ÷ 7 ≈ 17.89, so the pooled standard deviation is sp ≈ 4.23, sitting between the two group SDs, pulled slightly toward the larger class, exactly as designed.
When pooling is legitimate: and when it is not
Pooling assumes the two population variances are genuinely equal. If one group's spread is wildly larger (a common rule: the bigger variance is more than about 4× the smaller), the assumption fails and the honest tool is Welch's t-test, which keeps the variances separate. Check the two SDs on this page before you pool: if they look like siblings, pool away; if they look like strangers, don't.
Frequently asked questions
What is pooled variance used for?
It provides the single variance estimate required by the two-sample t-test and by ANOVA, under the assumption that both populations share a variance.
Why is pooled variance weighted by n − 1?
Each sample variance carries n − 1 degrees of freedom of information. Weighting by degrees of freedom gives larger samples proportionally more influence over the pooled estimate.
When should I not pool variances?
When the group variances are clearly unequal: as a rough guide, when the larger is more than about four times the smaller. Welch's t-test is the safer alternative then.