Pooled Variance Calculator
It calculates the combined variance from two groups with equal variances, as well as the standard deviation of the difference between the means. Includes step-by-step calculation
Pooled variance calculator
Calculates the pooled variance for equal variances, and the standard deviation of the difference between two means, for equal variances and for unequal variances.A pooled variance is the sample variance of two or more groups when the variances of all groups are equal.
The sample variance for all the groups is calculated, regardless of the group, since you assume the variances are equal.
Pooled variance formula
| Sp2 = | (n1 - 1)S12 + (n₂ - 1)S₂2 |
| n1 + n₂ - 2 |
Variance of the difference between two means formula
For independent random variables:σ²(X - Y) = σ²(X) + σ²(Y)
Sx̄₁ - x̄₂² = Sx̄₁² + Sx̄₂²
The variance of the average:
| Sx̄² = | S² |
| n |
Unequal variances formula
| Sx̄₁ - x̄₂² = | S₁² | + | S₂² | |
| n₁ | n₂ |
Equal variances formula
Since the variances are equal:Sp² = S₁² = S₂²
| Sx̄₁ - x̄₂² = ( | Sp² | + | Sp² | ) |
| n₁ | n₂ |
| Sx̄₁ - x̄₂² = Sp²( | 1 | + | 1 | ) |
| n₁ | n₂ |