# 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