# 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

S_{p}^{2} = | (n_{1} - 1)S_{1}^{2} + (n₂ - 1)S₂^{2} |

n_{1} + n₂ - 2 |

### Variance of the difference between two means formula

*For independent random variables:*

σ²(X - Y) = σ²(X) + σ²(Y)

S

_{x̄₁ - x̄₂}² = S

_{x̄₁}² + S

_{x̄₂}²

*The variance of the average:*

S_{x̄}² = | S² |

n |

#### Unequal variances formula

S_{x̄₁ - x̄₂}² = | S₁² | + | S₂² | |

n₁ | n₂ |

#### Equal variances formula

*Since the variances are equal:*

S

_{p}² = S₁² = S₂²

S_{x̄₁ - x̄₂}² = ( | S_{p}² | + | S_{p}² | ) |

n₁ | n₂ |

S_{x̄₁ - x̄₂}² = S_{p}²( | 1 | + | 1 | ) |

n₁ | n₂ |