Continuous probability distribution
F (Fisher–Snedecor) distribution
X ~ F(d₁, d₂)
The ratio of two scaled chi-squared variables. It is the distribution behind ANOVA and any test that compares two variances or assesses overall regression significance.
Explore it interactivelyKey facts
- Notation
- X ~ F(d₁, d₂)
- Type
- continuous
- Parameters
- d₁ — numerator degrees of freedom; d₂ — denominator degrees of freedom
- Support
- [0, ∞)
- Ratio of two independent χ² variables, each divided by its degrees of freedom
- Mean
- d₂ / (d₂ − 2), for d₂ > 2
- Variance
- 2 d₂² (d₁ + d₂ − 2) / [d₁ (d₂ − 2)² (d₂ − 4)], for d₂ > 4
When to use it
- Analysis of variance (ANOVA)
- Comparing two sample variances
- Overall F-test of a regression