F-Distribution Calculator
df₁ (numerator)
df₂ (denominator)
F statistic
✓F-Distribution Result
Critical Value α=0.05 (approx)
3.33
F=3.33 ≤ 3.33 → Fail to reject H₀
The F-distribution arises in statistical tests that compare variances or mean squares, such as ANOVA and regression analysis. The F-statistic is the ratio of two chi-squared distributions divided by their degrees of freedom.
- 1F = (s₁²/σ₁²) / (s₂²/σ₂²)
- 2Degrees of freedom: df₁ (numerator) and df₂ (denominator)
- 3If F > critical value: reject H₀ at chosen α
- 4F-test used in ANOVA, regression significance
F=3.5, df₁=3, df₂=20, α=0.05=Critical value ≈ 3.10; F > critical, reject H₀
F=1.2, df₁=5, df₂=10=Fail to reject H₀ — not significant
| df₁/df₂ | 5 | 10 | 20 | ∞ |
|---|---|---|---|---|
| 1 | 6.61 | 4.96 | 4.35 | 3.84 |
| 3 | 5.41 | 3.71 | 3.10 | 2.60 |
| 5 | 4.39 | 3.33 | 2.71 | 2.21 |
| 10 | 3.33 | 2.98 | 2.35 | 1.83 |
References
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