How to use it
- Type the values of each group, separated by commas or spaces.
- Put a semicolon or a new line between groups.
- Read F and the p-value. Compare p with your α.
How it works
The total variation splits into two parts. SSB = Σ nᵢ(x̄ᵢ − x̄)² measures how far the group means are from the grand mean. SSW = Σ (x − x̄ᵢ)² measures the spread inside each group. Dividing by their degrees of freedom (k − 1 and N − k) gives the mean squares, and F is their ratio. The p-value is the upper tail of the F distribution with those degrees of freedom. Eta squared is SSB / (SSB + SSW).
Worked example
Groups 6, 8, 4, 5, 3, 4; 8, 12, 9, 11, 6, 8; 13, 9, 11, 8, 7, 12 have means 5, 9 and 10 and a grand mean of 8.
- SSB = 6 × (9 + 1 + 4) = 84, SSW = 16 + 24 + 28 = 68
- Degrees of freedom: 2 and 15, so MSB = 42 and MSW ≈ 4.533
- F ≈ 9.265 and p ≈ 0.0024
Tips
- With two groups, ANOVA gives the same p-value as a pooled two-sided t-test (F = t²).
- A significant F does not tell you how large the difference is. Look at eta squared and the group means.