ANOVA calculator
When you compare three or more groups, running repeated t-tests inflates the false-positive rate. ANOVA tests all the means at once by dividing the between-group variation by the within-group variation, and this calculator reports the F ratio, the p-value and the share of variance explained.
| Source | SS | df | MS |
|---|---|---|---|
| Between groups | 24.00 | 2 | 12.00 |
| Within groups | 6.00 | 6 | 1.00 |
| Total | 30.00 | 8 | — |
A large F means the group means differ by more than the within-group noise explains.
MS_between / MS_within · Signal divided by noise.
SS_between / SS_total · Share of variance explained by the groups.
1 − F_cdf(F; df1, df2) · Probability of a ratio this large by chance.
A clear path from inputs to results.
When you compare three or more groups, running repeated t-tests inflates the false-positive rate. ANOVA tests all the means at once by dividing the between-group variation by the within-group variation, and this calculator reports the F ratio, the p-value and the share of variance explained.
How to use
- Enter three observations for each of three groups.
- Read the F ratio and p-value.
- Check eta squared for the size of the effect.
- Look at the group standard deviations to judge noise.
The formula
Reference: One-way analysis of variance; F distribution with (k−1, N−k) degrees of freedom.
Worked example
Three groups of three observations
- Group 1: 10, 11, 12.
- Group 2: 12, 13, 14.
- Group 3: 14, 15, 16.
- 1
Group means 11, 13, 15; grand mean 13.
- 2
SS between: 3 × (4 + 0 + 4) = 24.
- 3
SS within: 2 + 2 + 2 = 6.
- 4
MS between 12, MS within 1, F = 12.
- 5
p = 0.008; eta squared 0.80.
F 12.00 · p 0.008 · 80% of variance explained.
Interpreting the result
F is a signal-to-noise ratio: between-group spread divided by within-group spread. A large F with a small eta squared means the effect is real but small relative to total variation — statistically significant is not the same as practically important.
Assumptions & limitations
- Independent observations.
- Normally distributed residuals.
- Equal variance across groups.
- Three observations per group in this form.
Frequently asked questions
Why not three t-tests?
Each test carries a 5% false-positive risk, so three tests push the family error rate to about 14%.
What if the data are not normal?
Use a Kruskal–Wallis test instead.
What does eta squared mean?
The share of total variance explained by the grouping.
Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.