One-Way ANOVA Calculator
Run a one-way ANOVA test on up to four groups.
Calculate the F-statistic and p-value to determine if group means differ significantly.
One-Way ANOVA (Analysis of Variance)
One-way ANOVA tests whether the means of three or more independent groups are equal. It answers: “Is at least one group mean significantly different from the others?”
The null hypothesis (H₀): All group means are equal. The alternative hypothesis (H₁): At least one group mean differs.
How it works: partitioning variance:
| Source | Sum of Squares | df | Mean Square | F |
|---|---|---|---|---|
| Between groups | SSB | k − 1 | MSB = SSB/dfB | F = MSB/MSW |
| Within groups | SSW | N − k | MSW = SSW/dfW | |
| Total | SST | N − 1 |
Where k = number of groups, N = total observations.
Formulas:
Grand mean x̄ = (sum of all values) / N
SSB = Σᵢ nᵢ × (x̄ᵢ − x̄)² (between-group variance)
SSW = Σᵢ Σⱼ (xᵢⱼ − x̄ᵢ)² (within-group variance)
F = MSB / MSW
Interpreting the result:
A large F-statistic (and small p-value) suggests at least one group mean is different. The conventional threshold is p < 0.05 for statistical significance. If significant, use a post-hoc test (Tukey, Bonferroni) to find which specific groups differ.
Assumptions:
- Observations are independent
- Residuals are approximately normally distributed
- Groups have similar variances (homoscedasticity)
- If variances differ, use Welch’s ANOVA instead
Enter data as comma-separated numbers per group. Example: Group 1 → 23, 25, 28, 22, 27
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This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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