ANOVA Calculator (One-Way)
Compare the means of three or more groups with a one-way ANOVA, with the full ANOVA table.
What a one-way ANOVA tests
Analysis of variance (ANOVA) tests whether the means of three or more groups are all equal. It compares the variation between the group means with the variation inside the groups. If the between-group variation is much larger, the F statistic is large and the p-value is small. Use it instead of running several t-tests, which would raise the chance of a false positive.
Entering your data
- Data tab: type each group on its own line, with the values separated by spaces or commas.
- Summary tab: enter the sample size, mean and standard deviation of 2 to 4 groups. Leave unused groups at 0.
Worked example
Three teaching methods are tried, each with 6 students. The scores are 23, 25, 21, 28, 24, 26 (mean 24.5), 30, 33, 29, 35, 31, 32 (mean 31.67) and 27, 24, 29, 26, 28, 25 (mean 26.5).
| Source | Sum of squares | df | Mean square | F | p |
|---|---|---|---|---|---|
| Between groups | 164.11 | 2 | 82.06 | 17.50 | 0.00012 |
| Within groups | 70.33 | 15 | 4.69 | ||
| Total | 234.44 | 17 |
The result is F(2, 15) = 17.50, p < .001, η² = 0.70, a large effect. At least one method has a different mean. ANOVA does not say which groups differ, so follow a significant result with a post-hoc test such as Tukey’s HSD.
Formulas and assumptions
- SS between = Σ n × (group mean − grand mean)², SS within = Σ (n − 1) × s².
- F = (SS between ÷ (k − 1)) ÷ (SS within ÷ (N − k)).
- Eta squared = SS between ÷ SS total. About 0.01 is small, 0.06 medium and 0.14 large.
- Assumptions: independent observations, roughly normal data in each group and similar variances. With very unequal variances or sample sizes, Welch’s ANOVA is safer. For ordinal or very skewed data, the Kruskal-Wallis test is the alternative.
To look up the critical F value, use the F-table.
How to cite this page
CalcPulse. (2026). ANOVA Calculator. https://calcpulse.com/anova-calculator/
Frequently asked questions
What is a one-way ANOVA?
A test of whether the means of three or more independent groups are equal, using one grouping variable.
Why not use several t-tests?
Each extra test raises the chance of a false positive. ANOVA tests all the groups at once with one overall error rate.
What do I do after a significant ANOVA?
Use a post-hoc test, such as Tukey's HSD, to find which pairs of groups differ.
What is eta squared?
The share of the total variation explained by the groups. It is a measure of effect size.
What are the assumptions of ANOVA?
Independent observations, roughly normal data in each group, and similar variances across groups.
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