Statistics / Tests
One-Way ANOVA Calculator
Test whether three or more group means differ with a one-way analysis of variance: paste each group on its own line and get F, the p-value, η², the ANOVA table, and each group's mean and SD.
One-Way ANOVA Calculator: ANOVA splits the total variation into variation between group means and variation within groups. F is the between-group mean square divided by the within-group mean square, with k − 1 and N − k degrees of freedom; the p-value comes from the F distribution. For the three example groups, F = 22.68 and p = 0.000016. η² is the share of total variation that lies between groups. Runs 100% locally in your browser with zero server file uploads.
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| Source | SS | df | MS | F |
|---|---|---|---|---|
| Between groups | 4.4007 | 2 | 2.2003 | 22.6795 |
| Within groups | 1.6493 | 17 | 0.097 |
| Group | n | Mean | SD |
|---|---|---|---|
| 1 | 8 | 5.4875 | 0.4016 |
| 2 | 7 | 4.9143 | 0.241 |
| 3 | 5 | 6.14 | 0.2074 |
Significant at the 5% level (p < 0.05): the result would be unlikely if there were no real difference.
One-way analysis of variance tests whether several group means are all equal, by comparing the variation between groups with the variation within them: F = MS between ÷ MS within. A small p-value says at least one mean differs, not which; follow up with pairwise tests and a correction such as Tukey's or Bonferroni's. It assumes independent observations, roughly normal data, and similar variances.
Worked example
Three groups of plant heights, means 5.49, 4.91, and 6.14, with similar spreads: F(2, 17) = 22.68 and p < 0.0001, so the groups do not share one mean. η² = 0.73 means most of the variation lies between the groups.
For just two groups, the t-test calculator gives the same answer and also handles unequal variances.
Effect size
η² of about 0.01 is usually called small, 0.06 medium, and 0.14 large, following Cohen's guidelines; they are rough labels, so interpret them in the context of your field.
For categorical outcomes instead of measurements, use the chi-square calculator.
How to use it
- Paste each group's values on its own line.
- Read the F statistic, its degrees of freedom, the p-value, and η².
- Check the ANOVA table and the group summaries.
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Frequently asked questions
What does a significant ANOVA tell me?
That at least one group mean differs from the others, not which one. Follow up with pairwise comparisons corrected for multiple testing, such as Tukey's HSD.
Can I use ANOVA with two groups?
Yes: with two groups it is equivalent to Student's t-test, with F = t².
What if the variances differ a lot?
Welch's ANOVA, which does not assume equal variances, is safer; this calculator runs the classic one-way ANOVA.
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