One-Way ANOVA Calculator
Paste your groups, one per line, and the calculator runs a one-way analysis of variance. You get the F statistic, its degrees of freedom, the p-value, the critical value, a full ANOVA table, eta squared and omega squared, a table of group means and standard deviations, and pairwise comparisons with Bonferroni adjusted p-values so you can see which groups differ. Groups can have different sizes. Everything runs in your browser.
The group means are not all equal: the differences are larger than chance variation would usually give (F = 4.846, p below 0.05). ANOVA does not say which groups differ, so look at the pairwise comparisons.
| Source | Sum of squares | df | Mean square | F |
|---|---|---|---|---|
| Between groups | 3.7663 | 2 | 1.8832 | 4.846 |
| Within groups | 10.492 | 27 | 0.3886 | |
| Total | 14.258 | 29 |
| Group | n | Mean | Std dev |
|---|---|---|---|
| Control | 10 | 5.032 | 0.58309 |
| Treatment 1 | 10 | 4.661 | 0.79368 |
| Treatment 2 | 10 | 5.526 | 0.44257 |
| Treatment 1 minus Control | -0.371 | p 0.583 |
| Treatment 2 minus Control | 0.494 | p 0.263 |
| Treatment 2 minus Treatment 1 | 0.865 | p 0.0134 |
One-way ANOVA tests whether the means of two or more groups are all equal. It compares the variation between the group means with the variation within the groups: the F statistic is the between-group mean square divided by the within-group mean square, and a large F means the group means are spread out more than the scatter inside the groups would explain. A significant result says at least one mean differs, not which one, so the pairwise table compares each pair using the pooled error with a Bonferroni adjustment. The test assumes independent observations, roughly bell-shaped data in each group and similar spread across groups. The example is R's PlantGrowth data, which gives F = 4.846 and p = 0.0159. Everything is worked out in your browser.
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Student ToolsAbout the One-Way ANOVA Calculator
A one-way ANOVA asks whether several group means are all equal. It splits the total variation into the part between the group means and the part within the groups. The between-group sum of squares measures how far each group mean is from the overall mean, weighted by group size, and the within-group sum of squares measures the scatter around each group's own mean. Dividing each by its degrees of freedom, k minus 1 between and N minus k within, gives the mean squares, and the F statistic is the ratio of between to within. A large F means the means are spread out more than the scatter in the groups would explain. The p-value comes from the F distribution, computed from the regularized incomplete beta function. As a check, R's PlantGrowth data, three groups of ten plant weights, give F = 4.846 with 2 and 27 degrees of freedom and p = 0.01591, the same figures as R's aov function. With only two groups ANOVA gives the same answer as a pooled two-sample t-test, with F equal to t squared. A significant F says at least one mean differs, not which, so the pairwise table uses the pooled error with a Bonferroni adjustment. Eta squared is the share of the total variation that lies between groups. The test assumes independent observations, roughly normal data in each group and similar variances.
What does a one-way ANOVA test?▾
It tests whether the means of three or more groups are all the same. The null hypothesis is that they are equal, and a small p-value is evidence that at least one group mean differs from the others.
Why not just run several t-tests?▾
Each test has a chance of a false positive, and with many comparisons those chances add up. ANOVA tests all the groups at once with a single, controlled error rate, and follow-up comparisons are then adjusted for the number of pairs.
What does the F statistic mean?▾
It is the variation between the group means divided by the variation within the groups. If the group means were really equal, F would usually be near 1. A value well above 1, and above the critical value, points to real differences.
What do I do after a significant ANOVA?▾
Look at the pairwise comparisons to see which groups differ, and report an effect size such as eta squared. The calculator adjusts each pairwise p-value for the number of comparisons with the Bonferroni method.
Is my data uploaded?▾
No. The calculation runs in your browser and nothing you enter is sent anywhere.