Summary statistics are enough
You do not need the raw observations, only each group's mean, standard deviation, and n.
Tools / ANOVA Calculator
ANOVA Calculator
Compare three or more group means at once. Enter each group's mean, standard deviation, and size to get the F-statistic and p-value.
F = MS between ÷ MS within · df₁ = k − 1 · df₂ = N − k
Enter values to see the result
- 1
Enter each group
Mean, standard deviation, and sample size per group. Leave trailing rows blank if you have fewer than five groups.
- 2
Add more groups if needed
Every group you fill in needs a whole sample size of 2 or more: an undersized one stops the calculation rather than being dropped from it. Leave a row blank to leave it out.
- 3
Read F and the p-value
A small p-value means at least one group mean differs from the others, though not which one.
Why ANOVA instead of several t-tests
Each extra pairwise t-test adds another chance of a false positive. One-way ANOVA asks the question once, across all groups.
Both degrees of freedom shown
Between-groups and within-groups df are reported, which is what you need to write up the result as F(df1, df2).
Controls the error rate
One omnibus test at 5% instead of several pairwise tests each at 5%.
When to run ANOVA
Comparing three or more variants
Average order value across four pricing pages, or satisfaction across three support channels.
Regional or segment comparisons
Test whether average scores differ across offices, plans, or cohorts.
Experiments with several arms
Any design where one factor has more than two levels.
One-way ANOVA
F = MS_between ÷ MS_within · df₁ = k − 1 · df₂ = N − k
MS_between is the variance of the group means around the grand mean, weighted by group size. MS_within pools the variance inside each group. k is the number of groups and N the total observations.
After a significant ANOVA
- The test says at least one mean differs, not which one. Follow up with pairwise comparisons.
- Adjust those follow-up tests for multiple comparisons, for example with a Bonferroni correction.
- ANOVA assumes roughly normal data and similar variances across groups.
- Very unequal group sizes combined with very unequal variances make the F-test unreliable.
Related calculators
Frequently asked questions
What does one-way ANOVA test?
Whether the means of three or more groups are all equal. The null hypothesis is that every group shares the same population mean.
A small p-value means at least one group differs, but the test does not identify which.
How is the F-statistic calculated?
Divide the between-group mean square by the within-group mean square:
F = MS_between ÷ MS_within
Between-group variation is how far each group mean sits from the grand mean, weighted by group size. Within-group variation is the pooled spread inside the groups. A large F means the groups are further apart than their internal noise explains.
Why not just run t-tests on every pair?
Because each test carries its own 5% false positive risk. Three groups means three comparisons and roughly a 14% chance of at least one false positive. Five groups means ten comparisons and about 40%.
ANOVA asks once, then you follow up with corrected pairwise tests only if it is significant.
What do I do after a significant result?
Run post-hoc pairwise comparisons with an adjustment for multiple testing. The t test calculator handles each pair; divide your 0.05 threshold by the number of comparisons for a simple Bonferroni correction.
What are the assumptions?
Independent observations, roughly normal distributions within each group, and similar variances across groups.
ANOVA tolerates mild departures, especially with balanced group sizes. Badly unequal variances combined with unequal n is the case to avoid.
Can I use it with only two groups?
Yes, and it will give the same p-value as a pooled two-sample t-test, since F = t² in that case. The t test calculator is the more natural tool there because it also reports the difference of means.
Are my numbers stored?
No. Everything is calculated locally.
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