About ANOVA Calculator
This ANOVA calculator is free, needs no sign-up and runs in your browser, so your data is never uploaded. It runs a one-way analysis of variance on two or more groups and gives the full ANOVA table with sums of squares, degrees of freedom, mean squares, F, the p-value and the effect size η².
Paste the groups as columns from Excel or Google Sheets, with the group names in the first row. Groups can have different sizes: leave the empty cells blank. When F is significant, the Tukey HSD table shows which pairs of groups differ, with the q statistic and an adjusted p-value for every pair.
Group statistics and box plots are drawn beside the table, so you can see the spread and the overlap that the F test is judging.
How to use ANOVA Calculator
- Paste your data with one group per column. A text first row names the groups. Use "Groups in rows" if your groups run across the page.
- Choose the significance level α, usually 0.05.
- Read the ANOVA table: F is the ratio of between-group to within-group variance, and p says how surprising that ratio is if all group means were equal.
- If p is below α, read the Tukey HSD table to see which pairs of groups differ.
- Check the group statistics and the box plots. Very different spreads or heavy outliers weaken the test.
- Copy the summary line for your report.
Features
- One-way ANOVA table with SS, df, MS, F and p.
- Effect size η², the share of the total variance that is between groups.
- Tukey HSD post-hoc test for every pair, with Tukey-Kramer for unequal group sizes.
- Group sizes, means and standard deviations.
- Box plots by group with whiskers and outliers.
- Paste columns straight from a spreadsheet, with blank cells for uneven groups.
- Plain-English reading of the result.
- Three bundled examples to try.
The one-way ANOVA formulas
ANOVA splits the total variation into the part between the group means and the part within the groups. F compares the two after dividing each by its degrees of freedom. If all group means were equal, F follows an F distribution with k - 1 and N - k degrees of freedom.
Tukey HSD compares every pair of means using the studentized range distribution, which keeps the overall error rate at α across all the comparisons.
SSB = Σ n_i (mean_i − grand mean)²
SSW = Σ Σ (x − mean_i)²
F = (SSB / (k − 1)) / (SSW / (N − k))
eta² = SSB / (SSB + SSW)
q = |mean_i − mean_j| / sqrt((MSW / 2)(1/n_i + 1/n_j))Worked examples
Three methods with 6 scores each gives F(2, 15) = 9.265, p = 0.002
SS between = 84, SS within = 68, η² = 0.553. The means are 5, 9, 10.
Tukey HSD for the same data gives Method A vs Method B: p = 0.014; Method A vs Method C: p = 0.003; Method B vs Method C: p = 0.701
Pairs with p below 0.05 are different at the 5% level, with the error rate controlled across all three comparisons.
Layout of the ANOVA table
| Source | SS | df | MS | F |
|---|---|---|---|---|
| Between groups | SSB | k - 1 | SSB / (k - 1) | MSB / MSW |
| Within groups | SSW | N - k | SSW / (N - k) | |
| Total | SSB + SSW | N - 1 |
Reading eta squared
| η² | Effect |
|---|---|
| About 0.01 | Small |
| About 0.06 | Medium |
| 0.14 or more | Large |
Good to know
What ANOVA assumes
The observations are independent, each group is roughly normal, and the groups have similar variances. ANOVA is fairly forgiving when group sizes are equal. This calculator shows standard deviations and box plots so you can look at the assumptions, but it does not run a Levene, Bartlett or normality test. With strongly unequal variances or skewed data, a Welch ANOVA or a Kruskal-Wallis test is safer.
What it does not do
It handles one factor only: no two-way ANOVA, no repeated measures and no covariates. Between 2 and 12 groups are accepted. A significant F tells you that some mean differs, not which one: use the Tukey table for that.
Privacy: how it works
- Everything is calculated by code running in your browser tab. Your data is not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- With only two groups, ANOVA gives the same p-value as a two-sided t test with equal variances, and F equals t squared.
- Do not run many separate t tests on the same groups. The chance of a false positive grows, which is the problem Tukey HSD solves.
- Report F with both degrees of freedom, the p-value and η², for example F(2, 15) = 9.26, p = 0.002, η² = 0.55.
- Make sure each column is a different group of independent people or items, not the same people measured repeatedly.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your data are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your data are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What does one-way ANOVA test?
It tests whether three or more group means are all equal. The null hypothesis is that they are; a small p-value is evidence that at least one group mean differs.
What is a good p-value for ANOVA?
Below your chosen α, which is usually 0.05. That means the differences between group means are larger than chance variation would normally produce.
What is Tukey HSD?
A post-hoc test that compares every pair of group means after a significant ANOVA while keeping the overall false positive rate at α.
Can groups have different sizes?
Yes. Leave the empty cells blank. The F test handles unequal sizes and the post-hoc test automatically becomes Tukey-Kramer.
What is eta squared?
The proportion of the total variation that lies between the groups. An η² of 0.55 means the group explains 55% of the variation.
Why is my result not significant when the means look different?
Small samples or large spread inside the groups make differences hard to tell from chance. The box plots show how much the groups overlap.