About the ANOVA Calculator
ANOVA Calculator runs a one-way analysis of variance. Paste your data, one group per line, and the page tests whether the groups have the same mean. It gives the full ANOVA table, the sums of squares, degrees of freedom and mean squares between and within the groups, the F statistic, the p-value from the F distribution and the effect size η², together with the count, mean and standard deviation of each group. A small p-value (below 0.05) means at least one group mean differs from the others. It suits school statistics, lab work and quick checks.
Updated October 2026
How to use the ANOVA Calculator
- 1Type or paste each group on its own line, with numbers separated by spaces or commas.
- 2Use at least two groups with at least two values each.
- 3Read the F statistic and the p-value.
- 4Check the ANOVA table and the group summaries.
- 5Copy the result for your report.
The idea of ANOVA
Suppose three classes take the same test. The scores vary from student to student, which is the variation within each class. The class averages also differ, which is the variation between classes. ANOVA asks whether the difference between class averages is larger than you would expect from the ordinary variation among students. If it is, the classes probably differ.
Reading the table
The between-groups sum of squares measures how far each group mean is from the overall mean. The within-groups sum of squares measures how far each value is from its own group mean. Dividing each by its degrees of freedom gives the mean squares, and the ratio MSB / MSW is the F statistic. The p-value is the chance of an F at least as large if all the means were equal.
- Between groups: k − 1 degrees of freedom
- Within groups: N − k degrees of freedom
- F = MS between ÷ MS within
- p < 0.05: the means differ at the 5% level
Good practice
Plot your data first, for example with the Box Plot Maker, to see the spread and outliers. Report the F value, both degrees of freedom, the p-value and the effect size, such as F(2, 12) = 5.43, p = 0.021, η² = 0.47. If ANOVA is significant, follow it up with pairwise comparisons.
Related tools
Work out the p-value directly with the P-Value Calculator, compare two groups with the T-Test Calculator and see how spread out a group is with the Standard Deviation Calculator. The Chi-Square Calculator handles counts instead of measurements.
Features
- Two to twelve groups
- Sum of squares, degrees of freedom, mean squares
- F statistic and exact p-value
- Effect size η²
- Group n, mean and standard deviation
- Private: nothing is uploaded
Frequently asked questions
What does a one-way ANOVA test?
The null hypothesis that all the groups have the same population mean. The alternative is that at least one mean is different.
How do I read the p-value?
If p is below your significance level, commonly 0.05, you reject the null hypothesis and conclude that the means differ. If it is above, you have not found enough evidence of a difference.
What is the F statistic?
The ratio of the variation between the groups to the variation within the groups. A large F means the groups differ more than chance would suggest.
Does ANOVA tell me which groups differ?
No. A follow-up test, such as Tukey's HSD, compares pairs of groups. This calculator gives the overall test only.
What are the assumptions?
The observations are independent, each group is roughly normally distributed and the groups have similar variances. ANOVA is fairly robust when groups are of similar size.
What is η²?
Eta squared, the share of the total variation explained by the group differences. Values around 0.01, 0.06 and 0.14 are often described as small, medium and large.
Can I compare only two groups?
Yes. The result is equivalent to a two-sided t-test (F equals t squared).
Is my data uploaded?
No. The test runs in your browser.