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One-Way ANOVA Calculator
Determine if there are statistically significant differences between the means of three or more independent groups. Build your groups, enter your data, and instantly generate an ANOVA summary table.
How to use this calculator
- Set your groups: The calculator defaults to 3 groups, but you can use the + Add Group and – Remove Group buttons to match your experimental design.
- Enter your data: Paste your raw data into each group’s text box. Groups do not need to have the exact same number of data points (unequal sample sizes are fully supported).
- Set your parameters: Choose your significance level ($\alpha$). If you aren’t sure, 0.05 is the standard default for most research.
One-Way ANOVA
Test for differences between three or more group means.
| Source of Variation | SS (Sum of Squares) | df (Degrees of Freedom) | MS (Mean Square) | F-Statistic | P-Value |
|---|---|---|---|---|---|
| Between Groups | 0 | 0 | 0 | 0 | 0 |
| Within Groups (Error) | 0 | 0 | 0 | – | – |
| Total | 0 | 0 | – | – | – |
*Technical note: P-values are calculated using a JavaScript implementation of the regularised incomplete beta function mapping to the F-distribution.
Understanding Your Results
An Analysis of Variance (ANOVA) tests the null hypothesis that all group means are equal. It does this by comparing the variance between the groups to the variance within the groups.
- F-Statistic ($F$): The ratio of the Mean Square Between to the Mean Square Within. An F-statistic close to 1 suggests the group means are equal. A larger F-statistic suggests that at least one group mean is significantly different from the others.
- Degrees of Freedom ($df$): You will see two $df$ values. Between $df$ is based on the number of groups ($k - 1$). Within $df$ is based on your total sample size minus the number of groups ($N - k$).
- P-Value: The probability of obtaining an F-statistic this large if the null hypothesis (that all groups are identical) were true.
- Conclusion: If the p-value is less than your chosen significance level, the result is statistically significant. Note: ANOVA is an omnibus test. A significant result tells you that at least one group is different, but it does not tell you which specific groups differ from each other. (That requires a post-hoc test like Tukey's HSD).