How to use the ANOVA Calculator
- 1. Enter groupsOne group per line: a name, a colon and its values.
- 2. Choose αPick the significance level for the decision.
- 3. Run ANOVASee the ANOVA table, group means and SDs, η² and the decision.
How one-way ANOVA works
ANOVA compares variation between group means with variation within groups. The between-groups sum of squares (SSB) adds up each group's size times the squared gap between its mean and the grand mean. The within-groups sum of squares (SSW) adds each value's squared distance from its own group mean. Dividing each by its degrees of freedom (k − 1 and N − k) gives mean squares, and F = MSB ÷ MSW. A large F means the groups differ more than chance would explain. The p-value comes from the F distribution, and η² = SSB ÷ SST is the share of variation explained by group membership.
Worked example
Three teaching methods, each tested on 10 students: Method A averages 82, B 73.5 and C 88.5. SSB = 1131.67 on 2 df and SSW = 309 on 27 df, so MSB = 565.833, MSW = 11.4444 and F(2, 27) = 49.442. The p-value is 9.415 × 10⁻¹⁰, far below 0.05, so at least one method's mean differs. η² = 0.7855: about 79% of the variation in scores is explained by the method.
Before you trust the result
- ANOVA assumes independent observations, roughly normal data within each group and similar variances (check the SDs).
- A significant F says some means differ, not which ones; follow up with a post-hoc test such as Tukey's HSD.
- F and p match SciPy's f_oneway, checked on 40 random datasets.
Frequently asked questions
Can groups be different sizes?
Yes. One-way ANOVA handles unequal group sizes; each group needs at least two values.
Is ANOVA with two groups the same as a t-test?
Yes. With two groups F equals t² from a pooled-variance t-test, and the p-values match.
Is the ANOVA calculator free?
Yes. You can open the ANOVA calculator and enter everything without signing up. When you run an ANOVA for the first time, we ask once for your name and WhatsApp number; after that it, and every other Uncodemy tool, opens straight away.