One-Way ANOVA Calculator
This one-way ANOVA calculator tests whether two or more group means differ. Paste each group into its own box to get the between- and within-group sums of squares, the F statistic, a right-tailed p-value, and η² (eta-squared) as a simple effect-size measure.
One-way ANOVA calculator
Paste one group in each box to get the ANOVA table: sums of squares, mean squares, F, and the p-value. Empty boxes are ignored. At least two groups are required.
Working
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One-way ANOVA formulas
SSbetween = Σ ni (ȳi − ȳ)², with dfbetween = k − 1.
SSwithin = Σ Σ (xij − ȳi)², with dfwithin = N − k.
MS = SS / df, and F = MSbetween / MSwithin.
The p-value is P(Fk−1, N−k ≥ F). η² = SSbetween / SStotal.
One-way ANOVA assumes independent observations, roughly normal groups, and similar group variances. With only two groups, the F test is equivalent to a pooled two-sample t-test (F = t²).
Worked example
Group 1: 6, 8, 7, 9, 7. Group 2: 4, 5, 6, 4, 5. Group 3: 8, 9, 10, 8, 9.
The group means are 7.4, 4.8, and 8.8, and the grand mean is 7.0. SSbetween = 41.2 and SSwithin = 10.0, so F = 24.72 with df 2 and 12. The p-value is about 0.000056, and η² is about 0.805. The means are not all the same.
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Frequently asked questions
It tests the null hypothesis that all group means are equal, against the alternative that at least one mean differs. It does not tell you which groups differ; that takes a follow-up comparison.
No. Unequal group sizes are allowed. Each group just needs at least one observation, and you need more observations than groups so that the within-group degrees of freedom are positive.
η² is the share of the total variation that lies between the groups. It is a simple effect-size statistic and should be read with the p-value, not instead of it.
The p-value here is the right tail of the same F distribution used in an F table or a critical F calculator. If F is larger than the critical value at your α, the p-value is smaller than α.
Yes. Once the calculator script is in place, the Add a group button appends another box. You can also leave Group 4 empty if you only have two or three groups.