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One-Way ANOVA Calculator

Test whether the means of 2 to 10 independent groups differ. Paste one group per line and get the full ANOVA table (sums of squares, degrees of freedom, mean squares, F and p-value), effect sizes, group statistics and every step of the working.

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2 to 10 groups. Optional name before a colon. Separate values with spaces, commas or semicolons. Groups may have different sizes.

Enter your values to see the result.
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How to use the One-Way ANOVA Calculator

  1. Enter one group per line. Values can be separated by spaces, commas or semicolons; you may start a line with a name and a colon.
  2. Choose α (0.05 by default).
  3. Click Calculate or just type: results update instantly.
  4. Read F and the p-value. If p is below α, at least one group mean differs from the others.
  5. Check the effect size and group summary, then copy the results or download the tables as CSV.

One-way ANOVA formulas

SourceSum of squaresdfMean squareF
Between groupsSSB = Σ nᵢ (x̄ᵢ − x̄)²k − 1MSB = SSB ÷ (k − 1)MSB ÷ MSW
Within groupsSSW = Σᵢ Σⱼ (xᵢⱼ − x̄ᵢ)²N − kMSW = SSW ÷ (N − k)
TotalSST = Σ (xᵢⱼ − x̄)² = SSB + SSWN − 1

Here k is the number of groups, nᵢ and x̄ᵢ the size and mean of group i, N the total number of values and x̄ the grand mean. The p-value is the upper-tail area of the F distribution with (k − 1, N − k) degrees of freedom beyond the observed F.

Reading the result

  • p < α: reject the null hypothesis; the group means are not all equal. Follow up with a post-hoc test (Tukey HSD, Bonferroni-corrected t-tests) to see which pairs differ.
  • p ≥ α: the data do not show a difference between the means. This is not proof that the means are equal; small samples have little power.
  • Effect size: report η² or ω² alongside F and p, e.g. “F(2, 15) = 15.63, p < .001, η² = .68”.
η² (eta squared)Conventional label
about 0.01Small
about 0.06Medium
0.14 or moreLarge

Frequently asked questions

What does a one-way ANOVA test?

It tests the null hypothesis that all group means are equal (μ₁ = μ₂ = … = μₖ) against the alternative that at least one differs. It compares the variation between group means with the variation inside the groups.

How is the F statistic calculated?

F = MSB ÷ MSW, where MSB = SSB ÷ (k − 1) is the between-group mean square and MSW = SSW ÷ (N − k) is the within-group mean square. SSB = Σ nᵢ(x̄ᵢ − x̄)² and SSW is the sum of squared deviations of each value from its own group mean.

How do I interpret the p-value?

The p-value is the probability of an F at least this large if all population means were equal. If p < α (usually 0.05) the result is significant: at least one mean differs. ANOVA does not say which groups differ; use a post-hoc test such as Tukey's HSD for that.

What are the assumptions of one-way ANOVA?

Independent observations, roughly normal data within each group (less critical with larger samples), and similar variances across groups. If the largest standard deviation is more than about twice the smallest, especially with unequal group sizes, Welch's ANOVA is safer.

What is eta squared?

Eta squared (η² = SSB ÷ SST) is the share of the total variance explained by group membership. Common rough benchmarks are 0.01 small, 0.06 medium and 0.14 large. Omega squared (ω²) is a less biased version for estimating the population effect.

Is ANOVA with two groups the same as a t-test?

Yes. With two groups the one-way ANOVA F equals the square of the pooled two-sample t statistic, and the p-values are identical.

Is my data uploaded?

No. All calculations run in your browser; nothing you paste is sent anywhere.

Are all the tools on FreeToolCabin tested for quality and accuracy?

Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.

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