One-Way ANOVA Calculator: F-Test, p-Value & Table

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Formula at a glance

ANOVA Calculator: F statistic — F = MS_between / MS_within. Example: Three teaching methods → F statistic: 0.2042007 — How the ANOVA Calculator works: F statistic — F = MS_between / MS_within

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📘 About the One

One-way analysis of variance (ANOVA) tests whether several group means are all equal — for example the scores of students taught by three methods, or the yield of four fertilisers. It compares the variation between the group means with the variation within the groups; a large ratio F means the groups really differ.

Paste each group’s values. The calculator gives the ANOVA table (sums of squares, degrees of freedom, mean squares), F, the p-value, the critical F, the η² effect size and each group’s mean and SD. A significant result says at least one mean differs — a post-hoc test shows which.

🧮 Formula

F statistic

F = MS_between / MS_within

Between groups

SS_B = Σ nᵢ(x̄ᵢ − x̄)², df = k − 1

Within groups

SS_W = ΣΣ (x − x̄ᵢ)², df = N − k

✏️ Worked examples

Three teaching methods

You enter
Group 1	85, 86, 88, 75, 78, 94, 98
Group 2	91, 92, 93, 85, 87, 84, 82
Group 3	79, 78, 88, 94, 92, 85, 83
Significance level α	0.05 (95%)

You get
F statistic	0.2042007
p-value	0.817161
Decision	Not significant at α = 0.05 — do not reject the null hypothesis (p = 0.817161 ≥ 0.05)
Critical F at α = 0.05	3.55456
Effect size η²	0.02219 (2.22% of variation is between groups)
Group 1 mean (n = 7)	86.285714 · SD 8.13868
Group 2 mean (n = 7)	87.714286 · SD 4.30946
Group 3 mean (n = 7)	85.571429 · SD 6.13344

F = 0.2042007, p = 0.817161.

Clearly different groups

You enter
Group 1	4, 5, 6, 5
Group 2	8, 9, 7, 8
Group 3	12, 11, 13, 12
Significance level α	0.05 (95%)

You get
F statistic	74
p-value	0.000002585
Decision	Significant at α = 0.05 — reject the null hypothesis (p = 0.000002585 < 0.05) — at least one group mean differs
Critical F at α = 0.05	4.25649
Effect size η²	0.9427 (94.3% of variation is between groups)
Group 1 mean (n = 4)	5 · SD 0.816497
Group 2 mean (n = 4)	8 · SD 0.816497
Group 3 mean (n = 4)	12 · SD 0.816497

F = 74, p = 0.000002585.

🧭 How to use this calculator

What you enter

Group 1Separate numbers with commas, spaces or new lines.
Group 2
Group 3
Group 4 (optional)
Group 5 (optional)
Group 6 (optional)
Significance level α

What you get

F statistic
p-value
Decision
Critical F at α = 0.05
Effect size η²
Group 1 mean (n = 7)
Group 2 mean (n = 7)
Group 3 mean (n = 7)

❓ Frequently asked questions

Why not just do several t-tests?

Each extra test adds a chance of a false positive. ANOVA tests all groups at once at your chosen α.

What does the F value mean?

How many times larger the variation between group means is than the variation inside groups. F near 1 suggests no real difference.

What are the assumptions?

Independent observations, roughly normal data in each group and similar variances.

What people are saying

★★★★★

Anonymous · 13 Nov 2026

F One-Way ANOVA Calculator