One-Way ANOVA Calculator
F, p and η² — the last one first.
Work out One-Way ANOVA. F, p and η² — the last one first. Names the misconception directly.
F statistic
21.5556
p = 0.00011 · η² = 0.7823
One-way ANOVA compares the variation between group means against the variation within groups. A large F means the groups are further apart than their internal scatter would explain, and the p-value puts a probability on that under the null hypothesis of equal means. It answers only whether some difference exists, not which groups differ. That takes a post-hoc test — Tukey's HSD is the usual choice — and running individual t-tests between every pair instead is how the false positive rate climbs above the level you thought you were testing at. η² is the effect size, and it is the number worth reading first. It says what share of the total variation group membership accounts for, which is a question the F statistic does not answer at all. The test assumes roughly normal groups with similar variances.
How the One-Way ANOVA Calculator works
One-way ANOVA across two to four groups, with the full sum-of-squares table and η² alongside the F statistic. η² says what share of variation group membership explains, which the F statistic does not answer at all.
Also known as: compare three group means · one way anova online · f test for groups · which groups are different
Frequently asked questions
What does ANOVA test?
Whether the means of several groups differ by more than their internal scatter would explain. A large F means the groups are further apart than chance would predict under the null hypothesis of equal means.
Which groups actually differ?
ANOVA does not say — only that some difference exists. Finding which pairs takes a post-hoc test such as Tukey's HSD, and running individual t-tests between every pair instead inflates the false positive rate.
What is eta squared?
The effect size: the proportion of total variation explained by group membership. It is the number worth reading first, since a significant F with a tiny η² means a real but trivial difference.
What assumptions does ANOVA make?
Roughly normal distributions within groups, similar variances across them, and independent observations. It is fairly robust to the first two with equal group sizes and much less so when sizes are unbalanced.
Why not just run t-tests?
Because each test carries its own false positive risk. Three groups means three pairwise tests, and at 0.05 each the chance of at least one spurious result is over 14% rather than 5%.
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