One-Way ANOVA Calculator
Tests whether three or more group means differ by more than chance variation would explain.
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The formula
F = (SS between ÷ (k − 1)) ÷ (SS within ÷ (N − k))
F compares the variation between group means with the variation inside the groups. Eta squared is the share of the total variation that lies between groups.
What to watch out for
With exactly two groups, the F statistic is the square of the pooled t statistic and the p-values match. After a significant result, a post-hoc test such as Tukey’s shows which groups differ.
Frequently Asked Questions
What is the critical F value for 2 and 15 degrees of freedom at 5%?
3.682.
Why not run several t-tests?
Each test carries its own risk of a false positive, so the overall risk grows with the number of tests. ANOVA tests all the groups at once.
What is a worked example?
The three groups filled in above give F = 9.2647, with 2 and 15 degrees of freedom.