One-Way ANOVA Calculator
Compare the means of three or more groups at once. Paste each group’s data on its own line and get the full ANOVA table — sums of squares, degrees of freedom, mean squares, the F statistic, p-value and η² — matching R’s aov().
How to use it
What ANOVA does
A t-test compares two groups; one-way ANOVA compares three or more at once, in a single test that keeps your false-positive rate under control. It asks: is there any difference among the group means?
- A significant F (small p) means at least one group differs — but not which. Follow up with a post-hoc test such as Tukey’s HSD that corrects for multiple comparisons.
- η² (eta-squared) is the effect size: the proportion of total variance explained by the grouping.
- ANOVA assumes roughly normal residuals and similar variances across groups. If variances differ badly, use Welch’s ANOVA; if normality fails, the Kruskal–Wallis test.
Don’t run many pairwise t-tests instead of one ANOVA — that inflates your error rate.
Do it in R
y <- c(g1, g2, g3)
grp <- factor(rep(1:3, c(length(g1), length(g2), length(g3))))
summary(aov(y ~ grp))Full walkthrough: One-way ANOVA in R with post-hoc tests.
FAQ
Frequently asked questions
The F-test is significant — which groups differ?
ANOVA only tells you a difference exists somewhere. Run a post-hoc test (Tukey’s HSD is common) to find which specific pairs differ, with the multiple-comparison correction built in.
Why not just run t-tests between every pair?
Each test carries a 5% false-positive risk, so several tests push your overall error rate well above 5%. ANOVA asks the “any difference?” question once, at the right error rate.
Comparing groups in your own data — with assumptions checked and a report written? That’s our work.