ANOVA Calculator

In short A one-way ANOVA asks whether several groups could all have come from populations with the same mean. It works by splitting the total variation in two — the part BETWEEN the group means and the part WITHIN the groups — and taking their ratio. The three groups loaded above give F = 38.40 on 2 and 9 degrees of freedom, p = 3.9 × 10⁻⁵, with sums of squares of 128 between and 15 within, adding to 143 total. That split is exact by construction and is the whole of what ANOVA does. The obvious question is why not just run a t-test on every pair, and the answer is the reason ANOVA exists: each test carries its own false-positive risk, so three groups mean three tests and about a 14% chance of at least one false alarm at α = 0.05. ANOVA asks the question once. What it does NOT tell you is WHICH groups differ — a significant F says only that they are not all alike, and finding the pair needs a follow-up test with a correction. Report η² alongside F, not instead of it: here η² = 0.8951, meaning 89.51% of the variation sits between the groups. F and p both grow with sample size and η² does not, which is why the effect size is the number that travels.