📊 One-Way ANOVA Calculator
Compare means across 2–5 groups. Computes SS_between, SS_within, F-statistic, degrees of freedom, p-value, and a complete ANOVA table.
ANOVA Table
| Source | SS | df | MS | F |
|---|---|---|---|---|
| Between Groups | — | — | — | — |
| Within Groups | — | — | — | — |
| Total | — | — | — | — |
ANOVA Formulas
Frequently Asked Questions
Analysis of Variance (ANOVA) tests whether the means of three or more groups are statistically equal. It partitions total variability into between-group and within-group components, then compares them using the F-distribution.
H₀: all group means are equal (μ₁ = μ₂ = ... = μk). The alternative hypothesis H₁ is that at least one group mean differs. A significant F-test rejects H₀ but does not identify which groups differ.
ANOVA assumes: (1) observations are independent; (2) each group is normally distributed; (3) groups have equal variances (homoscedasticity). Levene's test or Bartlett's test can check variance equality.
A significant F-test only tells you that at least one group mean differs. Post-hoc tests (Tukey HSD, Bonferroni, Scheffé) are used to identify which specific pairs of groups are significantly different.
The F-statistic is the ratio of between-group variance (MS_between) to within-group variance (MS_within). A large F indicates that group means differ more than would be expected by chance.
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