ANOVA (Analysis of Variance)
Omnibus test for means across three or more groups — F statistic from between-group vs. within-group variance.
Also known as: analysis of variance, one-way ANOVA, F-test (ANOVA)
Analysis of Variance (ANOVA) tests whether the means of several groups differ. It is an omnibus test: a significant result tells you at least one mean differs — not which one. That is what post-hoc tests (Tukey HSD, Bonferroni, Scheffé) are for.
- One-way ANOVA — one factor with k levels; H₀: μ₁ = μ₂ = ... = μ_k
- Multi-way ANOVA — two or more factors; also estimates interactions
- Block designs / repeated measures — with a structured error component
See also
Used in
In the Algorithm Lab
Sources
- Fisher, R. A. — Statistical Methods for Research Workers, 1925
- Montgomery, D. C. — Design and Analysis of Experiments, 10th Edition, Chapter 3
- Kutner, M., Nachtsheim, C., Neter, J. & Li, W. — Applied Linear Statistical Models, 5th Edition