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