Definition
ANOVA (analysis of variance) tests whether the means of three or more groups differ. It splits the total variability of the data into the part explained by a factor (between groups) and the random part (within groups); their ratio yields the F statistic and a p-value. Factorial ANOVA additionally reveals interactions between factors.
Statistical tests
A significant ANOVA only says that at least one group differs — which ones is shown by post-hoc tests (Tukey, Scheffé). The assumptions are normal residuals and equal variances; when violated, a transformation or the nonparametric Kruskal–Wallis ANOVA helps.
Two-way and factorial ANOVA are the backbone of designed experiments: besides main effects (temperature, material) they test the interaction — whether the effect of one factor depends on the level of another. Repeated-measures ANOVA handles the case where the same units are measured several times.
In Statistica
The Statistics → ANOVA module offers one-way, factorial and repeated-measures ANOVA with a wizard that guides you from variable selection to plots of means with confidence intervals. For more complex designs (unbalanced data, covariates) use General Linear Models (GLM).
Related terms
- Post-hoc testsPost-hoc tests follow a significant ANOVA and compare groups pairwise to show which ones really differ.
- t-testThe t-test compares means: the one-sample version compares a mean with a fixed value, the two-sample version the means…
- Nonparametric testsNonparametric tests do not assume a normal distribution — they work with the ranks of values rather than the values themselves.
- Effect sizeEffect size expresses how large a difference is or how strong an association is — independently of sample size.
- Design of experiments (DOE)Design of experiments (DOE) is a systematic way to find out, with a minimum of runs, which factors (temperature…
Knowledgebase guides
FAQ
- ANOVA is significant — am I done?
- No. Post-hoc tests come next to tell which pairs of groups differ, plus an effect size (η²) to tell how much.
- When should I use repeated-measures ANOVA?
- When each unit is measured under several conditions or over time — e.g. patients before treatment, after a month and after a year.
- What is an interaction between factors?
- A situation where the effect of one factor depends on the level of another — a drug helps only younger patients. In a plot of means it appears as non-parallel lines.
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Statistical tests
Updated: September 2026.