Analysis of variance

Analysis of variance (ANOVA) partitions observed variability into components associated with modeled effects and residual error. It tests hypotheses about group means or other effects using ratios of variance estimates.

F-test: A statistical test that compares variance estimates through their ratio, evaluated against an F distribution. ANOVA typically tests effects by comparing model and residual mean squares with an F statistic.
Statistical hypothesis testing: A framework for evaluating a claim about a population using sample data and a specified decision rule. ANOVA uses a test statistic and null hypothesis to assess modeled differences.
One-way analysis of variance: An ANOVA design that tests a response against one categorical explanatory factor. It is the basic form for comparing means across several independent groups.
Student's t-test: A statistical test commonly used to compare means, especially between two groups. For two groups, the classical ANOVA F test and a two-sided pooled t-test give equivalent results.
Ronald Fisher: A British statistician and geneticist who developed foundational methods for experimental design and statistical inference. Fisher developed analysis of variance as part of a framework for analyzing experiments.
Sum of squares: The sum of squared deviations used to measure variability in data or model residuals. ANOVA decomposes sums of squares among modeled effects and unexplained variation.
Null hypothesis: A statistical hypothesis specifying a baseline condition, often that an effect or difference is absent. The ANOVA null commonly states that the tested group means or modeled effects are equal to zero.
Two-way analysis of variance: An ANOVA design that models two categorical factors and may include their interaction. It separates each factor's effects from the possibility that their effects depend on each other.
Kruskal–Wallis test: A rank-based test for differences among independent groups that does not require normally distributed outcomes. It is a common alternative when the assumptions of ordinary one-way ANOVA are unsuitable.
F distribution: A probability distribution for ratios of independent scaled chi-squared variables. Under the classical null model, ANOVA's ratio of mean squares follows an F distribution.

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