📊ANOVA

NEW

Also known as: Analysis of Variance

Statistical framework testing whether group means differ significantly using variance decomposition and F-tests.

DESCRIPTION

ANOVA assesses whether differences among group means could arise by chance by comparing between-group to within-group variability. One-way ANOVA tests one factor; two-way extends to two factors and interactions. Assumptions include independence, homoscedasticity, and normality of residuals. Post-hoc procedures (Tukey, Bonferroni) localize differences after a significant omnibus test. Nonparametric alternatives like Kruskal–Wallis apply when assumptions are violated.

ALTERNATIVE DEFINITIONS

Wikipedia

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures used to analyze the differences among group means in a sample.

Defines ANOVA as models and procedures for group mean differences.

Source

Penn State STAT 501

ANOVA is a method for comparing several population means by analyzing sample variances.

Emphasizes variance decomposition to compare means.

Source

RELATED TERMS

F-test Multiple Comparisons Post-hoc Tests Assumptions Linear Model Effect Size Two-way ANOVA Repeated Measures ANOVA

COMPETING TERMS

t-test Kruskal–Wallis Test

RELATIONS

• Broader: Linear Model
• Narrower: Repeated Measures ANOVA

KNOWLEDGE AREAS

Mathematics Data Science

TARGET AUDIENCE

Data Scientist Data Analyst BI Specialist Information Analyst

EXTERNAL SOURCES

• Wikipedia - Analysis of variance
• NIST/SEMATECH e-Handbook - ANOVA overview and assumptions
• Statsmodels - ANOVA in Python examples

TOP QUESTIONS

When should I use ANOVA instead of multiple t-tests?

Use ANOVA to control Type I error when comparing three or more groups, then apply post-hoc tests to identify specific differences.

Category: Guidance

What assumptions underpin ANOVA?

Independent observations, normally distributed residuals, and equal variances across groups are standard assumptions.

Category: Assumptions

How do I proceed after a significant ANOVA?

Run post-hoc pairwise comparisons with multiple testing corrections to locate which groups differ.

Category: Procedure

What if ANOVA assumptions are violated?

Consider transformations, Welch’s ANOVA for unequal variances, or nonparametric Kruskal–Wallis.

Category: Alternatives

What is the F-statistic in ANOVA?

It’s the ratio of between-group mean square to within-group mean square; larger values suggest group differences.

Category: Concept

Can ANOVA handle multiple factors?

Yes. Two-way and factorial ANOVA test main effects and interactions between factors.

Category: Scope

How large should samples be for ANOVA?

Power depends on effect size, variance, and alpha. Use power analysis to estimate needed per-group sample sizes.

Category: Requirements

What is repeated measures ANOVA?

It handles correlated measurements from the same subjects over conditions or time, increasing power by modeling within-subject variance.

Category: Variant

How to report ANOVA results?

Include F-value, degrees of freedom, p-value, effect size (e.g., eta-squared), and post-hoc results with corrections.

Category: Reporting