---
title: "One-way ANOVA"
method_id: SM.DIF.PAR.KIND.ANOVA1
family: Difference
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/one_way_anova.md
source: Clarus method library
---

# One-way ANOVA

> A classical statistical method in the Clarus library (Difference family).
> Clarus selects, assumption-checks and runs this method on your data with a
> deterministic rule engine and real numerical libraries (scipy / statsmodels);
> it never generates numbers, citations or results.

**Also known as:** one-factor ANOVA; between-subjects ANOVA; single-factor analysis of variance; Fisher's ANOVA.

## Hypotheses

- **Null (H0):** mu_1 = mu_2 = ... = mu_k
- **Alternative (H1):** at least one group mean differs (NOT all mu_i are equal)

## When to use it

Use this method when your goal is to:
- compare three or more independent group means

## Data it expects

- **dependent:** 1 continuous
- **independent:** 1 nominal/3+ levels
- **pairing:** independent

## Assumptions Clarus checks

- **normality** (gate: shapiro_wilk; severity: warning; on violation: reroute)
- **variance homogeneity** (gate: levene; severity: warning; on violation: reroute)
- **independence** (severity: warning; on violation: warn_only)

## Effect size reported

- **eta squared** (Cohen (1988))

## Honest limitations

- A significant ANOVA only tells you that at least one group mean differs; it does not say which ones. Read the post-hoc comparisons.
- Large n can pair statistical significance with a trivial effect — read eta-squared and omega-squared.
- A significant difference is not causal unless participants were randomly assigned to groups.
- Unequal group sizes combined with unequal variances can distort the F test; in that case Welch's ANOVA is preferred.
- Results generalize only to the sampled population.

## Primary sources

- Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd.
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
- Tukey, J. W. (1949). Comparing individual means in the analysis of variance. Biometrics, 5(2), 99-114. https://doi.org/10.2307/3001913
- Games, P. A., & Howell, J. F. (1976). Pairwise multiple comparison procedures with unequal n's and/or variances. Journal of Educational Statistics, 1(2), 113-125. https://doi.org/10.3102/10769986001002113
- Levene, H. (1960). Robust tests for equality of variances. In Contributions to Probability and Statistics (pp. 278-292). Stanford University Press.
- Hays, W. L. (1963). Statistics for Psychologists. Holt, Rinehart and Winston.
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). Sage.

## How to cite this

To cite this Clarus method page (the page itself — for the method's own primary sources, see above):

**Plain text**

Clarus, "One-way ANOVA", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/one_way_anova.md

**APA**

Clarus. (2026). One-way ANOVA (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/one_way_anova.md

**BibTeX**

```bibtex
@misc{clarus-one-way-anova,
  author       = {Clarus},
  title        = {One-way ANOVA},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/one_way_anova.md}
}
```

_No DOI is minted for Clarus method pages yet; this citation uses the canonical URL, version and date. Cite the primary sources above for the method's scientific provenance._

---

METHOD SM.DIF.PAR.KIND.ANOVA1 · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library