Robust ANOVA (Welch-Yuen trimmed means)

Coming soon

ANOVA

This test is implemented and is currently going through StatMinds’ production verification: every statistic is independently checked against a trusted reference (scipy / R), locked with regression tests, and the screen is exercised across assumption-met/violated and significant/non-significant scenarios before it opens up.

See what’s live now

Omnibus comparison of 3+ independent-group TRIMMED MEANS using a Welch-Yuen-style F statistic with Winsorised variances and Welch-Satterthwaite degrees of freedom.

Default 20% trim (drops top + bottom 20% per group) downweights outliers and heavy tails while retaining the language of means. Reports the trimmed-means F, Welch-Satterthwaite df, p, and per-group trimmed means + Winsorised SE. Substantially more efficient than rank-based alternatives under heavy-tailed Gaussian-with-contamination models, and only slightly less efficient than classical F under clean Gaussian data.

Worked example

Do groups differ when outliers and non-normality threaten ANOVA?

A robust (trimmed-means) ANOVA compares groups using trimmed means and Winsorised variances, resisting outliers.

Result

Groups differed on the trimmed means, Ft = 6.1, p = .004.

How you'd report it (APA)

A robust trimmed-means ANOVA showed a significant group difference, Ft = 6.1, p = .004.

When to use it

3+ independent groups with heavy tails or outliers
An RCT compares response time across four catalysts (n ≈ 20 each).
Outlier-contaminated k-group continuous DV
Reaction-time experiment: 4 conditions × n = 25.

When NOT to — use instead

Two groups only
Robust ANOVA is k ≥ 3. → Yuen's Trimmed-Mean Test (robust)
Paired / repeated measures
This robust ANOVA is between-subjects only. → One-Way RM-ANOVA (3+ measurements)
Clean Gaussian data
Classical ANOVA is more efficient when assumptions hold — use it for parsimony. → One-Way ANOVA (3+ groups)
Effect concentrated in tails
Trimming discards the tail signal. → Quantile Regression \u2014 \u03b2(\u03c4) at requested quantiles (median + tails)

Hypotheses

H₀: the population trimmed means are equal — μ_t1 = μ_t2 = … = μ_tk (for γ% symmetric trim).

Hₐ: at least one pair of trimmed means differs.

Parameter tested: set of population trimmed means {μ_t_j}

Assumptions (and what to do if they fail)

Each group retains ≥ 5 observations after the γ·2 trim (h_j = n_j − 2·⌊γ·n_j⌋).medium

Check: Report h_j per group.

If violated: Too few observations after trimming make the Winsorised-variance SE unstable.

Each group's Winsorised variance is strictly positive (no point mass after trimming).medium

Check: Report SD_W per group.

If violated: Point mass in a trimmed group breaks the SE computation.

Ready to run a Robust ANOVA (Welch-Yuen trimmed means) on your own data?

Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.

Run this test →

🔎 Worked example

✓ When to use it

✗ When NOT to — use instead

Hypotheses

Assumptions (and what to do if they fail)

Worked example

When to use it

When NOT to — use instead