ART Factorial ANOVA (aligned rank transform)

Verified

Nonparametric ANOVA

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

Run this test straight away on a free built-in teaching dataset — no data of your own needed — or bring your own. Either opens the guided workspace: variable setup, assumption diagnostics, results with effect sizes and confidence intervals, figures, and APA-ready reporting.

Loading teaching datasets…

Or use your own dataset

Loading your datasets…

Factorial nonparametric ANOVA supporting main effects AND interactions.

Per Wobbrock et al. (2011), each effect is tested by aligning residuals for that effect (subtracting the estimated contributions of all OTHER effects), ranking them, and running a classical ANOVA on the ranked aligned residuals. Fills a real gap: Kruskal-Wallis handles one factor, Friedman one within-factor — ART handles 2- or 3-way between-subjects factorial nonparametrically.

Worked example

Do two factors interact when the data are non-normal?

The Aligned Rank Transform lets a factorial ANOVA — including the interaction — run on ranked, non-normal data.

Result

A significant A × B interaction emerged on the aligned ranks, F(1, 76) = 6.4, p = .013.

How you'd report it (APA)

An ART ANOVA showed a significant A × B interaction on aligned ranks, F(1, 76) = 6.4, p = .013.

When to use it

  • 2- or 3-way factorial with non-normal DV
    A 2 × 2 study of drug (active / placebo) × condition (fasted / fed) on reaction time (right-skewed) with n = 25 per cell.
  • Ordinal Likert outcome in factorial design
    HCI study: 2 (Interface: A/B) × 3 (Task difficulty: easy/med/hard) on 7-point usability ratings.

When NOT to — use instead

Hypotheses

H₀: the population DV distributions are the same across cells of the factorial — no main effects, no interactions.
Hₐ: at least one main effect or interaction is non-zero.

Parameter tested: factorial structure on the joint distribution

Assumptions (and what to do if they fail)

Cell sample sizes are balanced or approximately balanced (recommended for ART).medium

Check: Report per-cell n and max/min ratio.

If violated: Unbalanced ART can inflate Type I error on interaction effects.

Each cell has ≥ 5 observations (recommended ≥ 10).medium

Check: Report min cell n.

If violated: Very small cells undermine the ART F distribution.

Ready to run a ART Factorial ANOVA (aligned rank transform) on your own data?

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

Run this test →