One-Way MANOVA (multivariate k groups)

Verified

Multivariate

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.

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Multivariate omnibus test for k ≥ 3 independent groups on p ≥ 2 continuous DVs.

Returns FOUR multivariate statistics (Wilks' Λ, Pillai's trace, Hotelling-Lawley, Roy's largest root) that triangulate the evidence — Pillai's is most robust when assumptions are uncertain. Per-DV univariate follow-ups with Bonferroni correction localise which DVs drive the multivariate effect. Pre-checks multivariate normality (Mardia), homogeneity of covariance (Box's M), and outliers in p-dimensional space.

Worked example

Do three diets differ across several health outcomes at once?

Weight, blood pressure and cholesterol (correlated outcomes) were compared across three diets with MANOVA, followed by univariate tests.

Result

The diets differed on the combined outcomes, Pillai's trace = .27, F = 4.5, p < .001.

How you'd report it (APA)

A MANOVA showed a significant multivariate effect of diet on the health outcomes, Pillai's trace = .27, F = 4.5, p < .001.

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • k groups × p continuous correlated DVs
    Manufacturing study compares 4 production shifts (n = 25 each) on 3 quality metrics (defect rate, cycle time, yield).
  • Psychometric battery comparison across k groups
    Big Five subscale comparison across 4 occupational groups (n = 50 each) on 5 trait scores.

When NOT to — use instead

Hypotheses

H₀: the population mean vectors are equal across all k groups.
Hₐ: at least one group's mean vector differs.

Parameter tested: set of group mean vectors {μ_j}

Assumptions (and what to do if they fail)

Per-group multivariate normality of the DVs.medium

Check: Per-DV Shapiro-Wilk per group.

If violated: MANOVA is fairly robust to mild MVN violations with balanced n; severe non-normality inflates Type I error.

All k groups share a common covariance matrix (Box's M test).high

Check: Report Box's M χ² and p.

If violated: Heterogeneous covariance matrices inflate Type I error under unbalanced n.

Ready to run a One-Way MANOVA (multivariate k groups) on your own data?

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

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