MANOVA — Multivariate Analysis of Variance
MANOVA compares two or more groups on multiple dependent variables simultaneously. Where ANOVA tests group means on one outcome, MANOVA tests group means on a multivariate vector of outcomes.
Step 1 — Provide your data
- One categorical grouping variable (the factor)
- Two or more dependent variables (the multivariate outcome)
Supports Excel Import, Sample Data Generator, and Manual Entry.
Step 2 — Results
Multivariate test:
- Wilks' Lambda with F-statistic, df, p-value
- Partial eta-squared (multivariate effect size)
Box's M Test:
- Tests homogeneity of covariance matrices
- F approximation with p-value
- Guidance on Pillai's Trace if assumption violated
Univariate F-tests (follow-up):
- Per-variable ANOVA: F-value, df, p-value, eta-squared
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Statistical methods used
Wilks' Lambda
Lambda = det(E) / det(E + H) where E = within-groups SSCP, H = between-groups SSCP.
Rao's F approximation for p-value.
Hypothesis: H0: all group mean vectors equal. H1: at least one differs. alpha = 0.05.
Effect size: eta2_partial = 1 - Lambda^(1/s)
| eta2 | Label |
|---|---|
| < 0.06 | Small |
| 0.06 - 0.14 | Medium |
| >= 0.14 | Large |
Box's M Test — formal test of equal covariance matrices across groups. p < 0.001 suggests violation.
Univariate follow-ups — separate one-way ANOVA per dependent variable (no Bonferroni correction applied).