MANOVA (GLM Multivariate)
Tests whether groups differ on a set of related numeric outcomes considered together, then shows the univariate ANOVA for each outcome.
Menu: Analyze → General Linear Model → Multivariate…
When should I use it?
- Do three therapy groups differ on anxiety, depression and stress scores taken together?
- Does a training programme change several performance measures at once?
What are the assumptions?
- Independent observations; more cases per cell than outcomes.
- Multivariate normality within cells (robust with balanced, moderate-sized groups).
- Equal covariance matrices (Box's M; it is very sensitive, so judge at the .001 level).
- Outcomes are moderately correlated — not unrelated and not nearly identical.
How do I run it in StatLab?
- Move two or more outcomes to Dependent variables and the grouping variable(s) to Fixed factor(s).
- Keep Box's M and homogeneity tests under Options.
- Request post hoc tests if a factor has more than two levels.
- A WLS weight, Type II / IV sums of squares and the extra post hoc tests (Dunnett, S-N-K, R-E-G-W-Q, Tamhane) are available as for the univariate model.
How do I read the output?
| Output | Meaning |
|---|---|
| Box's Test | Sig. < .001 suggests unequal covariance matrices; then report Pillai's trace. |
| Multivariate Tests | Pillai's trace, Wilks' lambda, Hotelling's trace and Roy's largest root for each effect, with F, df, Sig. and partial eta squared. |
| Tests of Between-Subjects Effects | Follow-up ANOVA for each outcome. |
Worked example
On the practice survey dataset (File → Sample dataset), this command — which the dialog's Paste button also produces — runs the procedure:
PROC glmMulti /deps=(score post) /factors=(group) /covs=() /wls='' /phFactors=() /ss=3 /model=full /emm=YES /compare='' /ph_tukey=YES /ph_bonferroni=NO /ph_scheffe=NO /ph_snk=NO /ph_regwq=NO /ph_dunnett=NO /dunnettSide=two /control=last /ph_gameshowell=NO /ph_tamhane=NO /desc=YES /levene=YES /eta=YES /power=NO /params=NO /plot=YES /boxm=YES.
Output tables: Between-Subjects Factors · Descriptive Statistics · Box's Test of Equality of Covariance Matrices · Multivariate Tests · Levene's Test of Equality of Error Variances · Tests of Between-Subjects Effects · Grand Mean · group.
How would I report it in APA style?
A one-way MANOVA on Wellbeing score, Post-test score (N = 150) using Pillai's trace: group, V = .07, F(4, 294) = 2.50, p = .043, partial η² = .03.
Computed by StatLab's validated procedure code when this page was built. The example only illustrates the steps; choose variables that fit your own research question.
What are common mistakes?
- Reporting only Wilks' lambda when Box's M is significant — Pillai's trace is more robust.
- Treating significant univariate follow-ups as independent findings without adjusting for the number of outcomes.