MANOVA in SPSS: Setup, Assumptions, and Follow-Up

MANOVA (multivariate analysis of variance) tests whether group means differ across two or more continuous outcome variables analyzed together, rather than one at a time. In SPSS it runs through Analyze > General Linear Model > Multivariate — a different menu entry than the Univariate procedure used for ordinary one-way and two-way ANOVA. This guide covers when MANOVA is the right tool instead of running several separate ANOVAs, how to set it up in SPSS, the assumption checks specific to the multivariate case (Box’s M and multivariate normality), how to read the four multivariate test statistics SPSS reports, and how to decide whether — and how — to run univariate follow-up tests after a significant multivariate effect.

Why use MANOVA instead of several ANOVAs?

If a study measures three related outcomes — say, anxiety, depression, and stress scores from the same intervention — the intuitive approach is to run three separate one-way ANOVAs, one per outcome. That approach has two problems MANOVA is built to address:

• Inflated Type I error. Running three independent tests at α = .05 each pushes the study-wise false-positive rate above 5%, the same multiple-comparisons problem that motivates Bonferroni-style corrections elsewhere. A single MANOVA tests all outcomes in one omnibus test, controlling the overall error rate directly rather than after the fact.
• Ignoring the correlation between outcomes. Separate ANOVAs treat each dependent variable (DV) as if it were unrelated to the others. When the DVs are correlated — which is exactly the situation where a researcher tends to measure them together — a multivariate test can detect a combined effect across the outcomes that no single univariate test reaches significance on its own, because it accounts for the shared variance between them.

MANOVA is the right tool when the DVs are conceptually related and at least moderately correlated. If the outcomes are conceptually unrelated or essentially uncorrelated, combining them into one multivariate test doesn’t add power and can make the result harder to interpret — separate ANOVAs are the better choice in that case.

Setting up MANOVA in SPSS

Go to Analyze > General Linear Model > Multivariate. Move your continuous outcomes into the Dependent Variables box (this box accepts multiple variables — that’s what distinguishes the Multivariate procedure from Univariate) and your categorical predictor(s) into Fixed Factor(s). Any continuous covariates go into the Covariate(s) box if you’re running a MANCOVA instead of a plain MANOVA. Leave the Model tab on its default, Full factorial, unless you have a specific reason to drop an interaction term.

Before clicking OK, two tabs matter for a complete MANOVA run:

• Options — move your factor(s) into Display Means for, and check Descriptive statistics, Estimates of effect size, Homogeneity tests (this is what produces Box’s M), and SSCP matrices if you want to inspect the sum-of-squares-and-cross-products matrices directly.
• Post Hoc — this tab is grayed out for multivariate factors and only applies to between-subjects factors with more than two levels; it does not substitute for the DV-level follow-up testing covered below.

Click OK. SPSS returns, in order, a Box’s Test of Equality of Covariance Matrices table (if Homogeneity tests was checked), a Multivariate Tests table, and a Tests of Between-Subjects Effects table — the same univariate-style table the Univariate GLM procedure produces, but now repeated once per dependent variable.

Checking the assumptions specific to MANOVA

MANOVA carries the same baseline assumptions as ordinary ANOVA (independent observations, reasonably continuous DVs, no extreme outliers) plus two that only apply once there is more than one outcome variable:

Box’s M: homogeneity of covariance matrices

Box’s M tests whether the variance-covariance matrix of the dependent variables is equal across groups — the multivariate equivalent of a Levene’s test for a single DV. SPSS reports it in the Box’s Test of Equality of Covariance Matrices table when Homogeneity tests is checked on the Options tab. A significant result (commonly evaluated at a stricter threshold than .05, since Box’s M is known to be oversensitive with large samples) suggests the covariance matrices differ across groups.

Box’s M is sensitive to violations of multivariate normality as well as to unequal covariance, and it is known to be overly sensitive in large samples — a significant result doesn’t automatically invalidate the analysis. Two practical points follow from this:

• With equal or near-equal group sizes, MANOVA is fairly robust to a Box’s M violation, and Wilks’ Lambda (the default-reported statistic) remains reasonably trustworthy.
• With unequal group sizes, a significant Box’s M is a real concern. The standard recommendation is to rely on Pillai’s Trace instead of Wilks’ Lambda in that situation, since Pillai’s Trace is the most robust of the four multivariate statistics to violations of the covariance-homogeneity and normality assumptions.

Multivariate normality

MANOVA assumes the dependent variables follow a multivariate normal distribution within each group — each DV normally distributed, and every linear combination of the DVs also normally distributed. SPSS’s GLM Multivariate procedure does not produce a single built-in multivariate normality test or p-value, so this assumption is normally checked with a combination of approaches rather than one dialog checkbox:

• Check univariate normality for each DV within each group first (see testing normality in SPSS) — univariate non-normality is a strong indicator that the multivariate assumption fails too, and it’s the cheapest check to run first.
• Screen for multivariate outliers using Mahalanobis distance, since a small number of extreme multivariate outliers can distort MANOVA results even when each DV looks acceptable in isolation. Mahalanobis distance can be saved as a variable from the Save options of the Linear Regression dialog (regressing case ID on the DV set) and then evaluated against a chi-square critical value with degrees of freedom equal to the number of DVs.

MANOVA is reasonably robust to moderate normality violations, particularly with larger and more balanced group sizes, but it is not robust to combined violations of normality and covariance homogeneity together — which is exactly why Box’s M and normality are checked as a pair, not independently.

Multicollinearity and singularity among the DVs

The dependent variables should be correlated enough to justify analyzing them jointly, but not so highly correlated that they are effectively measuring the same thing. Two DVs correlated above roughly .8–.9 introduce multicollinearity into the multivariate test (parallel to the multicollinearity check on predictors in multiple regression) and can produce an unstable or non-invertible covariance matrix. Check the DV correlations in advance with a Pearson correlation matrix; if two DVs are near-redundant, consider dropping one or combining them into a composite rather than entering both.

Reading the Multivariate Tests table

SPSS reports four multivariate test statistics for each effect in the model, all in the same Multivariate Tests table: Pillai’s Trace, Wilks’ Lambda, Hotelling’s Trace, and Roy’s Largest Root. Each is a different way of summarizing how much the groups are separated across the combined set of DVs, and each converts to an approximate F-statistic with its own Sig. value.

• Wilks’ Lambda is the most commonly reported statistic by convention and is exact (not approximate) when there are two groups or two DVs. It is what most published MANOVA results cite by default.
• Pillai’s Trace is the most robust of the four to violations of multivariate normality and homogeneity of covariance, and is the recommended choice when Box’s M is significant, group sizes are unequal, or there is reason to doubt normality.
• Hotelling’s Trace and Roy’s Largest Root are reported less often in applied work; Roy’s Largest Root in particular is the least robust of the four and the most sensitive to a single dominant dimension of group separation, so a discrepancy between it and the other three is worth investigating rather than reporting at face value.

With two groups, all four statistics test the same thing and will agree. With three or more groups, they can occasionally disagree at the margin because they weight the multiple discriminant dimensions differently — when they do, favor whichever statistic matches the assumption-check results above rather than picking whichever one is significant.

Univariate follow-up after a significant multivariate effect

A significant multivariate result tells you the groups differ on some combination of the DVs — it does not say which individual DV, or DVs, is driving that difference. The standard follow-up is to examine the Tests of Between-Subjects Effects table SPSS produces automatically alongside the Multivariate Tests table: this is a separate univariate ANOVA F-test for each DV against the same factor(s).

Two decisions matter at this stage:

• Only interpret the univariate follow-ups if the multivariate test was significant. Running and interpreting the per-DV ANOVAs regardless of the multivariate result defeats the purpose of using MANOVA in the first place — it reintroduces the same inflated Type I error rate that running separate ANOVAs from the start would have produced. The multivariate test is the gatekeeper.
• Adjust alpha across the univariate follow-ups. Because you are now running one F-test per DV, apply a Bonferroni correction (divide .05 by the number of DVs) or a comparable correction to the follow-up significance threshold, rather than evaluating each at the uncorrected .05 level. Some researchers use discriminant function analysis instead of univariate follow-ups specifically to avoid this correction step, but the Bonferroni-adjusted univariate approach is the more commonly reported one in applied research.

Report effect size (SPSS’s Options tab reports partial eta squared for both the multivariate and univariate tests when Estimates of effect size is checked) alongside significance at every stage — see effect size: choosing, reporting and interpreting it for the general reporting conventions this follows.

Reporting MANOVA results

A typical APA-style report states the multivariate result first, then the univariate follow-ups for whichever DVs were significant:

“A one-way MANOVA was conducted to examine group differences across [DV1] and [DV2]. There was a statistically significant effect of group on the combined dependent variables, Wilks’ Λ = .XX, F(df1, df2) = X.XX, p = .XXX, partial η² = .XX. Follow-up univariate ANOVAs, evaluated at a Bonferroni-adjusted alpha of .025, indicated a significant effect on [DV1], F(df1, df2) = X.XX, p = .XXX, but not on [DV2], F(df1, df2) = X.XX, p = .XXX.”

Report Wilks’ Lambda by default; if Box’s M was significant with unequal group sizes, report Pillai’s Trace instead and say so explicitly, since a reviewer who expects Wilks’ Lambda by convention will otherwise wonder why it was substituted.

Frequently asked questions

What’s the difference between MANOVA and running several ANOVAs?

MANOVA tests all dependent variables together in one omnibus test, controlling the overall Type I error rate and accounting for correlation between the DVs; running separate ANOVAs tests each DV independently, inflating the study-wise error rate and ignoring how the DVs relate to each other. See ANOVA (Analysis of Variance) for the single-DV case this builds on.

Which multivariate statistic should I report: Wilks’ Lambda or Pillai’s Trace?

Wilks’ Lambda by convention and default, unless Box’s M is significant and group sizes are unequal, in which case Pillai’s Trace is the more robust and defensible choice.

What do I do if Box’s M is significant?

Check whether group sizes are roughly equal first — if they are, MANOVA is reasonably robust to the violation and Wilks’ Lambda remains usable. If group sizes are unequal, switch to reporting Pillai’s Trace, which is the most robust of the four statistics to this violation.

Do I need to correct for multiple comparisons in the univariate follow-up tests?

Yes — apply a Bonferroni correction (or equivalent) across the per-DV follow-up tests, since each is now its own significance test drawn from a set. See Bonferroni correction and multiple comparisons for how to apply it.

Can I run MANOVA with a covariate in SPSS?

Yes — enter continuous covariates in the Covariate(s) box of the same Analyze > General Linear Model > Multivariate dialog; this turns the analysis into a MANCOVA and adds an adjustment for the covariate to both the multivariate and univariate output.