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SPSS command: SPSS GLM

MANOVA (GLM Multivariate) in your browser

MANOVA tests whether groups differ on several correlated outcomes at once, controlling the error rate that separate ANOVAs would inflate.

Try with example dataRun on your own file

Free · No account · Files stay on your device · Updated 18 October 2026

What it tells you

Crosstabs runs SPSS GLM with two to ten dependent variables on your device and reports the four multivariate statistics, Box's test of equal covariance matrices, Bartlett's test of sphericity and a univariate F for each outcome.

  • Whether a factor shifts the combination of outcomes, judged by Pillai's trace, Wilks' lambda, Hotelling's trace and Roy's largest root.
  • Which individual outcomes carry the difference, from the Type I–IV univariate tests reported for each dependent variable.
  • Whether the outcomes' covariance matrices are similar across groups (Box's M), an assumption behind the multivariate tests.
  • Whether the outcomes are correlated enough to justify a joint analysis, via Bartlett's test of sphericity on the residual matrix.

When to use it

Use it when

  • Two or more related scale outcomes measured on the same cases, such as speed and accuracy, or several satisfaction dimensions.
  • You want one overall test before looking at outcomes one by one, to limit false positives.
  • One to four fixed factors, optionally with covariates (MANCOVA).

Use something else when

  • The outcomes are the same measure at different times: use repeated-measures ANOVA, which models the time structure.
  • The outcomes are essentially uncorrelated: separate GLM Univariate analyses are simpler to report.
  • You want to predict group membership from the outcomes: use discriminant analysis.
  • Very small groups relative to the number of outcomes: the error matrix becomes unstable and Box's M cannot be computed.

How to run it in Crosstabs

  1. 01

    Open your data

    Open the file in the workspace and switch to Statistics mode.

  2. 02

    Choose GLM Multivariate

    In the General linear model group, pick GLM Multivariate.

  3. 03

    Assign the variables

    Tick two to ten Dependent variables, up to four Fixed factors and up to five Covariates.

  4. 04

    Set the model

    Choose Full factorial, Main effects only or Custom under Model, and a Sum of squares type (Type III is the default).

  5. 05

    Pick the options and run

    Keep Homogeneity tests ticked for Levene's test per outcome, optionally tick Observed power, then click Run analysis. Missing values are excluded listwise across all selected variables.

Run GLM Multivariate (MANOVA) in your browser

Worked example

Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.

Try with example data

Data

45 synthetic trainees, 15 in each of three training programmes (A, B, C). Each has two outcomes — task speed and accuracy — generated with a shared component so they correlate, from a fixed seed. Programme B was built to be faster and programme C more accurate.

Box's Test of Equality of Covariance Matrices
StatisticValue
Box's M5.603
F0.869
df16
df243964.3
Sig..516
Multivariate Tests: programme
ItemValueFHypothesis dfError dfSig.Partial Eta Squared
Pillai's Trace0.4305.751484<.0010.215
Wilks' Lambda0.6055.845482<.0010.222
Hotelling's Trace0.5935.930480<.0010.229
Roy's Largest Root0.4689.824242<.0010.319
Tests of Between-Subjects Effects: programme
Dependent VariableType III Sum of SquaresdfMean SquareFSig.Partial Eta Squared
speed103.60251.802.654.0820.112
accuracy296.862148.437.952.0010.275

How to read it

Box's M = 5.60 (p = .516) gives no sign that the covariance matrices differ across programmes. The joint test of the two outcomes gives Pillai's trace = 0.430, F(4, 84) = 5.75, p < .001; Wilks' lambda = 0.605. The univariate follow-ups show which outcome carries the difference: speed F = 2.65 (p = .082) and accuracy F = 7.95 (p = .001).

Output tables explained

Box's Test of Equality of Covariance Matrices
Box's M with its F approximation. The test is very sensitive in large samples, so it is usually judged at p < .001; the footnote shows how many cells had non-singular covariance matrices.
Multivariate Tests
For each effect, Pillai's trace, Wilks' lambda, Hotelling's trace and Roy's largest root with F, hypothesis and error df, significance and partial eta squared. Exact F values are flagged; Roy's F is an upper bound.
Levene's Test of Equality of Error Variances
One table per dependent variable, based on the mean and on the median, when the model has factors and no covariates.
Tests of Between-Subjects Effects
The univariate follow-up: every effect tested on every dependent variable, with R² for each outcome in the footnotes.
Bartlett's Test of Sphericity
Tests whether the residual covariance matrix is proportional to an identity matrix; a small p value means the outcomes are correlated after the model.

Assumptions and notes

  • Cases are independent and the outcomes are jointly (multivariate) normal within each cell.
  • Covariance matrices of the outcomes are equal across cells; Pillai's trace is the most robust statistic when Box's M suggests otherwise.
  • Each cell needs more cases than dependent variables for its covariance matrix to enter Box's M.
  • The panel offers no estimated marginal means or post hoc tests for MANOVA; run GLM Univariate on an outcome for those.

How the results are validated

The four multivariate statistics, their F approximations, df and p values match R 4.6 car 3.1.5 Type III multivariate tests (values and F to a relative 1e-9, p to 1e-7); Pillai, Wilks and Roy also match statsmodels 0.15 mv_test. Box's M and Bartlett's test are checked against independent NumPy implementations of the SPSS formulas (1e-9), and the univariate follow-ups against the reference Type III sums of squares. Validation evidence

Questions

Which multivariate statistic should I report?

Pillai's trace is the most robust to unequal covariance matrices and small or unequal groups, so it is the safe default. Wilks' lambda is the most commonly cited; with one hypothesis df all four give the same exact F.

Box's M is significant — is my MANOVA invalid?

Not necessarily. Box's M flags small differences in large samples, so the usual threshold is p < .001. If it is below that and group sizes are unequal, rely on Pillai's trace.

Why run MANOVA instead of one ANOVA per outcome?

Separate ANOVAs inflate the chance of a false positive and ignore the correlation between outcomes. MANOVA gives one protected overall test and can detect a difference that shows only in the combination of outcomes.

Can I add covariates (MANCOVA)?

Yes. Tick up to five Covariates; they enter the model and appear as their own rows in the Multivariate Tests and the univariate table. Levene's test is not shown when covariates are present.

Is my data uploaded?

No. The file is parsed and the MANOVA computed in your browser; nothing is uploaded to Crosstabs servers.

Related procedures

Run GLM Multivariate (MANOVA) on your own data

Open a .sav, CSV or Excel file. Everything runs in your browser; the file never leaves your device.

Open the workspace

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