MANOVA
Compare groups on two or more numeric outcomes in one test.
When to use it
Use MANOVA when groups might differ on several related outcomes, and you want one test of the set before you look at each outcome alone. For example: do lecture and workshop students differ on recall and confidence together?
Running a separate t-test on every outcome inflates the chance of a false positive. MANOVA asks first whether the group difference shows up in the combination. A significant multivariate test does not name which outcome did the work. Tensr follows it with a one-way ANOVA per outcome.
Assumptions
Each outcome is numeric. Observations are independent. The outcomes should be roughly multivariate normal, and the pattern of variances and correlations should be similar in each group.
Tensr does not test those assumptions. There is no Box’s M, no Shapiro–Wilk, and no effect-size column on the MANOVA table.
Running it in Tensr
Options
Prop
Type
Reading the output
Teaching method on two outcomes at once: exam score and a confidence rating. Both shift a little with method.
| Effect | Test | Value | F | df | p-value |
|---|---|---|---|---|---|
| Intercept | Pillai's trace | 0.973 | 1647 | 2,92 | < .001 |
| method | Pillai's trace | 0.151 | 3.797 | 4,186 | .005 |
| Dependent variable | F | p-value |
|---|---|---|
| score | 4.033 | .021 |
| confidence | 5.003 | .009 |
A significant multivariate effect of method on the combined outcome of score, confidence was found (Pillai's trace = 0.151, F = 3.797, p = .005).
The multivariate effect was driven primarily by score, confidence — method significantly predicts these outcomes. A significant multivariate effect of method on the combined outcome of score, confidence was found (Pillai's trace = 0.151, F = 3.797, p = .005).
The multivariate effect was driven primarily by score, confidence — method significantly predicts these outcomes. Metrics: Groups = 3; Cases = 96.
Reporting (APA 7)
A significant multivariate effect of method on the combined outcome of score, confidence was found (Pillai's trace = 0.151, F = 3.797, p = .005).
The multivariate effect was driven primarily by score, confidence — method significantly predicts these outcomes. Report the estimate in the table. This procedure is not summarised by one p-value.
Coming from SPSS
Analyze → General Linear Model → Multivariate.
SPSS prints Pillai’s trace, Wilks’ lambda, Hotelling’s trace, and Roy’s largest root. Tensr prints Pillai’s trace only. SPSS also offers post-hoc tests and effect sizes. Tensr’s follow-up is the uncorrected univariate F and p.
Related
One outcome: one-way ANOVA. Two groups and several outcomes is also what Hotelling’s T² tests. A covariate: ANCOVA, which takes one outcome.