Compare groups on multiple outcomes simultaneously while controlling for one or more covariates.
MANCOVA extends MANOVA by statistically controlling for one or more continuous covariates before testing group differences on a set of related outcome variables. It combines the covariate control of ANCOVA with the multivariate protection of MANOVA, making it useful when you have multiple DVs and want to partial out a nuisance variable (e.g., controlling for pre-test scores when comparing groups on multiple post-test measures).
StatRyx tests the homogeneity of regression slopes assumption, computes multivariate test statistics (Pillai's trace, Wilks' lambda), and reports follow-up univariate ANCOVAs for each DV with adjusted means.
MANCOVA tests whether groups differ on a combination of several related outcomes after adjusting for one or more covariates. It first gives a multivariate test (Wilks' Λ, Pillai's trace) of the overall group difference; only if that is significant do you examine each outcome with a univariate ANCOVA. Its assumptions combine those of MANOVA (multivariate normality, equal covariance matrices — Box's M) with those of ANCOVA (linear covariates, homogeneous regression slopes).
| Test | Value | F | p | partial η² |
|---|---|---|---|---|
| Wilks' Lambda | 0.74 | 7.83 | < .001 | .15 |
| Pillai's Trace | 0.27 | 7.31 | < .001 | .14 |
A one-way MANCOVA controlling for pre-test scores revealed a significant multivariate group effect, Wilks' Λ = 0.74, F(4, 184) = 7.83, p < .001, partial η² = .15. Follow-up univariate ANCOVAs indicated significant group differences on both anxiety (F(2, 93) = 9.12, p < .001) and depression (F(2, 93) = 6.44, p = .002).
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StatRyx supports multiple covariates. However, each covariate consumes degrees of freedom; use only theoretically justified covariates.
Report the multivariate test with its F approximation and partial η², then the univariate follow-ups: "Controlling for pre-test scores, there was a significant multivariate effect of group, Wilks' Λ = 0.74, F(4, 184) = 7.83, p < .001, partial η² = .15."
Wilks' Λ is the most commonly reported. Pillai's trace is more robust when group sizes are unequal or Box's M test shows unequal covariance matrices, so it is the safer choice in those cases. With two groups all four multivariate statistics give the same F.
Each covariate costs a degree of freedom and must relate to the outcomes to be worth including. Use only covariates measured before the intervention and justified by theory — usually one to three.