Compare groups on multiple outcome variables simultaneously while controlling the Type I error rate.
Multivariate Analysis of Variance (MANOVA) extends One-Way ANOVA to situations where you have two or more continuous dependent variables measured simultaneously. Instead of running a series of separate ANOVAs — which inflates Type I error — MANOVA tests whether group membership explains variance in the entire set of outcome variables considered jointly. This is powerful when your outcomes are theoretically related and you want a single omnibus test.
MANOVA is common in educational research (comparing schools on reading, math, and science scores simultaneously), clinical psychology (comparing treatment groups on depression, anxiety, and quality of life), and organizational behavior (comparing management styles on employee satisfaction, commitment, and performance). The test produces multivariate test statistics — Wilks' lambda, Pillai's trace, Hotelling's trace, and Roy's largest root — each reflecting the group separation in multivariate space.
StatRyx handles MANOVA automatically: it checks multivariate normality (Box's M test for homogeneity of covariance matrices), selects Pillai's trace as the default statistic (most robust), computes the F approximation, reports effect sizes (partial eta-squared), and runs follow-up univariate ANOVAs on each dependent variable with appropriate alpha corrections.
| Test | Value | F | Hypothesis df | Error df | p | Partial η² |
|---|---|---|---|---|---|---|
| Pillai's Trace | 0.31 | 8.41 | 4.00 | 194.00 | < .001 | .15 |
| Wilks' Lambda | 0.71 | 8.76 | 4.00 | 192.00 | < .001 | .15 |
| Hotelling's Trace | 0.43 | 9.13 | 4.00 | 190.00 | < .001 | .16 |
A one-way MANOVA was conducted to examine the effect of intervention type on anxiety and depression scores. The multivariate test was significant, Wilks' Λ = 0.71, F(4, 192) = 8.76, p < .001, partial η² = .15. Follow-up univariate ANOVAs indicated significant group differences for both anxiety, F(2, 97) = 11.23, p < .001, and depression, F(2, 97) = 7.84, p = .001.
Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.
No coding required. You specify your grouping variable and your outcome variables in plain English, and StatRyx handles the entire multivariate analysis — including assumption checks like Box's M test — automatically.
A common guideline is to have at least 20 observations per cell (combination of group and dependent variable). With more dependent variables, you need larger samples. Smaller samples make Box's M test for homogeneity of covariance matrices unreliable.
Pillai's Trace is the most robust to violations of MANOVA assumptions and is generally recommended when sample sizes are unequal or Box's M is significant. Wilks' Lambda is more commonly reported in older literature. StatRyx reports all four statistics and highlights the recommended one for your data.
MANOVA is appropriate when your dependent variables are theoretically related and you want to control Type I error inflation. If your outcomes are conceptually independent and you have strong a priori hypotheses about each separately, individual ANOVAs with Bonferroni correction may be more interpretable and equally defensible.