MANOVA asks whether groups differ on several outcome variables at once, accounting for the correlation among them. It is a statement about a vector of means, which is why it has four different test statistics and why the choice among them matters less than people fear.
A multivariate analysis of variance (MANOVA) tests whether one grouping factor produces differences on two or more dependent variables considered together. Instead of running one ANOVA per outcome and multiplying the chances of a false positive, it tests a single hypothesis about the vector of group means while accounting for the correlations among the outcomes.
There are four classical test statistics — Pillai's trace, Wilks' lambda, Hotelling-Lawley trace and Roy's greatest root — and Magic Stat reports all four with their F, degrees of freedom and p-value. They rarely disagree in practice; Pillai's trace is often suggested because it is comparatively robust to assumption violations, while Roy's greatest root is the most sensitive to violations of the assumptions. Reporting all four lets the reader see that the conclusion does not hinge on the choice.
Where MANOVA stops being the right tool: with many outcomes and a modest sample it can be underpowered, and it assumes multivariate normality and homogeneous covariance matrices. A permutational alternative, PERMANOVA, is computed alongside. If the question is classification rather than group difference, discriminant analysis is the better fit.
Design: one-way — a single grouping factor with two or more levels, and two or more numeric dependent variables.
Statistics: Pillai's trace · Wilks' lambda · Hotelling-Lawley trace · Roy's greatest root, each with F, df1, df2 and p.
Effect size: partial eta-squared, computed from Pillai's trace.
Companion test: PERMANOVA (Euclidean distance, permutational), with R², reported in the same tab.
They usually lead to the same conclusion. Pillai's trace is the common recommendation because it is comparatively robust to violations of the assumptions; Wilks' lambda is the classical default; Roy's greatest root is the most sensitive to violations. Reporting all four, as the app does, makes the choice transparent.
MANOVA tests one combined hypothesis about the vector of means and controls the error rate across correlated outcomes; separate ANOVAs each test a narrower question but multiply the false-positive risk. With many outcomes and a small sample, though, MANOVA can be underpowered — running the univariate tests as a follow-up is standard.
MANOVA is parametric: it relies on multivariate normality and homogeneous covariance matrices. PERMANOVA makes no normality assumption and works from a distance matrix. The app computes both for the same factor, so you can see whether the conclusion depends on the distributional assumptions.
The MANOVA in this app is one-way: a single grouping factor. For a factorial multivariate design with interactions, R (for example car::Anova on an mlm object) is the better route — being honest about that is more useful than pretending the dialog covers it.
No. The computation runs on your computer; the only automatic signal is an anonymous installation counter.