MANOVA Multivariate ANOVA Calculator

Advanced MANOVA engine for researchers and students analyze multiple dependent variables across groups compute Wilks lambda Pillai trace Hotelling Lawley trace and Roy largest root interpret results with clear matrices visualize distributions export clean reports and learn assumptions controls designed for reliability transparency and reproducibility on real experimental datasets including power tips examples tutorials

Data Input
Header required. First column is often the factor. Numeric columns are dependents.
What Is MANOVA Multivariate ANOVA?

Multivariate analysis of variance (MANOVA) extends the one‑way or two‑way ANOVA to situations with multiple dependent variables measured on the same subjects. Rather than testing each outcome separately and inflating Type I error, MANOVA builds a set of contrasts that compare group mean vectors jointly. It partitions total variability into between‑group and within‑group scatter matrices and evaluates their ratio through four classical tests: Wilks’ lambda, Pillai’s trace, Hotelling–Lawley trace, and Roy’s largest root. When assumptions hold—independence, multivariate normality, and equal covariance matrices—the tests are powerful screens for overall differences. Significant results can be followed by univariate ANOVAs or discriminant analyses to locate effects. This tool computes the matrices, eigenvalues, test statistics, and approximate p‑values from a tidy table input input.

FAQs

1) What input format does this tool expect?
A header row with column names and rows of observations. One column is a categorical factor. Two or more columns are numeric dependents.

2) Can I analyze more than one factor?
This version handles a single fixed factor across groups. You can run separate analyses for different factors or reshape data for factorial designs.

3) Which statistic should I report?
Many researchers favor Pillai’s trace for robustness while Wilks’ lambda is common historically. Report the full set and describe which guided your conclusion.

4) How are p‑values computed?
Wilks uses Bartlett’s chi‑square approximation. Pillai and Hotelling–Lawley use F approximations with derived degrees of freedom. Roy uses a conservative F approximation.

5) What assumptions does MANOVA require?
Independent observations, multivariate normality within each group, and equal covariance matrices across groups. Check diagnostics before interpreting results.

6) What if the within matrix is nearly singular?
Increase the ridge value to stabilize inversion or reduce the number of dependent variables relative to sample size.

7) Can I export the matrices and statistics?
You can copy tables directly. For programmatic use, copy results into your analysis notebook or save the page as HTML.

8) How do I follow up a significant MANOVA?
Conduct univariate ANOVAs with correction, examine canonical variates, and consider post‑hoc contrasts or discriminant analysis to locate group differences.

Quick Tips
  • At least 2 dependents and 2 groups are required.
  • Ensure each dependent is numeric and measured on comparable scales.
  • Balanced designs improve robustness of approximations.
  • Use a small ridge if warned about near‑singularity.
CSV Template
Group,Y1,Y2,Y3
A,5.1,2.9,1.3
A,4.8,3.0,1.5
B,6.4,3.2,1.8
B,6.9,3.1,1.7
C,5.7,2.5,1.4
C,6.0,2.7,1.6
Assumptions
  • Independence across rows/subjects.
  • Multivariate normality within each group.
  • Homogeneity of covariance matrices across groups.
  • No extreme multicollinearity among dependents.

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.