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MANOVA CALCULATOR

One-way MANOVA calculator for several dependent variables.

Test whether groups differ on two or more outcomes at once. Get Pillai's trace, Wilks' lambda, Hotelling's trace and Roy's largest root with F approximations, partial eta squared, follow-up ANOVAs and APA text.

DATA

Group column, then the dependent variables

MULTIVARIATE

The first row must be a header: group name, then one name per dependent variable. One row per participant.

METHOD

One-way MANOVA: statistics, assumptions, and APA reporting

What is a MANOVA?

A multivariate analysis of variance (MANOVA) tests whether groups differ on two or more related dependent variables considered together. Instead of running a separate ANOVA for each outcome, it uses the correlations between the outcomes, which controls the overall Type I error rate and can detect differences that no single outcome shows.

The four test statistics

Pillai V = Σ λᵢ/(1+λᵢ), Wilks Λ = Π 1/(1+λᵢ), Hotelling T = Σ λᵢ, Roy θ = λ₁

λᵢ are the eigenvalues of E⁻¹H, where H is the between-groups and E the within-groups sums-of-squares-and-cross-products matrix. Each statistic is converted to an approximate F; Roy's F is an upper bound.

Worked example: three groups, three scores

30 students in three groups with reading, writing and maths scores (the sample data).

  1. Pillai's V = .386, F(6, 52) = 2.07, p = .072, partial η² = .19.
  2. Wilks' Λ = .624, F(6, 50) = 2.22, p = .056.
  3. Roy's largest root is significant (p = .008), but it is the least conservative statistic.
  4. Reporting Pillai's trace, the groups do not differ significantly on the combined outcomes at α = .05.
  5. Follow-up ANOVAs should therefore be treated as exploratory.

Assumptions to check

  • Independent observations
  • At least as many participants per group as dependent variables
  • Multivariate normality (check each outcome for outliers)
  • Homogeneity of covariance matrices (Box's M; Pillai's trace is robust when group sizes are equal)
  • Moderate, not extreme, correlations between the dependent variables

How to report it (APA style)

“A one-way MANOVA showed no statistically significant difference between groups on the combined dependent variables, Pillai's V = .39, F(6, 52) = 2.07, p = .072, partial η² = .19.”

References

  • Tabachnick, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). Pearson.
  • Olson, C. L. (1976). On choosing a test statistic in multivariate analysis of variance. Psychological Bulletin, 83(4), 579–586.
  • Rao, C. R. (1951). An asymptotic expansion of the distribution of Wilks' criterion. Bulletin of the International Statistical Institute, 33(2), 177–180.

ABOUT THIS TOOL

MANOVA Calculator

Test whether groups differ on two or more outcomes together, with all four multivariate statistics and their F approximations, partial eta squared, follow-up ANOVAs and an APA write-up.

  • Compare reading, writing and maths scores across schools
  • Test a programme's effect on several wellbeing measures
  • Analyse a questionnaire with several related subscales

KEY FUNCTIONS

Pillai's trace, Wilks' lambda, Hotelling's trace and Roy's rootF approximations with exact dfMultivariate partial eta squaredFollow-up univariate ANOVAsAPA 7 report sentence
Browse research statistics & survey tools →

USE IN YOUR THESIS

Cite this calculator and export your results

APA 7 reference for software or an online tool. Cite the statistical method in your text as well.

SolveGrid. (2026). MANOVA Calculator [Online calculator]. https://solvegrid.online/manova-calculator

LEARN THE METHOD

Guides for this calculator workflow

GUIDEHow to report ANOVA results in APA styleCopy-ready APA templates for one-way, Welch, repeated-measures, and two-way ANOVA with effect sizes and post hoc tests.Read →GUIDEHow to choose a statistical testSeparate descriptive statistics, t-tests, correlation, and one-way ANOVA by the question and data type.Read →

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