How to Report a MANOVA in APA 7 (With Example)

A MANOVA (multivariate analysis of variance) tests whether groups differ on two or more continuous outcome variables considered together. The write-up is where people slip, because you have to report a multivariate test first and only then the follow-up univariate tests. This guide gives you the exact APA 7 format, a worked example you can copy, and the mistakes reviewers catch.

What you need before you write a single word

An APA 7 write-up of a one-way MANOVA needs these values from your output:

1. The mean (M) and standard deviation (SD) for each group on each dependent variable.
2. A multivariate test statistic, most often Wilks' Λ (report Pillai's Trace instead when assumptions are shaky).
3. The multivariate F approximation with its two degrees of freedom (hypothesis df and error df).
4. The exact p value for the multivariate test.
5. A multivariate effect size, usually partial eta squared.
6. The follow-up univariate ANOVAs (one per dependent variable), each with its own F, df, p, and effect size, ideally with a corrected alpha.

The APA 7 format template

Report the multivariate result first, in running text:

A one-way MANOVA revealed a significant multivariate effect of [independent variable] on the combined dependent variables, Wilks' Λ = .XX, F(df1, df2) = X.XX, p = .XXX, partial η² = .XX.

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Formatting rules reviewers actually check:

• Italicize the statistical symbols: M, SD, F, p.
• Report both degrees of freedom for the multivariate F in parentheses, hypothesis df first: F(4, 172).
• No leading zero on p, on Wilks' Λ, or on partial η² (none can exceed 1).
• Round the F and Wilks' Λ to two decimals; report p to two or three decimals, and if it is below .001, write p < .001.
• Name the multivariate statistic you used. Wilks' Λ is the default; Pillai's Trace is more robust when group sizes are unequal or the covariance assumption is violated.

A worked example

Suppose you compared three teaching methods on two outcomes measured together, exam score and course satisfaction, with 30 students per group.

• Multivariate result: Wilks' Λ = .82, F(4, 172) = 4.41, p = .002, partial η² = .09
• Follow-up ANOVAs (Bonferroni-corrected alpha = .025): exam score, F(2, 87) = 5.83, p = .004, partial η² = .12; satisfaction, F(2, 87) = 2.10, p = .129.

Written up in APA 7, that becomes:

A one-way MANOVA revealed a significant multivariate effect of teaching method on the combined outcomes, Wilks' Λ = .82, F(4, 172) = 4.41, p = .002, partial η² = .09. Follow-up univariate ANOVAs with a Bonferroni-corrected alpha of .025 showed a significant effect on exam score, F(2, 87) = 5.83, p = .004, partial η² = .12, but not on course satisfaction, F(2, 87) = 2.10, p = .129.

The multivariate sentence establishes that the groups differ on the outcomes as a set; the univariate sentences say which specific outcome carries the effect.

The APA 7 table (recommended for MANOVA)

With several groups and several outcomes, a descriptives table earns its place:

Note. The multivariate effect of teaching method was significant, Wilks' Λ = .82, F(4, 172) = 4.41, p = .002, partial η² = .09.

Mistakes reviewers catch

• Skipping the multivariate test. Reporting only the univariate ANOVAs defeats the purpose of a MANOVA. Report the multivariate result first.
• Not correcting the follow-ups. Running one ANOVA per outcome at alpha = .05 inflates the false-positive rate. Use a Bonferroni-corrected alpha or another correction.
• Not naming the statistic. Say whether you used Wilks' Λ or Pillai's Trace, and why.
• A leading zero on Wilks' Λ, p, or partial η². APA drops it for values that cannot exceed 1.
• Using MANOVA when the outcomes are unrelated. MANOVA is for outcomes that are conceptually and statistically correlated; for unrelated outcomes, separate ANOVAs with a correction are cleaner.

Before you report: did the test's assumptions hold?

A one-way MANOVA assumes:

• Independence of observations.
• Multivariate normality of the dependent variables within each group.
• Homogeneity of the variance-covariance matrices across groups, checked with Box's M test. If Box's M is significant, especially with unequal group sizes, report Pillai's Trace rather than Wilks' Λ.
• Linear relationships among the dependent variables and no severe multicollinearity.

When the multivariate effect is significant, the usual follow-up is a set of univariate one-way ANOVAs, one per outcome. See the assumptions guide for how to check each condition, and the effect size guide for choosing and formatting partial eta squared.

Let KyroStat do the write-up for you

A MANOVA has a lot of moving parts: the multivariate statistic, two sets of degrees of freedom, Box's M, and corrected follow-up tests. KyroStat runs the MANOVA on your data, checks the assumptions, applies a correction to the follow-ups, and hands you the finished APA 7 sentences, a publication-ready table, the plots, and the underlying Python or R code. Upload your spreadsheet, and the report is done in seconds.

Run a MANOVA yourself, in the browser

Here is a real one, runnable in your browser with no installation. iris ships with R: 150 flowers from three species, measured on four variables. This asks whether the species differ on sepal length and petal length together.

# MANOVA: do the three iris species differ across
# sepal length and petal length together?
fit <- manova(cbind(Sepal.Length, Petal.Length) ~ Species, data = iris)
summary(fit)

Running that gives:

Df Pillai approx F num Df den Df    Pr(>F)    
Species     2 0.9885   71.829      4    294 < 2.2e-16 ***
Residuals 147                                            
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Every number in the write-up above comes from output like this. If you want the mechanics rather than the reporting, the free R lesson on this walks through it step by step, and the playground is there whenever you want to try something.

Frequently asked questions

Wilks' Λ or Pillai's Trace? Wilks' Λ is the conventional default. Switch to Pillai's Trace when group sizes are unequal or Box's M is significant, because it is more robust to those violations.

Why is my Wilks' Λ smaller when the effect is bigger? Wilks' Λ is the proportion of variance not explained by the grouping, so smaller values mean a stronger effect. That is the opposite direction to F, which is why you report both.

Do I always run follow-up ANOVAs? Only if the multivariate test is significant. If it is not, you stop there rather than fishing through the individual outcomes.

Which effect size do I report for a MANOVA? Partial eta squared for the multivariate effect, reported without a leading zero, for example partial η² = .09.

What do I report if MANOVA is not the right fit? With a single outcome, a one-way ANOVA or, with two factors, a two-way ANOVA. When the same participants give every outcome at several time points, a repeated-measures ANOVA fits better. Report the multivariate effect size as partial eta squared, and check normality per outcome with Shapiro-Wilk.

Which related guides might I need? Often these: mixed ANOVA, post hoc tests and Levene's test.