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' Lambda (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' Lambda = .XX, F(df1, df2) = X.XX, p = .XXX, partial eta-squared = .XX.

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' Lambda, or on partial eta-squared (none can exceed 1).
• Round the F and Wilks' Lambda 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' Lambda 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' Lambda = .82, F(4, 172) = 4.41, p = .002, partial eta-squared = .09
• Follow-up ANOVAs (Bonferroni-corrected alpha = .025): exam score, F(2, 87) = 5.83, p = .004, partial eta-squared = .12; satisfaction, F(2, 87) = 2.10, p = .128.

Written up in APA 7, that becomes:

A one-way MANOVA revealed a significant multivariate effect of teaching method on the combined outcomes, Wilks' Lambda = .82, F(4, 172) = 4.41, p = .002, partial eta-squared = .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 eta-squared = .12, but not on course satisfaction, F(2, 87) = 2.10, p = .128.

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' Lambda = .82, F(4, 172) = 4.41, p = .002, partial eta-squared = .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' Lambda or Pillai's Trace, and why.
• A leading zero on Wilks' Lambda, p, or partial eta-squared. 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' Lambda.
• 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.

Frequently asked questions

Wilks' Lambda or Pillai's Trace? Wilks' Lambda 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' Lambda smaller when the effect is bigger? Wilks' Lambda 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 eta-squared = .09.