How to Interpret MANOVA Output in SPSS (and Report It in APA 7)

A MANOVA (multivariate analysis of variance) compares groups on two or more continuous outcomes measured together. SPSS's GLM > Multivariate procedure prints several tables, and the main result sits in the Multivariate Tests table, but you must also check Box's M test, the univariate follow-ups, and Levene's test for each outcome. This guide reads every table row by row with a worked example (three teaching methods, exam score and course satisfaction), flags the misreadings that cost marks, and ends with the APA 7 write-up. For the reporting format on its own, see the MANOVA APA guide.

What SPSS gives you

Analyze > General Linear Model > Multivariate, with the outcomes in Dependent Variables, the grouping factor in Fixed Factor(s), Descriptive Statistics and Homogeneity Tests ticked under Options, and Display Means for your factor, produces:

1. Between-Subjects Factors: the grouping variable and group counts.
2. Descriptive Statistics: N, mean, and standard deviation for each group on each outcome, plus totals.
3. Box's Test of Equality of Covariance Matrices: whether the groups have similar variance-covariance structures, judged at α = .001.
4. Multivariate Tests: four statistics (Pillai's Trace, Wilks' Λ, Hotelling's Trace, Roy's Largest Root) for the intercept and factor, each with F, df, p, and partial eta squared. This is the main result.
5. Levene's Test of Equality of Error Variances: homogeneity of variance for each outcome separately.
6. Tests of Between-Subjects Effects: univariate ANOVA tables for each outcome.

The worked example

Sixty-nine students took an exam and rated course satisfaction after one of three teaching methods (Lecture, Video, or Interactive; 23, 22, and 24 per group). Exam score ranged 0 to 100; satisfaction 1 to 5.

Table 1: Descriptive Statistics

• Video had the highest exam mean and highest satisfaction; Lecture the lowest on both.
• These are raw (unadjusted) means. The multivariate test considers both outcomes together.

Table 2: Box's Test of Equality of Covariance Matrices

Box's test checks whether the groups have similar variance-covariance structures. Sig. = .331 is well above the α = .001 used for this test, so there is no evidence against equal covariance matrices; it does not prove they are equal. The very large df2 is normal: SPSS uses an F approximation whose second df grows with the sample. This Sig. is not your MANOVA result.

Table 3: Multivariate Tests

• Intercept block: grand mean. Not reported.
• teaching_method block: your effect. Report Wilks' Λ by convention: Λ = .735, F(4, 130) = 5.41, p < .001, partial η² = .14. Teaching method accounted for about 14% of variance in the combined outcomes.
• Partial eta squared by statistic (each has its own formula):
  • Wilks' Λ: 1 − Λ^(1/s) where s = min(k−1, p) = 2. So 1 − .735^(1/2) = .143.
  • Pillai's Trace: V/s = .265/2 = .133.
  • Hotelling's Trace: (T/s) / ((T/s) + 1) = .153.
  • Roy's Largest Root: θ / (1 + θ) = .265.

When the multivariate test is significant, run univariate follow-ups (Table 5).

Table 4: Levene's Test of Equality of Error Variances

Levene's test checks equal variance per outcome. Both Sig. values are above .05, so there is no evidence that the assumption is violated. If Levene's were significant, interpret that univariate F cautiously.

Table 5: Tests of Between-Subjects Effects

Follow-up univariate ANOVAs with Bonferroni-corrected alpha = .025 (α = .05 / 2 outcomes).

• Exam Score: F(2, 66) = 10.84, p < .001, partial η² = .25. Significant at .025. Teaching method affects exam scores.
• Satisfaction: F(2, 66) = 1.91, p = .156, partial η² = .05. Not significant at .025. No significant effect of teaching method on satisfaction.

The multivariate test is significant because the exam effect is strong. Satisfaction alone is not significant, but their combination shows a multivariate effect.

Misreadings that cost marks

• Reporting Box's M p as the MANOVA result. Box's M tests assumptions; the multivariate result is Table 3.
• Using wrong partial eta squared. For Wilks' Λ, η² = 1 − Λ^(1/s) = .14, not Roy's .27 or 1 − Λ.
• Reporting all four multivariate statistics. Use Wilks' Λ by default. Saying all four agree is unnecessary.
• Writing p = .000. Write p < .001.
• One df only. Report both: F(4, 130).
• Skipping Bonferroni correction. Two outcomes mean α = .025 per test, not .05.
• Not checking Levene's test. If significant, the univariate F for that outcome needs caution.
• Mixing univariate effect sizes. Report partial η² from Tests of Between-Subjects Effects for each outcome, not from the multivariate block.

The APA 7 format template

A one-way MANOVA revealed a significant multivariate effect of [independent variable] on the combined outcomes, Wilks' Λ = .XX, F(df1, df2) = X.XX, p = .XXX, partial η² = .XX. Follow-up univariate ANOVAs with Bonferroni-corrected alpha = .025 showed [which outcomes were significant and which were not].

The write-up for this example

A one-way MANOVA revealed a significant multivariate effect of teaching method on the combined outcomes (exam score and course satisfaction), Wilks' Λ = .73, F(4, 130) = 5.41, p < .001, partial η² = .14. Follow-up univariate ANOVAs with Bonferroni-corrected alpha = .025 showed a significant effect of teaching method on exam score, F(2, 66) = 10.84, p < .001, partial η² = .25, but not on course satisfaction, F(2, 66) = 1.91, p = .156. Descriptively, the Video group scored highest on the exam (M = 80.14, SD = 5.77), followed by Interactive (M = 75.33, SD = 5.87) and Lecture (M = 70.52, SD = 8.72).

Let KyroStat do the write-up for you

A MANOVA has many moving parts: four multivariate statistics, two df sets, Box's M, univariate follow-ups with Bonferroni correction, and multiple effect sizes. KyroStat runs the MANOVA on your data, checks assumptions, applies the correction, and hands you the finished APA 7 sentences, a publication-ready table, diagnostic plots, and the underlying Python code.

Also useful for the write-up (affiliate links): Proofreading for your thesis or paper (20% off with code PAP20): Paperpal

Frequently asked questions

Which statistic should I report? Wilks' Λ by default. Switch to Pillai's Trace when Box's M is significant (at .001), especially with unequal group sizes: it is the most robust of the four to that violation.

Why do the partial eta squared values differ among the four statistics? Each statistic has its own partial eta squared formula. Wilks' uses 1 − Λ^(1/s), Pillai uses V/s, and so on. They measure effect size differently.

My multivariate test is significant but some univariate tests are not. Is that possible? Yes. The multivariate test considers outcomes together; univariate tests look at each alone. A strong effect on one outcome combined with weak effects on others can produce a significant multivariate test.

Box's M is significant at .05. Should I worry? Box's M is judged at α = .001, not .05. If it is significant at .001, there is evidence against equal covariance matrices; then report Pillai's Trace instead of Wilks' Λ.

Do I always report univariate ANOVAs? Only if the multivariate test is significant. If it is not, you stop there.

What is the Bonferroni correction? Divide α = .05 by the number of dependent variables. With 2 outcomes, α = .025 per test. This controls the family-wise error rate.

Can I use MANOVA with unequal group sizes? Yes, but check Box's M carefully and consider reporting Pillai's Trace. Unequal sizes can reduce power and introduce bias if assumptions are violated.

Which related guides might I need? One-way ANOVA output, ANCOVA output, Levene's test, post hoc tests, partial eta squared, and the MANOVA reporting guide.