Reporting MANOVA Results in SPSS
One Result From Two Layers of Output
Reporting MANOVA results in SPSS means telling a multivariate result and its univariate follow-ups as one account: the statistic chosen and the reason, its F with both df, partial eta squared, and the adjusted tests for each outcome.
IN SHORT
The Elements of a Two-Layer MANOVA Result
A MANOVA report names the multivariate statistic and the reason for choosing it, gives its F with both degrees of freedom, the p-value and partial eta squared, and then reports the follow-up as it was actually run, usually univariate tests against an adjusted criterion or a discriminant follow-up. For reporting MANOVA results in SPSS, the values come from the Multivariate Tests table and the Tests of Between-Subjects Effects table of the General Linear Model, Multivariate procedure, and labels differ between releases. A table of means for each outcome by group completes the account. Reports built on two layers of output are among the tasks that in-house PhD-level statisticians at OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, prepare or check against the saved output.
In This Guide
METHOD SUPPORT
Pages for the Analysis Behind the Report
Whether the comparison stays multivariate or turns to discriminant functions sets what the report can say, and each route has its own method page.
MANOVA
Several related outcomes compared across groups in one model, with the design, assumptions and follow-up strategy settled for your data.
Discriminant Analysis
The combination of outcomes that best separates the groups, used as a follow-up to a multivariate result or as a method on its own.
BEFORE THE RESULT IS TOLD
Choices That Shape the Multivariate Account
These choices are made before the follow-up tables are read, because they decide what is reported and which criterion the univariate tests are held to.
Which Multivariate Statistic Four statistics are printed. Choose one in advance and name it. The one most robust to unequal covariance matrices is a common choice, and with two groups all four give the same F.
The Follow-Up Strategy Say before the tables are read whether the follow-up is univariate tests with an adjusted criterion, a discriminant analysis or another approach, and report the one that was run.
The Adjusted Criterion SPSS does not adjust the p-values of the univariate tests. A Bonferroni criterion of alpha divided by the number of outcomes is applied by hand, and the report states it.
Covariance Matrices Box's Test of Equality of Covariance Matrices is judged with the group sizes, since it is sensitive to non-normality and often significant in large samples. The report says what was concluded.
IN SPSS
Building the Account From Two Tables
IBM SPSS prints the multivariate and univariate layers separately, and the choice of test and follow-up is explained in One-Way MANOVA in SPSS: Checks and Reporting.
Take the Multivariate Statistic
From the Multivariate Tests table, take the row of the factor, not the Intercept, with the statistic you named: its Value, F, Hypothesis df, Error df and Sig.
Check: Use the Hypothesis df and Error df of the same row as the two degrees of freedom of F, and read the footnotes to see whether that F is exact or approximate before wording it.
Take Partial Eta Squared
Take Partial Eta Squared, printed when Estimates of effect size is ticked under Options, from the same row of the Multivariate Tests table, and name it as the multivariate partial eta squared.
Watch: Partial eta squared in this table is derived from the statistic of its own row, so it changes if another of the four is reported. Quote the value belonging to the statistic you named.
Take the Univariate Tests
From Tests of Between-Subjects Effects, take F, df and Sig. on the factor row for each outcome, and Partial Eta Squared when requested, leaving out Intercept and Corrected Model.
Watch: These p-values are not adjusted. Compare each with the criterion you set, such as alpha divided by the number of outcomes, and report which outcomes passed it.
Take the Means for Each Outcome
From the Descriptive Statistics table, take the mean, Std. Deviation and N of each outcome in each group.
Tip: One table of means and standard deviations for all outcomes, with the univariate F beside it, lets the multivariate and univariate layers read as a single result.
Take the Pairwise or Discriminant Output
If groups are compared pairwise, take the Multiple Comparisons table for each outcome, or the discriminant output if that was the follow-up.
Check: Report pairwise comparisons only as the plan allowed, for instance for outcomes that passed the adjusted criterion, and state how many comparisons the adjustment covered.
Join the Two Layers in the Text
Begin with the multivariate clause, then add one clause per outcome from the frame below, and check the clauses and the table shell against the output.
Check: The outcomes named in the sentence, the table and the follow-up paragraph should form one list, in one order. A missing outcome is hard for a reader to spot.
READING THE OUTPUT
Where Each MANOVA Output Value Goes in the Report
The output runs from Box's test through the multivariate rows to the univariate rows, and the write-up keeps that order.
| Output value | Where SPSS prints it | Where it goes and what to check |
|---|---|---|
| Box’s M, F, df1, df2 and Sig. | Box’s Test of Equality of Covariance Matrices | A clause on the covariance matrices, read together with the group sizes |
| Levene’s statistic for each outcome | Levene’s Test of Equality of Error Variances | A brief mention, outcome by outcome, where the univariate tests are interpreted |
| Pillai’s Trace, Wilks’ Lambda, Hotelling’s Trace, Roy’s Largest Root | Multivariate Tests, factor row | One statistic is named and reported; the others are not listed in the sentence |
| F, Hypothesis df, Error df and Sig. | Multivariate Tests table | F(df1, df2) of the named statistic, with p |
| Partial Eta Squared, multivariate | Multivariate Tests table | Named as multivariate partial eta squared, for the statistic that was reported |
| Correlations among the outcomes | Residual SSCP matrix option, or Bivariate Correlations | A short matrix or a sentence showing why a joint test suited the outcomes |
| F, Sig. and Partial Eta Squared per outcome | Tests of Between-Subjects Effects | The univariate layer, reported against the adjusted criterion |
| Mean and Std. Deviation | Descriptive Statistics | The table of means for every outcome by group |
| Mean Difference (I-J) with 95% Confidence Interval | Multiple Comparisons | Pairwise results for each outcome, with the adjustment named |
REPORTING
A Two-Layer Result Sentence and a Table of Means
The first sentence carries the multivariate result, the second the univariate follow-ups, and the table shows every outcome by group.
In MANOVA APA format the multivariate result comes first, with the statistic named, for example Wilks’ Λ = ___, F(___, ___) = ___, p = ___, partial η² = ___. The univariate layer follows, and reporting multivariate and univariate results together means stating the adjusted criterion before the outcome-by-outcome values. The frame below is for one factor with several outcomes, and a factorial design reports the interaction before the main effects. Pairwise comparisons, if run, carry their adjustment. A table lists the mean and standard deviation of each outcome by group, with its univariate F beside it.
A one-way MANOVA on [outcome 1], [outcome 2] and [outcome 3] showed [a statistically significant / no statistically significant] effect of [factor], [Wilks’ Λ / Pillai’s V] = ___, F(___, ___) = ___, p = ___, partial η² = ___. Univariate tests used a Bonferroni-adjusted criterion of α = ___. [Outcome 1] differed between groups, F(___, ___) = ___, p = ___, partial η² = ___, whereas [outcome 2] did not meet the adjusted criterion, F(___, ___) = ___, p = ___. Group means are given in Table 1.
| Table 1. Means and Standard Deviations of [Outcomes] by [Group], With Univariate Tests | |||
|---|---|---|---|
| Outcome | [Group A] M (SD) | [Group B] M (SD) | F(___, ___), p, partial η² |
| [Outcome 1] | ___ (___) | ___ (___) | ___, ___, ___ |
| [Outcome 2] | ___ (___) | ___ (___) | ___, ___, ___ |
| [Outcome 3] | ___ (___) | ___ (___) | ___, ___, ___ |
| Note. Multivariate test: [statistic] = ___, F(___, ___) = ___, p = ___. Univariate tests are judged against α = ___ (adjusted for ___ outcomes). | |||
The multivariate partial eta squared describes the strength of association between the factor and the outcomes taken together, and its value depends on which of the four statistics produced it. The univariate partial eta squared values describe each outcome alone and do not add up to the multivariate value. Each is named as such and the two are not mixed in one sentence. Where the follow-up was a discriminant analysis, the report gives the standardized coefficients or structure correlations, the functions retained and their tests, and describes the separation of the groups without a causal ordering.
COMMON MISTAKES
When the Two Layers Disagree in Print
Reading the finished paragraph against both tables, the multivariate and the univariate, shows where the two layers part company.
Roy's Bound Read as an Exact p The F for Roy's Largest Root carries a footnote calling it an upper bound, which makes its p-value a lower bound. Quoted without that caveat it overstates the evidence, and another statistic is usually the better one to name.
Statistic Left Unnamed Four statistics are printed, and their F and p can differ when there are more than two groups. A result without the name of the one reported cannot be checked.
Univariate df Attached to the Multivariate F The df on an outcome's row of Tests of Between-Subjects Effects belong to that univariate F alone. Attached to the multivariate statistic they misreport it, because its own df are the Hypothesis df and Error df of its row.
Follow-Ups Called Protected A significant multivariate test controls the error rate only under the overall null, so univariate tests that follow it are not called protected, and the adjustment is still reported.
Outcomes Listed Differently A different set of outcomes in the text, the table and the follow-up paragraph confuses the reader. One list, in one order, runs through all three, and it matches the design.
Partial Eta Squared Mixed Across Layers The multivariate and univariate values describe different things. A univariate value quoted beside a multivariate F, without saying which, misstates the result.
Multivariate and univariate F values sharing one paragraph? Independent Statistical Review checks that every value carries the df and effect size of its own table.
FREQUENTLY ASKED QUESTIONS
Correlated Outcomes, Adjustment and a Null Joint Test
Correlated outcomes are what a joint test is for, the adjusted criterion governs the univariate follow-ups, and a null multivariate result limits what one outcome can claim.
Should the correlations among the outcomes be reported?
Usually yes, as a short matrix or a sentence, since they show why a joint test suited these outcomes. Near-zero correlations suggest that separate analyses may serve as well, and very high ones redundant measures. GLM does not print them by default; the Residual SSCP matrix option prints the pooled within-group correlations, under wording that varies by release.
Do I adjust the univariate p-values after a significant MANOVA?
Usually yes: the criterion is adjusted for the number of outcomes, since SPSS prints unadjusted p-values. A Bonferroni criterion is the simplest, and the report states it. A discriminant follow-up is an alternative when the outcomes are strongly correlated and the aim is to describe how they separate the groups together.
What if the multivariate test is not significant but one outcome is?
That univariate result is not presented as a finding unless it was specified in advance. If the univariate tests were planned as primary, they are reported with their adjustment and the multivariate result is described as it came. Presenting a single significant outcome after a null multivariate test as a discovery is selective reporting.
What is checked when a MANOVA report arrives with its output?
Four points are compared with the output: the statistic named, the df taken from its row, the criterion on the univariate tests and the means table. An in-house PhD-level statistician at OnlineSPSS checks each, or prepares the report when no draft exists. The service is Results Reporting & Interpretation, and interpreting the outcomes is the researcher’s task.
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