METHOD GUIDE
Two-Way MANOVA in SPSS
Reading the Interaction Before the Main Effects
Several outcomes turn one interaction into a question asked of the set and of each outcome, and the number of follow-up tests grows with every outcome added. Cell sizes, a reading order for the multivariate blocks and an adjustment planned in advance keep that work manageable.
IN SHORT
What a Two-Factor Multivariate Model Tests
A two-way MANOVA tests the effects of two categorical factors, and of their interaction, on a set of related continuous outcomes taken together, and it asks whether the pattern of group means across the outcomes depends on the combination of both factors. To run two-way MANOVA in SPSS, open Analyze, General Linear Model, Multivariate, enter the outcomes as Dependent Variables and both factors as Fixed Factors, request profile plots under Plots, and read the interaction block of the multivariate tests before either main effect. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, carries out and reviews this analysis through an in-house PhD-level statistician.
ANALYSIS SUPPORT
Analysis Support for This Method
A factorial model with several outcomes has more places to go wrong than either idea alone. Support starts from the design, and it also shows where a simpler model would answer the question.
MANOVA
Several outcomes analyzed jointly across two factors within your study design, with the cell structure, the interaction and its follow-up across outcomes agreed for your data.
Comparative & Hypothesis Testing
The group-comparison family that holds factorial designs, for when the number of outcomes or the design is not yet settled and the model still has to be chosen.
BEFORE YOU RUN IT
Design Questions That Come Before the Model
Two factors and several outcomes make the structure of the design the first thing to examine, and these four questions shape every table that follows.
Cell Sizes Every cell of the cross needs more cases than there are outcomes. Empty or tiny cells make the covariance matrix unreliable, and unequal sizes change how the effects are tested.
Balanced or Not With unequal cell sizes the factors overlap, and SPSS uses Type III sums of squares by default. Whether that suits the question is judged from how the imbalance arose, not from convenience.
Fixed Factors Both factors should be fixed, with levels the study chose. A factor whose levels are a sample of many possible ones, such as classrooms, calls for a mixed or multilevel model.
A Plan for the Interaction Decide in advance what a significant interaction will lead to: simple effects of one factor within the levels of the other, for which outcomes, and under what adjustment.
IN SPSS
How to Run Two-Way MANOVA in SPSS
This outline follows IBM SPSS and stops at the settings that change the output. Check the dialog labels against your own version.
- Check the cross of the two factors: one row per case, both factors coded, outcomes in separate columns.
- Open Analyze, General Linear Model, Multivariate, and enter the outcomes and both Fixed Factors.
- Under Plots, add profile plots of the cell means for each outcome, with one factor on the horizontal axis and the other as separate lines.
- Under Options, ask for descriptives, effect size estimates and homogeneity tests.
- Read Box’s test, then the blocks of the multivariate tests in order: the interaction first, then the main effects.
- Where the interaction calls for simple effects, request them through pasted syntax, since the dialog compares marginal means for main effects only.
READING THE OUTPUT
The Tables in Reading Order, From the Interaction Outward
The SPSS multivariate tests table has one block of four statistics per model term, and the order in which the blocks are read changes what each one means.
| Output element | What it tells you | What to check |
|---|---|---|
| Between-Subjects Factors | The levels of each factor and the number of cases at each level | That every cell of the cross holds cases, since the counts here are by factor, not by cell |
| Box’s Test of Equality of Covariance Matrices | Whether the covariance matrices are equal across all cells of the design | That a significant result is weighed against the cell sizes, as unequal cells make it matter more |
| Multivariate Tests, interaction block | The four statistics for the joint effect of the two factors on the set of outcomes | That it is read before the main effects, and that the one statistic named in advance is the one quoted |
| Multivariate Tests, main effect blocks | The effect of each factor on the outcome set, averaged over the levels of the other | That a main effect is described as an average only where the interaction does not qualify it |
| Tests of Between-Subjects Effects | A univariate two-way ANOVA for each outcome, including its interaction row | That it is a follow-up under a stated adjustment, as the interaction can appear for one outcome and not another |
| Descriptive Statistics | The mean, standard deviation and N in each cell for each outcome | That cell means, not marginal means, are used to describe an interaction |
| Profile Plots | One plot of cell means for each outcome | That non-parallel lines are judged with the test or an interval, not by eye alone |
REPORTING
Reporting the Multivariate Interaction and the Main Effects It Qualifies
The interaction leads the write-up, and each main effect is reported only with the qualification the interaction requires.
Report the interaction first, with the statistic chosen in advance and its degrees of freedom: Wilks’ Λ = ___, F(df1, df2) = ___, p = ___, partial η² = ___. Then give the same for each main effect, qualifying any main effect that an interaction contradicts. Partial eta squared comes without an interval in the GLM output, so any interval is taken from another program. If the interaction is followed up, say for which outcomes, which simple effects were tested and what adjustment covered both outcomes and comparisons. Add a table of cell means and standard deviations for each outcome with the cell sizes, include the profile plots, and name the type of sums of squares when the cells are unequal.
COMMON MISTAKES
Errors That Surface When Two Factors Meet Several Outcomes
Most points reviewers raise concern the interaction: how it was read, which outcomes it was followed up for and how many tests that created.
Univariate Rows Read Before the Joint Test Opening the Tests of Between-Subjects Effects first and reporting whichever outcome shows an interaction skips the joint test the model was chosen for. The multivariate interaction block is read first, and the univariate rows follow it as planned.
Interaction Missed by Power A non-significant interaction in a design with small cells is not evidence that there is none, and the plot may still show a clear departure. The wording says what the data can and cannot exclude.
Family Counted Within One Outcome An adjustment that covers the simple effects within one outcome ignores the same tests repeated across the others. The family is defined across outcomes and comparisons together, and the report states its size.
Empty or Thin Cells A cell with few cases, or none, makes the covariance matrix unreliable and Box's test uninformative. The count per cell is checked before the model is run, not after the output arrives.
Marginal Post Hoc After Interaction Post hoc comparisons of a factor's marginal means average over the other factor. After a significant interaction they can describe an average that fits no single level of that factor.
One Story for All Outcomes A significant multivariate interaction does not mean that every outcome shows it. The pattern in each outcome is described on its own before the interpretation is written.
Analysis finished? Independent Statistical Review examines the interaction handling, the follow-up and the tables you plan to submit.
FREQUENTLY ASKED QUESTIONS
Questions About Two-Factor Multivariate Output
Simple effects across several outcomes, unbalanced cells and a covariate added to the model are the output questions taken first.
How are MANOVA interaction effects followed up in SPSS?
A significant multivariate interaction is followed up with simple effects of one factor within each level of the other, tested for the outcomes your plan names. The univariate interaction rows show which outcomes carry it, the profile plots show its shape, and the simple effects, usually requested through pasted syntax, test it. The adjustment has to count both the outcomes and the comparisons, and it is decided before the results are read.
Should I worry that my cells have unequal sizes?
Unequal sizes are manageable, but they change what the main effects mean and make Box’s test matter more. SPSS uses Type III sums of squares by default, a common choice for unbalanced factorial designs, which tests each effect adjusting for the others. If the sizes differ because of dropout related to the outcome, the problem lies in the design and not in the output, and it is reported as a limitation.
Can I add a covariate to a two-way MANOVA?
Yes, by placing the covariate in the Covariate(s) box of the Multivariate dialog, which makes the model a MANCOVA. The covariate should be measured independently of the factors, and its relation to each outcome should be similar across cells. A covariate that the factors themselves influence can distort the adjusted comparison instead of improving it.
Could a statistician set the simple-effects plan across all my outcomes?
Yes. An in-house PhD-level statistician can check the cell sizes, settle the order of reading and the simple-effects plan before results are interpreted, and carry out the model or review one you have run. Results Reporting & Interpretation covers the tables and the wording alone. The interpretation and the conclusions remain with you.
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