METHOD GUIDE
Two-Way ANOVA in SPSS
Read the Interaction First, Then Follow Up
The interaction row decides how every other row in the output can be read. This guide covers the design checks, the order in which to read the tables, the follow-up of simple main effects, the effect sizes with intervals and the APA 7 write-up.
IN SHORT
What the Design Asks and Where the Answer Sits
A two-way ANOVA crosses two between-subjects factors and asks three questions at once: whether the outcome differs across the first factor, across the second, and whether the effect of one factor depends on the level of the other. That last question is the interaction, and it comes first, because a main effect averaged over a changing pattern can mislead. To run a two-way ANOVA in SPSS, open Analyze, General Linear Model, Univariate, enter both factors as fixed factors, and read the interaction row of the Tests of Between-Subjects Effects table 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 sits within a wider family of group comparisons. These pages describe support for the factorial analysis itself, and One-Way ANOVA covers the single-factor case.
Comparative & Hypothesis Testing
The family of group comparisons where factorial designs are supported, with the model, the follow-up of an interaction and the reporting agreed for your design.
ANCOVA
The group comparison adjusted for baseline covariates, for when a continuous baseline measure belongs in the model next to the factors.
BEFORE YOU RUN IT
Decisions for a Factorial Model
A factorial model is easy to fit and easy to misread, so these four decisions are made first, and they determine which rows of the output can be interpreted at all.
Two Between-Subjects Factors Each participant falls in exactly one cell of the crossing. If one factor is measured repeatedly on the same people, the design is a mixed one and needs a different model.
Cell Sizes and Sums of Squares With unequal cell sizes, the test of a main effect depends on the type of sum of squares. SPSS uses Type III by default, and you should know what hypothesis that tests.
The Interaction as the Question State beforehand whether you expect the effect of one factor to depend on the other. That keeps the interaction a hypothesis of the study and not a result found by looking.
Manipulated or Observed Factors A randomized factor supports causal wording, while an observed factor such as sex or site supports only a description of differences. A baseline covariate may call for ANCOVA instead.
IN SPSS
How to Run a Two-Way ANOVA in SPSS
The outline is for IBM SPSS. Labels vary by version, and the follow-up of simple effects is easiest through the pasted syntax, so it is named and not walked through.
- Confirm the design: one continuous outcome and two between-subjects factors, with every cell filled.
- Open Analyze, General Linear Model, Univariate, and place the factors under Fixed Factor(s).
- Under Plots, request a profile plot of the cell means, and under Options request descriptives, effect size estimates and homogeneity tests.
- Under EM Means, request the marginal means for the interaction.
- Paste the syntax and add a COMPARE and an adjustment for the simple effects, if the interaction is present.
- Read the Tests of Between-Subjects Effects table starting with the interaction row.
READING THE OUTPUT
What Each Part of the SPSS Factorial Output Tells You
Read these elements in order, starting with the interaction row, because every main effect and marginal mean depends on what that row shows.
| Output element | What it tells you | What to check |
|---|---|---|
| Descriptive Statistics | The mean, standard deviation and N in every cell of the crossing | That no cell is empty and that cell sizes are noted, since they affect the tests |
| Levene’s Test of Equality of Error Variances | Whether the spread differs across the cells | That it is a signal only, read with the cell sizes, since unequal spread matters most when the cells are also unequal |
| Tests of Between-Subjects Effects | An F test for each factor and for the interaction, with Type III sums of squares by default | That the interaction row is read before the two main-effect rows |
| Profile Plots | The cell means drawn by level of each factor | That non-parallel lines are confirmed by the interaction test, with error bars added where your version offers them |
| Estimated Marginal Means | Model-based means with intervals for cells and for each factor | That marginal means are interpreted as averages over the other factor, which is only sensible without a strong interaction |
| Pairwise Comparisons | Differences between estimated marginal means, with an adjustment you select | That the adjustment and the family of comparisons are named |
| Partial Eta Squared | The share of variance for an effect relative to that effect plus error | That the value is labeled partial, since it is not additive across effects |
REPORTING
The APA 7 Template for a Factorial Result
The wording below is a frame with blanks, and your own output fills each one. It does not report a result.
Start with the interaction: F(df1, df2) = ___, p = ___, partial eta squared = ___, adding a 95% CI [___, ___] where the journal asks for one. The GLM output prints no interval, so it is computed from the F value and its degrees of freedom in another program. If the interaction is supported, describe the pattern and report simple main effects in SPSS as mean differences with their adjusted intervals, naming the adjustment and the comparisons it covers. If the interaction is not supported, report the main effects and say that the interaction was examined. Give the cell means, standard deviations and sizes in a table, and note the type of sums of squares if the design was unbalanced. Include an interaction plot in SPSS or another program, drawn with intervals.
COMMON MISTAKES
Mistakes Reviewers Find in Reported Factorial Analyses
Six errors draw most reviewer queries on a two-factor model, and most come from the order of reading or the scope of the follow-up.
Main Effects Read First When the interaction is present, a main effect describes an average over levels where the effect differs. Interpreting it alone can hide a reversal that the interaction shows.
Plot as the Test Lines that look parallel in a plot of means do not show that there is no interaction, because a plot is not a test and small cells leave wide uncertainty. The interaction row and its effect size decide.
Unadjusted Simple Effects Simple effects run through many separate comparisons multiply the chance of a false positive. The adjustment is chosen beforehand, and the text names it and the family of comparisons.
Sums of Squares Ignored In an unbalanced design the main-effect tests change with the type of sum of squares. Reporting results without knowing which type was used leaves the hypothesis tested unclear.
Every Cell Against Every Cell Comparing all cells pairwise in a large factorial table swamps the question with comparisons. The follow-up is limited to the contrasts that the interaction suggests and the theory supports.
Causal Wording on Observed Factors A difference between observed groups, such as sites or age bands, can reflect many things besides the factor. Causal wording belongs only to factors that were randomly assigned.
Fitted the model already? Independent Statistical Review checks the interaction, the follow-up and the wording of the effects before you submit.
FREQUENTLY ASKED QUESTIONS
Questions About Two-Way ANOVA Output
Short answers to what researchers ask once the factorial table appears, from reading the interaction and following it up to confidentiality and the assessment.
What do I do when the interaction is significant?
Describe the pattern of the interaction and follow it up with simple main effects, which compare the levels of one factor within each level of the other. The main effects are then interpreted with caution, because they average over levels that behave differently. The follow-up comparisons are limited to the ones the research question needs and are adjusted for their number.
Can I interpret main effects when the interaction is not significant?
Usually yes, with some care. A non-significant interaction is not proof that there is none, particularly in a study with small cells, so the size of the interaction effect is worth reporting. Main effects are interpreted as averages across the levels of the other factor, and the text says so.
How do I obtain the follow-up comparisons for an interaction?
The dialog does not offer them directly. They are requested through the pasted syntax by adding a comparison of the marginal means within each level of the other factor, with an adjustment such as Bonferroni. Doing this for each factor in turn gives the simple effects in SPSS, and the output appears in the Pairwise Comparisons table.
Can OnlineSPSS follow up the interaction in my factorial model?
Yes. An in-house PhD-level statistician can confirm that the model matches your design, run the simple main effects with an adjustment agreed in advance and prepare the cell means table and reporting from your own output. An existing model can also be reviewed. For the tables and reporting alone, Results Reporting & Interpretation covers that stage. The interpretation remains yours.
How do you protect my research data and confidentiality?
Your data and project details are handled confidentially, and project information is not published. Researcher names and institutions are not used publicly without permission. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, such as the dataset or the output you have, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Planning the Follow-Up
of Your Interaction?
Describe the two factors, how participants were allocated and the output you have. The model, the simple effects and the reporting are agreed with you before any work begins.
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