How do you run a two-way ANOVA in SPSS?

Open Analyze, then General Linear Model, then Univariate. Put your continuous outcome in Dependent Variable and both categorical predictors in Fixed Factors. Request descriptives, effect size, and a profile plot, then click OK and read the Tests of Between-Subjects Effects table, starting with the interaction row.

What does the interaction in a two-way ANOVA tell you?

The interaction tests whether the effect of one factor depends on the level of the other. If it is significant, you cannot interpret the main effects in isolation and should break it down into simple effects. If it is not significant, you interpret each main effect on its own, as in a one-way design.

How do you do simple effects in SPSS after a significant interaction?

SPSS does not offer simple effects through the menus, so use the EMMEANS subcommand in syntax with COMPARE and a Bonferroni adjustment. This produces the effect of one factor at each level of the other, which is the correct follow-up to a significant interaction rather than the raw main effects.

What effect size do you report for a two-way ANOVA?

Report partial eta squared for each main effect and the interaction. Request it by ticking Estimates of effect size under Options, or add the ETASQ keyword in syntax. It expresses the proportion of variance in the outcome that each effect explains after accounting for the other terms in the model.

Two-Way ANOVA in SPSS: Interaction and Simple Effects

To run a two-way ANOVA in SPSS, you use Analyze > General Linear Model > Univariate, enter one continuous outcome and two categorical factors, and read the Tests of Between-Subjects Effects table for two main effects and, most importantly, their interaction. The interaction is the reason you ran a two-way design rather than two separate analyses, so reading it first, and following it with simple effects, is what makes the result interpretable. This guide covers the full procedure, the output, and the reporting.

When a two-way ANOVA earns its place

A two-way analysis of variance tests the effect of two categorical independent variables on one continuous outcome at the same time. It returns three results: the main effect of each factor, plus the interaction that asks whether the effect of one factor depends on the level of the other. That interaction is something a single one-way ANOVA in SPSS cannot see, and it is the whole reason to choose this design. If one of your predictors is continuous rather than categorical and you want to control for it, you move instead to analysis of covariance.

Setting up the model in General Linear Model

Open Analyze > General Linear Model > Univariate. Move the continuous outcome into Dependent Variable and both grouping variables into Fixed Factor(s). Under Options (or EM Means in newer versions), request Descriptive statistics, Estimates of effect size, and Homogeneity tests; under Plots, put one factor on the horizontal axis and the other as separate lines to build the profile plot that makes an interaction visible. The reproducible syntax, including the simple-effects comparisons you will need if the interaction is significant, is:

UNIANOVA score BY method level
  /PLOT=PROFILE(method*level)
  /EMMEANS=TABLES(method*level) COMPARE(method) ADJ(BONFERRONI)
  /PRINT=DESCRIPTIVE ETASQ HOMOGENEITY
  /CRITERIA=ALPHA(.05)
  /DESIGN=method level method*level.

The assumptions for a factorial design

The model assumes the outcome is normally distributed within each cell of the design, that the cells share a common variance, and that observations are independent. Because each cell can be small, check normality on the residuals saved from the model rather than cell by cell. SPSS prints Levene's Test across all cells when you request homogeneity tests; a result above .05 supports equal variances. Unequal cell sizes complicate the picture, because they make the choice of sums of squares matter, and the SPSS default of Type III is the right one for most unbalanced factorial designs.

Reading the interaction before the main effects

Go straight to the Tests of Between-Subjects Effects table and read the interaction row first, because it changes how you interpret everything else. If the interaction is significant, the effect of one factor genuinely depends on the other, so the standalone main effects can be misleading and you should not over-interpret them. If the interaction is not significant, you interpret the two main effects on their own terms, each as you would in a one-way design. Each row gives an F, its degrees of freedom, the significance, and, because you requested it, partial eta squared as the effect size. The wider art of reading these tables is covered in our walkthrough of SPSS output.

Following up a significant interaction with simple effects

When the interaction is significant, the correct follow-up is an analysis of simple effects: the effect of one factor at each level of the other. SPSS does not offer these through the menus, which is why the syntax above uses the /EMMEANS subcommand with COMPARE and a Bonferroni adjustment to produce them. Read the resulting pairwise comparison tables to say, for example, that the teaching method mattered for advanced students but not for beginners. This decomposition, rather than the raw main effects, is the finding your reader actually wants. Support it with the profile plot, where non-parallel lines are the visual signature of an interaction.

Reporting a two-way ANOVA in APA style

Report each effect in the form F(effect degrees of freedom, error degrees of freedom) = value, the exact p-value, and partial eta squared, leading with the interaction. A clean passage reads: there was a significant interaction between teaching method and prior level, F(2, 114) = 4.88, p = .009, partial eta squared = .079. Simple-effects analysis showed that the blended method outperformed lecture for advanced students, p = .001, but the methods did not differ for beginners, p = .43. State which sums of squares you used if your design was unbalanced. The decimal and italics conventions are in the APA conventions for statistics, and the passage becomes part of your dissertation's results chapter.

Common mistakes in a factorial analysis

The recurring errors are interpreting main effects while ignoring a significant interaction, forgetting to request an effect size, reading cell-by-cell normality on tiny cells instead of the residuals, and skipping the simple-effects breakdown that gives the interaction meaning. Plan the design with balanced cells where you can, decide your follow-up comparisons in advance, and lead the write-up with the interaction. Treated this way, the two-way ANOVA tells a richer story than two separate group comparisons ever could.

How to run a two-way ANOVA in SPSS