Two-Way ANOVA and Interactions: How to Read, Interpret and Report Them

When to use a two-way ANOVA, what a main effect and an interaction are, how to run it in SPSS (Univariate), how to read an interaction plot, simple effects and APA reporting.

Part of the series: Statistical Analysis for a Seminar Paper or Thesis: The Complete Guide

A two-way ANOVA tests the effect of two categorical independent variables on a continuous outcome - and above all the interaction between them. For example: does exam anxiety depend on gender, on exam type (oral/written), and is the oral-written difference different for men and women?

Three questions in one analysis

1. Main effect of A (gender): do men and women differ in anxiety, averaged over exam types?
2. Main effect of B (exam type): do oral and written differ, averaged over genders?
3. A×B interaction: does the effect of exam type depend on gender?

The interaction is usually why you run a two-way ANOVA rather than two separate analyses - and often it's the central hypothesis.

In SPSS

Analyze → General Linear Model → Univariate. Outcome in Dependent Variable, both factors in Fixed Factor(s). - Plots: one factor on Horizontal Axis, the other in Separate Lines → Add. That's the interaction plot. - Options: Descriptive statistics, Estimates of effect size, Homogeneity tests. - EM Means: move the interaction (A*B) across and tick Compare simple main effects.

Reading the output

Levene's Test: as in a one-way ANOVA - if significant, say so; with similar group sizes the analysis is fairly robust.

Tests of Between-Subjects Effects is the key table: for each of the three rows (A, B, AB), F, df, Sig. and Partial Eta Squared*.

The important order: look at the interaction first. If it's significant, main effects can mislead - "no difference on average" can hide large differences in opposite directions.

Reading the interaction plot

• Parallel lines: no interaction - B has the same effect at every level of A.
• Converging or diverging lines: an interaction - B's effect is stronger in one group.
• Crossing lines: a strong, sometimes reversed interaction - B works one way in one group and the opposite way in the other.

The plot alone isn't enough; you need the significance of the A*B row.

Simple effects

When the interaction is significant, test one factor's effect at each level of the other: does exam type matter for women? For men? The EM Means Pairwise Comparisons table gives exactly that, Bonferroni-corrected.

Reporting in APA

"There was a significant gender × exam type interaction, F(1, 156) = 8.21, p = .005, ηp² = .05. Simple-effects analysis showed that among women, anxiety before an oral exam (M = 3.92, SD = 0.58) was higher than before a written one (M = 3.24, SD = 0.66), p < .001, whereas among men exam type made no difference (p = .41). The main effect of exam type was significant, F(1, 156) = 12.40, p < .001, ηp² = .07, but should be read in light of the interaction."

Include the plot as a figure.

Common mistakes

• Interpreting main effects without qualification when the interaction is significant.
• Calling partial η² plain η² (or vice versa) - Univariate gives partial η²; write ηp².
• Two separate one-way analyses instead of a two-way - you miss the interaction.
• Confusing it with moderation in regression: if one variable is continuous (e.g. age), it's moderation in PROCESS, not ANOVA.

FAQ

The same people measured in every condition? That's a repeated-measures (or mixed) ANOVA - GLM → Repeated Measures.

Only one independent variable with 3 levels? Then it's a one-way ANOVA.

Where does it fit? Step 4 of 7: Statistical analysis for a seminar paper: the complete guide; on effect sizes: Effect sizes. An interaction you can't make sense of? Tell us.

Last updated: 2026-10-01