Two-Way ANOVA: How to Run It Online and Report It in APA7
Two-way ANOVA tests the effects of two categorical factors on a continuous outcome, including whether the two factors interact.
What is Two-Way ANOVA?
Two-way ANOVA tests the effects of two categorical factors on a continuous outcome, including whether the two factors interact.
When to use it
Use it for factorial designs, for example teaching method (A, B) × class size (small, medium, large), with different participants in each combination.
Example question: Do teaching method and class size affect scores, and does the effect of method depend on class size?
Preparing your data
Long format: one row per participant, two factor columns and one outcome column.
Example dataset (simulated; first rows of 120): id, method (Lecture or Active), class_size (Small, Medium, Large), score; long format, 20 per cell.
| id | method | class_size | score |
|---|---|---|---|
| 1 | Lecture | Small | 73.0 |
| 2 | Lecture | Small | 69.0 |
| 3 | Lecture | Small | 71.0 |
| 4 | Lecture | Small | 82.0 |
| 5 | Lecture | Small | 62.0 |
| 6 | Lecture | Small | 80.0 |
Download the full example CSV to practise. If the tool asks for a different layout, follow the instructions on its page.
How to run it on StatFas
- Open the Two-Way ANOVA tool. You do not need an account to run an analysis.
- Enter your data or upload your file, laid out as described in Preparing your data.
- Select your variables. Select the outcome and the two factors. Include the interaction term.
- Choose any options the tool offers (for example the confidence level, a post hoc test or the error bar type) and run the analysis.
- Read the results on the page. Check the assumptions first, then the test statistic, the p-value and the effect size.
- To save your results, log in or create a free account. Every analysis stays free; the account is only needed to download.
Assumptions and checks
- Independent observations; each person appears in one cell only.
- Roughly normal residuals in each cell.
- Homogeneity of variance across cells (Levene's test).
- Check cell sizes: unequal cell sizes need Type III sums of squares, and very small cells weaken the test.
Key numbers to look at
- Main effect of factor A, main effect of factor B and the A × B interaction, each with F, df and p.
- Partial η2 for each effect.
- Cell means and an interaction plot.
- Simple effects or post hoc tests if the interaction is significant.
Effect size
Partial η2 ≈ .01 small, .06 medium, .14 large.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Two-Way ANOVA in APA7 style
Template
Worked example (simulated data)
The numbers below were computed from the example CSV above, so you can reproduce them. They illustrate the format and are not real findings.
| Method | Class size | Cell mean |
|---|---|---|
| Lecture | Small | 71.7 |
| Lecture | Medium | 68.2 |
| Lecture | Large | 65.6 |
| Active | Small | 83.5 |
| Active | Medium | 72.4 |
| Active | Large | 71.0 |
APA7 reminders: italicise statistical symbols (M, SD, t, F, p, r), report exact p-values to two or three decimals (use p < .001 for very small values), omit the leading zero for values that cannot exceed 1 (.45, not 0.45), and put degrees of freedom in parentheses. See the APA7 cheat sheet.
Common mistakes
- Interpreting main effects without checking the interaction first.
- Using it when the same participants appear in several cells (use a repeated-measures or mixed ANOVA).
- Ignoring unequal cell sizes.
Related analyses and alternatives
- One-way ANOVA: One factor.
- Two-way ANOVA with repeated measures: Repeated measures.
- Moderation: A continuous moderator.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
What is an interaction?
The effect of one factor differs across the levels of the other. In the plot, the lines are not parallel.
If the interaction is significant, can I still report main effects?
Interpret the interaction first. Main effects may be misleading when the interaction is strong.
References
American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
This guide is for learning and for preparing results for your own reports. You remain responsible for choosing an appropriate analysis, checking its assumptions and interpreting the results. Follow the formatting rules of your journal or institution where they differ from APA7.