Two-way ANOVA calculator with interaction effects.

What is a two-way ANOVA?

A two-way ANOVA tests how two categorical factors, such as teaching method and gender, affect one numeric outcome. It gives three results: a main effect for each factor and an interaction effect, which shows whether the effect of one factor depends on the level of the other.

Formula

Each effect's sum of squares is found by comparing the full model with a model that leaves that effect out (Type III, sum-to-zero coding). Degrees of freedom are (a − 1), (b − 1) and (a − 1)(b − 1), with N − ab for the error term.

Worked example: method × gender

The sample data has 3 teaching methods × 2 genders with 3 students per cell (N = 18).

1. Interaction: F(2, 12) = 0.30, p = .748, partial η² = .047, so not significant.
2. Main effect of method: F(2, 12) = 21.99, p < .001, partial η² = .786.
3. Main effect of gender: F(1, 12) = 21.24, p < .001, partial η² = .639.
4. Because the interaction is not significant, interpret the two main effects directly and follow up method with post hoc tests.

Assumptions to check

• Outcome is numeric and observations are independent
• Residuals are roughly normal in each cell (check with Shapiro-Wilk)
• Similar variances across cells (Levene's test)
• Every combination of factor levels has data

How to report it (APA style)

Start with the interaction, then the main effects: “There was no significant interaction between method and gender, F(2, 12) = 0.30, p = .748, partial η² = .05. There was a significant main effect of method, F(2, 12) = 21.99, p < .001, partial η² = .79, and of gender, F(1, 12) = 21.24, p < .001, partial η² = .64.”

References

• Maxwell, S. E., Delaney, H. D., & Kelley, K. (2018). Designing experiments and analyzing data (3rd ed.). Routledge.
• Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). SAGE.