Examine the effects of two independent factors and their interaction on a continuous outcome.
Two-Way ANOVA (Factorial ANOVA) extends One-Way ANOVA to designs with two independent variables (factors). It simultaneously tests three null hypotheses: no main effect of Factor A, no main effect of Factor B, and no interaction between A and B. The interaction test is the most important and unique feature — it reveals whether the effect of one factor depends on the level of the other.
This design is used whenever a researcher wants to study two factors simultaneously with greater statistical efficiency than running two separate One-Way ANOVAs. Examples include testing the effects of both teaching method and student gender on exam scores, or examining the combined effect of drug dose and time point on blood pressure.
StatRyx computes the full two-way ANOVA table, partial eta-squared for each effect, Tukey HSD post-hoc tests for significant main effects, and an interaction plot — all in APA 7 format.
Read a two-way ANOVA from the interaction down. If the A × B interaction is significant, the main effects can mislead — the effect of one factor depends on the other, so you probe simple effects (the effect of A at each level of B) and describe the pattern with an interaction plot. Only when the interaction is not significant do the main effects summarise the data on their own. Report partial η² for each effect: .01 is small, .06 medium and .14 large.
| Source | SS | df | MS | F | p | partial η² |
|---|---|---|---|---|---|---|
| Teaching Method (A) | 1243.7 | 2 | 621.9 | 9.14 | < .001 | .14 |
| Gender (B) | 287.4 | 1 | 287.4 | 4.22 | .042 | .04 |
| A × B | 793.1 | 2 | 396.6 | 5.83 | .004 | .09 |
| Error | 7756.1 | 114 | 68.0 |
A two-way ANOVA revealed a significant interaction between teaching method and gender on exam scores, F(2, 114) = 5.83, p = .004, partial η² = .09. Main effects were also significant for teaching method, F(2, 114) = 9.14, p < .001, partial η² = .14, and gender, F(1, 114) = 4.22, p = .042, partial η² = .04.
Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.
An interaction means the effect of Factor A on the outcome depends on the level of Factor B. For example, a teaching method might benefit female students but not male students.
Aim for at least 20 participants per cell (unique combination of factor levels). Unequal cell sizes are supported but reduce power.
A one-way ANOVA has one grouping factor. A two-way ANOVA has two factors and also tests their interaction — whether the effect of one factor changes across the levels of the other. Running two separate one-way ANOVAs cannot detect an interaction.
Unequal cells are common and fine. Use Type III sums of squares (the SPSS default), which test each effect after adjusting for the others. Very small cells reduce power and make the homogeneity-of-variance assumption more important, so check Levene's test.
Run a Two-Way ANOVA on your data →