The Two-Way ANOVA is similar to the One-Way ANOVA, but is used when comparing groups on two different categorical variables (i.e. gender and level of education). The biggest difference between the One-Way and the Two-Way ANOVA is that in a Two-Way ANOVA, you are interpreting main effects and interaction effects.
Running One-Way ANOVA in SPSS
Interpreting the Output
Reporting Results in APA Style
A Two-Way ANOVA was conducted to determine to what extent gender and education level have an effect on income. There was a statistically significant interaction between the effects of gender and education level on income (F(2, 37) = 5.21, p < .01). Simple main effects analysis showed that females earned significantly lower incomes than males when higher levels of education had been pursued (p = .003), but there was no difference noted with only high school (p = .42) or undergraduate levels of education (p = .19).