The Two-Way ANOVA is used to determine whether the subgroups formed by two categorical variables differ in means on a continuous outcome variable. It is the extension of the One-Way ANOVA to two independent variables. Next to the main effects of both variables, the Two-Way ANOVA also tests for the interaction between them. This interaction term in a Two-Way ANOVA tells you whether the effect of one of your independent variables on the dependent variable differs among the groups of your other independent variable. The two assumptions that need to be checked are for the subgroups to have equal variances and to have an approximate normal distribution in the outcome variable.