A two-factor between-subjects ANOVA examines the effect of two independent variables (A & B) and the interaction of those variables (AxB). What is the proper course of analysis to follow if the AxB interaction is statistically significant? Conduct post-hoc comparison of the main effect means for A and B, if they are statistically significant, before examining the AxB interaction. Conduct post-hoc comparison of the "simple main effect means" for levels of A within B, (and vice versa) and ignore the overall main effects. First, conduct post-hoc comparison of the "simple main effect means" for levels of A within B, (and vice versa) and then examine the overall main effects of A & B if they are significant and have three or more levels. The order is irrelevant, you have to conduct post-hoc comparison of the "simple main effect means" for levels of A within B, (and vice versa) and the overall main effects of A & B if they are significant and have three or more levels