First, I suggest that you explain more about your research. What I got is that you have two independent variables each of which has three levels, one dependent variable, and you want to compare these groups. In this case, you may use two-way ANOVA to compare the mean scores of these groups. However, if you'd like to have more technical answers--as I am not a statistician-- you can mention Prof. David L Morgan.
Use a factorial (or Multiway) ANOVA. It provides statistics for both main and interaction effects. Make sure that your groups are large enough, though.