I am trying to develop a function to simulate datasets, in order to perform power analysis on a Factorial Design (for example 3x5 design). In my case, I'll be interested in testing both differences in the main effects (A and B), as well as for the interaction (A*B). I will also work under the assumption of a balanced design across all 15 groups.
In this scenario, which type of ANOVA should be the one to use? I have read several sites on Type I vs Type II vs Type III but, mostly state such difference is important mostly on unbalanced designs, with some places stating "on a balanced design, they will give the same results", which does not seem to be the case.
Thanks in advance