IM,
Thank you for your post. I honestly don't think I understand what your faculty member is suggesting that you do, nor do I understand how it would help with power.
I agree with your assessment of your design:
In my mind, this is a 4 (Group; between-subjects) by 4 (Time; within-subjects) mixed design.
I have an experiment with four groups that I measure on variable A on four occasions. In my mind, this is a 4 (Group; between-subjects) by 4 (Time; within-subjects) mixed design. However, a faculty suggested that I divide the groups into two dummy-variables of two levels each such that group 1 can be described as 0,0, group 2 as 0,1, and so on. This would result in a 2 (Dummy 1, between) by 2 (Dummy 2, between) by 4 (Time, within) design. According to the faculty, this design would increase my statistical power.
As much as I try, I fail to see how this design increases my power. While it is true that it is easier to follow up a variable of only two levels given a significant ANOVA, I am now contending with the chance/risk of a three-way interaction as well. Any advice on how to approach this would be greatly appreciated. G*Power offer little guidance on how to compare the two different options in terms of statistical power, as far as I can tell. Thank you in advance.