# Power of interactions in factorial ANOVA using G*Power

I’m using GPower to perform a priori power analysis. Let’s say that I want to do a 2x2 factorial ANOVA. I’m interested in the power of the interaction. I set effect size f to .25, alpha value to .05, power to .80. The degree of freedom of my interaction is 1 and I have 2x2 = 4 groups. GPower calculates that I need 128 participants, 32 per cell.

Now, let’s say I have a 2x2x2x2 factorial ANOVA. The degree of freedom of any one of the interactions, including the AxBxCxD, is still 1 and I now have 2x2x2x2 = 16 groups! Yet, GPower still calculates that I need 128 participants, namely only 8 participants per cell.

I’m a bit confused with this result. It seems to me that 8 participants per cell is very few to correctly power a AxBxCxD interaction…? If I set 30 groups, I still have 129 participants as a total sample size, that is less than 5 people per cell!

Does anyone could explain such a result? Am I wrong in using GPower or is there something I didn’t get with power?