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I have installed the R package "pwr" and I am looking to use it for my experiment to see how much power the tests will have.

The experiment is a $3^3$ factorial design ($3$ factors, each with $3$ levels)

At the moment we have planned to do $3$ replications of each combination (so each of the $27$ possible combinations will be repeated three times for a total of $81$ runs)

From my understanding, if I am testing if each factor is significant and if each of the 1st order interactions are significant and if 2nd order is significant, I would need to find multiple powers since I am conducting multiple hypothesis tests?

I am using the question How do I do an a priori power analysis for a 2x3 factorial anova? as a basis for trying to figure this out on my own but I am not making any progress. I also seen this question here: power analysis for factorial design but no one has answered it but basically is asking the same question.

I do see that G.Power is used in many other examples but preferably I would like to see how I could do this in R.

Thank You.

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