I’ve been intensely reviewing the DeclareDesign documentation, Library, and tutorials, but it would be great to check my understanding with the community before I dive in.

I would like to declare a design wherein respondents are shown a factorial vignette with .5 probability; for those who see the vignette, there are k factors with two levels each, with probabilities of .5. My primary questions are:

- Is there enough power to compare outcomes for interactions between the factors in the vignette?
- Is there enough power to compare outcomes for those who do not see the vignette (control) with each unique combination of factorial treatments?

My thinking is that I could use factorial_designer() to answer question #1 about power for the factorial vignette. Then, I could use multi_arm_designer() to answer question #2, with (1 + 2^k) arms (1 for control and 2^k for each unique combination of factorial treatments).

Does this make sense? Thanks!