I am a newbie and have a question on power analysis.

I would like to measure the effect of an intervention on various measures and have several control variables. I believe it is the best to use a multiple linear regression model with a dummy variable for the treatment.

Therefore, I have a linear model y = beta_0 + beta_1 * x_1 + ... beta_k * x_k and would like to calculate the required sample size. I have 3 independent variables (one of them is the treatment dummy, and two variables for moderating effects) plus a few control variables. The hypotheses I would like to test are whether some of the betas are larger than 0. The estimated effect size is weak to medium (suggested Cohen's d of around 0.4).

I am using G*Power and don't know which option to choose for the linear multiple regression. These are the following options:

1) t-Test: Fixed model, single regression coefficient
2) F-Test: Fixed model, R2 deviation from zero
3) F-Test: Fixed model, R2 increase
4) Exact: Random model

Can anybody explain the differences to me? Which option should I choose? The calculated sample sizes are very different depending on the option I choose...

I'd recommend running a series of tests from different families and examine the consistency of the sample size estimates. If the question is about the difference between fixed and random effects models, then here is a good clarification by Richard Williams -- https://www3.nd.edu/~rwilliam/stats3...edVsRandom.pdf

The power analysis is a priori to calculate the required sample. Depending on the model I choose, the sample can be around 30-40 or even 150. I can't just gather all data first and then check whether 30-40 would have been enough. Therefore, I need to run the analysis first, but don't know which model to choose.

Concerning random/fixed effects I am bit confused, because I do not have panel data. My data will only be measured once. Hence, I think I don't know in which way to distinguish between the two options?