calculating sample size - which test?

#1
Hello everyone,

I have a question on calculating the sample size. I am writing a research proposal. Someone else once already calculated the appropriate sample size but didn't include the calculation in the proposal that was written before. So now I need to redo it to double check it. Also they both report a cohen's d of 0.3 and 0.4 in the old proposal, and I need to figure out which one it really is. However, whatever I do, I cannot get the same result of n=73 per group.

The study is a (stepped care) psychological intervention that will be tested. The design is as follows:
- there is 1 intervention group and 1 control group (parallel design).
- Both groups are tested at 4 moments in time with the same measurement instruments (about 6-8):

1. Baseline test
- intervention group gets intervention A
2. Post-assesment 1
- if people in the intervention group did not improve enough, they get intervention B
3. Post-assesment 2
4. Follow-up assessment

Given information from the original proposal:
It is a repeated measurements design. power = 0.8, alpha = 0.05, test two-sided, rho = 0.9. Minimum sample size per group is 73.
Sometimes it says cohen's d is 0.3 and sometimes 0.4.

My questions:
1) Which test do I use to get a sample size of n=73 per group, and why?
First I thought I have one outcome variable (improved vs not improved), but now i'm thinking that because of all the test instruments i maybe have two or more? And there is 1 predictor variable which is categorical (intervention vs no intervention, right?) --> MANOVA. Am I correct?

2) I have acces to STATA, SPSS, and the Gpower tool. If I go for MANOVA in Gpower, I can't figure out if I need to choose between factors/within factors/both. Which one do I need?

3) How do I find out which is the right cohen's d?


If I use Gpower and I choose 'MANOVA, repeated measures, within-between interaction', I can get a total sample size of 73, but not 73 per group:

1612637831154.png

So as an effect size I filled in 0.4, guessing that is the correct cohen's d (do i do this correct?)

But they don't ask if I'm testing one or two-sided, and they don't ask for rho. This makes me wonder why they reported that then in the proposal, and so I'm guessing I don't have the correct test?


I'm very much hoping someone can tell me what I do wrong. All other tests I tried also didn't give me a sample size of 146.

Thanks!