Let's say there was an intervention delivered using method A and method B. There was a post test asking participants about satisfaction on a Likert scale immediately after each method was delivered. We want to know which was better (i.e. higher mean satisfaction score).
Let's say 25 schools participated, with 2 individuals per school. One person got intervention A only, and the other got both A and B.
Now, if I only looked at the 25 people who got both interventions, I could probably compare their A & B satisfaction scores using a paired t-test. But that wouldn't work if I want to include observations for folks who only took A since they only have observations in 1 data set, right? There would also have to be adjustments for clustering probably?
Advice on what stat tests/ adjustments are best for this scenario?
There's also the age old question of parametric vs. non-parametric tests for skewed Likerts with somewhat small sample sizes. There's so much conflicting advice out there & simulations seem to show that it's kind of a wash, but if there's something I'm missing please let me know.
Thanks in advance!!