Use paired t-test to compare mean scores of 2 interventions, if 1 group got only 1 and another got both? 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!!
 A: So there are 25 schools, 50 students and 75 measurements. Create the data set in following format:
  School  Student  Method  Y    other covariates
     1       1      A      1      ...
     1       2      A      2      ...
     1       2      B      4      ...
     2       3      A      3      ...
   ..................................
    25      50      B      4       ...

Let consider linear mixed model first:
$$Y_{ijk}= \beta_0 +\beta_1 X_1 + \text{ other covariates } + \gamma_{1i} +\gamma_{2j} +\epsilon_{ijk}$$
where $i$ indicates the school, $j$ student, $k$ the order of measurement. $X_1 = 1$ for methods B and = 0 for method A. $\gamma_{1j}$ is random school specific intercept, and $\gamma_{2j}$ is random school specific intercept, $\epsilon_{ijk}$ is error term. All of them following the normal distribution with mean 0 and variances $\sigma_1^2$, $\sigma_2^2$, and $\sigma_3^2$, and they are independent from each other. 
Based on this structure, the variance-covariance of 3 $Y$s from the same school is:
$$Cov(Y_{111}, Y_{121}, Y_{122})=\left(\begin{matrix} \sigma_1^2+\sigma_2^2+\sigma_3^2& \sigma_1^2 &\sigma_1^2\\
\sigma_1^2 &\sigma_1^2+\sigma_2^2+\sigma_3^2& \sigma_1^2+\sigma_2^2\\
\sigma_1^2&\sigma_1^2+\sigma_2^2&\sigma_1^2+\sigma_2^2+\sigma_3^2\end{matrix}\right)
$$
It indicates that relation between $Y$ from the same student is stronger than that from different students from the same school. $Y$s from the different schools are independent. In this model $\beta_1$ is the difference between method A and B, and you can estimate and test it.
If you think the linear model is not good, especially $y$ does not follow normal distribution, you can select other distribution and/or link function and keep the fixed and random effects parts not change.
$$\beta_0 +\beta_1 X_1 + \text{ other covariates } + \gamma_{1i} +\gamma_{2j}$$
