Which test to use? Repeated measures with binary outcomes

Question

I would like your opinion about which analyses to use for the research question.

I've got a repeated measures with binary data. N = 20

H0 = there is no difference between pre and post measurement

HA = there is a difference between pre and post measurement

So, I first wanted to go for the McNemar-test or maybe a Fisher's test because of the small sample size. But now I looked into it, I'm not sure if any of these is the right test. Because within the experiment it's really unlikely that someone scores 1 at T1.

These are my predictions (by rule of thumb)

              T2   
          |0   |1  |
     T1|0 |15  |5  |
       |1 |0   |0  |
prediction if H0 is correct

             T2   
          |0   |1  |
     T1|0 |2   |18 |
       |1 |0   |0  |
prediction if HA is correct

Answer 1

This is an interesting question. My intuitive thinking is goodness of fit $\chi^2$ test:

1. Merge these two contingency table
2. Calculate $$\sum_{i=1}^4\frac{(O_i - E_i)^2}{E_i}$$ Here $O_i$ is the observed counts and $E_i$ is the expected counts.

if there is no difference between pre/post measurement, the above statistic should follow a $\chi^2_3$ distribution, where the degree of freedom is calculated as 4 - 1.