I'm not sure how to estimate the confidence interval (CI) for a change in a small sample size binomial proportion using the same sample set both times. 

I have two methods that I would like to compare (A and B). I have tested both methods on the same sample ($n=28$) from a large population. 

Method A gave the correct result 11 times but method B gave the correct result 17 times. I think that this indicates that method B is 17/11-1 = 55% better than method A. As well as this point estimate for the difference between the methods, I would like to understand the uncertainty caused by my small number of samples. How can I construct a 95% CI for the 55% improvement in performance please?

- In 11 cases, both test A and test B worked.

- In no cases, test A did work but test B didn't work.

- In 6  cases, test A didn't work but test B did work.

- In 11 cases, both test A and test B didn't work.

These proportions all relate to the same sample ($n=28$). They are not independent of each other. 

Is there a way to calculate CIs that doesn't assume independence please? I would be happy with confidence intervals or with credible intervals and would also be interested in arguments as to why such measures of uncertainty were not appropriate.