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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.

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.

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'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.

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.

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?