Large sample approximations do not work well in a small sample setting. Exact tests have to be developed for better estimation in that case.
Since we know X (positive cell count for response) follows binomial, without making normal approximation, we can go for exact inference, by calculating the confidence intervals from the quantiles of a binomial distribution.
Since we know X (positive cell count for response) follows binomial, without making normal approximation, we can go for exact inference, by calculating the confidence intervals from the quantiles of a binomial distribution.
