document: Approximate confidence intervals for one proportion and difference of two proportions Constructing a confidence interval for a binomial proportion or the difference of two proportions is a routine exercise in daily data analysis . The best-known method is the Wald interval based on the asymptotic normal approximation to the distribution of the observed sample proportion , though it is known to have bad performance for small to medium sample sizes . Agresti et al. -LRB- 1998 , 2000 -RRB- proposed an Adding-4 method : 4 pseudo-observations are added with 2 successes and 2 failures and then the resulting -LRB- pseudo - -RRB- sample proportion is used . The method is simple and performs extremely well . Here we propose an approximate method based on a t-approximation that takes account of the uncertainty in estimating the variance of the observed -LRB- pseudo - -RRB- sample proportion . It follows the same line of using a t-test , rather than z-test , in testing the mean of a normal distribution with an unknown variance . For some circumstances our proposed method has a higher coverage probability than the Adding-4 method
doc_bio_tags: B I I O O O O B I I I O O O O O O B I O O B I I I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I O O O O
extractive_keyphrases: approximate confidence intervals binomial proportion difference of two proportions data analysis uncertainty normal distribution coverage probability
abstractive_keyphrases: t-approximation variance estimation t-test pseudo-sample proportion