TY - JOUR
T1 - Approximate confidence intervals for one proportion and difference of two proportions
AU - Pan, Wei
PY - 2002/7/28
Y1 - 2002/7/28
N2 - 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 a bad performance for small to medium sample sizes. Recently, Agresti and his co-workers proposed an Adding-4 method: 4 pseudo-observations are added with 2 successes and 2 failures and then the resulting (pseudo-)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 (pseudo-)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.
AB - 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 a bad performance for small to medium sample sizes. Recently, Agresti and his co-workers proposed an Adding-4 method: 4 pseudo-observations are added with 2 successes and 2 failures and then the resulting (pseudo-)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 (pseudo-)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.
KW - Binomial
KW - Satterthwaite's method
KW - Wald
KW - t-distribution
UR - http://www.scopus.com/inward/record.url?scp=0037189766&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037189766&partnerID=8YFLogxK
U2 - 10.1016/S0167-9473(01)00107-4
DO - 10.1016/S0167-9473(01)00107-4
M3 - Article
AN - SCOPUS:0037189766
SN - 0167-9473
VL - 40
SP - 143
EP - 157
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 1
ER -