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

VL - 40

SP - 143

EP - 157

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 1

ER -