Premium
A NON‐ITERATIVE ACCURATE ASYMPTOTIC CONFIDENCE INTERVAL FOR THE DIFFERENCE BETWEEN TWO PROPORTIONS
Author(s) -
WALLENSTEIN SYLVAN
Publication year - 1997
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/(sici)1097-0258(19970630)16:12<1329::aid-sim567>3.0.co;2-i
Subject(s) - confidence interval , mathematics , statistics , binomial proportion confidence interval , binomial (polynomial) , nominal level , coverage probability , quadratic equation , cdf based nonparametric confidence interval , confidence region , tolerance interval , variance (accounting) , robust confidence intervals , negative binomial distribution , geometry , accounting , business , poisson distribution
I propose a new confidence interval for the difference between two binomial probabilities that requires only the solution of a quadratic equation. The procedure is based on estimating the variance of the observed difference at the boundaries of the confidence interval, and uses least squares estimation rather than maximum likelihood as previously suggested. The proposed procedure is non‐iterative, agrees with the conventional test of equality of two binomial probabilities, and, even for fairly small sample sizes, appears to yields actual 95 per cent confidence intervals with mean or median probabilities of coverage very close to 0⋅95. The Yates continuity correction appears to generate confidence intervals with the conditional probability of coverage at least equal to nominal levels. © 1997 by John Wiley & Sons, Ltd.