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Confidence Intervals for the Weighted Sum of Two Independent Binomial Proportions
Author(s) -
Decrouez Geoffrey,
Robinson Andrew P.
Publication year - 2012
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2012.00680.x
Subject(s) - mathematics , confidence interval , binomial proportion confidence interval , statistics , binomial (polynomial) , wald test , robust confidence intervals , continuity correction , negative binomial distribution , nominal level , binomial distribution , binomial test , statistical hypothesis testing , beta binomial distribution , poisson distribution
Summary Confidence intervals for the difference of two binomial proportions are well known, however, confidence intervals for the weighted sum of two binomial proportions are less studied. We develop and compare seven methods for constructing confidence intervals for the weighted sum of two independent binomial proportions. The interval estimates are constructed by inverting the Wald test, the score test and the Likelihood ratio test. The weights can be negative, so our results generalize those for the difference between two independent proportions. We provide a numerical study that shows that these confidence intervals based on large‐sample approximations perform very well, even when a relatively small amount of data is available. The intervals based on the inversion of the score test showed the best performance. Finally, we show that as for the difference of two binomial proportions, adding four pseudo‐outcomes to the Wald interval for the weighted sum of two binomial proportions improves its coverage significantly, and we provide a justification for this correction.