Confidence Intervals for the Difference between Two Proportions by Sampling Importance Resampling Algorithm
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Abstract
Confidence intervals for the difference between two proportions ( p1 – p2 ) have gained interest by statisticians from past to present. Several researchers have proposed and compared the confidence intervals. Nowadays, computers play an important role in computational statistics. Methods of confidence interval constructions could employ algorithms instead of direct analytical method. In this research, Sampling Importance Resampling (SIR) algorithm frequently found in Bayesian statistics is applied to construct the confidence intervals which are then compared to those obtained from Bayes, hybrid, and Wald confidence intervals. The results show that the confidence intervals obtained from SIR give the coverage probabilities similar to those of Bayes and hybrid methods, and these 3 methods are superior to the Wald method in all population characteristics and sample sizes. Because SIR algorithm directly uses samples of p1 and p2, the confidence intervals of p1 – p2 are definitely in [–1, +1]. In case of , SIR algorithm is able to construct a confidence interval while the Wald interval is not when the standard error equals zero. The characteristic of population also affects the length of intervals. If p1 and p2 are close to .5 (symmetric), the interval length tends to be greater than that calculated from skewed population, for example p1 = p2 = .05. To conclude, in many situations, SIR algorithm is able to produce a good confidence interval similar to Bayes and hybrid method, one of the most efficient methods in literature review.
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