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Interval estimation for the difference between independent proportions: comparison of eleven methods
1University of Wales College of Medicine, Heath Park, Cardiff, U.K.
Statistics in Medicine
|May 22, 1998
Summary
Several confidence interval methods for comparing two binomial proportions have flaws. New methods, including a Wilson score interval approach, offer better accuracy and are easier to compute, especially for large sample sizes.
Area of Science:
- Biostatistics
- Statistical inference
Background:
- Accurate confidence intervals for the difference between binomial proportions are crucial in statistical analysis.
- Existing unconditional methods often exhibit computational simplicity at the cost of coverage properties and reliability.
Purpose of the Study:
- To evaluate existing unconditional confidence interval methods for the difference between binomial proportions.
- To develop and assess novel methods that mitigate common aberrations and improve coverage.
Main Methods:
- Evaluation of established unconditional confidence interval methods.
- Development and assessment of two new methods: a tail area profile likelihood approach and a combined Wilson score interval method.
Main Results:
- Simpler computational methods demonstrate poor coverage properties and aberrations.
- The Mee-Miettinen-Nurminen methods perform well but necessitate computational programs.
- The tail area profile likelihood method offers excellent coverage but is computationally intensive.
- The combined Wilson score interval method shows good performance and is easily implemented across sample sizes.
Conclusions:
- Many existing methods for confidence intervals of binomial proportion differences are unreliable.
- A new method combining Wilson score intervals provides a practical and accurate solution for comparing binomial proportions, regardless of sample size.