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Exact one-sided confidence limits for the difference between two correlated proportions
Chris J Lloyd1, Max V Moldovan
1Melbourne Business School, Carlton, Australia. c.lloyd@mbs.edu
Statistics in Medicine
|February 23, 2007
Summary
This study develops exact confidence bounds for the difference between two probabilities from matched binary data. The signed root likelihood ratio statistic provides the most accurate and practical confidence intervals.
Area of Science:
- Statistics
- Biostatistics
- Probability Theory
Background:
- Confidence bounds are crucial for estimating the difference between two probabilities in matched binary data.
- Existing approximate methods may lack exact coverage probabilities.
Purpose of the Study:
- To construct exact and optimal one-sided upper and lower confidence bounds for the difference between two probabilities.
- To compare the performance of different exact confidence limits based on their mean size.
Main Methods:
- Utilized Buehler's optimality theory for constructing exact confidence bounds.
- Adjusted five approximate lower and upper limits to achieve exact nominal coverage probability.
- Employed the signed root likelihood ratio statistic.
Main Results:
- Developed exact one-sided confidence bounds for the difference between two probabilities.
- Identified exact limits based on the signed root likelihood ratio statistic as superior.
- Demonstrated that these exact bounds achieve the desired nominal coverage level.
Conclusions:
- Exact confidence bounds are essential for reliable inference with matched binary pairs.
- The signed root likelihood ratio statistic offers preferred exact confidence intervals for practical applications.
- This method ensures accurate coverage probability for the difference between two probabilities.
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