A non-iterative accurate asymptotic confidence interval for the difference between two proportions

Area of Science:

• Biostatistics
• Statistical Inference

Background:

• Comparing two binomial probabilities is crucial in various scientific fields.
• Existing methods can be computationally intensive or less accurate for small samples.

Purpose of the Study:

• To introduce a novel, computationally efficient confidence interval for the difference between two binomial probabilities.
• To provide a method that ensures accurate coverage probabilities, especially for small sample sizes.

Main Methods:

• Developed a new confidence interval based on solving a quadratic equation.
• Employed least squares estimation for variance at confidence interval boundaries.
• Investigated the effect of Yates continuity correction.

Main Results:

• The proposed method is non-iterative and aligns with conventional equality tests.
• Achieved actual 95% confidence intervals with coverage probabilities near 0.95, even for small sample sizes.
• Yates continuity correction enhanced conditional coverage probability.

Conclusions:

• The new confidence interval offers a practical and accurate alternative for comparing binomial proportions.
• The method simplifies statistical analysis without compromising precision.
• Recommended for use in biostatistical and other comparative studies.