Approximate interval estimation of the difference in binomial parameters: correction for skewness and extension to...

Area of Science:

• Biostatistics
• Statistical Inference

Background:

• Approximate interval estimation for binomial parameters is crucial in statistical analysis.
• Mee's modification of Anbar's method offers a viable approach for small sample sizes.

Purpose of the Study:

• To evaluate the score theory's applicability for correcting skewness in interval estimation.
• To extend interval estimation methods to stratified and multiple-table binomial data.
• To provide a unified theoretical framework for estimating differences, ratios, and odds ratios.

Main Methods:

• Utilizing score theory (Bartlett) for approximate interval estimation of binomial parameter differences.
• Applying skewness correction derived from score theory.
• Extending the score theory approach to stratified and multiple-table scenarios.

Main Results:

• The skewness correction is less critical for differences than for ratios of binomial parameters.
• Score theory effectively extends interval estimation to complex (stratified/multiple-table) data.
• The method provides good approximate interval estimates for differences, ratios, and odds ratios.

Conclusions:

• Score theory provides a robust framework for approximate interval estimation in binomial data.
• The derived methods offer accurate interval estimates for various binomial parameter comparisons.
• A unified approach from score theory simplifies the estimation of differences, ratios, and odds ratios.