REVOLUTIONIZING STATISTICAL INFERENCE: ADVANCEMENTS IN CRAFTING SUPERIOR CONFIDENCE INTERVALS

Abstract

Statistical inference frequently involves the construction of confidence intervals for binomial parameters, particularly the proportion (p). The conventional approach, utilizing the Wald interval, has proven limitations, particularly when p is close to 0 or 1 and with small sample sizes. To address these challenges, alternative methods have been developed, each with its strengths and weaknesses. This article provides a comprehensive review of these methods, offering insights into their applicability and robustness.

The Clopper-Pearson "exact" interval ensures a coverage probability of at least 1 - α for all possible p values, presenting a reliable alternative. The Score method, initially proposed by Wilson and refined by Guan, exhibits enhanced robustness and reduced fluctuations, making it a valuable tool. Bayesian approaches, including methods like Arcsin, Logit, Jeffres prior intervals, and non-informative Bayesian priors, contribute to the diverse toolbox of confidence interval construction techniques.This review not only outlines the theoretical foundations of these methods but also explores their practical applications in constructing confidence intervals for binomial proportions and related linear functions. The article underscores the complexities inherent in seemingly simple statistical inference tasks, emphasizing the pivotal role of selecting appropriate methods based on sample characteristics and desired confidence levels.