ADVANCEMENTS IN CONFIDENCE INTERVALS: A BETTER SOLUTION

Statistical inference often involves the construction of confidence intervals for binomial parameters, particularly the proportion (p). The most widely used approach is the Wald interval, which relies on sample proportion (p̂), sample size (n), and the quantile of the standard normal distribution (zα) to determine the interval. While seemingly straightforward, this method has limitations, especially when p is close to 0 or 1, and it performs poorly with small sample sizes. To address these issues, various alternative methods for building confidence intervals for p have been developed. The Clopper-Pearson "exact" interval guarantees a coverage probability of at least 1 - α for all possible p values. The Score method, discussed by Wilson and further improved by Guan, offers robustness and reduced fluctuations. Bayesian approaches have also proven effective. Additionally, methods like Arcsin, Logit, and Jeffres prior intervals, along with non-informative Bayesian priors, contribute to the toolbox of confidence interval construction techniques. This article reviews these methods, discusses their strengths and weaknesses, and explores their applications in constructing confidence intervals for binomial proportions and related linear functions. It sheds light on the complexities underlying seemingly simple statistical inference tasks, emphasizing the importance of choosing appropriate methods based on sample characteristics and desired confidence levels. Keywords: Confidence intervals, binomial parameter, Wald interval, Clopper-Pearson interval, Score method, Bayesian methods