A comparative study of various methods of testing single binomial Proportion

Abstract

Frequentist and Bayesian methodologies are two major paradigms of theoretical and newlinepractical aspects of statistical inference. Though optimum procedures are prescribed newlinein theory, practical challenges always provide ample scope to devise competing newlinemethods from the house of theoretical statisticians. Exact and approximate methods newlineare the illuminating examples and the advent of computers and powerful algorithms newlineare further enhancing the communication between theory and practice. This work has newlineexploited all these observations to one of the most important quantities of interest, newlinebinomial proportion; associated inferential prospects in the light of sparseness and newlinebehavior of an array of procedures in boundaries of the parameters are considered in newlinethe study. The relation of latter with observed sample data augments this study newlineobjective. Necessary and possible improvements for frequentist method and carefully newlineconceived priors in Bayesian are the noted insights of the work supplemented with newlinecomprehensive data analyses using practical data sets extracted from real world newlinephenomena implemented through the computing platforms R, SAS, and WinBUGS. newlineThe objective of the present work is summarized as newline1. Provide a framework for the analysis of binomial proportion distinct data newlinecharacteristics such as sparseness in terms of zero successes for the underlying newlineBernoulli events. newline2. Include an effort in understanding the essential ingredients of p-values and its newlineassociated impacts due to exact and approximate frequentist methods newline3. Explore the major areas of a Bayesian study design; the choice of appropriate newlinepriors and the computational strategies involved in the analysis of a problem in newlinepractice. newline4. Emphasize the need and relevance of the complete research design and its newlineimplementations with the help of carefully extracting practical data sets. newline5. Develop necessary computational tools in widely practicing platforms and newlineaugment the findings with appropriate usage of Monte-Carlo simulation newlinetechniques newline