Methods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods

Chapter 34

Proportions: Inferences and Comparisons

Jason T. Connor and Peter B. Imrey

34.1 Introduction

Binomially based inferences about one proportion, or about two proportions using data from independent samples, are among the most common tasks in statistical analysis, taught in every elementary course. However, despite the ease with which these tasks can be described and the frequency with which they are encountered, they remain controversial and inconsistently handled in statistical practice.

Numerous papers in theoretical and applied publications have covered binomial point estimation, interval estimation, and hypothesis testing using exact, approximate, and Bayesian methods. Yet, even with the advanced computational power now widely available, no single approach to this set of tasks has emerged as clearly preferable. The methodological choices regarding testing equality of two independently sampled proportions, or estimating any disparity between them, can also be perplexing.

For example, it is now well-understood that clearly superior alternatives to two of the most basic and popular of all methods of statistical inference, the Wald confidence interval for a single proportion and Fisher’s exact test for comparing two proportions, are available for almost any practical application. However, no alternative to either dominates its competitors on all reasonable theoretical and performance criteria. Buttressed by scientific tradition, the long shelf life of statistical texts, ...