Statistical Inference for a Single Proportion

Abstract

Most studies compare two or more proportions, but occasionally we need to draw statistical inferences about a single problem. This chapter presents a brief survey of inferential methods, and lays a formal groundwork for statistical ideas use throughout this and other chapters. We begin with a discussion of methods of testing hypotheses about the parameter of a binomial distribution, using exact binomial calculations. We continue with a discussion of confidence intervals. We present methods that are approximate, based on large sample normal theory, which require only pencil-and-paper calculations, or at most a hand-held calculator. We then consider the important question of sample size planning for a single sample study. Next, we discuss how to calculate approximate standard errors by the delta method. We also discuss different ways of determining p-values and confidence intervals for discrete and asymmetrical distributions. A problem solving section appears at the end of the chapter.