One-Sample and Paired-Sample Inferences Based on the Binomial Distribution

Abstract

The goal of statistical inference procedures is to use sample data to obtain information, albeit uncertain, about some larger population or data-generating process. The inferences may concern any aspect of a suitably defined population (or process) from which observations are obtained, for example, the form or shape of the probability distribution of some variable in the population, or any definable properties, characteristics or parameters of that distribution, or a comparison of some related aspects of two or more populations. Procedures are usually classified as nonparametric when some of their important properties hold even if only very general assumptions are made or hypothesized about the probability distribution of the observations. The word “distribution-free” is also frequently used in this context. We will not attempt to give an exact definition of “nonparametric” now or later, as it is only this general spirit, rather than any exact definition, which underlies the topics covered in this book.