Mathematical properties and finite-population correction for the Wilson score interval

TL;DR

This paper analyzes the mathematical properties of the Wilson score interval, extends it to finite populations, and discusses the finite population correction, providing practical R implementations.

Contribution

It introduces generalized forms of the Wilson score interval for finite populations and examines their properties, enhancing inference accuracy in various population contexts.

Findings

Generalized Wilson intervals maintain monotonicity and consistency.

Finite population correction impacts the interval's properties.

R implementation makes the methods accessible for practical use.

Abstract

In this paper we examine the properties of the Wilson score interval, used for inferences for an unknown binomial proportion parameter. We examine monotonicity and consistency properties of the interval and we generalise it to give two alternative forms for inferences undertaken in a finite population. We discuss the nature of the "finite population correction" in these generalised intervals and examine their monotonicity and consistency properties. This analysis gives the appropriate confidence interval for an unknown population proportion or unknown unsampled proportion in a finite or infinite population. We implement the generalised confidence interval forms in a user-friendly function in R.