Exact Confidence Bounds when Sampling from Small Finite Universes

This book tackles a fundamental statistical challenge that arises when drawing conclusions from small, finite populations where the total number of items possessing a certain attribute is unknown. It moves beyond large-sample approximations to provide exact methods for quantifying the uncertainty about this unknown quantity, offering precise confidence bounds derived directly from the hypergeometric distribution. The text is built around a core problem that is deceptively simple to state but rich in statistical implications, making it a crucial resource for anyone working with limited data sets. This approach is essential for fields like quality control, ecological studies, and audit sampling, where populations are small and every data point carries significant weight.

What distinguishes this work is its rigorous focus on exact solutions for small universes, a scenario where common asymptotic methods often fail or provide misleading results. The author systematically unpacks the mathematical framework, making the derivations of confidence intervals transparent and grounded in first principles of probability. It will resonate most with statisticians, data scientists, and researchers in applied fields who require methodological precision and cannot rely on the "large N" assumptions of classical statistics. By mastering the techniques within, readers gain a powerful and definitive toolkit for making reliable inferences from inherently limited information.