Testing Statistical Hypotheses

This chapter presents the basic concepts and results of the theory of testing statistical hypotheses. The generalized likelihood ratio tests that are discussed can be applied to testing in the presence of nuisance parameters. Besides the likelihood ratio tests, for testing in the presence of nuisance parameters one can use conditional tests. The chapter also presents the motivation for steps of the proof of the randomization principle theorem. It considers the case of a single observation, but the extension to the case of n observations will be obvious. The chapter presents an approach that requires unbiasedness and explains how the theory of testing statistical hypotheses is related to the theory of confidence intervals. It reviews the major testing procedures for parameters of normal distributions and is intended as a convenient reference for users rather than an exposition of new concepts or results.