Testing Statistical Hypotheses

A mathematical theory of hypothesis testing in which tests are derived as solutions of clearly stated optimum problems was developed by Neyman and Pearson in the 1930’s and since then has been considerably extended. The purpose of the present book is to give a systematic account of this theory and of the closely related theory of confidence sets, together with their principal applications. These include the standard one- and two-sample problems concerning normal, binomial, and Poisson distributions; some aspects of the analysis of variance and of regression analysis (linear hypothesis); certain multivariate and sequential problems. There is also an introduction to non-parametric tests, although here the theoretical approach has not yet been fully developed. One large area of methodology, the class of methods based on large-sample considerations, in particular chi-squared and likelihood ratio tests, essentially has been omitted because the approach and the mathematical tools used are so different that an adequate treatment would require a separate volume. Thetheory ofthese tests is only briefly indicated at the end of Chapter 7.