Fisher, Neyman, and the Creation of Classical Statistics

verfasst von: Erich L. Lehmann

Verlag: Springer New York

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Classical statistical theory—hypothesis testing, estimation, and the design of experiments and sample surveys—is mainly the creation of two men: Ronald A. Fisher (1890-1962) and Jerzy Neyman (1894-1981). Their contributions sometimes complemented each other, sometimes occurred in parallel, and, particularly at later stages, often were in strong opposition. The two men would not be pleased to see their names linked in this way, since throughout most of their working lives they detested each other. Nevertheless, they worked on the same problems, and through their combined efforts created a new discipline.

This new book by E.L. Lehmann, himself a student of Neyman’s, explores the relationship between Neyman and Fisher, as well as their interactions with other influential statisticians, and the statistical history they helped create together. Lehmann uses direct correspondence and original papers to recreate an historical account of the creation of the Neyman-Pearson Theory as well as Fisher’s dissent, and other important statistical theories.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

As background to a study of their work, this section briefly sketches some of the main features of the lives of these two men.

Erich L. Lehmann

Chapter 2. Fisher’s Testing Methodology

Abstract

We saw in Sect. 1.3 that Student in 1908a brought a new point of view to statistical inference by determining the small-sample (exact) distribution of what he called z, now called t, under the assumption of normality. Student found the correct form of this distribution but was not able to prove it.

Erich L. Lehmann

Chapter 3. The Neyman-Pearson Theory

Abstract

How the Neyman-Pearson collaboration came about was told in Sects. 1.1 and 1.4. We are lucky to have several sources that enable us to follow the development of their joint work in some detail. They are a paper by Pearson (1966), “The Neyman-Pearson Story,” Neyman’s account reported in Constance Reid’s (1982) Neyman biography, and Neyman’s letters to Pearson.

Erich L. Lehmann

Chapter 4. Fisher’s Dissent

Abstract

The preceding two chapters describe the two stages of the founding of the field of hypothesis testing. The first stage consisted of Fisher’s development of a cohesive methodology of basic tests under the assumption of normality. It was followed by the Neyman-Pearson theory of optimal tests, which as its major application provided a justification of the tests Fisher had proposed on intuitive grounds. What, one wonders, was Fisher’s reaction to this new perspective.

Erich L. Lehmann

Chapter 5. The Design of Experiments and Sample Surveys

Abstract

As mentioned toward the end of Sect. 2.3, the last pages of SMRW dealt not with significance testing but with a new subject: the planning of experiments. Fisher extended this brief sketch in a 1926 survey paper, “The arrangement of field experiments.” His interest in experimental design grew out of his work at Rothamsted and resulted in many papers dealing with the new ideas and techniques he developed in this context. In 1935, he gave a systematic account of the new science of experimental design he had created in a book, “The Design of Experiments” (DOE). Instead of following the details of his work on the subject, the present and following sections will provide a discussion of this enormously influential book.

Erich L. Lehmann

Chapter 6. Estimation

Abstract

Throughout the nineteenth century, the most commonly used statistical procedure was estimation by means of least squares. In 1894, Karl Pearson broke new ground by proposing an alternative approach: the method of moments. Of this method, Fisher, in his fundamental paper of 1922 [18] (discussed in Sect. 1.5), wrote that it is “without question of great practical utility.” On the other hand, he points out that it requires the population moments involved to be finite, and “that it has not been shown, except in the case of a normal curve, that the best values will be obtained by the method of moments.” And he asserts that “a more adequate criterion is required.” For this purpose, he proposes the method of maximum likelihood.

Erich L. Lehmann

Chapter 7. Epilog

Abstract

As stated in the Preface, it is the aim of this book to trace the creation of classical statistics, and to show that it was principally the work of two men, Fisher and Neyman. Since the main story is somewhat lost in the details, let us now review their contributions to hypothesis testing, estimation, design, and the philosophy of statistics.

Erich L. Lehmann

Backmatter

Titel: Fisher, Neyman, and the Creation of Classical Statistics
verfasst von: Erich L. Lehmann
Verlag: Springer New York
Electronic ISBN: 978-1-4419-9500-1
Print ISBN: 978-1-4419-9499-8
DOI: https://doi.org/10.1007/978-1-4419-9500-1