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A Chronicle of Permutation Statistical Methods

1920–2000, and Beyond

verfasst von: Kenneth J. Berry, Janis E. Johnston, Paul W. Mielke Jr.

Verlag: Springer International Publishing

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

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Über dieses Buch

The focus of this book is on the birth and historical development of permutation statistical methods from the early 1920s to the near present. Beginning with the seminal contributions of R.A. Fisher, E.J.G. Pitman, and others in the 1920s and 1930s, permutation statistical methods were initially introduced to validate the assumptions of classical statistical methods.

Permutation methods have advantages over classical methods in that they are optimal for small data sets and non-random samples, are data-dependent, and are free of distributional assumptions. Permutation probability values may be exact, or estimated via moment- or resampling-approximation procedures. Because permutation methods are inherently computationally-intensive, the evolution of computers and computing technology that made modern permutation methods possible accompanies the historical narrative.

Permutation analogs of many well-known statistical tests are presented in a historical context, including multiple correlation and regression, analysis of variance, contingency table analysis, and measures of association and agreement. A non-mathematical approach makes the text accessible to readers of all levels.

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Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract

This chapter introduces permutation statistical methods. This first chapter begins with a brief description of the advantages of permutation methods from statisticians who are advocates of permutation tests, followed by a description of the methods of permutation tests including exact, moment-approximation, and resampling-approximation permutation tests. The chapter continues with an example that contrasts the well-known Student t test and results from exact, moment-approximation, and resampling-approximation permutation tests using historical data. The chapter concludes with a brief overview of the remaining chapters.

Kenneth J. Berry, Janis E. Johnston, Paul W. Mielke Jr.

2. 1920–1939

Abstract

This chapter chronicles the development of permutation statistical methods from 1920 to 1939, when the earliest discussions of permutation methods appeared in the literature. In this period J. Spława-Neyman, R.A. Fisher, R.C. Geary, T. Eden, F. Yates, and E.J.G. Pitman laid the foundations of permutation methods as we know them today. As is evident in this period, permutation methods had their roots in agriculture and, from the beginning, were widely recognized as the gold standard against which conventional methods could be verified and confirmed.

Kenneth J. Berry, Janis E. Johnston, Paul W. Mielke Jr.

3. 1940–1959

Abstract

This chapter chronicles the development of permutation statistical methods from 1940 to 1959. This period may be considered a bridge between the early years of 1920–1939 where permutation tests were first conceptualized and the next period, 1960–1979, in which gains in computer technology provided the necessary tools to successfully employ permutation tests. The recognition of permutation methods as the gold standard against which conventional statistical methods were to be evaluated, while often implicit in the 1920s and 1930s, is manifest in many of the publications on permutation methods that appeared between 1940 and 1959. Also, a number of researchers turned their attention during this time period to rank tests, which simplified the calculation of exact probability values; other researchers continued work on calculating exact probability values, creating tables for small samples; and still others continued the theoretical work begun in the 1920s.

Kenneth J. Berry, Janis E. Johnston, Paul W. Mielke Jr.

4. 1960–1979

Abstract

This chapter chronicles the development of permutation statistical methods from 1960 to 1979. This was a period that witnessed dramatic improvements in computer technology, a process that was integral to the development of permutation tests. Prior to 1960, computers were based on vacuum tubes and were large, slow, expensive, and availability was severely limited. Between 1960 and 1979 computers became based on transistors and were smaller, faster, more affordable, and more readily available to researchers. During this period, work on permutation tests fell primarily into three categories: writing algorithms that efficiently generated permutation sequences; designing exact permutation probability values for known statistics; and, for the first time, the development of statistics specifically designed for permutation methods.

Kenneth J. Berry, Janis E. Johnston, Paul W. Mielke Jr.

5. 1980–2000

Abstract

This chapter chronicles the period from 1980 to 2000. Progress on the development of permutation methods continued unabated during this period, paralleling advancements in high-speed computing and the subsequent wide-spread availability of both university mainframes and, later in the period, personal desktop computers. Also, a number of books were published that introduced permutation methods to a wide variety of audiences and there was a decided shift in the literature away from computer science journals into discipline journals. These progressions were accompanied by an increasing emphasis on statistical applications of permutation methods, both exact and resampling, since efficient permutation generators were readily available.

Kenneth J. Berry, Janis E. Johnston, Paul W. Mielke Jr.

6. Beyond 2000

Abstract

This chapter chronicles the period from 2001 to 2010. By the beginning of this period, permutation statistical methods had come of age and advances were comprised more of application and expansion into new fields and disciplines than the development of new permutation methods that characterized earlier years. In this period computing power was sufficient to accommodate the needs of computational statisticians utilizing permutation statistical methods, including both exact and Monte Carlo permutation tests.

Kenneth J. Berry, Janis E. Johnston, Paul W. Mielke Jr.

Backmatter

Titel: A Chronicle of Permutation Statistical Methods
verfasst von: Kenneth J. Berry
Janis E. Johnston
Paul W. Mielke Jr.
Copyright-Jahr: 2014
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-02744-9
Print ISBN: 978-3-319-02743-2
DOI: https://doi.org/10.1007/978-3-319-02744-9

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