Kenneth J Berry Janis E Johnston Paul W Mielke Jr A Chronicle of Permutation Statistical Methods 1920–2000, and Beyond A Chronicle of Permutation Statistical Methods Kenneth J Berry • Janis E Johnston • Paul W Mielke Jr A Chronicle of Permutation Statistical Methods 1920–2000, and Beyond 123 Kenneth J Berry Department of Sociology Colorado State University Fort Collins, CO USA Janis E Johnston U.S Government Alexandria, VA USA Paul W Mielke Jr Department of Statistics Colorado State University Fort Collins, CO USA Additional material to this book can be downloaded from http://extra.springer.com ISBN 978-3-319-02743-2 ISBN 978-3-319-02744-9 (eBook) DOI 10.1007/978-3-319-02744-9 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2014935885 © Springer International Publishing Switzerland 2014 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer Permissions for use may be obtained through RightsLink at the Copyright Clearance Center Violations are liable to prosecution under the respective Copyright Law The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made The publisher makes no warranty, express or implied, with respect to the material contained herein Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) For our families: Nancy T Berry, Ellen E Berry, Laura B Berry, Lindsay A Johnston, James B Johnston, Roberta R Mielke, William W Mielke, Emily (Mielke) Spear, and Lynn (Mielke) Basila Preface The stimulus for this volume on the historical development of permutation statistical methods from 1920 to 2000 was a 2006 Ph.D dissertation by the second author on ranching in Colorado in which permutation methods were extensively employed [695] This was followed by an invited overview paper on permutation statistical methods in Wiley Interdisciplinary Reviews: Computational Statistics, by all three authors in 2011 [117] Although a number of research monographs and textbooks have been published on permutation statistical methods, few have included much historical material, with the notable exception of Edgington and Onghena in the fourth edition of their book on Randomization Tests published in 2007 [396] In addition, David provided a brief history of the beginnings of permutation statistical methods in a 2008 publication [326], which was preceded by a more technical and detailed description of the structure of permutation tests by Bell and Sen in 1984 [93] However, none of these sources provides an extensive historical account of the development of permutation statistical methods As Stephen Stigler noted in the opening paragraph of his 1999 book on Statistics on the Table: The History of Statistical Concepts and Methods: [s]tatistical concepts are ubiquitous in every province of human thought they are more likely to be noticed in the sciences, but they also underlie crucial arguments in history, literature, and religion As a consequence, the history of statistics is broad in scope and rich in diversity, occasionally technical and complicated in structure, and never covered completely [1321, p 1] This book emphasizes the historical and social context of permutation statistical methods, as well as the motivation for the development of selected permutation tests The field is broadly interpreted and it is notable that many of the early pioneers were major contributors to, and may be best remembered for, work in other disciplines and areas Many of the early contributors to the development of permutation methods were trained for other professions such as mathematics, economics, agriculture, the military, or chemistry In more recent times, researchers from atmospheric science, biology, botany, computer science, ecology, epidemiology, environmental health, geology, medicine, psychology, and sociology have made significant contributions to the advancement of permutation statistical methods Their common characteristic was an interest in, and capacity to use, quantitative methods on problems judged to be important in their respective disciplines vii viii Preface The purpose of this book is to chronicle the birth and development of permutation statistical methods over the approximately 80-year period from 1920 to 2000 As to what the state of permutation methods will be 80 years in the future—one can only guess Not even our adult children will live to see the permutation methods of that day As for ourselves, we have to deal with the present and the past It is our hope in this writing that knowledge of the past will help the reader to think critically about the present Those who write intellectual history, as Hayden White maintained, “do not build up knowledge that others might use, they generate a discourse about the past” (White, quoted in Cohen [267, pp 184–185]) Although the authors are not historians, they are still appreciative of the responsibility historians necessarily assume when trying to accurately, impartially, and objectively interpret the past Moreover, the authors are acutely aware of the 1984 Orwellian warning that “Who controls the past controls the future” [1073, p 19] The authors are also fully cognizant that there are the records of the past, then there is the interpretation of those records The gap between them is a source of concern As Appleby, Hunt, and Jacob noted in Telling the Truth About History, “[a]t best, the past only dimly corresponds to what the historians say about it” [28, p 248] In writing this book, the authors were reminded of the memorable quote by Walter Sellar and Robert Yeatman, the authors of 1066 and All That: A Memorable History of England: “History is not what you thought It is what you can remember” [1245, p vii].1 In researching the development of permutation methods, the authors constantly discovered historical events of which they were not aware, remembered events they thought they had forgotten, and often found what they thought they remembered was incorrect Debates as to how to present historical information about the development of permutation methods will likely be prompted by this volume What is not up for debate is the impact that permutation methods have had on contemporary statistical methods Finally, as researchers who have worked in the field of statistics for many years, the authors fondly recall a sentient quote by Karl Pearson: I feel how wrongful it was to work for so many years at statistics and neglect its history [1098, p 1] A number of books and articles detailing the history of statistics have been written, but there is little coverage of the historical development of permutation methods While many of the books and articles have briefly touched on the development of permutation methods, none has been devoted entirely to the topic Among the many important sources on the history of probability and statistics, a few have served the authors well, being informative, interesting, or both Among these we count Natural Selection, Heredity and Eugenics: Selected Correspondence of R.A Fisher with Leonard Darwin and Others and Statistical Inference and Analysis: Selected Correspondence of R.A Fisher by J.H Bennett [96, 97]; “A history of statistics in the social sciences” by V Coven [289]; A History of Inverse Probability from Thomas Bayes to Karl Pearson by A.I Dale [310]; Games, Gods, Emphasis in the original Preface ix and Gambling: The Origin and History of Probability and Statistical Ideas from the Earliest Times to the Newtonian Era by F.N David [320]; “Behavioral statistics: An historical perspective” by A.L Dudycha and L.W Dudycha [361]; “A brief history of statistics in three and one-half chapters” by S.E Fienberg [428]; The Making of Statisticians edited by J Gani [493]; The Empire of Chance: How Probability Changed Science and Everyday Life by G Gigerenzer, Z Swijtink, T.M Porter, and L Daston [512]; The Emergence of Probability and The Taming of Chance by I Hacking [567, 568]; History of Probability and Statistics and Their Applications Before 1750 and A History of Mathematical Statistics from 1750 to 1930 by A Hald [571,572]; “The method of least squares and some alternatives: Part I,” “The method of least squares and some alternatives: Part II,” “The method of least squares and some alternatives: Part III,” “The method of least squares and some alternatives: Part IV,” “The method of least squares and some alternatives: Addendum to Part IV,” “The method of least squares and some alternatives: Part V,” and “The method of least squares and some alternatives: Part VI” by H.L Harter [589–595]; Statisticians of the Centuries edited by C.C Heyde and E Seneta [613]; Leading Personalities in Statistical Sciences: From the Seventeenth Century to the Present edited by N.L Johnson and S Kotz [691]; Bibliography of Statistical Literature: 1950–1958, Bibliography of Statistical Literature: 1940–1949, and Bibliography of Statistical Literature: Pre 1940 by M.G Kendall and A.G Doig [743–745] Also, Studies in the History of Statistics and Probability edited by M.G Kendall and R.L Plackett [747]; Creative Minds, Charmed Lives: Interviews at Institute for Mathematical Sciences, National University of Singapore edited by L.Y Kiang [752]; “A bibliography of contingency table literature: 1900 to 1974” by R.A Killion and D.A Zahn [754]; The Probabilistic Revolution edited by L Krüger, L Daston, and M Heidelberger [775]; Reminiscences of a Statistician: The Company I Kept and Fisher, Neyman, and the Creation of Classical Statistics by E.L Lehmann [814,816]; Statistics in Britain, 1865–1930: The Social Construction of Scientific Knowledge by D MacKenzie [863]; The History of Statistics in the 17th and 18th Centuries Against the Changing Background of Intellectual, Scientific and Religious Thought edited by E.S Pearson [1098]; Studies in the History of Statistics and Probability edited by E.S Pearson and M.G Kendall [1103]; The Rise of Statistical Thinking, 1820–1900 by T.M Porter [1141]; Milestones in Computer Science and Information Technology by E.D Reilly [1162]; The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century by D Salsburg [1218]; Bibliography of Nonparametric Statistics by I.R Savage [1225]; Theory of Probability: A Historical Essay by O.B Sheynin [1263]; American Contributions to Mathematical Statistics in the Nineteenth Century, Volumes and 2, The History of Statistics: The Measurement of Uncertainty Before 1900, and Statistics on the Table: The History of Statistical Concepts and Methods by S.M Stigler [1318– 1321], Studies in the History of Statistical Method by H.M Walker [1409], and the 44 articles published by various authors under the title “Studies in the history of probability and statistics” that appeared in Biometrika between 1955 and 2000 In addition, the authors have consulted myriad addresses, anthologies, articles, autobiographies, bibliographies, biographies, books, celebrations, chronicles, Subject Index Symbols A, Berry–Mielke’s 301, 302 C , Dixon’s 115 F , Bartlett’s 232 F , Snedecor’s 20, 35–37, 104, 180, 238, 244, 303, 334, 425, 427, 428 Fmax , Hartley’s 232 H , Kruskal–Wallis’s 180 H , Lehmann–Stein’s 162 Q, Cochran’s 245, 249, 280, 313, 316, 327 Q, Yule’s 152, 282 R, Spearman’s 327, 329–331 Rh , Wald–Wolfowitz’s 123, 130 Rn , Siegel–Tukey’s 233 S, Kendall’s 148–150, 152 S, Whitfield’s 148, 149 T , Hotelling’s 221, 280, 352, 353 U , Hoeffding’s 256, 265 U , Mann–Whitney’s 144, 145, 148–150, 152, 171, 245, 249 U , Wald–Wolfowitz’s 118 W , Kendall’s 381, 382 W , Wilcoxon’s 133, 134, 144, 148, 170, 171 Z, Fisher’s 358–361