Kenneth J. Berry Janis E. Johnston Paul W. Mielke Jr. A .
Kenneth J. BerryJanis E. JohnstonPaul W. Mielke Jr.A Chronicle ofPermutationStatistical Methods1920–2000, and Beyond
A Chronicle of PermutationStatistical Methods
Kenneth J. Berry Janis E. Johnston Paul W. Mielke Jr.A Chronicle ofPermutation StatisticalMethods1920–2000, and Beyond123
Kenneth J. BerryDepartment of SociologyColorado State UniversityFort Collins, COUSAJanis E. JohnstonU.S. GovernmentAlexandria, VAUSAPaul W. Mielke Jr.Department of StatisticsColorado State UniversityFort Collins, COUSAAdditional material to this book can be downloaded from http://extra.springer.com.ISBN 978-3-319-02743-2ISBN 978-3-319-02744-9 (eBook)DOI 10.1007/978-3-319-02744-9Springer Cham Heidelberg New York Dordrecht LondonLibrary of Congress Control Number: 2014935885 Springer International Publishing Switzerland 2014This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part ofthe 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 informationstorage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodologynow known or hereafter developed. Exempted from this legal reservation are brief excerpts in connectionwith reviews or scholarly analysis or material supplied specifically for the purpose of being enteredand executed on a computer system, for exclusive use by the purchaser of the work. Duplication ofthis publication or parts thereof is permitted only under the provisions of the Copyright Law of thePublisher’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. Violationsare liable to prosecution under the respective Copyright Law.The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoes not imply, even in the absence of a specific statement, that such names are exempt from the relevantprotective 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 ofpublication, neither the authors nor the editors nor the publisher can accept any legal responsibility forany errors or omissions that may be made. The publisher makes no warranty, express or implied, withrespect to the material contained herein.Printed on acid-free paperSpringer 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.
PrefaceThe stimulus for this volume on the historical development of permutation statisticalmethods from 1920 to 2000 was a 2006 Ph.D. dissertation by the second author onranching in Colorado in which permutation methods were extensively employed[695]. This was followed by an invited overview paper on permutation statisticalmethods in Wiley Interdisciplinary Reviews: Computational Statistics, by all threeauthors in 2011 [117]. Although a number of research monographs and textbookshave been published on permutation statistical methods, few have included muchhistorical material, with the notable exception of Edgington and Onghena in thefourth edition of their book on Randomization Tests published in 2007 [396]. Inaddition, David provided a brief history of the beginnings of permutation statisticalmethods in a 2008 publication [326], which was preceded by a more technical anddetailed 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 thedevelopment of permutation statistical methods.As Stephen Stigler noted in the opening paragraph of his 1999 book on Statisticson the Table: The History of Statistical Concepts and Methods:[s]tatistical concepts are ubiquitous in every province of human thought. they are morelikely 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 andrich in diversity, occasionally technical and complicated in structure, and never coveredcompletely [1321, p. 1].This book emphasizes the historical and social context of permutation statisticalmethods, 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 weremajor contributors to, and may be best remembered for, work in other disciplinesand areas. Many of the early contributors to the development of permutationmethods were trained for other professions such as mathematics, economics,agriculture, the military, or chemistry. In more recent times, researchers fromatmospheric science, biology, botany, computer science, ecology, epidemiology,environmental health, geology, medicine, psychology, and sociology have madesignificant contributions to the advancement of permutation statistical methods.Their common characteristic was an interest in, and capacity to use, quantitativemethods on problems judged to be important in their respective disciplines.vii
viiiPrefaceThe purpose of this book is to chronicle the birth and development of permutationstatistical methods over the approximately 80-year period from 1920 to 2000. As towhat the state of permutation methods will be 80 years in the future—one can onlyguess. Not even our adult children will live to see the permutation methods of thatday. As for ourselves, we have to deal with the present and the past. It is our hope inthis writing that knowledge of the past will help the reader to think critically aboutthe present. Those who write intellectual history, as Hayden White maintained,“do not build up knowledge that others might use, they generate a discourse aboutthe past” (White, quoted in Cohen [267, pp. 184–185]). Although the authors arenot historians, they are still appreciative of the responsibility historians necessarilyassume when trying to accurately, impartially, and objectively interpret the past.Moreover, the authors are acutely aware of the 1984 Orwellian warning that “Whocontrols the past . . . controls the future” [1073, p. 19]. The authors are also fullycognizant that there are the records of the past, then there is the interpretation ofthose 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 dimlycorresponds 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 RobertYeatman, 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 Inresearching the development of permutation methods, the authors constantly discovered historical events of which they were not aware, remembered events theythought they had forgotten, and often found what they thought they remembered wasincorrect. Debates as to how to present historical information about the developmentof permutation methods will likely be prompted by this volume. What is not up fordebate is the impact that permutation methods have had on contemporary statisticalmethods. Finally, as researchers who have worked in the field of statistics for manyyears, the authors fondly recall a sentient quote by Karl Pearson:I do 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 beenwritten, but there is little coverage of the historical development of permutationmethods. While many of the books and articles have briefly touched on thedevelopment of permutation methods, none has been devoted entirely to the topic.Among the many important sources on the history of probability and statistics, afew have served the authors well, being informative, interesting, or both. Amongthese we count Natural Selection, Heredity and Eugenics: Selected Correspondenceof R.A. Fisher with Leonard Darwin and Others and Statistical Inference andAnalysis: Selected Correspondence of R.A. Fisher by J.H. Bennett [96, 97]; “Ahistory of statistics in the social sciences” by V. Coven [289]; A History of InverseProbability from Thomas Bayes to Karl Pearson by A.I. Dale [310]; Games, Gods,1Emphasis in the original.
Prefaceixand Gambling: The Origin and History of Probability and Statistical Ideas from theEarliest Times to the Newtonian Era by F.N. David [320]; “Behavioral statistics: Anhistorical perspective” by A.L. Dudycha and L.W. Dudycha [361]; “A brief historyof statistics in three and one-half chapters” by S.E. Fienberg [428]; The Makingof Statisticians edited by J. Gani [493]; The Empire of Chance: How ProbabilityChanged 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 byI. Hacking [567, 568]; History of Probability and Statistics and Their ApplicationsBefore 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 methodof least squares and some alternatives: Part II,” “The method of least squares andsome 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 ofleast squares and some alternatives: Part VI” by H.L. Harter [589–595]; Statisticiansof the Centuries edited by C.C. Heyde and E. Seneta [613]; Leading Personalitiesin Statistical Sciences: From the Seventeenth Century to the Present edited byN.L. Johnson and S. Kotz [691]; Bibliography of Statistical Literature: 1950–1958,Bibliography of Statistical Literature: 1940–1949, and Bibliography of StatisticalLiterature: 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 atInstitute for Mathematical Sciences, National University of Singapore edited byL.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 byL. Krüger, L. Daston, and M. Heidelberger [775]; Reminiscences of a Statistician:The Company I Kept and Fisher, Neyman, and the Creation of Classical Statistics byE.L. Lehmann [814,816]; Statistics in Britain, 1865–1930: The Social Constructionof Scientific Knowledge by D. MacKenzie [863]; The History of Statistics in the17th and 18th Centuries Against the Changing Background of Intellectual, Scientificand Religious Thought edited by E.S. Pearson [1098]; Studies in the History ofStatistics and Probability edited by E.S. Pearson and M.G. Kendall [1103]; The Riseof Statistical Thinking, 1820–1900 by T.M. Porter [1141]; Milestones in ComputerScience 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 ofProbability: A Historical Essay by O.B. Sheynin [1263]; American Contributionsto Mathematical Statistics in the Nineteenth Century, Volumes 1 and 2, The Historyof Statistics: The Measurement of Uncertainty Before 1900, and Statistics on theTable: 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 the44 articles published by various authors under the title “Studies in the history ofprobability 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,
xPrefacecollections, commentaries, comments, compendiums, compilations, conversations,correspondences, dialogues, discussions, dissertations, documents, essays, eulogies,encyclopedias, festschrifts, histories, letters, manuscripts, memoirs, memorials,obituaries, remembrances, reports, reviews, speeches, summaries, synopses, theses,tributes, web sites, and various other sources on the contributions of individualstatisticians to permutation methods, many of which are listed in the references atthe end of the book.No preface to a chronicle of the development of permutation statistical methodswould be complete without acknowledging the major contributors to the field,some of whom contributed theory, others methods and algorithms, and still otherspromoted permutation methods to new audiences. At the risk of slighting someoneof importance, in the early years from 1920 to 1939 important contributions weremade by Thomas Eden, Ronald Fisher, Roy Geary, Harold Hotelling, Joseph Irwin,Jerzy Neyman, Edwin Olds, Margaret Pabst, Edwin Pitman, Bernard Welch, andFrank Yates. Later, the prominent names were Bernard Babington Smith, GeorgeBox, Meyer Dwass, Eugene Edgington, Churchill Eisenhart, Alvan Feinstein, LeonFestinger, David Finney, Gerald Freeman, Milton Friedman, Arthur Ghent, JohnHaldane, John Halton, Wassily Hoeffding, Lawrence Hubert, Maurice Kendall,Oscar Kempthorne, William Kruskal, Erich Lehmann, Patrick Leslie, Henry Mann,M. Donal McCarthy, Cyrus Mehta, Nitin Patel, Henry Scheffé, Cedric Smith,Charles Spearman, Charles Stein, John Tukey, Abraham Wald, Dirk van der Reyden,W. Allen Wallis, John Whitfield, Donald Whitney, Frank Wilcoxon, Samuel Wilks,and Jacob Wolfowitz. More recently, one should recognize Alan Agresti, BrianCade, Herbert David, Hugh Dudley, David Freedman, Phillip Good, Peter Kennedy,David Lane, John Ludbrook, Bryan Manly, Patrick Onghena, Fortunato Pesarin, JonRichards, and Cajo ter Braak.Acknowledgments. The authors wish to thank the editors and staff at SpringerVerlag. A very special thanks to Federica Corradi Dell’Acqua, Assistant Editor,Statistics and Natural Language Processing, who guided the project through frombeginning to end; this book would not have been written without her guidance andoversight. We also wish to thank Norm Walsh who answered all our LATEX questions.We are grateful to Roberta Mielke who read the entire manuscript and made manyhelpful comments, and Cristi MacWaters, Interlibrary Loan Coordinator at MorganLibrary, Colorado State University, who retrieved many of the manuscripts weneeded. Finally, we wish to thank Steve and Linda Jones, proprietors of the RainbowRestaurant, 212 West Laurel Street, Fort Collins, Colorado, for their gracioushospitality; the bulk of this book was written at table 20 in their restaurant adjacentto the campus of Colorado State University.Fort Collins, COAlexandria, VAFort Collins, COAugust 2013Kenneth J. BerryJanis E. JohnstonPaul W. Mielke Jr.
dimensionalAmerican Association for the Advancement of ScienceAssociation for Computing MachineryAtomic Energy CommissionAlgorithmic computer languageApproximate Multivariate Association ProcedureAnalysis of varianceA programming languageAsymptotic relative efficiencyAdvanced Research Projects Agency networkAutomatic sequence controlled calculatorAutomatic send and receiveBritish Association for the Advancement of ScienceBeginners All-Purpose Symbolic Instruction CodeBernard Babington SmithBInary digiTCity College of New YorkColumbia Broadcasting SystemControl Data CorporationCumulative distribution functionCollege Entrance Examination BoardCorrection factor (analysis of variance)California Institute of TechnologyCorrection factorCommon business oriented languageCentral processing unitCompany sergeant majorComputing Tabulating Recording CorporationDefense Advanced Research Projects AgencyDigital Equipment CorporationDepartment of Health and Social SecurityDepartment of DefenseThe design of experiments (Fisher)xi
MANOVAMCMMITAcronymsEmpirical cumulative distribution functionExact chi-squared testExploratory data analysisElectronic delay storage automatic calculatorElectroencephalogramEngineer of minesExact multivariate association procedureElectronic numerical integrator and computerEnvironmental Protection AgencyEidgenössische Technische HochschuleEducational Testing ServiceFisher exact probability testFast Fourier transformFloating operations per secondFood and Nutrition ServiceFormula TranslationFellow of the Royal SocietyGovernment Communications Head QuartersGermaniumGeneral electricGeneralized logistic (distribution)Goodness of fitGeneralized Pareto distributionGraphical user interfaceInstitute for Advanced Study (Princeton)International Business Machines (Corporation)Imperial Chemical IndustriesInstitute of Electrical and Electronics EngineeringInteger Matrix LibraryInstitute of Mathematical StatisticsInternet protocolImagery Randomized Block AnalysisKappa sigma (fraternity)Least absolute deviation (regression)Los Alamos National LaboratoryLos Alamos Scientific LaboratoryLyons Electronic OfficeLibrascope General PurposeLaboratory Instrument ComputerLawrence Livermore National LaboratoryLeast sum of Euclidean distancesMathematical analyzer, numerical integrator and computerMultivariate analysis of varianceMicro computer machinesMassachusetts Institute of Technology
FMTSIAMSIMDSiO2SKxiiiMicro Instrumentation Telemetry SystemsMassively parallel processingMultivariate randomized block permutation proceduresMulti-response permutation proceduresMean square (analysis of variance)Multivariate sequential permutation analysesMersenne TwisterMultivariate extended hypergeometricNational Basketball AssociationNational Bureau of StandardsNational Center for Atmospheric ResearchNational Cash Register CompanyNational Football LeagueNational Homeland Security Research CenterNational Institute of Standards and TechnologyNational Institutes of HealthNational Research CouncilNational Science FoundationNational Science Foundation NETworkNew York UniversityOrder of the British EmpireOrganization for Economic Cooperation and DevelopmentOrdinary least squares (regression)Office of Naval ResearchOak Ridge Automatic Computer and Logical EngineOffice of Scientific Research and DevelopmentPersonal computerProgrammed data processorPersonal Electronic Transactor (Commodore PET)Phi kappa theta (fraternity)Programme for International Student AssessmentPhenylketonuriaPseudo random number generatorStatisticians in the Pharmaceutical IndustryRoyal Air ForceResearch and Development (Corporation)Random errorRelative to an identified distributionSemi-Automatic Ground EnvironmentScholastic aptitude testSIMD-Oriented Fast Mersenne TwisterSociety for Industrial and Applied MathematicsSingle instruction [stream], multiple data [stream]Silicon oxideSymmetric kappa (distribution)
ACUSDAWMWAcronymsSuper Little ChipSandia National LaboratoriesStatistical Package for the Social SciencesSouthern Regional Education BoardStatistical Research Group (Columbia University)Stanford Research InstituteSum of squares (analysis of variance)Spanish Supercomputing NetworkStanford University
N.L. Johnson and S. Kotz [691]; Bibliography of Statistical Literature: 1950–1958, Bibliography of Statistical Literature: 1940–1949,andBibliography of Statistical Literature: Pre 1940by M.G. Kendall and A.G. Doig [743–745]. Also, Studies in the H
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