This page intentionally left blank THECAMBRIDGEDICTIONARYOFSTATISTICS FOURTHEDITION Ifyouworkwithdataandneedeasyaccesstoclear,reliabledefinitionsandexplanationsof modernstatisticalandstatistics-relatedconcepts,thenlooknofurtherthanthisdictionary. Nearly4000termsaredefined,coveringmedical,survey,theoreticalandappliedstatistics, including computational and graphical aspects. Entries are provided for standard and specializedstatisticalsoftware.Inaddition,shortbiographiesofover100importantstatis- ticians aregiven.Definitionsprovide enough mathematical detail toclarify conceptsand give standard formulae when these are helpful. The majority of definitions then give a referencetoabookorarticlewheretheusercanseekfurtherormorespecializedinforma- tion,andmanyareaccompaniedbygraphicalmaterialtoaidunderstanding. B. S. EVERITT is Professor Emeritus of King’s College London. He is the author of almost 60 books on statistics and computing, including Medical Statistics from A to Z, alsofromCambridgeUniversityPress. A.SKRONDALisSeniorStatisticianintheDivisionofEpidemiology,NorwegianInstitute ofPublicHealthandProfessorofBiostatisticsintheDepartmentofMathematics,University ofOslo.PreviouspositionsincludeProfessorofStatisticsandDirectorofTheMethodology InstituteattheLondonSchoolofEconomics. THE CAMBRIDGE DICTIONARY OF Statistics Fourth Edition B.S. EVERITT InstituteofPsychiatry,King’sCollegeLondon A. SKRONDAL NorwegianInstituteofPublicHealth DepartmentofMathematics,UniversityofOslo CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521766999 © B. S. Everitt and A. Skrondal 2010 First, Second and Third Editions © Cambridge University Press 1998, 2002, 2006 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2010 ISBN-13 978-0-511-78827-7 eBook (EBL) ISBN-13 978-0-521-76699-9 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. TothememoryofmydearsisterIris B.S.E. TomychildrenAstridandInge A.S. Prefacetofourthedition In the fourth edition of this dictionary many new entries have been added reflecting, in particular, the expanding interest in Bayesian statistics, causality and machine learning. There has also been a comprehensive review and, where thought necessary, subsequent revisionofexistingentries.Thenumberofbiographiesofimportantstatisticianshasbeen increased by including many from outside the UK and the USA and by the inclusion of entriesforthosewhohavediedsincethepublicationofthethirdedition.Butperhapsthe most significant addition to this edition is that of a co-author, namely Professor Anders Skrondal. Prefacetothirdedition InthisthirdeditionoftheCambridgeDictionaryofStatisticsIhaveaddedmanynewentries andtakentheopportunitytocorrectandclarifyanumberofthepreviousentries.Ihavealso added biographies of important statisticians whom I overlooked in the first and second editionsand,sadly,Ihavehadtoincludeanumberofnewbiographiesofstatisticianswho havediedsincethepublicationofthesecondeditionin2002. B.S.Everitt,2005 Prefacetofirstedition The Cambridge Dictionary of Statistics aims to provide students of statistics, working statisticiansandresearchersinmanydisciplineswhoareusersofstatisticswithrelatively concisedefinitionsofstatisticalterms.Allareasofstatisticsarecovered,theoretical,applied, medical,etc.,although,asinanydictionary,thechoiceofwhichtermstoincludeandwhich toexcludeislikelytoreflectsomeaspectsofthecompiler’smainareasofinterest,andIhave noillusionsthatthisdictionaryisanydifferent.Myhopeisthatthedictionarywillprovidea usefulsourceofreferenceforbothspecialistsandnon-specialistsalike.Manydefinitions necessarilycontainsomemathematicalformulaeand/ornomenclature,otherscontainnone. Butthedifferenceinmathematicalcontentandlevelamongthedefinitionswill,withluck, largelyreflectthetypeofreaderlikelytoturntoaparticulardefinition.Thenon-specialist looking up, for example, Student’s t-tests will hopefully find the simple formulae and associatedwrittenmaterialmorethanadequatetosatisfytheircuriosity,whilethespecialist vii seeking a quick reminder about spline functions will find the more extensive technical materialjustwhattheyneed. Thedictionarycontainsapproximately3000headwordsandshortbiographiesofmore than100importantstatisticians(fellowstatisticianswhoregardthemselvesas‘important’ butwhoarenotincludedhereshouldnotethesinglecommoncharacteristicofthosewho are).Severalformsofcross-referencingareused.Termsinslantedromaninanentryappear asseparateheadwords,althoughheadwordsdefiningrelativelycommonlyoccurringterms such as random variable, probability, distribution, population, sample, etc., are not referred to in this way. Some entries simply refer readers to another entry. This may indicate thatthe termsaresynonymsor,alternatively,thatthe termismore conveniently discussed under another entry. In the latter case the term is printed in italics in the main entry. Entriesareinalphabeticalorderusingtheletter-by-letterratherthantheword-by-word convention. In terms containing numbers or Greek letters, the numbers or corresponding English word are spelt out and alphabetized accordingly. So, for example, 2 × 2 table is foundundertwo-by-twotable,andα-trimmedmean,underalpha-trimmedmean.Only headings corresponding to names are inverted, so the entry for William Gosset is found underGosset,WilliambutthereisanentryunderBox–Müllertransformationnotunder Transformation,Box–Müller. Forthosereadersseekingmoredetailedinformationaboutatopic,manyentriescontain eitherareferencetooneorotherofthetextslistedlater,oramorespecificreferencetoa relevant book or journal article. (Entries for software contain the appropriate address.) Additional material is also available in many cases in either the Encyclopedia of StatisticalSciences,editedbyKotzandJohnson,ortheEncyclopediaofBiostatistics,edited byArmitageandColton,bothpublishedbyWiley.Extendedbiographiesofmanyofthe peopleincludedinthisdictionarycanalsobefoundinthesetwoencyclopediasandalsoin LeadingPersonalitiesinStatisticalSciencesbyJohnsonandKotzpublishedin1997again byWiley. Lastly and paraphrasing Oscar Wilde ‘writing one dictionary is suspect, writing two bordersonthepathological’.ButbeforereadersjumptoanobviousconclusionIwouldlike tomakeitveryclearthatananorakhasneverfeaturedinmywardrobe. B.S.Everitt,1998 Acknowledgements FirstlyIwouldliketothankthemanyauthorswhohave,unwittingly,providedthebasisofa largenumberofthedefinitionsincludedinthisdictionarythroughtheirbooksandpapers. Nextthanksareduetomanymembersofthe‘allstat’mailinglistwhohelpedwithreferences toparticularterms.Iamalsoextremelygratefultomycolleagues,DrSophiaRabe-Hesketh and Dr Sabine Landau, for their careful reading of the text and their numerous helpful suggestions.LastlyIhavetothankmysecretary,MrsHarrietMeteyard,formaintainingand typing the many files that contained the material for the dictionary and for her constant reassurancethatnothingwaslost! viii