This page intentionally left blank THE CAMBRIDGE DICTIONARY OF STATISTICS THE CAMBRIDGE DICTIONARY OF Statistics Second Edition B. S. EVERITT Institute ofPsychiatry, King’s College, University ofLondon    Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge  , United Kingdom Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521810999 © Cambridge University Press 1998, 2002 This book 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 2002 -  isbn-13 978-0-511-06437-1 eBook (NetLibrary) -  isbn-10 0-511-06437-3 eBook (NetLibrary) -  isbn-13 978-0-521-81099-9 hardback -  isbn-10 0-521-81099-X hardback Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Reprinted with corrections 2003 To the memory of my dear sister Iris Preface TheCambridgeDictionaryofStatisticsaimstoprovidestudentsofstatistics,working statisticians and researchers in many disciplines who are users of statistics with relatively concise definitions of statistical terms. All areas of statistics are covered, theoretical,applied,medical,etc.,although,asinanydictionary,thechoiceofwhich termstoincludeandwhichtoexclude,islikelytoreflectsomeaspectsofthecompi- ler’smainareasofinterest,andIhavenoillusionsthatthisdictionaryisanydiffer- ent.Myhopeisthatthedictionarywillprovideausefulsourceofreferenceforboth specialistsandnon-specialistsalike.Manydefinitionsnecessarilycontainsomemath- ematical formulae and/or nomeclature, others contain none. But the difference in mathematicalcontentandlevelamongthedefinitionswill,withluck,largelyreflect thetypeofreaderlikelytoturntoaparticulardefinition.Thenon-specialistlooking up, for example, Student’s t-tests will hopefully find the simple formulae and asso- ciated written material more than adequate to satisfy their curiosity, while the spe- cialist seeking a quick reminder about spline functions will find the more extensive technical materialjust whattheyneed. Thedictionarycontainsapproximately3000headwordsandshortbiographiesof morethan100importantstatisticians(fellowstatisticianswhoregardthemselvesas ‘important’butwhoarenotincludedhereshouldnotethesinglecommoncharacter- isticsofthosewhoare).Severalformsofcross-referencingareused.Termsinslanted romanin an entry appear as a separate headword, although headwords defining relatively commonly occurring terms such as random variable, probability, distribu- tion,population,sample,etc.,arenotreferredtointhisway.Someentriessimplyrefer readers to another entry. This may indicate that the terms are synonyms or, alter- natively, that the term is more conveniently discussed under another entry. In the lattercasethe termis printedin italics in the mainentry. 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(cid:1)2 table is found under two-by-two table, and (cid:1)-trimmed mean, under alpha-trimmed mean. Only headings corresponding to names are inverted, so the entry for William Gossett is found under Gosset, William. but there is an entry underBox–Mu¨llertransformation not underTransformation, Box–Mu¨ller. Forthosereadersseeking moredetailed information abouta topic, manyentries containeitherareferencetooneorotherofthetextslistedlater,oramorespecific reference to a 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 Statistical Sciences, edited by Kotz and Johnson, or the Encyclopedia of Biostatistics, edited by Armitage and Colton, both published by Wiley. Extended biographies of many of the people included in this dictionary can also be found in these two encyclopedias and also in Leading Personalities in Statistical Sciencesby JohnsonandKotz published in 1997againbyWiley. vii Lastly and paraphrasing Oscar Wilde ‘writing one dictionary is suspect, writing twobordersonthepathological’.ButbeforereadersjumptoanobviousconclusionI wouldliketomakeitveryclearthatananorakhasneverfeaturedinmywardrobe. B. S.Everitt, 1998 Preface to second edition InthissecondeditionoftheCambridgeDictionaryofStatisticsIhaveaddedapproxi- mately500newentriesandtakentheopportunitytocorrectandclarifyanumberof thepreviousentries.IhavealsoaddedbiographiesofimportantstatisticianswhomI overlooked in the first edition and, sadly, I have had to include a number of new biographiesofstatisticianswhohavediedsincethepublicationofthefirsteditionin 1998. IwouldliketothankProfessorPakShamforprovidinganumberoftheentrieson genetics, Professor David Hand for putting me straight about data mining and relatedtechniques,ProfessorDavidFinneyforpointingoutproblemswithanumber of the definitions in the first edition and Dr Phillip Sedgwick for leading me to the correct (Ihope)definition of censored observations. B. S.Everitt, 2001 Acknowledgements FirstlyIwouldliketothankthemanyauthorswhohave,unwittingly,providedthe basis of a large number of the definitions included in this dictionary through their booksandpapers.Nextthanksareduetomanymembersofthe‘allstat’mailinglist who helped with references to particular terms. I am also extremely grateful to my colleagues,DrSophiaRabe-HeskethandDrSabineLandau,fortheircarefulread- ing of the text and their numerous helpful suggestions. Lastly I have to thank my secretary, Mrs Harriet Meteyard, for maintaining and typing the many files that contained the material for the dictionary and for her constant reassurance that nothing waslost! viii