Statistics:AVeryShortIntroduction VERYSHORTINTRODUCTIONSareforanyonewantingastimulatingand accessiblewayintoanewsubject.Theyarewrittenbyexperts,andhavebeen publishedinmorethan25languagesworldwide. Theseriesbeganin1995,andnowrepresentsawidevarietyoftopicsin history,philosophy,religion,science,andthehumanities.Overthenext fewyearsitwillgrowtoalibraryofaround200volumes–aVeryShort IntroductiontoeverythingfromancientEgyptandIndianphilosophyto conceptualartandcosmology. VeryShortIntroductionsavailablenow: AFRICANHISTORY CHOICETHEORY MichaelAllingham JohnParkerandRichardRathbone CHRISTIANART BethWilliamson AMERICANPOLITICALPARTIES CHRISTIANITY LindaWoodhead ANDELECTIONS L.SandyMaisel CITIZENSHIP RichardBellamy THEAMERICANPRESIDENCY CLASSICS MaryBeardand CharlesO.Jones JohnHenderson ANARCHISM ColinWard CLASSICALMYTHOLOGY ANCIENTEGYPT IanShaw HelenMorales ANCIENTPHILOSOPHY JuliaAnnas CLAUSEWITZ MichaelHoward ANCIENTWARFARE THECOLDWAR RobertMcMahon HarrySidebottom CONSCIOUSNESS SusanBlackmore ANGLICANISM MarkChapman CONTEMPORARYART THEANGLO-SAXONAGE JohnBlair JulianStallabrass ANIMALRIGHTS DavidDeGrazia CONTINENTALPHILOSOPHY Antisemitism StevenBeller SimonCritchley ARCHAEOLOGY PaulBahn COSMOLOGY PeterColes ARCHITECTURE AndrewBallantyne THECRUSADES ChristopherTyerman ARISTOTLE JonathanBarnes CRYPTOGRAPHY ARTHISTORY DanaArnold FredPiperandSeanMurphy ARTTHEORY CynthiaFreeland DADAANDSURREALISM THEHISTORYOFASTRONOMY DavidHopkins MichaelHoskin DARWIN JonathanHoward ATHEISM JulianBaggini THEDEADSEASCROLLS AUGUSTINE HenryChadwick TimothyLim AUTISM UtaFrith DEMOCRACY BernardCrick BARTHES JonathanCuller DESCARTES TomSorell BESTSELLERS JohnSutherland DESIGN JohnHeskett THEBIBLE JohnRiches DINOSAURS DavidNorman THEBRAIN MichaelO’Shea DOCUMENTARYFILM BRITISHPOLITICS AnthonyWright PatriciaAufderheide BUDDHA MichaelCarrithers DREAMING J.AllanHobson BUDDHISM DamienKeown DRUGS LeslieIversen BUDDHISTETHICS DamienKeown THEEARTH MartinRedfern CAPITALISM JamesFulcher ECONOMICS ParthaDasgupta CATHOLICISM GeraldO’Collins EGYPTIANMYTH GeraldinePinch THECELTS BarryCunliffe EIGHTEENTH-CENTURYBRITAIN CHAOS LeonardSmith PaulLangford THEELEMENTS PhilipBall INTERNATIONALMIGRATION EMOTION DylanEvans KhalidKoser EMPIRE StephenHowe INTERNATIONALRELATIONS ENGELS TerrellCarver PaulWilkinson ETHICS SimonBlackburn ISLAM MaliseRuthven THEEUROPEANUNION JohnPinder JOURNALISM IanHargreaves andSimonUsherwood JUDAISM NormanSolomon EVOLUTION JUNG AnthonyStevens BrianandDeborahCharlesworth KABBALAH JosephDan EXISTENTIALISM ThomasFlynn KAFKA RitchieRobertson FASCISM KevinPassmore KANT RogerScruton FEMINISM MargaretWalters KIERKEGAARD PatrickGardiner THEFIRSTWORLDWAR THEKORAN MichaelCook MichaelHoward LAW RaymondWacks FOSSILS KeithThomson LINGUISTICS PeterMatthews FOUCAULT GaryGutting LITERARYTHEORY JonathanCuller FREEWILL ThomasPink LOCKE JohnDunn THEFRENCHREVOLUTION LOGIC GrahamPriest WilliamDoyle MACHIAVELLI QuentinSkinner FREUD AnthonyStorr THEMARQUISDESADE JohnPhillips FUNDAMENTALISM MaliseRuthven MARX PeterSinger GALAXIES JohnGribbin MATHEMATICS TimothyGowers GALILEO StillmanDrake THEMEANINGOFLIFE GameTheory KenBinmore TerryEagleton GANDHI BhikhuParekh MEDICALETHICS TonyHope GEOGRAPHY JohnA.Matthewsand MEDIEVALBRITAIN DavidT.Herbert JohnGillinghamandRalphA.Griffiths GEOPOLITICS KlausDodds MEMORY JonathanFoster GERMANLITERATURE MODERNART DavidCottington NicholasBoyle MODERNCHINA RanaMitter GLOBALCATASTROPHES BillMcGuire MODERNIRELAND SeniaPašeta GLOBALIZATION ManfredSteger MOLECULES PhilipBall GLOBALWARMING MarkMaslin MORMONISM THEGREATDEPRESSIONAND RichardLymanBushman THENEWDEAL EricRauchway MUSIC NicholasCook HABERMAS JamesGordonFinlayson MYTH RobertA.Segal HEGEL PeterSinger NATIONALISM StevenGrosby HEIDEGGER MichaelInwood NELSONMANDELA EllekeBoehmer HIEROGLYPHS PenelopeWilson THENEWTESTAMENTAS HINDUISM KimKnott LITERATURE KyleKeefer HISTORY JohnH.Arnold NEWTON RobertIliffe HISTORYofLife MichaelBenton NIETZSCHE MichaelTanner THEHISTORYOFMEDICINE NINETEENTH-CENTURYBRITAIN WilliamBynum ChristopherHarvieand HIV/AIDS AlanWhiteside H.C.G.Matthew HOBBES RichardTuck NORTHERNIRELAND HUMANEVOLUTION BernardWood MarcMulholland HUMANRIGHTS AndrewClapham NUCLEARWEAPONS HUME A.J.Ayer JosephM.Siracusa IDEOLOGY MichaelFreeden THEOLDTESTAMENT INDIANPHILOSOPHY SueHamilton MichaelD.Coogan INTELLIGENCE IanJ.Deary PARTICLEPHYSICS FrankClose PAUL E.P.Sanders SCHIZOPHRENIA PHILOSOPHY EdwardCraig ChrisFrithandEveJohnstone PHILOSOPHYOFLAW SCHOPENHAUER RaymondWacks ChristopherJanaway PHILOSOPHYOFSCIENCE SCIENCEANDRELIGION SamirOkasha ThomasDixon PHOTOGRAPHY SteveEdwards SCOTLAND RabHouston PLATO JuliaAnnas SEXUALITY VéroniqueMottier POLITICALPHILOSOPHY SHAKESPEARE GermaineGreer DavidMiller SIKHISM EleanorNesbitt POLITICS KennethMinogue SOCIALANDCULTURAL POSTCOLONIALISM RobertYoung ANTHROPOLOGY POSTMODERNISM ChristopherButler JohnMonaghanandPeterJust POSTSTRUCTURALISM SOCIALISM MichaelNewman CatherineBelsey SOCIOLOGY SteveBruce PREHISTORY ChrisGosden SOCRATES C.C.W.Taylor PRESOCRATICPHILOSOPHY THESPANISHCIVILWAR CatherineOsborne HelenGraham PSYCHIATRY TomBurns SPINOZA RogerScruton PSYCHOLOGY STATISTICS DavidJ.Hand GillianButlerandFredaMcManus STUARTBRITAIN JohnMorrill THEQUAKERS PinkDandelion TERRORISM CharlesTownshend QUANTUMTHEORY THEOLOGY DavidF.Ford JohnPolkinghorne THEHISTORYOFTIME RACISM AliRattansi LeofrancHolford-Strevens RELATIVITY RussellStannard TRAGEDY AdrianPoole RELIGIONINAMERICA TimothyBeal THETUDORS JohnGuy THERENAISSANCE JerryBrotton TWENTIETH-CENTURYBRITAIN RENAISSANCEART KennethO.Morgan GeraldineA.Johnson THEUNITEDNATIONS ROMANBRITAIN PeterSalway JussiM.Hanhimäki THEROMANEMPIRE THEVIETNAMWAR ChristopherKelly MarkAtwoodLawrence ROUSSEAU RobertWokler THEVIKINGS JulianRichards RUSSELL A.C.Grayling WITTGENSTEIN A.C.Grayling RUSSIANLITERATURE CatrionaKelly WORLDMUSIC PhilipBohlman THERUSSIANREVOLUTION THEWORLDTRADE S.A.Smith ORGANIZATION AmritaNarlikar AvailableSoon: APOCRYPHALGOSPELS PaulFoster NOTHING FrankClose BEAUTY RogerScruton PHILOSOPHYOFRELIGION Expressionism KaterinaReed-Tsocha JackCopelandandDianeProudfoot FREESPEECH NigelWarburton SUPERCONDUCTIVITY MODERNJAPAN StephenBlundell ChristopherGoto-Jones Formoreinformationvisitourwebsites www.oup.com/uk/vsi www.oup.com/us DavidJ.Hand Statistics A Very Short Introduction 1 1 GreatClarendonStreet,OxfordOX26DP OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwidein Oxford NewYork Auckland CapeTown DaresSalaam HongKong Karachi KualaLumpur Madrid Melbourne MexicoCity Nairobi NewDelhi Shanghai Taipei Toronto Withofficesin Argentina Austria Brazil Chile CzechRepublic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore SouthKorea Switzerland Thailand Turkey Ukraine Vietnam OxfordisaregisteredtrademarkofOxfordUniversityPress intheUKandincertainothercountries PublishedintheUnitedStates byOxfordUniversityPressInc.,NewYork (cid:2)c DavidJ.Hand2008 Themoralrightsoftheauthorhavebeenasserted DatabaserightOxfordUniversityPress(maker) FirstPublished2008 Allrightsreserved.Nopartofthispublicationmaybereproduced, storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans, withoutthepriorpermissioninwritingofOxfordUniversityPress, orasexpresslypermittedbylaw,orundertermsagreedwiththeappropriate reprographicsrightsorganization.Enquiriesconcerningreproduction outsidethescopeoftheaboveshouldbesenttotheRightsDepartment, OxfordUniversityPress,attheaddressabove Youmustnotcirculatethisbookinanyotherbindingorcover andyoumustimposethesameconditiononanyacquirer BritishLibraryCataloguinginPublicationData Dataavailable LibraryofCongressCataloginginPublicationData Dataavailable ISBN978–0–19–923356–4 1 3 5 7 9 10 8 6 4 2 TypesetbySPIPublisherServices,Pondicherry,India PrintedinGreatBritainby AshfordColourPressLtd,Gosport,Hampshire Contents Preface ix Listofillustrations xi 1 Surroundedbystatistics 1 2 Simpledescriptions 21 3 Collectinggooddata 36 4 Probability 55 5 Estimationandinference 75 6 Statisticalmodelsandmethods 92 7 Statisticalcomputing 110 Furtherreading 115 Endnote 117 Index 119 This page intentionally left blank Preface Statisticalideasandmethodsunderliejustabouteveryaspectof modernlife.Sometimestheroleofstatisticsisobvious,butoften thestatisticalideasandtoolsarehiddeninthebackground.In eithercase,becauseoftheubiquityofstatisticalideas,itisclearly extremelyusefultohavesomeunderstandingofthem.Theaimof thisbookistoprovidesuchunderstanding. Statisticssuffersfromanunfortunatebutfundamental misconceptionwhichmisleadspeopleaboutitsessentialnature. Thismistakenbeliefisthatitrequiresextensivetediousarithmetic manipulation,andthat,asaconsequence,itisadryanddusty discipline,devoidofimagination,creativity,orexcitement.But thisisacompletelyfalseimageofthemoderndisciplineof statistics.Itisanimagebasedonaperceptiondatingfrommore thanhalfacenturyago.Inparticular,itentirelyignoresthefact thatthecomputerhastransformedthediscipline,changingit fromonehingingaroundarithmetictoonebasedontheuseof advancedsoftwaretoolstoprobedatainasearchfor understandingandenlightenment.Thatiswhatthemodern disciplineisallabout:theuseoftoolstoaidperceptionand providewaystoshedlight,routestounderstanding,instruments formonitoringandguiding,andsystemstoassistdecision-making. Allofthese,andmore,areaspectsofthemoderndiscipline.