统计方法描述统计推断统计参数估计假设检验.pptVIP

2019/12/12,安徽大学数学科学学院,1,Mindonstatistics,MaoJunJunAnHuiUniversity,2019/12/12,安徽大学数学科学学院,2,1Measureforteaching,ZH31020(专业核心课)双语(18X4)课件(中，英）教案（英）作业（英）考试（英）(70%+30%)Note:周二、周四第1-18周博南B401;,2019/12/12,安徽大学数学科学学院,3,Teachingmaterial,MindOnStatisticsJESSICAM.UTTSHowisthisbookdifferent?TwobasicpremisesoflearningOnepremiseisthatnewmaterialismucheasiertolearnandrememberifitisrelatedtosomethinginterestingorpreviouslyknownThesecondpremiseisthatnewmaterialismucheasiertolearnifyouactivelyaskquestionsandanswerthemforyourself.,2019/12/12,安徽大学数学科学学院,4,MindOnStatisticsisdesignedtohelpyoulearnstatisticalideasbyactivelythinkingaboutthem,2019/12/12,安徽大学数学科学学院,5,Teachingreference,(1)D.A.BerryandB.W.Lindgren,StatisticsTheoryandMethods,DuxburyPress,1995,ISBN0-534-50479-5.(2)G.CasellaandJ.O.Berger,StatisticalInference,2ndEdition,BrooksCole,2001,ISBN0-534-24312-6.(3)M.H.DeGroot,ProbabilityandStatistics,3rdedition,Addison-Wesley,2001,ISBN0-201-52488-0.,2019/12/12,安徽大学数学科学学院,6,(4)W.Mendenhall,R.L.ScheafferandD.D.Wackerly,MathematicalStatisticswithApplications,DuxburyPress,6thEdition,2002,ISBN0-534-37741-6.(5)J.A.Rice,MathematicalStatisticsandDataAnalysis,2ndedition,DuxburyPress,1994,ISBN0-534-20934-3.(6)G.W.Snedecor,W.G.Cochran,StatisticalMethods,IowaStateUniversityPress,8thEdition,1989,ISBN0-813-81561-4.,2019/12/12,安徽大学数学科学学院,7,中文参考,(1)统计学高等教育出版社袁卫等（2）应用数理统计学人民大学出版社周复恭等（3）统计学习题与案例高等教育出版社袁卫，庞皓等（4）统计学原理标准化题型习题集东北财经大学出版社栗方忠,2019/12/12,安徽大学数学科学学院,8,TeachingAim,Wewillstudytechniquesforcollectingdata,estimatingparameters,fittingmodels,andtestinghypotheses,andsoon.However,aswestudythesetechniquesweshouldbeawarethatapracticingstatisticianneedsmorethansimplyaknowledgeofmathematicaltechniques.Thecollectionandinterpretationofdataisasubtleart.Itrequirescommonsense.Itcansometimesraisephilosophicalquestions.,2019/12/12,安徽大学数学科学学院,9,Althoughthiscourseisprimarilyconcernedwithmathematicaltechniques,Iwillalsotry,bymeansofexamplesanddigressions,tointroduceyoutosomeofthenon-mathematicalaspectsofStatistics.Inaword:Notonlyholdmindonstatisticsbutalsoapplymodelswhenwefaceactualproblem,2019/12/12,安徽大学数学科学学院,10,Teachingcontents,Chapter1PrefaceChapter2TurningDataIntoInformationChapter3GatheringUsefulData,2019/12/12,安徽大学数学科学学院,11,Ch4samplingCh5relationshipsbetweenquantitative/categoricalvariablesCh61415RegressionAnalysisandCorrelationanalysisCh7Probability,2019/12/12,安徽大学数学科学学院,12,Chapter8randomvariablesChapter91012SamplingDistributionandEstimating(confidenceintervals),2019/12/12,安徽大学数学科学学院,13,Chapter1113HypothesisTestingChapter16VarianceAnalysisChapterTimeSeriesAnalysisChapterIndexAnalysis,2019/12/12,安徽大学数学科学学院,14,E-mail,QQ:401784750(院外交流)maojunjunahu(学生交作业)maojunjun(答疑),2019/12/12,安徽大学数学科学学院,15,几点要求,2019/12/12,安徽大学数学科学学院,16,谢谢合作！,2019/12/12,安徽大学数学科学学院,17,Chapter1Preface,2019/12/12,安徽大学数学科学学院,18,Learningobjects,BackgroundofthestatisticsWhatisthestatistics(EmphasesandDifficulties)Branchesofthestatistics,2019/12/12,安徽大学数学科学学院,19,【1.1】Background,1662（JohnGraunt)1676(WilliamPatty)1710(AdolpheQuetlet),2019/12/12,安徽大学数学科学学院,20,JacobBernoulli(伯努利)(16541705)DeMoivre(棣莫弗)(16671754)ThomasBayes(贝叶斯)(17021761)LeonhardEuler(欧拉)(17071783)PierreSimonLaplace(拉普拉斯)(17491827)AdrienMarieLegendre(勒让德)(17521833),2019/12/12,安徽大学数学科学学院,21,statistics,FriedrichGauss(高斯)(17771855)W.S.GOSSET(格赛特)T统计量KarlPearson(皮尔逊)(18571936)：CHI统计量RonaldAylmerFisher(费希尔)(18901962)F统计量，方差分析JerzyNeyman（奈曼）(18941981)置信区间EgonSharpePearson(皮尔逊)(18951980)假设检验A.Wald(沃尔德)(19061970).序贯抽样,2019/12/12,安徽大学数学科学学院,22,NOW,Informationdevelopedthroughtheuseofstatisticshasenhancedourunderstandingofhowlifeworks,helpeduslearnabouteachother,allowedcontroloversomesocietalissues,andhelpedindividualsmakeinformeddecisions.Thereisalmostnoareaofknowledgethathasnotbeenadvancedbystatisticalstudies.,2019/12/12,安徽大学数学科学学院,23,Statisticalmethodshavecontributedtoourunderstandingofhealth,physics,medicine,engineering,psychology,ecology,politics,music,business,lifestylechoices,anddozensofothertopics.,2019/12/12,安徽大学数学科学学院,24,Althoughstatisticscoursesareoftenofferedthroughmathematicsdepartments,statisticsisnotabranchofmathematics.Mathematicsistostatisticsaswood,hammer,andnailsaretoahouse:apartialsetofmaterialsandtools.Inadditiontomathematics,statisticsalsodrawsmaterialsandtoolsfromphilosophy,graphics,computing,psychology,andlanguage.,2019/12/12,安徽大学数学科学学院,25,(1.2)Whatisstatistics(p1),Whenyouheartheword“statistics”,youprobablythinkoflifelessorgruesomenumbers.Theword“statistics”however,actuallyisusedtomeandifferentthings.Thebetter-knowndefinitionisthat:Define1(p1):numbersmeasuredforsomepurpose(data),2019/12/12,安徽大学数学科学学院,26,Amorecompletedefinitionisthefollowing:Define2(p1):acollectionofproceduresandprinciplesforgatheringdataandanalyzinginformationinordertohelppeoplemakedecisionswhenfacedwithuncertaintythatistosay:,2019/12/12,安徽大学数学科学学院,27,FivebasicstepsP7AskingtherightquestionsCollectingusefuldataSummarizingandanalyzingdataMakingdecisionsandgeneralizationsTurningthedataandsubsequentdecisionsintonewknowledgeOR:,2019/12/12,安徽大学数学科学学院,28,Step1:Defineproblem:ThedefinitionoftheproblemisverycrucialatthestartofaninvestigationasitactsastheobjectiveofinvestigationStep2:Designexperiment:Thisincludesdecidingwhethertousethepopulationorselectasample.Oneshouldalsodefinewhatitisthatisbeingobservedandhowitshouldbemeasured.,2019/12/12,安徽大学数学科学学院,29,Step3:Collectdata:Theresearchermustdecidehowtocollecttheprimarydataandsecondarydata.Step4:Analysisdata:thefocusofthecourse.Theaimisturningdataintoinformation.Step5:Reportresults:Thereportingofresultsisoneofthemostimportantexerciseintheexperiment.Resultsshouldbepresentedinsuchawaythatthereceivercanunderstandthemwithaslittledifficultyaspossible.,2019/12/12,安徽大学数学科学学院,30,Define3:Statisticsisabodyofprincipleandmethodsconcernedwithextractingusefulinformationfromasetofnumericaldata.SuchasBayesTheorem.,2019/12/12,安徽大学数学科学学院,31,Statistics的定义(不列颠百科全书),Statistics:thescienceofcollecting,analyzing,presenting,andinterpretingdata.,2019/12/12,安徽大学数学科学学院,32,什么是统计学?,1.数据搜集：取得数据2.数据分析：分析数据3.数据表述：图表展示数据数据解释：结果的说明,收集、整理、显示和分析数据的科学,2019/12/12,安徽大学数学科学学院,33,实际问题,2019/12/12,安徽大学数学科学学院,34,(1.3)Branchesofstatistics,(a)DescriptiveStatistics(b)Inductive(inferential)Statisticsor(A)TheoreticalStatistics(B)Appliedstatistics,2019/12/12,安徽大学数学科学学院,35,DescriptiveStatistics:DescriptiveStatisticsdealswiththevariousmeasuresthatcanbeusedtodescribeasetofdata.Thesemeasureslookatwherethefocalpointofthedatais,forexample:mean,andhowthedatafluctuates,forexample:median,lowerquartile,upperquartile,standarddeviation.Story1.11.2,2019/12/12,安徽大学数学科学学院,36,CaseStudy1.1WhoAreThoseSpeedyDrivers?,Question:Whatsthefastestyouhaveeverdrivenacar?mph.Data:87maleand102femalestudentsfromlargestatisticsclassatUniversity.,Whichgenderhasdrivenfaster?Howtosummarizedata?,2019/12/12,安徽大学数学科学学院,37,Males:1101099014010515012011011090115951451401101058595100115124951001251408512011510512510285120110120115941258085140120921301251109011011095951101058010011013010510512090100105100120100100801001201056012512010011595110101801121201101151255590Females:807583801001009075958590859090120851001207585807085110857510595757090708285100907590110808011011095751309511011080901059011075100901108590808085508010080808095100901009580805088909085709030858587859085759010280100951108095908090,2019/12/12,安徽大学数学科学学院,38,CaseStudy1.1WhoAreThoseSpeedyDrivers?,Dotplot:eachdotrepresentstheresponseofanindividualstudent.,2019/12/12,安徽大学数学科学学院,39,2019/12/12,安徽大学数学科学学院,40,CaseStudy1.1WhoAreThoseSpeedyDrivers?,Five-numbersummary:thelowestvalue,thecutoffpointsfor,andofthedata,andthehighestvalue.,Note:ofmenhavedriven95mphormore,onlyofwomenhavedoneso.,2019/12/12,41,可编辑,2019/12/12,安徽大学数学科学学院,42,2019/12/12,安徽大学数学科学学院,43,Moral:Simplesummariesofdatacantellaninterestingstoryandareeasiertodigestthanlonglists.Definitions:datamedianlowerquarterupperquarter,2019/12/12,安徽大学数学科学学院,44,CaseStudy1.2SafetyintheSkies?,“Planesgetcloserinmidairastrafficcontrolerrorsrise”“Errorsbyairtrafficcontrollersclimbedfrom746infiscal1997to878infiscal1998,an18%increase.”USAToday,Levin,1999,2019/12/12,安徽大学数学科学学院,45,Soundsominous,but“Theerrorspermillionflightshandledbycontrollersclimbedfrom4.8to5.5.”Sotheoriginalrateoferrorsin1997,fromwhichthe18%increasewascalculated,waslessthan5errorspermillionflights.,2019/12/12,安徽大学数学科学学院,46,Moral:Whendiscussingthechangeintherateorriskofoccurrenceofsomething,makesureyoualsoincludethebaserateorbaselinerisk.Definitions:rateriskbaseratebaserisk,2019/12/12,安徽大学数学科学学院,47,InductiveorinferentialstatisticsInferentialstatisticsreferstoabodyofprinciplesthatenablesonetoinferorreachsomeconclusionsaboutapopulationbysimplyobservingasamplefromthatpopulation.Itmaybetimeconsuming,expensiveorinappropriatetolookatthepopulationatlarge.Story1.61.7,2019/12/12,安徽大学数学科学学院,48,“AccordingtoanewUSAToday/GallupPollofteenagersacrossthecountry,57percentofteenswhogooutondatessaytheyvebeenoutwithsomeoneofanotherraceorethnicgroup.”(Peterson,1997).SacramentoBeeheadlineread:“Interracialdatescommonamongtodaysteenagers.”,CaseStudy1.3DidAnyoneAskWhomYouveBeenDating?,2019/12/12,安徽大学数学科学学院,49,MillionsofteenagersinU.S.-Didpolltakersaskallofthem?No.Thearticlestates“theresultsofthenewpollof602teens,conductedOct.1320,reflecttheubiquity(普遍性）ofinterracialdatingtoday”Askedonly602teens.CouldsuchasmallsampletellusanythingaboutthemillionsofteenagersintheU.S.?Yesifthoseteensconstitutedarandomsamplefromthepopulation.,2019/12/12,安徽大学数学科学学院,50,CaseStudy1.3DidAnyoneAskWhomYouveBeenDating?,ThepercentofallteenagersintheUSwhodatethatwouldsaytheyhavedatedinterraciallyislikelytobeintherange57%5%,orbetween52%and62%.,Howaccuratecouldthissamplebe?Marginoferrorisabout5%.,2019/12/12,安徽大学数学科学学院,51,MoralStudy1.3:Arepresentativesampleofonlyafewthousand,orperhapsevenafewhundred,cangivereasonablyaccurateinformationaboutapopulationofmillions.,2019/12/12,安徽大学数学科学学院,52,CaseStudy1.4WhoAreThoseAngryWomen?,ShereHitesentquestionnairesto100,000womenaskingaboutlove,sex,andrelationships.Only4.5%ofthewomenresponded,andHiteusedthoseresponsestowriteherbook,WomenandLove.,“Thewomenwhorespondedwerefedupwithmenandeagertofightthem.Forexample,91%ofthosewhoweredivorcedsaidthattheyhadinitiatedthedivorce.Theangerofwomentowardmenbecamethethemeofthebook.”Moore(1997,p.11).,2019/12/12,安徽大学数学科学学院,53,Extensivenonresponsefromarandomsample,ortheuseofaself-selected(i.e.,all-volunteer)sample,willprobablyproducebiasedresults.MoralStudy1.4:Anunrepresentativesample,evenalargeone,tellsyoualmostnothingaboutthepopulation.,2019/12/12,安徽大学数学科学学院,54,CaseStudy1.5DoesPrayerLowerBloodPressure?,“AttendingreligiousserviceslowersbloodpressuremorethantuningintoreligiousTVorradio,anewstudysays”USATodayheadlineread:“Prayercanlowerbloodpressure.”(Davis,1998),2019/12/12,安徽大学数学科学学院,55,Basedonobservationalstudy,followed2391people6years.“PeoplewhoattendedareligiousserviceonceaweekandprayedorstudiedtheBibleonceadaywere40%lesslikelytohavehighbloodpressurethanthosewhodontgotochurcheveryweekandprayedandstudiedtheBibleless.”Researchersdidobservearelationship,butitsamistaketoconcludeprayeractuallycauseslowerbloodpressure.,2019/12/12,安徽大学数学科学学院,56,CaseStudy1.5DoesPrayerLowerBloodPressure?,Inobservationalstudies,groupscandifferinimportantwaysthatmaycontributetotheobservedrelationship.Peoplewhoattendedchurchregularlymayhavebeenlesslikelytosmokeordrinkalcohol;hadabettersocialnetwork;beensomewhathealthierandabletogotochurch.Theseotherfactorsarepossibleconfoundingvariables.,2019/12/12,安徽大学数学科学学院,57,Moral:Cause-and-effectconclusionscannotgenerallybemadebasedonanobservationalstudy.Definitions:observationalstudy(merelyobserved);variable;confoundingvariable,2019/12/12,安徽大学数学科学学院,58,CaseStudy1.6DoesAspirinReduceHeartAttackRates?,PhysiciansHealthStudy(1988)5-yearrandomizedexperiment22,071malephysiciansofage40-84;randomlyassignedtooneoftwotreatmentgroups;Group1=aspirineveryotherday;Group2=placebo;Physiciansblindedastowhichgrouptheywerein.,2019/12/12,安徽大学数学科学学院,59,CaseStudy1.6DoesAspirinReduceHeartAttackRates?,2019/12/12,安徽大学数学科学学院,60,Aspiringroup:9.42heartattacksper1000participantsPlacebogroup:17.13heartattacksper1000participantsRandomization=otherimportantfactors(age,diet,etc)shouldhavebeensimilarforbothgroups.Onlyimportantdifferenceshouldbewhethertheytookaspirinorplacebo.,2019/12/12,安徽大学数学科学学院,61,Moral:Unlikewithobservationalstudies,cause-and-effectconclusionscangenerallybemadeonthebasisofrandomizedexperiments.,2019/12/12,安徽大学数学科学学院,62,CaseStudy1.7DoestheInternetIncreaseLonelinessandDepression?,“greateruseoftheInternetwasassociatedwithdeclinesinparticipantscommunicationwithfamilymembersinthehousehold,declinesinsizeoftheirsocialcircle,andincreasesintheirdepressionandloneliness”(Krautetal.,1998,p.1017)NewYorkTimesheadlineread:“Sad,LonelyWorlddiscoveredinCyberspace.”(Harmon,1998),2019/12/12,安徽大学数学科学学院,63,Studyincluded169individualsfrom73householdsinPittsburghgivenfreecomputersandinternetservice.Participantsansweredquestionsatbeginningandeither1-2yearslateronsocialcontacts,stress,loneliness,depression.,2019/12/12,安徽大学数学科学学院,64,Changeswerequitesmall,althoughsignificant#ofpeoplein“localsocialnetwork”decreasedfromaverageof23.94to22.90people;onscale1to5,self-reportedlonelinessdecreasedfromaverageof1.99to1.89(lower=greaterloneliness).onascale0to3,self-reporteddepressiondroppedfromaverageof0.73to0.62(lower=higherdepression).,CaseStudy1.7DoestheInternetIncreaseLonelinessandDepression?,2019/12/12,安徽大学数学科学学院,65,Follow-upstudy:“UsingtheInternetathomedoesntmakepeoplemoredepressedandlonelyafterall.”(Elias,2001)Whetherthelinkeverexistedwillneverbeknown,butitisnotsurprising,giventhesmallmagnitudeoftheoriginalfinding,thatitsubsequentlydisappeared.,2019/12/12,安徽大学数学科学学院,66,Moral:A“statisticallysignificant”findingdoesnotnecessarilyhavepracticalimportance.Whenastudyreportsastatisticallysignificantfinding,findoutthemagnitudeoftherelationshipordifference.,CaseStudy1.7DoestheInternetIncreaseLonelinessandDepression?,2019/12/12,安徽大学数学科学学院,67,Asecondarymoraltothisstoryisthattheimplieddirectionofcauseandeffectmaybewrong.Inthiscase,itcouldbethatpeoplewhoweremorelonelyanddepressedweremorepronetousetheInternet.And,asthefollow-upresearchmakesclear,rememberthat“truth”doesntnecessarilyremainfixedacrosstime.,2019/12/12,安徽大学数学科学学院,68,Therefore,inferentialstatisticsplaysanImportantroleinenablingtheresearchertouseonlyasmallrandomlyselectedsampletopredictthecharacteristicsofpopulation.Forexample:randomsample,samplesurvey,marginoferror,HypothesisTesting,confidenceinterval,2019/12/12,安徽大学数学科学学院,69,统计方法,2019/12/12,安徽大学数学科学学院,70,描述统计(descriptivestatistics),研究数据收集、整理和描述的统计学分支内容搜集数据整理数据展示数据描述性分析目的描述数据特征找出数据的基本规律,2019/12/12,安徽大学数学科学学院,71,推断统计(inferentialstatistics),研究如何利用样本数据来推断总体特征的统计学分支内容参数估计假设检验目的对总体特征作出推断,2019/12/12,安徽大学数学科学学院,72,描述统计与推断统计的关系,反映客观现象的数据,描述统计（统计数据的搜集、整理、显示和分析等）,2019/12/12,安徽大学数学科学学院,73,(3)Branchesofstatistics,(A)TheoreticalStatistics(B)Appliedstatistics,2019/12/12,安徽大学数学科学学院,74,InSummary:Morals,1S