统计学的成功案例和警示故事

StatisticsSuccessStoriesandCautionaryTales统计学的成功案例和警示故事LESSON1第一课

1.1WHATISSTATISTICS?什么是统计学Statisticsisacollectionofproceduresandprincipleforgatheringdataandanalyzinginformationinordertohelppeoplemakedecisionswhenfacedwithuncertainty.统计学是一套收集数据和分析信息的方法和原则，以帮助人们在面对不确定性时制定决策。Theoddsoffindingtwoidenticalfingerprintswere1in64billion.—FrancisGalton两个随机个体具有相同DNA图形的概率为3×10-11；如果同时用两种探针进行比较，两个个体完全相同的概率小于5×10-19。每支枪的枪管都有独一无二的特征，这种特征影响了它所发射的每一发子弹。—司法弹道学航空公司通过抽样而省钱最早的英文原版《打败庄家》1.2SEVENSTATISTICALSTORIESWITHMORALS7个包含寓义的统计学故事Therearethreekindsoflies:lies,damnedliesandstatistics。BenjaminDisraeli(BritishPrimeMinister,1804–1881)CASESTUDY1WhoareThoseSpeedyDrivers?谁是快车手？“What’sthefastestyouhaveeverdrivenacar?”-PennStateUniversity,1994

11010990140105150120110110

9011595145140110105859510011512495100125140851201151051251028512011012011594125808514012092130125110901101109595110105801001101301051051209010010510012010010080100120105601251201001159511010180112120110115125559087Males

807583801001009075958590909012085100120758580708511085751059575709070828510090959011080801101109575130951101108090105901107510090110859080808550801008080

8095100901009580805088909085709030858587859085759010280100951108095908090102FemalesDotplotMALESFastestspeed(mph)FEMALESFastestspeed(mph)Five-numbersummaryMales(87Students)Females(102Students)Median11089Quartiles951208095Extremes5515030130一条平均水深0.4m河流绝不会比一个平均水深0.6m的游泳池更安全Five-numbersummaryMales(87Students)Females(102Students)Median11089Quartiles951208095Extremes5515030130Definition:Themedianisthevalueinthemiddlewhenthenumbersareputinorder.Thelowerquartileandupperquartileare(roughly)themediansofthelowerandupperhalvesofthedata.Moralofthestory1303015055Extremes958012095Quartiles89110MedianFemales(102Students)Males(87Students)Simplesummariesofdatacantellaninterestingstoryandareeasiertodigestthanlonglists.CASESTUDY2DisasterintheSkies?空中的灾难？“Planesgetcloserinmidairastrafficcontrolerrorsrise.Errorsbyairtrafficcontrollersclimbedfrom746infiscal1997to878infiscal1998,an18%increase”-USATODAY,Levin,1999“Theerrorspermillionflightshandledbycontrollersclimbedfrom4.8to5.5”5.54.8=114.6%Definition:Therateissimplythenumberoftimessomethingoccurspernumberofopportunitiesforittooccur.Baselinerateistherateatabeginningtimeperiodorunderspecificconditions.MoralofthestoryWhendiscussingthechangeintherateorriskofoccurrenceofsomething,makesureyoualsoincludethebaserateorbaselinerisk.CASESTUDY3Didanyoneaskyouwhomyou’vebeendating?“AccordingtoanewUSA

Today/GallupPollofteenagersacrossthecountry,57percentofteenswhogooutondatessaythey’vebeenoutwithsomeoneofanotherraceorethnicgroup.”-USATODAY,Perterson,1997CASESTUDY3“Inmostcases,parentsaren’tamajorobstacle.Sixty-fourpercentofteenssaystheirparentsdon’tmindthattheydateinterracially,orwouldn’tmindiftheydid.”-SacramentoBee,Hiram,1997Howcouldthepolltakersmanagetoasksomanyteenagersthesequestion?Question1Question2Question3Theresultsofthispollareaccuratetowithinamarginoferrorofabout4.5%(95%confidenceinterval).MoralofthestoryCASESTUDY4WhoAreThoseAngryWomen?“Awell-conductedsurveycanbeveryinformative,butapoorlyconductedonecanbeacompletedisaster.”-Statistics:ConceptsandControversives,DavidS.Moore“Thewomenwhorespondedwerefedupwithmenandeagertofightthem.Forexample,91%ofthosewhoweredivorcedsaidtheyhadinitiatedthedivorce.Theangerofwomentowardmenbecamethethemeofthebook.”-WomenandLove,Shere.HiteShereHitesentquestionnairesto100,000womenaskingaboutlove,sex,andrelationships.MoralofthestoryCASESTUDY5DoesPrayerLowerBloodpressure?PrayerCanLowerBloodPressure“AttendingreligiousserviceslowersbloodpressuremorethantuningintoreligiousTVorradio,anewstudysays.”-USATODAY,Davis,1998Peoplewhoattendedareligiousserviceonceaweekandprayedorstudiedthebibleonceadaywere40%lesslikelytohavehighbloodpressurethanthosewhodon’tgotochurcheveryweekandprayedandstudiedthebibleless.AnobservationalstudyconductedbytheU.S.NationalInstitutesofHealth,whichfollowed2391peopleaged65orolderforsixyears.BackgroundCriticismMoralofthestoryCause-and-effectconclusionscannotgenerallybemadebasedonanobservationalstudy.Definition:Anobservationalstudyisoneinwhichparticipantsaremerelyobservedandmeasured.Aconfoundingvariableisavariablethatisnotthemainconcernofthestudy,butmaybepartiallyresponsiblefortheobservedresults.CASESTUDY6DoesAspirinReduceHeartAttackRates?BackgroundTime:1983~1988Organizer:SteeringCommitteeofthePhysicians’HealthStudyResearchGroupObjective:Todetermineiftakingaspirinreducestheriskofaheartattack.Subject:22,071malephysiciansbetweentheagesof40and80Method:Afive-yearrandomizedexperimentMethod2x2factorialdesignactiveaspirinandactivebeta-carotene(5,517)activeaspirinandbeta-caroteneplacebo(5,520)aspirinplaceboandactivebeta-carotene(5,519)aspirinplaceboandbeta-caroteneplacebo(5,515)Aspirinreducedtheriskoffirstmyocardialinfarctionby44%(Plessthan0.00001).Thereweretoofewstrokesordeathsuponwhichtobasesoundclinicaljudgmentregardingaspirinandstrokeormortality.Result-NewEnglandJournalofMedicine,1989,321(3):18-185TreatmentHeartAttacksDoctorsinGroupAttacksPer1000DoctorsAspirin10411,0379.42Placebo18911,03417.13TheEffectofAspirinonHeartAttacks*Morethan170otherfindingshaveemergedfromthetrialsofar.MoralofthestoryUnlikewithobservationalstudies,cause-andeffectconclusionscangenerallybemadeonthebasisofrandomizedexperiments.CASESTUDY7DoestheinternetIncreaseLonelinessandDepression?“greateruseoftheinternetwasassociatedwithdeclinesinparticipants’communicationwithfamilymembersinthehousehold,declinesinsizeoftheirsocialcircle,andincreasesintheirdepressionandloneliness.”-Internetparadox:Asocialtechnologythatreducessocialinvolvementandpsychologicalwell-being?AmericanPsychologist,1998,53(9):1017-1031DavidS.MooreSad,LonelyWorldDiscoveredinCyberspace-AmyHarmon,August30,1998,SundayBackground:Thestudyincluded169individualsin73householdsinPittsburg,Pennsylvaniawhoweregivenfreecomputersandinternetservicein1995.Theparticipantsansweredaseriesofquestionsatthebeginningofthestudyan