Unit2高等数学英文 出国留学Word文件下载.docx
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Unit2高等数学英文 出国留学Word文件下载.docx
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▪Acensuscollectsdatafromeveryindividualinthepopulation.
▪Intherealworld,timeandcostconsiderationsusuallymakeitimpossibletoanalyzeanentirepopulation–whose“truth”isessentiallyunknowable.
•Asampleisasubsetofthepopulationthatisactuallybeingexaminedandusedtorepresentthepopulation.
▪Anynumericalvaluethatcomesfromasampleiscalledastatistic.Theideaistousestatisticstodrawconclusionsaboutunknownparameters.Whileapopulationparameterisafixedquantity,statisticsvarydependingontheparticularsamplechosen.
▪SampleSurvey:
Thedistinctionbetweenpopulationandsampleisbasictostatistics.Toderiveconclusionsaboutthelargepopulation,weneedtobeconfidentthatthesamplewehavechosenrepresentsthatpopulationfairly.
II.Bias
Samplingmethodsthat,bytheirnature,tendtoover-orunderemphasizesomecharacteristicsofthepopulationaresaidtobebiased.Conclusionsbasedonsamplesdrawnwithbiasedmethodsareinherentlyflawed.Biasisnotjustbadluckinonesample.Itistheresultofabadstudydesignthatwillconsistentlymissthetruthaboutthepopulationinthesameway.
Ø
Choosingindividualsfromthepopulationwhoareeasytoreachresultsinaconveniencesample.Manysurveydesignssufferfromunder-coverage,inwhichsomeportionofthepopulationisnotsampledatall,orhasasmallerrepresentationinthesamplethanithasinthepopulation.
Responsebiasreferstoanythinginthesurveydesignthatinfluencestheresponses.oItisatypeofcognitivebiaswhichcanaffecttheresultsofastatisticalsurvey.(e.g.,respondentsanswerquestionsinthewaytheythinkthequestionerwantsthemtoanswerratherthanaccordingtotheirtruebeliefs.)
oSuchcircumstancesleadtoanonrandomdeviationoftheanswersfromtheirtruevalue.Becausethisdeviationtakesonaveragethesamedirectionamongrespondents,itcreatesasystematicerrorofthemeasure,orbias
oThesebiasesaremostprevalentinthetypesofstudiesandresearchthatinvolveparticipantself-report,suchasstructuredinterviewsorsurveys.Asaresult,responsebiasescanhavealargeimpactonthevalidityofthequestionnaireorsurveytowhichtheparticipantisresponding.
Wordingbias:
Non-neutralorpoorlywordedquestionsmayleadtoanswersthatareveryunrepresentativeofthepopulation.
Voluntaryresponsebias:
samplesbasedonindividualswhooffertoparticipate,usuallybyrespondingtoageneralinvitation,typicallydisplaysexcessiveemphasizetopeoplewithstrongopinions,thusleadingtobias.
Non-responsebiasoccurswhenanindividualchosenforthesamplecan’tbecontactedorrefusestoparticipate.
oNon-responsetosurveysoftenexceeds50%,evenwithcarefulplanningandseveralfollow-upcalls.
oIfthepeoplewhoresponddifferfromthosewhodon’t,inawaythatisrelatedtotheresponse,biasresults.
oShort,easilyunderstoodsurveysgenerallyhavehigherresponserates
•Themaintechniquetoavoidbiasistoincorporaterandomnessintotheselectionprocess.Randomizingprotectsusfromtheinfluencesofallthefeaturesofourpopulationbymakingsurethat,onaverage,thesamplelooksliketherestofthepopulation.
•Thelargerthesample,thebettertheresults,butwhatiscriticalisthesamplesize,notthepercentageorfractionofthepopulation.Arandomsampleofsize500fromapopulationofsize100,000isjustasrepresentativeasarandomsampleofsize500fromapopulationofsize1,000,000.
III.Sampling1.RandomSampling
•Randomsamplinginvolvesusingachanceprocesstodeterminewhichmembersofapopulationareincludedinthesample.
•ASimplerandomsample(SRS)ofsizenischoseninsuchawaythateverypossiblegroupofnindividualsinthepopulationhasanequalchancetobeselectedasthesample.oAnSRSgiveseverypossiblesampleofthedesiredsizeanequalchancetobechosen.Italsogiveseachmemberofthepopulationanequalchancetobeincludedinthesample.
oAnSRSisthestandardagainstwhichwemeasureothersamplingmethods,andthesamplingmethodonwhichthetheoryofworkingwithsampleddataisbased.
ChoosinganSRSwithTechnology
Step1:
Label.Giveeachindividualinthepopulationadistinctnumericallabelfrom1toN
Step2:
Randomize.UseaRandomNumberGenerator(RNG)toobtainndifferentintegersfrom1toN.
•Samplesdrawnatrandomgenerallydifferonefromanother.Thesedifferencesleadtodifferentvaluesforthevariableswemeasure.Wecallthesesample-to-sampledifferencessamplingvariabilityorsamplingerror.
oDifferentsamplesgivedifferentsamplestatistics,allofwhichareestimatesofapopulationparameter.
oSamplingerrorrelatestonaturalvariationbetweensamples,canneverbeeliminated,canbedescribedusingprobability,andisgenerallysmallerifthesamplesizeislarger.
2.StratifiedSampling
•Instratifiedsamplingthepopulationisfirstdividedintohomogenous(meaningofsimilarifnotthesamefeatures)groups(knownasstrata),thentakeanSRSoutofeachstratumandcombinetheseSRSstoformthefullsample.
o
Choosethestratabasedonfactsknownbeforethesampleistaken.Forexample,inastudyofsleephabitsonschoolnights,thepopulationofstudentsinalargeuniversitymightbedividedintofreshmen,sophomore,junior,andseniorstrata.
oSamplestakenwithinastratumvaryless,sotheresultingestimatescanbemoreprecise.Thisreducedsamplingvariabilityisthemostimportantbenefitofstratifying.Stratifiedsamplesgiveusefulinformationabouteachstratum.
•Stratifiedrandomsamplingworksbestwhentheindividualswithineachstratumaresimilarwithrespecttowhatisbeingmeasuredandwhentherearelargedifferencesbetweenstrata.
•Wecouldfurtherdoproportionalsampling,wherethesizesoftherandomsamplesfromeachstratumdependontheproportionofthetotalpopulationrepresentedbythestratum.
3.ClusterSampling
Inclustersamplingthepopulationisdividedintorepresentative,heterogeneousgroups,knownasclusters.Wethenrandomlyselectoneormoreclusterstobethesample.
•SomestatisticianstakeanSRSfromeachclusterratherthanincludingallmembersofthecluster.
•Clustersareinternallyheterogeneous,eachresemblingtheoverallpopulation.Eachclustershouldbesimilartoeveryothercluster.
•Clustersamplesareoftenusedforpracticalreasons–savingtimeandcost.Clustersamplingworksbestwhentheclusterslookjustlikethepopulationbutonasmallerscale.
4.MultistageSampling
Multistagesamplingreferstoaprocedureinvolvingtwoormoresteps,eachofwhich(beingofSRS)couldinvolveanyofthevarioussamplingtechniques.
TheGalluporganization,forexample,oftenfollowsaprocedureinwhichnationwidelocationsarerandomlyselected,thenneighborhoodsarerandomlyselectedineachoftheselocations,andfinallyhouseholdsarerandomlyselectedineachoftheseneighborhoods.
IV.Experiments1.ObservationalStudy(OS)
Anobservationalstudyobservesindividualsandmeasurevariablesofinterestsbutdoesnotinfluencetheresponses.
●InanOS,subjectschoosetheirownactionsandresearchersobservewhattheydo.
●Asamplesurveyisanobservationalstudyinwhichwedrawconclusionsaboutanentirepopulationbyconsideringanappropriatelychosensampletolookat.
2.Experiment
●Anexperimentdeliberatelyimposessome“treatment”onindividualstomeasuretheirresponses.
⏹Atreatmentisaspecificconditionappliedtotheindividualsinanexperiment.
●Anexperimentisperformedonobjectscalledexperimentalunits,andiftheunitsarepeople,theyarecalledsubjects.
●Theexperimentalunitsorsubjectsaretypicallydividedintotwogroups:
treatmentandcontrol.
⏹TreatmentGroup:
thegroupthatreceivesatreatment
⏹ControlGroup:
thegroupthatreceivesnotreatmentorold,establishedtreatment.Acontrolgroupmustbeusedforcomparison.Forexample,ifyouaretestingatreatmentforasprainedankle,youmusthaveagroupthatgetsnotreatmentbecausesprainedanklesnaturallygetbetterovertime.Youneedtoshowthatthetreatmentgroupgetsbetterfasterthanthecontrolgroup.
⏹PlaceboGroup:
Acontrolgroupthatreceivesaplacebo(fakedrug)inexperimentsinvolvingmedicines.
◆Placeboeffectreferstothefactthatmanypeoplerespondtoanykindof“perceived”treatment.Thepurposeoftheplaceboistoseparategenuinetreatmenteffectsfrompossiblesubjectresponsesduetosimplybeingpartofanexperiment.
●Experimentsinvolveexplanatoryvariables,calledfactors,whicharebelievedtohaveaneffectonresponsevariables,whichmeasuretheoutcomesofanexperiment.
⏹Thechoicesyouhaveforeachfactorareknownaslevels.
⏹Thedifferentfactor-levelcombinationsaretreatments.
●Inanexperiment,westudytheeffectsofthespecifictreatmentsweareinterestedin,whiletryingtocontrolfortheeffectsofothervariables.
⏹Thepurposeofanexperimentistodeterminewhetherthetreatmentcausesachangeintheresponse.
⏹Theexperimentcomparestheresponsesinthetreatmentgrouptotheresponsesinthecontrolgroup.
●Someexperimentaldesignsdon’tincludeacontrolgroup.That’
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