概率论毕业论文外文翻译.docx

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概率论毕业论文外文翻译

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济南大学泉城学院毕业论文外文资料翻译

Statisticalhypothesistesting

AdrianaAlbu，LoredanaUngureanu

PolitehnicaUniversityTimisoara,adrianaa@aut.utt.ro

PolitehnicaUniversityTimisoara,loredanau@aut.utt.ro

AbstractInthisarticle,wepresentaBayesianstatisticalhypothesistestinginspection,testingtheoryandtheprocessMentionedhypothesistestingintherealworldandtheimportanceof,andsuccessfultestoftheNotes.

KeywordsBayesianhypothesistesting;Bayesianinference;TestofsignificanceIntroduction

Astatisticalhypothesistestisamethodofmakingdecisionsusingdata,whetherfromacontrolledexperimentoranobservationalstudy（notcontrolled）.Instatistics,aresultiscalledstatisticallysignificantifitisunlikelytohaveoccurredbychancealone,accordingtoapre-determinedthresholdprobability,thesignificancelevel.Thephrase"testofsignificance"wascoinedbyRonaldFisher:

"Criticaltestsofthiskindmaybecalledtestsofsignificance,andwhensuchtestsareavailablewemaydiscoverwhetherasecond

sampleisorisnotsignificantlydifferentfromthefirst."

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Hypothesistestingissometimescalledconfirmatorydataanalysis,incontrasttoexploratorydataanalysis.Infrequencyprobability,thesedecisionsarealmostalwaysmadeusingnull-hypothesistests.TheseareteststhatanswerthequestionAssumingthatthenullhypothesisistrue,whatistheprobabilityofobservingavaluefortheteststatisticthatisatleastasextremeasthevaluethatwasactuallyobserved?

）2Moreformally,theyrepresentanswerstothequestion,posedbeforeundertakinganexperiment,ofwhatoutcomesoftheexperimentwouldleadtorejectionofthenullhypothesisforapre-specifiedprobabilityofanincorrectrejection.Oneuseofhypothesistestingisdecidingwhetherexperimentalresultscontainenoughinformationtocastdoubtonconventionalwisdom.

Statisticalhypothesistestingisakeytechniqueoffrequentiststatisticalinference.TheBayesianapproachtohypothesistestingistobaserejectionofthehypothesisonthe

posteriorprobability.

[3][4]

Otherapproachestoreachingadecisionbasedondataare

availableviadecisiontheoryandoptimaldecisions.

Thecriticalregionofahypothesistestisthesetofalloutcomeswhichcausethenullhypothesistoberejectedinfavorofthealternativehypothesis.ThecriticalregionisusuallydenotedbytheletterC.

One-sampletestsareappropriatewhenasampleisbeingcomparedtothepopulationfromahypothesis.Thepopulationcharacteristicsareknownfromtheoryorarecalculatedfromthepopulation.

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济南大学泉城学院毕业论文外文资料翻译

Two-sampletestsareappropriateforcomparingtwosamples,typicallyexperimentalandcontrolsamplesfromascientificallycontrolledexperiment.

Pairedtestsareappropriateforcomparingtwosampleswhereitisimpossibletocontrolimportantvariables.Ratherthancomparingtwosets,membersarepairedbetweensamplessothedifferencebetweenthemembersbecomesthesample.Typicallythemeanofthedifferencesisthencomparedtozero.

Z-testsareappropriateforcomparingmeansunderstringentconditionsregardingnormalityandaknownstandarddeviation.

T-testsareappropriateforcomparingmeansunderrelaxedconditions（lessisassumed）.

Testsofproportionsareanalogoustotestsofmeans（the50%proportion）.Chi-squaredtestsusethesamecalculationsandthesameprobabilitydistributionfor

differentapplications:

Chi-squaredtestsforvarianceareusedtodeterminewhetheranormalpopulationhasaspecifiedvariance.Thenullhypothesisisthatitdoes.

Chi-squaredtestsofindependenceareusedfordecidingwhethertwovariablesareassociatedorareindependent.Thevariablesarecategoricalratherthannumeric.Itcanbeusedtodecidewhetherleft-handednessiscorrelatedwithlibertarianpolitics（ornot）.Thenullhypothesisisthatthevariablesareindependent.Thenumbersusedinthecalculationaretheobservedandexpectedfrequenciesofoccurrence（fromcontingencytables）.

Chi-squaredgoodnessoffittestsareusedtodeterminetheadequacyofcurvesfittodata.Thenullhypothesisisthatthecurvefitisadequate.Itiscommontodeterminecurveshapestominimizethemeansquareerror,soitisappropriatethatthegoodness-of-fitcalculationsumsthesquarederrors.

F-tests（analysisofvariance,ANOVA）arecommonlyusedwhendecidingwhethergroupingsofdatabycategoryaremeaningful.Ifthevarianceoftestscoresoftheleft-handedinaclassismuchsmallerthanthevarianceofthewholeclass,thenitmaybeusefultostudyleftiesasagroup.Thenullhypothesisisthattwovariancesarethesame-sotheproposedgroupingisnotmeaningful.

Thetestingprocess

Inthestatisticalliterature,statisticalhypothesistestingplaysafundamentalrole.Theusuallineofreasoningisasfollows:

1.Thereisaninitialresearchhypothesisofwhichthetruthisunknown.

2.Thefirststepistostatetherelevantnullandalternativehypotheses.Thisisimportantasmis-statingthehypotheseswillmuddytherestoftheprocess.Specifically,thenullhypothesisallowsattachinganattribute:

itshouldbechoseninsuchawaythatitallowsustoconcludewhetherthealternativehypothesiscan

eitherbeacceptedorstaysundecidedasitwasbeforethetest.

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3.Thesecondstepistoconsiderthestatisticalassumptionsbeingmadeaboutthesampleindoingthetest;forexample,assumptionsaboutthestatisticalindependenceorabouttheformofthedistributionsoftheobservations.Thisis

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济南大学泉城学院毕业论文外文资料翻译

equallyimportantasinvalidassumptionswillmeanthattheresultsofthetestareinvalid.

4.Decidewhichtestisappropriate,andstatetherelevantteststatisticT.

5.Derivethedistributionoftheteststatisticunderthenullhypothesisfromtheassumptions.Instandardcasesthiswillbeawell-knownresult.ForexampletheteststatisticmayfollowaStudent'stdistributionoranormaldistribution.

6.Selectasignificancelevel（α）,aprobabilitythresholdbelowwhichthenullhypothesiswillberejected.Commonvaluesare5%and1%.

7.ThedistributionoftheteststatisticunderthenullhypothesispartitionsthepossiblevaluesofTintothoseforwhichthenull-hypothesisisrejected,thesocalledcriticalregion,andthoseforwhichitisnot.Theprobabilityofthecriticalregionisα.

8.Computefromtheobservationstheobservedvaluet

obs

oftheteststatisticT.

9.Decidetoeitherfailtorejectthenullhypothesisorrejectitinfavorofthealternative.ThedecisionruleistorejectthenullhypothesisH0iftheobservedvaluetobsisinthecriticalregion,andtoacceptor"failtoreject"thehypothesisotherwise.

UseandImportance

Statisticsarehelpfulinanalyzingmostcollectionsofdata.Thisisequallytrueofhypothesistestingwhichcanjustifyconclusionsevenwhennoscientifictheoryexists.Realworldapplicationsofhypothesistestinginclude:

Testingwhethermorementhanwomensufferfromnightmares

Establishingauthorshipofdocuments

Evaluatingtheeffectofthefullmoononbehavior

Determiningtherangeatwhichabatcandetectaninsectbyecho

Decidingwhetherhospitalcarpetingresultsinmoreinfections

Selectingthebestmeanstostopsmoking

Checkingwhetherbumperstickersreflectcarownerbehavior

Testingtheclaimsofhandwritinganalysts

Statisticalhypothesistestingplaysanimportantroleinthewholeofstatisticsandinstatisticalinference.Forexample,Lehmann（1992）inareviewofthefundamentalpaperbyNeymanandPearson（1933）says:

"Nevertheless,despitetheirshortcomings,thenewparadigmformulatedinthe1933paper,andthemanydevelopmentscarriedoutwithinitsframeworkcontinuetoplayacentralroleinboththetheoryandpracticeofstatisticsandcanbeexpectedtodosointheforeseeablefuture".

Significancetestinghasbeenthefavoredstatisticaltoolinsomeexperimentalsocialsciences（over90%ofarticlesintheJournalofAppliedPsychologyduringtheearly1990s）.Otherfieldshavefavoredtheestimationofparameters.Editorsoftenconsidersignificanceasacriterionforthepublicationofscientificconclusionsbasedonexperimentswithstatisticalresults.

Cautions

Thesuccessfulhypothesistestisassociatedwithaprobabilityandatype-Ierrorrate.Theconclusionmightbewrong.

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济南大学泉城学院毕业论文外文资料翻译

Theconclusionofthetestisonlyassolidasthesampleuponwhichitisbased.Thedesignoftheexperimentiscritical.Anumberofunexpectedeffectshavebeenobservedincluding:

TheCleverHanseffect.Ahorseappearedtobecapableofdoingsimplearithmetic.TheHawthorneeffect.Industrialworkersweremoreproductiveinbetter

illumination,andmostproductiveinworse.

ThePlaceboeffect.Pillswithnomedicallyactiveingredientswereremarkablyeffective.

Astatisticalanalysisofmisleadingdataproducesmisleadingconclusions.Theissueofdataqualitycanbemoresubtle.Inforecastingforexample,thereisnoagreementonameasureofforecastaccuracy.Intheabsenceofaconsensusmeasurement,nodecisionbasedonmeasurementswillbewithoutcontroversy.

ThebookHowtoLiewithStatisticsisthemostpopularbookonstatisticseverpublished.Itdoesnotmuchconsiderhypothesistesting,butitscautionsareapplicable,including:

Manyclaimsaremadeonthebasisofsamplestoosmalltoconvince.Ifareportdoesnotmentionsamplesize,bedoubtful.

Hypothesistestingactsasafilterofstatisticalconclusions;Onlythoseresultsmeetingaprobabilitythresholdarepublishable.Economicsalsoactsasapublicationfilter;Onlythoseresultsfavorabletotheaut