Hyohesisesing假设检验讲义中英文版

HypothesisTesting1假设检验2ObjectivesExplainthedifferencesbetweendecisionmakingwithpopulationdataandsampledataExplaintherisksofsamplebaseddecisionmakingExplainwhatahypothesisisExplainwhyhypothesistestingisimportanttoprocessimprovement.Definetheterms“NullHypothesis”and“AlternativeHypothesis”.CompareHypothesistestingtoCourtroomDecisionMaking.Explaintheterms“arisk”and“brisk”.Explainwhata“pvalue”is3目标解释由全部数据或抽样数据所作出决策的不同解释根据抽样资料所作出决策的风险说明假设是什么说明假设检验对程序优化的重要性介定“原假设”和“备择假设”.比较假设检验和法庭式决策.说明术语“a

风险”和“b

风险”.说明什么是“p数值”4Population:TheUniverseDataorinformationthatdefinestheentiresetParameters(m,s)may,ormaynotbeknown.PopulationSampleSample:

Asubsetdataorinformationthatpossessesthesamecharacteristicsasthatofthepopulation.Wecancalculatestatistics(XBar,s).WemakedecisionsaboutthepopulationbasedonthesampleHowmanysamplesshouldbetaken?Whyshouldwetakeasample?Shouldthesampleberandom?Isitpossibletohavesamplingerror?PopulationsandSamples5总体:统计总体用以定义所有可知或不可知参数(m,s)的数据或信息PopulationSample样品:

总体中具有共同特征的子集。可以计算其形成的统计表（X）.我们以样本为基础做出总体决策应取多少样本？为何要选取样本？样本需要随机抽取吗？可能出现取样错误吗？总体和样本6Samples?WhyUseThem?Whyuseasampleinsteadofapopulation?UsingasamplereducestimeandcostCapturingdataontheentirepopulationmaybeverydifficult,ifnotimpossible.WhentouseasampleWeusesamplestoBaselineaprocessUsesamplestoevaluatetheresultsofacontrolledchangetoaprocess.Howshouldthesamplebetaken?Seesection5.7样本?为何使用样本?为何采用样本而非总体?采用样本可减少时间和成本消耗即使可能，获取总体数据也是非常困难的.何时采用样本？我们利用样本定流程基线利用样本对过程的可控变化结果进行评估.如何获取样本?请看第五部分.8SampleAAllprocesseshavevariation.Samplesfromagivenprocessmayvary.SampleBHowcanwedifferentiatebetweensamplebased“chance”variationandatrueprocessdifference?Howcanwedependonasample?9样本A所有的过程都有差异.来源于给定过程的样本也可能是多样化的.样本B我们怎样区分随机变化的样本和真实总体的差别呢?怎样使用样本？10ConfidenceIntervalsandPointEstimatesConfidenceintervalsidentifyarangeofplausiblevaluesforasamplestatisticofapopulationparameter.Theycanbeeitherone-sidedortwo-sided.SampleMeans,SampleStandarddeviation,SampleVariancesandothersamplestatisticsareknownasPointEstimatorsbecausetheyaresinglevaluesusedtorepresentpopulationparameters11可信区区间和和特征征值的的估计计可信区区间确定了了总体体参数数中样样本统统计可可能的的数值值范围围.它们可以以是单单边也也可是是双边边。样本均均值、、样本本标准准偏差差、样样本方方异和和其它它样本本统计计被称称为特特征值值评估估者。。因为为它们们是用用以代代表总总体参参数的的单一一数值。12HypothesisTestsPointEstimatesofparametersandConfidenceIntervalInterpretationarebothmeansformakinginferencesaboutsampledata.Hypothesistestsaredesignedtohelpusmakeaninferenceaboutthetruepopulationvalueatthedesiredlevelofconfidence.Wewilluseconfidenceintervalsandtestsofsamplemeans,variancesandsamplestandarddeviationtoinvestigatedifferenceandcause/effectrelationshipsusingdata.HypothesisTestshelpdetermineifanapparentdifferenceisrealorcouldbeduetochance.Byusingdataandhypothesistesting,wecanquantifyourlevelofconfidencethatthedifferenceisreal.13假设检检验对参数数特征征值估估计和和可信信区间间的诠诠释都都是得得出样样本数数据推推论的的路径径.假设检检验是是用以以帮助助我们们在需需要的的可信信度上上对真真实的的总体体数值进行行推论论的。。我们将将用可可信区区间和和样本本均值值、样本差差异及样本本标准准偏差差测验来研究究使用用数据据的差差別和和因果果关系系。假设检检验有有助于于判断断一个个明显显的差差别是是否真真实存存在还还是偶偶然的的，而而且还还可以以提高高差异异真实实性的的可信信度.14AStatisticalHypothesisAnassertionorconjectureaboutoneormoreparametersofthepopulationTodeterminewhetheritistrueorfalse,wemustexaminetheentirepopulation.Thisisimpossible!!Insteadusearandomsampletoprovideevidencethateithersupportsordoesnotsupportthehypothesis.Theconclusionisthenbaseduponstatisticalsignificance.Itisimportanttorememberthatthisconclusionisaninferenceaboutthepopulationdeterminedfromthesampledata.15统计计假假设设对于一一个个或或多多个个总总体体里的参参数数的的肯肯定定或或推推断断为了了判判断断它它的的正正误误，，我我们们必必须须检检查查总总体体的的全全部部。。这这是是不不可可能能的的！！！！我们们应应使使用用随随机机样样本本，，观观察察其其是是否否能能支支持持该该假假设设.从而而该该结结论论是是建建立立在在统统计计学学意意义义的的基基础础之之上上的的.必须须记记住住该该有有关关总总体体的的结结论论是是由由样样本本推推测测出出的的.16WhyDoHypothesisTesting?1.Toimproveprocesses,weneedtoidentifyfactorswhichimpactthemeanorstandarddeviation.2.Oncewehaveidentifiedthesefactorsandmadeadjustmentsforimprovement,weneedtovalidateactualimprovementsinourprocesses.3.Sometimeswecannotdecidegraphicallyorbyusingcalculatedstatistics(samplemeanandstandarddeviation)ifthereisastatisticallysignificantdifferencebetweenprocesses.4.Insuchcasesthedecisionwillbesubjective.5.Weperformaformalstatisticalhypothesistesttodecideobjectivelywhetherthereisadifference.Datahelpseveryonemakesthesamedecision.17为何要做假设设检验?1.为了改进过程程，我们需要要确定影响均均值和标准偏偏差的因素.2.一旦确定了这这些因素并对对改进措施进进行了调整，，我们就需要要验证其在过过程中的切实实效果。3.若过程中存在在统计上的重重大差别，有有时我们就不不能利用图表表或算得的统统计数据（样样本均值和样样本标准偏差差）作出决策策.4.在这种情况下下，决定可能能是主观的.5.我们采用正统假设检检验以以客观观地判判断是是否存存在差差別。。数据帮帮助每个人作出出同样样的决决定。。18NatureofHypothesesNullHypothesis(Ho):UsuallydescribesastatusquoTheoneyouassumeunlessotherwiseshownSignsusedinMinitab:=AlternativeHypothesis(Ha):UsuallydescribesadifferenceTheoneyouacceptorrejectbaseduponevidenceSignsusedinMinitab:not=or<or>PopulationSampleOrPopulationSampleItseitherNull(same)orAlternative(Different)19假设的种种类虚无性假设通常用以以描述现现状除非其它它方面有有所说明明，否则则就是人人为设想想的。在Minitab中用“=”表示示选择性假假设(Ha):通常用以以描述差差別以证据为为基础接接受或拒拒绝的类类型在Minitab中用“not=or<or>”表示PopulationSampleOrPopulationSample不是全虚性假设（相同））就是选择性性假设（相区区别的）20HypothesisTesting

Guiltyvs.InnocentExampleTheAmericanjusticesystemcanbeusedtoillustratetheconceptofhypothesistesting.InAmericaweassumeinnocenceuntilprovenguilty.Innocencecorrespondstothenullhypothesis.Itrequiresstrongevidence,“beyondareasonabledoubt,”toconvictthedefendant.Returningaguiltyverdictcorrespondstorejectingthenullhypothesisandacceptingthealternativehypothesis.Morespecifically,wehavesignificantevidencetosupportthatadifferenceexists.Ho:Personisinnocent.Ha:Personisguilty.Whatarethepossibleoutcomeswhenthetruthisknown?21假设检验有有罪vs.无罪的案例美国的司法体体系可以用于于阐述假设检检验的概念.在美国罪犯在在被判有罪之之前均是清白白的.清白对应虚无性假设.它需要强而有有力的证据，，必需“排除除所有合理的的怀疑”才能能把被告定罪罪.若陪审审团裁定被告告有罪则相当当于拒绝虚无性假设接受选择择性假设.更具体些,我们拥有重要要的证据证明明差別的存在在.Ho:被告是清白的的.Ha:被告有罪.当得知真相后后，可能的结结果是什么?22TruthVerdictHo,=Ha,not=Ho,=Ha,not=InnocentJailedGuilty

SetFreeInnocent

SetFreeGuilty

JailedSetFreeJailInnocentGuiltyTheTypeIError(aerror)isrejectingHowhenitistrue––

sometimescalledtheproducer’srisk.TheTypeIIError(berror)isfailingtorejectHowhenitisfalse–sometimescalledtheconsumer’srisk.DecisionType1ErrorType2ErrorCorrectDecisionCorrectDecisionTruthHo,=Ha,not=Ho,=Ha,not=RiskDecisionMakinginourCourtsandinBusiness23真相裁决Ho,=Ha,not=Ho,=Ha,not=清白监禁有罪释放清白释放有罪监禁释放监禁清白有罪TypeI错误(a错误)当Ho是无误时而拒绝–

有时称称作生产者风险TypeII错误(b错误)是当Ho有错误时却接受–有时称作消费者风险.DecisionType1错误Type2错误正确决定正确决定真相Ho,=Ha,not=Ho,=Ha,not=法庭和商业上上的决策风险险24ThepValueAnotherwaytomeasuretheriskinthedecisionisthroughthepValue.Thep-valueisknownastheObservedLevelofSignificanceforafactor.ItisthechanceofobservingthisamountofdifferenceThep-valueisalsotheprobabilityofbeingwrongifwerejecttheNullHypothesis(TypeIError.)Unlessthereisanexceptionbasedonengineeringjudgment,wewillsetanacceptancelevelofaTypeIerrorata=0.05.Thus,anyp-valuelessthan0.05meanswerejecttheNullhypothesis.25p值衡量量决决策策风风险险的的另另一一种种方方法法是是通通过过P值.当样本和总体相对时，P值是指观测到其中差別的机会率.P值也指如果拒绝虚无性假设可能发生错误的概率（错误I）除非在基于工程判断上的例外，我们将错误I的可接受水平定在a=0.05.从而，任何小于0.05的P值就表示虚无性假设被拒绝。DefiningHypothesesNullHypothesesHO:X1=TargHO:X1=mHO:X1-X2=0HO:m1-m2=0HO:X1=X2=X3=….XnHO:s1=s2HO:S1=S2HO:S1=S2=S3=….SnAlternativeHypothesesHA:m1¹m2InequalitiesaretwosidedtestsHA:X1¹X2HA:m1<m2HA:X1<X2OneSidedtestareusedfor<or>hypotheses.HA:m1>m2HA:X1>X2HA:X1-X2¹0___________________HA:X1-X2<0___________________HA:X1-X2>0___________________HA:s1¹¹HA:s1<s2_______________________HA:S1>S2_______________________Scr27定义义假假设设虚无性假假设设HO:X1=TargetHO:X1=mHO:X1-X2=0HO:m1-m2=0HO:X1=X2=X3=…….XnHO:s1=s2HO:S1=S2HO:S1=S2=S3=….Sn选择性假设HA:m1¹m2不等式是针对对两边的测试试HA:X1¹X2HA:m1<m2HA:X1<X2单边测试用于于<或>假设.HA:m1>m2HA:X1>X2HA:X1-X2¹0___________________HA:X1-X2<0___________________HA:X1-X2>0___________________HA:s1<s2_______________________HA:S1>S2_______________________把假设以等等式陈述很很有用.28HypothesisTestingProtocolThehypothesesarealwaysstatementsaboutthepopulationparameters.Stateyournullhypothesis(Ho)HO:TheheightofcitizensincountryAisequaltotheheightofcitizensincountryB(mA=mB).StateyourAlternativeHypothesis(Ha)HA:TheheightofDeterminetheappropriatestatisticaltestbasedontheHypothesisbeingtested.Determinethelevelofacceptablerisk.aRisk:usually5%(Default)bRisk:Usually10–20%(Default)29假设检验协协议假设总是关关于总体参参数的陈述.定明虚无性假设(Ho)HO:A国与B国居民身身高相等等HA:A国居民身高低于B国居民的身高

(mA<mB).基于在需被测试的假设上，决定适合的统计测试.决定可接受的风险程度.a

风险:通常5%(预设值)b

风险:通常10–20%(预设值)30HypothesisTestingProtocol(Cont)Determinethepropersamplesizeforthetest(Section5)Collectasampleofobservationsfromthepopulation.Calculatestatisticsbasedonthesample.Useastatisticaltesttotestalternativehypothesis.Basedonthetestresult,weacceptorrejectHobasedonthepreviouslydeterminedcriterion.Translatetheresults.Translatethestatisticalconclusiontoapracticalone.StatisticalConclusion:Canweprovedifferencestatistically.PracticalConclusion:Dowecareaboutthedifference?31假设检验验协议(续)决定适合合测试的的样本数数量(第第五部分分)从总体中中选取需需观察的的样本群群.计算样本本的统计计.用统计测测试方法法测验选选择性假假设.在测试结结果的基基础上，，根据先先前确定定的标准准，做出出选择或或拒绝Ho的决定.转化结果果.将将统计计的结论论转换为为现实的的结果.统计结论论:我我们能能从统计计的角度度证明差差別吗？？现实结果果:我我们需需注意这这些差別別吗?32We’llbeusinghypothesistestingasamethodtoprovechangeTargetordesiredvalueOneSampletAremultiplesamplesthesameMean:twosampletorANOVAVariation:FtestorTestforEqualVarianceProportionofOccurrence:ChiSquareC2

33我们将假假设检验验作为证证明差异异的一种种方法目标数值一个样本t若干样本是否一致一致:两个t样本或ANOVA不一致:用F测试或均等差异测试事情发生的概率:ChiSquareC2

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