假設(shè)檢驗(yàn)相關(guān)知識(shí)簡(jiǎn)介

HypothesisTesting1假設(shè)檢驗(yàn)2ObjectivesExplainthedifferencesbetweendecisionmakingwithpopulationdataandsampledataExplaintherisksofsamplebaseddecisionmakingExplainwhatahypothesisisExplainwhyhypothesistestingisimportanttoprocessimprovement.Definetheterms“NullHypothesis”and“AlternativeHypothesis”.CompareHypothesistestingtoCourtroomDecisionMaking.Explaintheterms“arisk”and“brisk”.Explainwhata“pvalue”is3目標(biāo)解釋由全部數(shù)據(jù)或抽樣數(shù)據(jù)所作出決策的不同解釋根據(jù)抽樣資料所作出決策的風(fēng)險(xiǎn)說明假設(shè)是什么說明假設(shè)檢驗(yàn)對(duì)程序優(yōu)化的重要性介定“原假設(shè)”和“備擇假設(shè)”.比較假設(shè)檢驗(yàn)和法庭式?jīng)Q策.說明術(shù)語“a

風(fēng)險(xiǎn)”和“b

風(fēng)險(xiǎn)”.說明什么是“p數(shù)值”4Population:TheUniverseDataorinformationthatdefinestheentiresetParameters(m,s)may,ormaynotbeknown.PopulationSampleSample:

Asubsetdataorinformationthatpossessesthesamecharacteristicsasthatofthepopulation.Wecancalculatestatistics(XBar,s).WemakedecisionsaboutthepopulationbasedonthesampleHowmanysamplesshouldbetaken?Whyshouldwetakeasample?Shouldthesampleberandom?Isitpossibletohavesamplingerror?PopulationsandSamples5總體:統(tǒng)計(jì)總體用以定義所有可知或不可知參數(shù)(m,s)的數(shù)據(jù)或信息PopulationSample樣品:

總體中具有共同特征的子集?？梢杂?jì)算其形成的統(tǒng)計(jì)表（X）.我們以樣本為基礎(chǔ)做出總體決策應(yīng)取多少樣本？為何要選取樣本？樣本需要隨機(jī)抽取嗎？可能出現(xiàn)取樣錯(cuò)誤嗎？總體和樣本6Samples?WhyUseThem?Whyuseasampleinsteadofapopulation?UsingasamplereducestimeandcostCapturingdataontheentirepopulationmaybeverydifficult,ifnotimpossible.WhentouseasampleWeusesamplestoBaselineaprocessUsesamplestoevaluatetheresultsofacontrolledchangetoaprocess.Howshouldthesamplebetaken?Seesection5.7樣本?為何使用樣本?為何采用樣本而非總體?采用樣本可減少時(shí)間和成本消耗即使可能，獲取總體數(shù)據(jù)也是非常困難的.何時(shí)采用樣本？我們利用樣本定流程基線利用樣本對(duì)過程的可控變化結(jié)果進(jìn)行評(píng)估.如何獲取樣本?請(qǐng)看第五部分.8SampleAAllprocesseshavevariation.Samplesfromagivenprocessmayvary.SampleBHowcanwedifferentiatebetweensamplebased“chance”variationandatrueprocessdifference?Howcanwedependonasample?9樣本A所有的過程都有差異.來源于給定過程的樣本也可能是多樣化的.樣本B我們?cè)鯓訁^(qū)分隨機(jī)變化的樣本和真實(shí)總體的差別呢?怎樣使用樣本？10ConfidenceIntervalsandPointEstimatesConfidenceintervalsidentifyarangeofplausiblevaluesforasamplestatisticofapopulationparameter.Theycanbeeitherone-sidedortwo-sided.SampleMeans,SampleStandarddeviation,SampleVariancesandothersamplestatisticsareknownasPointEstimatorsbecausetheyaresinglevaluesusedtorepresentpopulationparameters11可信區(qū)間間和特征征值的估估計(jì)可信區(qū)間間確定了總總體參數(shù)數(shù)中樣本本統(tǒng)計(jì)可可能的數(shù)數(shù)值范圍圍.它們可以是是單邊也也可是雙雙邊。樣本均值值、樣本本標(biāo)準(zhǔn)偏偏差、樣樣本方異異和其它它樣本統(tǒng)統(tǒng)計(jì)被稱稱為特征征值評(píng)估估者。因因?yàn)樗鼈儌兪怯靡砸源砜偪傮w參數(shù)數(shù)的單一一數(shù)值。12HypothesisTestsPointEstimatesofparametersandConfidenceIntervalInterpretationarebothmeansformakinginferencesaboutsampledata.Hypothesistestsaredesignedtohelpusmakeaninferenceaboutthetruepopulationvalueatthedesiredlevelofconfidence.Wewilluseconfidenceintervalsandtestsofsamplemeans,variancesandsamplestandarddeviationtoinvestigatedifferenceandcause/effectrelationshipsusingdata.HypothesisTestshelpdetermineifanapparentdifferenceisrealorcouldbeduetochance.Byusingdataandhypothesistesting,wecanquantifyourlevelofconfidencethatthedifferenceisreal.13假設(shè)檢驗(yàn)驗(yàn)對(duì)參數(shù)特特征值估估計(jì)和可可信區(qū)間間的詮釋釋都是得得出樣本本數(shù)據(jù)推推論的路路徑.假設(shè)檢驗(yàn)驗(yàn)是用以以幫助我我們?cè)谛栊枰目煽尚哦壬仙蠈?duì)真實(shí)實(shí)的總體體數(shù)值進(jìn)行推推論的。。我們將用用可信區(qū)區(qū)間和樣樣本均值值、樣本差異異及樣本標(biāo)標(biāo)準(zhǔn)偏差差測(cè)驗(yàn)來研究使使用數(shù)據(jù)據(jù)的差別別和因果果關(guān)系。。假設(shè)檢驗(yàn)驗(yàn)有助于于判斷一一個(gè)明顯顯的差別別是否真真實(shí)存在在還是偶偶然的，，而且還還可以提提高差異異真實(shí)性性的可信信度.14AStatisticalHypothesisAnassertionorconjectureaboutoneormoreparametersofthepopulationTodeterminewhetheritistrueorfalse,wemustexaminetheentirepopulation.Thisisimpossible!!Insteadusearandomsampletoprovideevidencethateithersupportsordoesnotsupportthehypothesis.Theconclusionisthenbaseduponstatisticalsignificance.Itisimportanttorememberthatthisconclusionisaninferenceaboutthepopulationdeterminedfromthesampledata.15統(tǒng)計(jì)假設(shè)設(shè)對(duì)于一個(gè)或或多個(gè)總總體里的參數(shù)的的肯定或或推斷為了判斷斷它的正正誤，我我們必須須檢查總總體的全全部。這這是不可可能的?。?！我們應(yīng)使使用隨機(jī)機(jī)樣本，，觀察其其是否能能支持該該假設(shè).從而該結(jié)結(jié)論是建建立在統(tǒng)統(tǒng)計(jì)學(xué)意意義的基基礎(chǔ)之上上的.必須記住住該有關(guān)關(guān)總體的的結(jié)論是是由樣本本推測(cè)出出的.16WhyDoHypothesisTesting?1.Toimproveprocesses,weneedtoidentifyfactorswhichimpactthemeanorstandarddeviation.2.Oncewehaveidentifiedthesefactorsandmadeadjustmentsforimprovement,weneedtovalidateactualimprovementsinourprocesses.3.Sometimeswecannotdecidegraphicallyorbyusingcalculatedstatistics(samplemeanandstandarddeviation)ifthereisastatisticallysignificantdifferencebetweenprocesses.4.Insuchcasesthedecisionwillbesubjective.5.Weperformaformalstatisticalhypothesistesttodecideobjectivelywhetherthereisadifference.Datahelpseveryonemakesthesamedecision.17為何要做做假設(shè)檢檢驗(yàn)?1.為了改進(jìn)進(jìn)過程，，我們需需要確定定影響均均值和標(biāo)標(biāo)準(zhǔn)偏差差的因素素.2.一旦確定定了這些些因素并并對(duì)改進(jìn)進(jìn)措施進(jìn)進(jìn)行了調(diào)調(diào)整，我我們就需需要驗(yàn)證證其在過過程中的的切實(shí)效效果。3.若過程中中存在統(tǒng)統(tǒng)計(jì)上的的重大差差別，有有時(shí)我們們就不能能利用圖圖表或算算得的統(tǒng)統(tǒng)計(jì)數(shù)據(jù)據(jù)（樣本本均值和和樣本標(biāo)標(biāo)準(zhǔn)偏差差）作出出決策.4.在這種情情況下，，決定可可能是主主觀的.5.我們采用用正統(tǒng)假設(shè)檢驗(yàn)驗(yàn)以客觀觀地判斷斷是否存存在差別別。數(shù)據(jù)幫助助每個(gè)人作出同同樣的決決定。18NatureofHypothesesNullHypothesis(Ho):UsuallydescribesastatusquoTheoneyouassumeunlessotherwiseshownSignsusedinMinitab:=AlternativeHypothesis(Ha):UsuallydescribesadifferenceTheoneyouacceptorrejectbaseduponevidenceSignsusedinMinitab:not=or<or>PopulationSampleOrPopulationSampleItseitherNull(same)orAlternative(Different)19假設(shè)的種種類虛無性假設(shè)通常用以以描述現(xiàn)現(xiàn)狀除非其它它方面有有所說明明，否則則就是人人為設(shè)想想的。在Minitab中用“=”表示示選擇性假假設(shè)(Ha):通常用以以描述差差別以證據(jù)為為基礎(chǔ)接接受或拒拒絕的類類型在Minitab中用“not=or<or>”表示PopulationSampleOrPopulationSample不是全虛性假設(shè)（相相同）就就是選擇擇性假設(shè)設(shè)（相區(qū)區(qū)別的））20HypothesisTestingGuiltyvs.InnocentExampleTheAmericanjusticesystemcanbeusedtoillustratetheconceptofhypothesistesting.InAmericaweassumeinnocenceuntilprovenguilty.Innocencecorrespondstothenullhypothesis.Itrequiresstrongevidence,“beyondareasonabledoubt,”toconvictthedefendant.Returningaguiltyverdictcorrespondstorejectingthenullhypothesisandacceptingthealternativehypothesis.Morespecifically,wehavesignificantevidencetosupportthatadifferenceexists.Ho:Personisinnocent.Ha:Personisguilty.Whatarethepossibleoutcomeswhenthetruthisknown?21假設(shè)檢驗(yàn)驗(yàn)

有罪罪vs.無罪的案案例美國(guó)的司司法體系系可以用用于闡述述假設(shè)檢檢驗(yàn)的概概念.在美國(guó)罪罪犯在被被判有罪罪之前均均是清白白的.清白對(duì)應(yīng)應(yīng)虛無性假設(shè).它需要強(qiáng)強(qiáng)而有力力的證據(jù)據(jù)，必需需“排除除所有合合理的懷懷疑”才才能把被被告定罪罪.若若陪審團(tuán)團(tuán)裁定被被告有罪罪則相當(dāng)當(dāng)于拒絕虛無性假設(shè)接受受選擇性性假設(shè).更具體些些,我們擁有有重要的的證據(jù)證證明差別別的存在在.Ho:被告是清清白的.Ha:被告有罪罪.當(dāng)?shù)弥嬲嫦嗪螅?，可能的的結(jié)果是是什么?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真相裁決Ho,=Ha,not=Ho,=Ha,not=清白監(jiān)禁有罪釋放清白釋放有罪監(jiān)禁釋放監(jiān)禁清白有罪TypeI錯(cuò)誤(a錯(cuò)誤)當(dāng)Ho是無誤時(shí)而拒絕–有有時(shí)稱作作生產(chǎn)者風(fēng)風(fēng)險(xiǎn)TypeII錯(cuò)誤(b錯(cuò)誤)是當(dāng)Ho有錯(cuò)誤時(shí)時(shí)卻接受–有時(shí)稱作作消費(fèi)者風(fēng)風(fēng)險(xiǎn).DecisionType1錯(cuò)誤Type2錯(cuò)誤正確決定正確決定真相Ho,=Ha,not=Ho,=Ha,not=法庭和商商業(yè)上的的決策風(fēng)風(fēng)險(xiǎn)24ThepValueAnotherwaytomeasuretheriskinthedecisionisthroughthepValue.Thep-valueisknownastheObservedLevelofSignificanceforafactor.Itisthechanceofobservingthisamountofdifferenceifthesampleisconsistentwiththepopulation.Thep-valueisalsotheprobabilityofbeingwrongifwerejecttheNullHypothesis(TypeIError.)Unlessthereisanexceptionbasedonengineeringjudgment,wewillsetanacceptancelevelofaTypeIerrorata=0.05.Thus,anyp-valuelessthan0.05meanswerejecttheNullhypothesis.25p值衡量決策風(fēng)風(fēng)險(xiǎn)的另一一種方法是是通過P值.P值是指一個(gè)個(gè)因素可測(cè)測(cè)的重要性性水平.當(dāng)樣本和總總體相對(duì)時(shí)，P值是指觀測(cè)測(cè)到其中差差別的機(jī)會(huì)率.P值也指如果果拒絕虛無性假設(shè)可能能發(fā)生錯(cuò)誤誤的概率（（錯(cuò)誤I）除非在基于于工程判斷斷上的例外外，我們將將錯(cuò)誤I的可接受水水平定在a=0.05.從而，任何何小于0.05的P值就表示虛無性假設(shè)被拒拒絕。26DefiningHypothesesNullHypothesesHO:X1=TargetHO: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:s11s2_______________________HA:s1<s2_______________________HA:S1>S2_______________________ScriptingHypothesesasequationsisusefulwhenstating.27定義假設(shè)虛無性假設(shè)HO:X1=TargetHO:X1=mHO:X1-X2=0HO:m1-m2=0HO:X1=X2=X3=….XnHO:s1=s2HO:S1=S2HO:S1=S2=S3=….Sn選擇性假設(shè)設(shè)HA:m11m2不等式是針針對(duì)兩邊的的測(cè)試HA:X11X2HA:m1<m2HA:X1<X2單邊測(cè)試用用于<或或>假設(shè).HA:m1>m2HA:X1>X2HA:X1-X210___________________HA:X1-X2<0___________________HA:X1-X2>0___________________HA:s11s2_______________________HA:s1<s2_______________________HA:S1>S2_______________________把假設(shè)以等等式陳述很很有用.28HypothesisTestingProtocolThehypothesesarealwaysstatementsaboutthepopulationparameters.Stateyournullhypothesis(Ho)HO:TheheightofcitizensincountryAisequaltotheheightofcitizensincountryB(mA=mB).StateyourAlternativeHypothesis(Ha)HA:TheheightofcitizensincountryAislessthantheheightofcitizensincountryB(mA<mB).DeterminetheappropriatestatisticaltestbasedontheHypothesisbeingtested.Determinethelevelofacceptablerisk.aRisk:usually5%(Default)bRisk:Usually10––20%(Default)29假設(shè)檢驗(yàn)協(xié)協(xié)議假設(shè)總是關(guān)關(guān)于總體參參數(shù)的陳述.定明虛無性假設(shè)(Ho)HO:A國(guó)與B國(guó)居民身高高相等(mA=mB).規(guī)定選擇性性假設(shè)(Ha)HA:A國(guó)居民身高高低于B國(guó)居民的身身高(mA<mB).基于在需被被測(cè)試的假假設(shè)上，決決定適合的的統(tǒng)計(jì)測(cè)試試.決定可接受受的風(fēng)險(xiǎn)程程度.a風(fēng)險(xiǎn):通通常5%(預(yù)設(shè)值)b風(fēng)險(xiǎn):通通常10––20%(預(yù)設(shè)值)30HypothesisTestingProtocol(Cont)Determinethepropersamplesizeforthetest(Section5)Collectasampleofobservationsfromthepopulation.Calculatestatisticsbasedonthesample.Useastatisticaltesttotestalternativehypothesis.Basedonthetestresult,weacceptorrejectHobasedonthepreviouslydeterminedcriterion.Translatetheresults.Translatethestatisticalconclusiontoapracticalone.StatisticalConclusion:Canweprovedifferencestatistically.PracticalConclusion:Dowecareaboutthedifference?31假設(shè)檢驗(yàn)協(xié)協(xié)議(續(xù))決定適合測(cè)測(cè)試的樣本本數(shù)量(第第五部分)從總體中選選取需觀察察的樣本群群.計(jì)算樣本的的統(tǒng)計(jì).用統(tǒng)計(jì)測(cè)試試方法測(cè)驗(yàn)驗(yàn)選擇性假假設(shè).在測(cè)試結(jié)果果的基礎(chǔ)上上，根據(jù)先先前確定的的標(biāo)準(zhǔn)，做做出選擇或或拒絕Ho的決定.轉(zhuǎn)化結(jié)果.將統(tǒng)統(tǒng)計(jì)的結(jié)論論轉(zhuǎn)換為現(xiàn)現(xiàn)實(shí)的結(jié)果果.統(tǒng)計(jì)結(jié)論:我們們能從統(tǒng)計(jì)計(jì)的角度證證明差別嗎嗎？現(xiàn)實(shí)結(jié)果:我們們需注意這這些差別嗎嗎?32We’llbeusinghypothesistestingasamethodtoprovechangeTargetordesiredvalueOneSampletAremultiplesamplesthesameMean:twosampletorANOVAVariation:FtestorTestforEqualVarianceProportionofOccurrence:ChiSquareC2

33我們將假設(shè)設(shè)檢驗(yàn)作為為證明差異異的一種方方法目標(biāo)數(shù)值一個(gè)樣本t若干樣本是否一致一致:兩個(gè)t樣本或ANOVA不一致:用F測(cè)試或均等差異測(cè)試事情發(fā)生的概率:ChiSquareC2

349、靜夜夜四無無鄰，，荒居居舊業(yè)業(yè)貧。。。12月月-2212月月-22Thursday,December29,202210、雨中中黃葉葉樹，，燈下下白頭頭人。。。03:49:5803:49:5803:4912/29/20223:49:58AM11、以以我我獨(dú)獨(dú)沈沈久久，，愧愧君君相相見見頻頻。。。。12月月-2203:49:5803:49Dec-2229-Dec-2212、故故人人江江海海別別，，幾幾度度隔隔山山川川。。。。03:49:5803:49:5803:49Thursday,December29,202213、乍見見翻疑疑夢(mèng)，，相悲悲各問問年。。。12月月-2212月月-2203:49:5803:49:58December29,202214、他鄉(xiāng)生白白發(fā)，舊國(guó)國(guó)見青山。。。29十二二月20223:49:58上上午03:49:5812月-2215、比不了了得就不不比，得得不到的的就不要要。。。十二月223:49上午午12月-2203:49December29,202216、行動(dòng)出出成果，，工作出出財(cái)富。。。2022/12/293:49:5803:49:5829December202217、做做前前，，能能夠夠環(huán)環(huán)視視四四周周；；做做時(shí)時(shí)，，你你只只能能或或者者最最好好沿沿著著以以腳腳為為起起點(diǎn)點(diǎn)的的射射線線向向前前。。。。3:49:58上上午午3:49上上午午03:49:5812月月-229、沒有有失敗敗，只只有暫暫時(shí)停停止成成功?。?。12月月-2212月月-22Thursday,December29,202210、很多多事情情努力力了未未必有有結(jié)果果，但但是不不努力力卻什什么改改變也也沒有有。。。03:49:5803:49:5803:4912/29/20223:49:58AM11、成成功功就就是是日日復(fù)復(fù)一一日日那那一一點(diǎn)點(diǎn)點(diǎn)點(diǎn)小小小小努努力力的的積積累累。。。。12月月-2203:49:5803:49Dec-2229-Dec-2212、世間成成事，不不求其絕絕對(duì)圓滿滿，留一一份不足足，可得得無限完完美。。。03:49:5803:49:5803:49Thursday,December