AddtheauthorandtheaccompanyingtitleConfidenceIntervals置信区间CopyrightRouteSixSigma,LLC2002*WhatIsaConfidenceIntervalAconfidenceintervaldescribesrangeofplausiblevaluesforapopulationparameter.Intervalsizeisbasedononeofseveralstatisticaldistributions.Forlargesamplesizes(>30)orwhenusingpopulationstatistics,generallytheZdistributionisused.Forsmallsamples(<30),thestudenttdistributioniscommonlyused.Theboundarybetweentheconfidenceintervalandtheareaofriskisdefinedbythelevelofriskwearewillingtoassume,a.aisalsocalledthesignificancelevelConfidenceintervalscanbedefinedwithtwoboundariesorwithasingleboundary.Ifthevaluefallsinthisregion,wetakearisktosaythatitdoesnotrepresentthetrueparametermeasurement.orCopyrightRouteSixSigma,LLC2002*什么是置信区间置信区间描述了总体参数可能的数值范围.置信区间的大小是以统计数据分布状态为基础的。当样本数量较多(>30)或使用总体统计方法时，通常采用Z分布当样本数量较少(<30)时,一般采用studentt分布.我们愿意接受的风险水平a决定了置信区间和风险区域的分界线.a也被称为显著水平采用双边或单边界定置信区间均可.若数值落于该区间，那么它可能并未反映真正的参数水平.orCopyrightRouteSixSigma,LLC2002*ExampleTwoSidedConfidenceInterval95%ofthesamplestakenfromapopulationwithamean“m”canbeobservedwithin±1.96ofm.Thisisknownasa95%confidenceinterval.ItiswrittenOrTheconstant1.96isaZValuetakenfromtheNormalDistributionTable.Find1.96.Notethatitcorrespondsto2.5E-02.Why.025?Forthisexample,theconfidenceintervaltakesthe95%fromthecenterofthedistribution.95%2.5%2.5%CopyrightRouteSixSigma,LLC2002*以双边置信区间为例从总体中提取的95%样本的均值“m”被测出为±1.96以內，称为95%的置信区间。该区间用公式
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达如下：或常数1.96是取于正态分布表的Z值.找到1.96.注意常数与2.5E-02相对应.为何是0.025呢?在此例中，置信区间在分布中心两端所占区域共计95%.95%2.5%2.5%CopyrightRouteSixSigma,LLC2002*ExampleOneSidedConfidenceIntervalIfwearetestingforthemeanbeinglessthananumber,we’lluseaonesidedtestasshownbelow.Ifwearetestingforthemeanbeinggreaterthananumber,we’lluseaonesidedtestasshownbelow.
ConfidenceIntervalRiskInthiscase,witha=.05,theentireriskareaisononeside.WritetheinequalityforeachusingtheappropriateZ.CopyrightRouteSixSigma,LLC2002*以单边置信区间为例若测试的均值是小于一定数值的，我们将采用如下所示的单边测试方法.若测试的均值是大于一定数值的，我们将采用如下所示的单边测试方法.<置信区间风险>置信区间风险在此a=.05的例子中，整体风险区域是在一边的.用适当的Z值写出相对应的不等式.CopyrightRouteSixSigma,LLC2002*TheEffectOfLevelofSignificance(a)OnConfidenceIntervalWhathappenswhenyouchangethedesiredsignificancelevel(a)?ConfidenceIntervalAsyouincreasetheriskofclaimingsomethingisdifferentwhenitisreallythesame(i.e.,rejectinggoodpartsattheassemblyline),agetslargerandtheconfidenceinterval(1-a)growssmaller.Astheyoudecreasetheriskbydecreasinga,theconfidenceinterval(1-a)increases.Minitabwillprovideapvaluewithallconfidenceintervalcalculations.pvalueistheobservedlevelofsignificance.Ifpa,ThereisinsufficientevidencetosupportrejectingHO.CopyrightRouteSixSigma,LLC2002*显著水平（a）对置信区间的影响当合意的显著水平（a）被改变时会发生什么情况呢？置信区间当增加把一致的零件视为不一的风险（如弃丟装配线中良好的零件）时,则a值变大而置信区间(1-a)变小.当通过减少a值来降低风险时，置信区间(1-a)就会增大.Minitab将为所有置信区间提供P值.p值是观测到的显著水平.若pa,则沒有足够的证据支持弃用HO.CopyrightRouteSixSigma,LLC2002*TheEffectofSampleSize(n)OnConfidenceIntervalWhathappenstotheconfidenceintervalasndecreases?ThesigmamultiplegrowslargerandtheresultantConfidenceintervalincreases.Whenthesamplesize(n)increases,theconfidenceintervaldecreases.CopyrightRouteSixSigma,LLC2002*样本多少对置信区间（n）的影响当n下降，置信区间会发生什么变化?Sigma倍数变大，最终置信区间增大.当样本数量(n)增加,置信区间变小.CopyrightRouteSixSigma,LLC2002*AnExampleThenominaltorqueofafinishedawningtensioneris200footlbs.Asampleof10partsfromoneofthetorsioningstationsyieldedanaveragetorsionof198.75lbswithans=2.333lbs.Arethepartsbeingmadetospec?Here’sthetestresultHowabouta30piecesample?Howdoestheanswerchangeifweincreasethesamplesizeto20withthesameresults?CopyrightRouteSixSigma,LLC2002*实例一个完工的布篷应张环的额定扭力是200英尺/lbs.从提取的10个部件样本显示：平均扭转度为198.75lbs与s=2.333lbs.这些部件符合规格
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吗?测试结果如下30个样本呢?若将样本大小增加到20个，结果如何呢?CopyrightRouteSixSigma,LLC2002*ConfidenceIntervalsCanBeCalculatedforaSingleSampleorforTwoSamplesOneSampleInasinglesampleanalysis,theactualparametermeasurementisthefocusoftheconfidenceinterval.Theconfidenceintervaldescribestherangeofplausiblevaluesoftheparameterandthatiscomparedtothetargetvalue(I.e.,thenominalpartsize).TheNullHypothesisalwaysincludesthetargetintheconfidenceinterval.TwoSamplesInatwosamplescenario,thedifferenceintheparametermeasurementsisthefocus.Ifthemeasurementsarethesame,thedifferencebetweenthemiszeroandthatisthetargetfortheConfidenceInterval.Insuchcase,thevaluezero(0)willalwaysbeincludedintheconfidenceinterval.CopyrightRouteSixSigma,LLC2002*置信区间可用于单个或两个样本计算一个样本在一个样本的分析中，确实地度量参数是置信区间的重点.置信区间描述了与目标值相比的总体参数的可能数值范围(如，理论上零件的大小).虚无假设总是含括了置信区间的目标。两个样本在两个样本的情况下，参数被度量到的差异是焦点.当测度方法一致时，两者之间的差异为零，而这也正是置信区间的目标所在.在此例中，数值零(0)总是含括在置信区间中的.CopyrightRouteSixSigma,LLC2002*CalculatingtheZValueWedefinetheconfidenceintervalastherangeofplausiblevaluesofastatisticforapopulationparameterbasedontheselectedvalueofa.Wethencomparethesamplestatistictotheconfidenceinterval.Whenweknowthepopulationstandarddeviations,weuseacalculationtofindthezvalueforthestatistic.CopyrightRouteSixSigma,LLC2002*Addtheauthorandtheaccompanyingtitle生活图标元素商务图标元素商务图标元素商务图标元素商务图标元素
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