Minitab Presentation.ppt

1,2008.Apr,StatisticalAnalysiswithMinitab,徐开荣,2,1、Minitab的基本操作,3,MinitabBasics-Layout,Minitab有五个标准窗口:SessionProjectManagerGraphDataWorksheet,1、Basics,4,Openaproject(worksheet):Fileopenproject(openworksheet)Filenewminitabproject(worksheet)KeyboardshortcutsShowworksheetsfolder:Ctrl+Alt+DShowgraphsfolder:Ctrl+Alt+GShowsessionfolder:Ctrl+Alt+MEditlastdialog:Ctrl+E,Openaprojectandshortcutkey,1、Basics,5,2、基本图形分析,6,Graph,常见图形ScatterplotHistogramBoxplotTimeseriesplot,Graph,2、Graph,7,GraphScatterplot,Batteries.MTW,1打开BATTERIES.MTW.2选择GraphScatterplot.3选择WithRegressionandGroups,然后OK.4在Yvariables,输入FlashRecov.在Xvariables,输入VoltsAfter.5在Categoricalvariablesforgrouping(0-3),输入Formulation.6单击Scale,然后选择ReferenceLines.7在ShowreferencelinesatYvalues,输入5.25.单击各对话框OK.,2、Graph,8,GraphScatterplot,Batteries.MTW,2、Graph,9,GraphHistogram,用CAP.MTW中的数据，创建柱形图以描述频率分布的形状)InMinitab:GraphHistogram,CAP.MTW,2、Graph,10,HistogramAnotherOption,1打开PULSE.MTW.2选择StatBasicStatisticsGraphicalSummary.3在Variables,输入Pulse1.选择OK.,选择“GraphicalSummary”,PULSE.MTW,2、Graph,11,GraphBoxplot,(BoxPlot是一种将所有的数值排序后的图形表示)（BoxPlot包含有箱子,胡须(whiskers),飞点(outliers)Whisker-(胡须)上下胡须是从四分位线延伸到上下限范围内的最高、最低值Outliers(飞点)超出上或下限的点)UpperLimit=Q3+1.5(Q3-Q1)LowerLimit=Q1-1.5(Q3-Q1),2、Graph,12,BoxplotExample,CARPET.MTW,1打开CARPET.MTW.2选择GraphBoxplot3选择OneY下的WithGroups.单击OK.4在Graphvariables,输入Durability.5在Categoricalvariablesforgrouping(1-4,outermostfirst),输入Carpet.6单击Labels,然后选中DataLabels.7在Label标签里,选择Medians.选中Usey-valuelabels.单击OK.8选中DataView.9在Categoricalvariablesforattributeassignment,输入Carpet.在各对话框单击OK.,2、Graph,13,BoxplotExample,CARPET.MTW,2、Graph,14,BoxplotAnotherOption,CARPET.MTW,2、Graph,15,GraphTimeSeriesPlot,1打开ABCSALES.MTW.2选择GraphTimeSeriesPlot或者StatTimeSeriesTimeSeriesPlot.3选择WithGroups,单击OK.4在Series,输入sales.5在Categoricalvariablesforgrouping(1-3),输入AdAgency.6单击Time/Scale.7在TimeScale选Calendar然后选择MonthYear.8在Month的开始值下输入1在Year下输入2000.9在各对话框单击OK.,ABCSALES.MTW,2、Graph,16,ABCSALES.MTW,GraphTimeSeriesPlot,2、Graph,17,StatBasicStatisticsNormalityTest,2、Graph,1打开CRANKSH.MTW.2选择StatBasicStatisticsNormalityTest.3在Variable,输入AtoBDist.单击OK.,18,StatBasicStatisticsNormalityTest,2、Graph,19,3.1、基本统计量分析,20,StatBasicStatisticsDisplayDescriptiveStatistics,3.1、StatBasicStatistics,1打开PULSE.MTW.2选择StatBasicStatisticsDisplayDescriptiveStatistics.3在Variables,输入Height.4在Byvariable,输入Sex.5单击Graphs选中BoxplotofdataandIndividualvalueplot.6在各对话框单击OK.,PULSE.MTW,21,3.1、StatBasicStatistics,StatBasicStatisticsDisplayDescriptiveStatistics,22,3.1、StatBasicStatistics,StatBasicStatisticsDisplayDescriptiveStatistics,Session窗口DescriptiveStatistics:HeightVariableSexNN*MeanSEMeanStDevMinimumQ1MedianQ3Height157070.7540.3422.58366.00069.00071.00073.000235065.4000.4332.56361.00063.00065.50068.000VariableSexMaximumHeight175.000270.000,平均的标准误差=/n,23,3.1、StatBasicStatistics,StatBasicStatisticsStoreDescriptiveStatistics,将所需要的分析性数据存储在worksheet中,24,3.2、相关与回归,25,Correlation,3.2、StatCorrelationandRegression,打开文件DMCorrelationRegression.mpj,worksheetCorrelationExample.mtw-Measurementdata我们先逐个分析X和Y,及X2和Y2之间的关系.,Correlations(Pearson)CorrelationofYandX=0.878,Correlations(Pearson)CorrelationofY2andX2=0.391,相关系数r,26,相关系数(r)为-1和+1之间的某个数值。-1表示有很强的负相关0表示完全不相关+1表示有很强的正相关判定规则:相关系数(r).80或者CorrelationandRegression,Correlation,27,Regression,R-Square,回归式,为更加明显的表示X(Predictor)与Y(Response)的关系，我们用FittedLinePlot进行分析打开DMCorrelationRegression.mpj,3.2、StatCorrelationandRegression,28,FromtheFittedLinePlot,wecanseethatastheageofthepropellantincreasestheShearStrengthdecreases.Thisisanexampleofaninverserelationship.WealsoseealinearequationandanR-Sqvalue.Whatarethese?Letsexplore!,3.2、StatCorrelationandRegression,Regression,29,Session窗口RegressionAnalysis:ShearStrength(psi)versusAgeofPropellant(weeks)TheregressionequationisShearStrength(psi)=2628-37.15AgeofPropellant(weeks)S=96.1061R-Sq=90.2%R-Sq(adj)=89.6%AnalysisofVarianceSourceDFSSMSFPRegression115274831527483165.380.000Error181662559236Total191693738,R-Square(决定系数)全体变动中根据回归直线能说明的变动.R-Square=90.2%,即是说ShearStrength(psi)的变化有90.2%的变动可由versusAgeofPropellant(weeks)变动来说明.而9.8%的变动是由其它的原因引起的变动.,回归式0:截距X是0的时候,预测的Y值上例中,AgeofPropellant(weeks)变动率是0的时候,ShearStrength(psi)是2628.1:偏差X增加1时,Y值的增加幅度上例中,AgeofPropellant(weeks)增加1,ShearStrength(psi)增加1,即,预想增加-37.15.,3.2、StatCorrelationandRegression,Regression,30,3.3、假设检验,31,HypothesisTesting,3.3、StatBasicStatistics,假设检验能帮助你通过数据作出决断，确定什么才是真正影响过程的因素介绍假设检验介绍假设检验程序学习以下假设检验方法VARIANCETESTING(方差检验)TestforequalvariancesMEANTESTING(均值检验)2samplet-testPROPORTIONSTESTING(比例检验)2proportionstest,32,Washington,DC-(AP)Globalwarmingcontinuestoincreaseatalarmingrates.TheEPAcontinuestodevelopplanstocurbC02outputatallU.S.manufacturingfacilities.,GlobalWarmingExample,3.3、StatBasicStatistics,33,正确处理一些有疑惑的事情减少主观判断提出设想筛选并丢弃冗长的信息有效的防止错误性结论的风险,假设检验的基本概念,3.3、StatBasicStatistics,Ho=NullHypothesisHa=AlternativeHypothesisP-Value=ProbabilityValue,它能,关键术语,34,3.3、StatBasicStatistics,假设检验是简单比较真实结果与假设的差异，通过询问:它们的结论相一致吗?假设检验步骤：通过表述零假设开始,(即两个总体的特征是相等的)Ho然后阐述备择假设(即两个总体的特征是不相同的，具有显著差异)Ha假设检验将通过样本数据决定零假设不为假的可能性PValue,假设检验的结论是针对总体参数的(而不是样本),假设检验的基本概念,35,One-wayANOVA:ClarityversusRegionSourceDFSSMSFPRegion20.03830.01921.270.295Error350.53030.0152Total370.5687S=0.1231R-Sq=6.74%R-Sq(adj)=1.41%PooledStDev=0.1231,无处不在的P值!,3.3、StatBasicStatistics,36,两种类型的错误,3.3、StatBasicStatistics,在假设检验过程中，我们可能会犯两类错误TypeIError(Risk,ProducersRisk)从同一个总体取出的两组数据，结论却是存在差异的可能性。TypeIIError(Risk,ConsumersRisk)从两个不同的总体中取出的两组数据，结论却是没有差异的可能性,YourDecision,AcceptHo,TheTruth,HoTrue,HoFalse,TypeIError-Risk),TypeIIError-Risk),Correct,Correct,RejectHo,37,PValueIsExtremelyImportantRememberThisKeySaying.,IfPisLow,HoMustGo!,pafailtorejecttheNullHypothesis(不能拒绝零假设)pBasicStatistics,假设检验的判定,38,Formostcaseswewilluse.05,如何设定P值?,Wewouldliketheretobelessthana10%chancethattheseobservationscouldhaveoccurredrandomly(=.10)Fivepercentismuchmorecomfortable(=.05)Onepercentfeelsverygood(=.01)Theselectionofthealphalevelisbasedontheconsequencesofanincorrectdecisiontorejectthenullhypothesisandacceptthealternativehypothesis.,Itdepends,3.3、StatBasicStatistics,39,1-SampleZ,2-Samplet,1-Samplet,Pairedt,t-test的选择,1-SampleZ在当我们想评价样本Data的平均和母集团(全体集团)的平均是否相同的时候.且当母集团的平均和标准偏差已知的时候适用.为了观察从D电子购买的部品的平均重量,随机抽取10个样本并对其重量进行测量.我们希望部品的重量为40g,到目前为止生产的部品的母标准偏差为3g.1-Samplet在当我们想评价样本Data的平均和母集团(全体集团)的平均是否相同的时候.且当母集团的平均已知而标准偏差未知的时候适用.为了观察从D电子购买的部品的平均重量,随机抽取10个样本并对其重量进行测量.我们希望部品的重量为40g,而部品的母标准偏差未知.2-Samplet在当我们想评价从两个相互不同的集团中取出的样本Data的平均是否相同的时候适用.为了评价从D公司和E公司购买的部品的平均重量是相同还是不同,从各公司购买的部品中各随机抽取10个并测量其重量.Pairedt在当我们想评价两个互相成对的样本Data的平均是否的时候适用.为了评价从D公司购买的部品的左侧厚度和右侧厚度的平均是相同还是不同,随机抽取10个并测量其左侧和右侧厚度.,StatBasicStatisticst-test,3.3、StatBasicStatistics,40,3.3、StatBasicStatistics,StatBasicStatistics2Samplet,FURNACE.MTW,1打开FURNACE.MTW.2选择StatBasicStatistics2-SampleT.3选择Samplesinonecolumn.4在Samples,输入BTU.In.5在Subscripts,输入Damper.6选中Assumeequalvariances.单击OK.,41,3.3、StatBasicStatistics,Session窗口Two-SampleT-TestandCI:BTU.In,DamperTwo-sampleTforBTU.InDamperNMeanStDevSEMean1409.913.020.4825010.142.770.39Difference=mu(1)-mu(2)Estimatefordifference:-0.23595%CIfordifference:(-1.450,0.980)T-Testofdifference=0(vsnot=):T-Value=-0.38P-Value=0.701DF=88BothusePooledStDev=2.8818,P-ValueP-Value0.05的时候可以推断出两个设备的Data平均相同.P-Value0.05的时候可以推断出两个设备的Data平均不相同.上例中的P-Value=0.701,比0.05大,可说明从BTU.In平均效率和Damper的平均效率相同.,95.0%CI:两个设备平均差异的95%信赖区间-上例中两个设备平均差异的95%信赖区间(-1.450,0.980),0在这个95%信赖区间以内.即,(BTU.In平均效率Damper平均效率=0)可以成立.从这两个设备中分别收集的Data的平均可以相等的意思.所以,安装的BTU.In和Damper平均效率是相等的.,StatBasicStatistics2Samplet,FURNACE.MTW,42,1-Proportion,2-Proportion,p-test的选择,1-Proportion在当我们想评价样本Data的比例和母集团(全体集团)的比例是否相同的时候.且当母集团的比例已知的时候适用.2-Proportion在当我们想评价互不相同的集团中取出的样品的比例是否相同的时候.,StatBasicStatisticsp-test,3.3、StatBasicStatistics,43,3.3、StatBasicStatistics,1选择StatBasicStatistics2Proportions.2选择Summarizeddata.3在Firstsample的Events里输入44.在Trials里输入50.4在Secondsample的Events里输入42.在Trials里输入50.单击OK.,StatBasicStatisticsp-test,44,3.3、StatBasicStatistics,Session窗口TestandCIforTwoProportionsSampleXNSamplep144500.880000242500.840000Difference=p(1)-p(2)Estimatefordifference:0.0495%CIfordifference:(-0.0957903,0.175790)Testfordifference=0(vsnot=0):Z=0.58P-Value=0.564Fishersexacttest:P-Value=0.774,P1=P2,StatBasicStatisticsp-test,45,1-Variance,2-Variance,-test的选择,1-Variance在当我们想评价样本Data的方差和母集团(全体集团)的方差是否相同的时候.且当母集团的方差已知的时候适用.2-Variance在当我们想评价互不相同的集团中取出的样品的方差是否相同的时候.,StatBasicStatistics-test,3.3、StatBasicStatistics,46,3.3、StatBasicStatistics,1打开FURNACE.MTW.2选择StatBasicStatistics2Variances.3选择Samplesinonecolumn.4在Samples,输入BTU.In.5在Subscripts,输入Damper.单击OK.,FURNACE.MTW,StatBasicStatistics-test,47,3.3、StatBasicStatistics,Session窗口TestforEqualVariances:BTU.InversusDamper95%BonferroniconfidenceintervalsforstandarddeviationsDamperNLowerStDevUpper1402.406553.019874.027262502.254472.767023.56416F-Test(NormalDistribution)Teststatistic=1.19,p-value=0.558LevenesTest(AnyContinuousDistribution)Teststatistic=0.00,p-value=0.996,1=2,StatBasicStatistics-test,48,3.4、方差分析（ANOVA),49,ANOVA,3.4、StatANOVA,One-Way,MainEffectsPlot,GeneralLinearModel,InteractionPlot,One-Way1打开EXH_AOV.MTW.2选择StatANOVAOne-Way.3在Response,输入Durability.在Factor,输入Carpet.4在各对话框中单击OK.,50,OneWayANOVA,3.4、StatANOVA,51,3.4、StatANOVA,Session窗口One-wayANOVA:DurabilityversusCarpetSourceDFSSMSFPCarpet3146.448.83.580.047Error12163.513.6Total15309.9S=3.691R-Sq=47.24%R-Sq(adj)=34.05%Individual95%CIsForMeanBasedonPooledStDevLevelNMeanStDev-+-+-+-+1414.4833.157(-*-)249.7353.566(-*-)3412.8071.506(-*-)4418.1155.435(-*-)-+-+-+-+10.015.020.025.0PooledStDev=3.691,结果分析-上例中的P-Value=0.047,比0.05小,可说明四种地毯中至少有一种地毯的耐久性的平均与其它三种不同.,P:P-ValueP-Value0.05的时候可推断出各集团间Data平均相同.P-Value0.05的时候可得知至少有一个集团Data平均与其它不同.上例中的P-Value=0.047,比0.05小,可说明四种地毯中至少有一种地毯的耐久性的平均与其它地毯不同.,OneWayANOVA,52,GeneralLinearModel,3.4、StatANOVA,GLM.MTW,53,3.4、StatANOVA,Session窗口GeneralLinearModel:BurntFrenchversusTemp,BasketDesig,CycleTimeFactorTypeLevelsValuesTempfixed2300,350BasketDesignfixed3A,B,CCycleTimefixed340,50,60AnalysisofVarianceforBurntFrenchFries,usingAdjustedSSforTestsSourceDFSeqSSAdjSSAdjMSFPTemp1136.963136.963136.96348.340.000BasketDesign26.0376.0373.0191.070.355CycleTime2743.815743.815371.907131.260.000Temp*BasketDesign217.37017.3708.6853.070.059Temp*CycleTime2228.926228.926114.46340.400.000BasketDesign*CycleTime460.51960.51915.1305.340.002Temp*BasketDesign*CycleTime418.74118.7414.6851.650.182Error36102.000102.0002.833Total531314.370S=1.68325R-Sq=92.24%R-Sq(adj)=88.58%,GeneralLinearModel,GLM.MTW,54,3.4、StatBasicStatistics,GeneralLinearModel,GLM.MTW,55,3.4、StatBasicStatistics,GeneralLinearModel,GLM.MTW,56,3.5、实验设计（DOE),57,实验计划法基础,3.5、StatDOE,CreateFactorialDesign:要因配置法实验设计DefineCustomFactorialDesign:在变更当前的实验计划而再指定时使用。AnalyzeFactorialDesign:得出实验分析结果FactorialPlot:主效果,交互效果plot作成Contour/Surface(Wireframe)Plots:展现实验的反应表面OverlaidContourPlot:以视觉性展示多个反应变量的妥协领域ResponseOptimizer:寻找满足目标值因子的最佳组合,以最少的实验次数迅速获得最大的信息量的计划方法.把以往的经验或者理论性、技术性知识等的原有技术与依照实验计划法的知识结合起来,Factorial:要因配置实验RSDesign:反应表面实验MixtureDesign:混合物实验ModifyDesign:对实验的修正DisplayDesign:实验计划后生成的内容通过Worksheet可见,58,DOE用语,因子(Factor)实验所用的输入要素(例)温度,湿度,水准(Level)各实验因子的设定值(例)温度100200(-)(+)反应值(Response)实验的数值性结果(一般用Y表示)(例)Y=267mm主效果(MainEffect)随一个独立因子的水准变化相应的(例)E1=2反应值的影响E2=-7交互效果两个以上的因子结合后对反应(例)E12=5(InteractionEffect)因子产生的影响解析度(Resolution)在部分实施法中表示实验设计的搅乱(例)III,IV,V程度的记号搅乱(Confounding)以两个以上因子的效果合并后(例)1+2产生的现象难以分离1+3,2+2,3.5、StatDOE,59,2K-RuntheExperimentandCollecttheData,3.5、StatDOE,60,2K-RuntheExperimentandCollecttheData,EnterthenumberofreplicatesInthiscase,wewillonlyconsider1replicateforthisexperiment;Leavethe“CenterPoints”and“Blocks”fieldsontheirdefaultsettings,PressOKandyouwillreturntothepreviousscreen,3.5、StatDOE,61,该例有两个定量性输入因子(TemperatureandTime)和一个定性输入因子(ChipMfr.)产生一个输出RatingThefactorsandlevels:Temp:160oC(-1),180oC(1)Time:(min):8(-1),12(1)Chip:BrandA(-1),BrandB(1)实验设计结果如下矩阵:,用1和-1代表因子的水平称为CodedUnits.因子的高水平为1低水平为-1.,该例为全因子实验,3.5、StatDOE,2KDOE,62,2KDOE,Select“Factors”andenteryourfactornames.Wecouldalsolisttheuncodedlevelshere,however,ourtaskwastousecodedlevels.,WhenfinishedpressOKonthismenuandthe“CreateFactorialDesign”menuTheoutputisintheworksheet,3.5、StatDOE,63,2KDOE,Ensureyouhaveselected“RandomizeRuns”andbesuretostoreyourdesigninaworksheet,3.5、StatDOE,64,2KDOE-Worksheet,3.5、StatDOE,65,2.IdentifytheTermstoincludeinthemodel.Initiallyincludeallfactorsandinteractions.,3.5、StatDOE,2KDOE-Analyze,66,4.IdentifytheNormalandParetoplots.ThedefaultvalueofAlphainMinitab14is0.05.,3.5、StatDOE,2KDOE-Analyze,67,Thesearethecontrastsyoupreviouslycalculated,NoticetherearenoF-valuesorP-valuesbecausethereisonlyonemeasurementineachcellandtheerrortermcannotbecalculated.,3.5、StatDOE,2KDOE-Analyze,68,WeseeherethattheEffectsassociatedwithA(Temp)andtheA*C(Temperature*Chip)Interactionareimportant.SowewillevaluatethehighestorderinteractionandnotworryabouttheMainEffect.,3.5、StatDOE,2KDOE-Analyze,69,Thischartparetostheeffectsandusesap0.05asacutoffYoucanseethattheAandA*CinteractionsareidentifiedasgoodcandidatesWecanalsoreducethemodelbyremovingtheABCinteractionandgetsomeanalyticalbasis,3.5、StatDOE,2KDOE-Analyze,70,Butwhatisthebasisfortheredline?TheHoisthattherearenosignificanteffects(noneofthetermsaresignificant)Therefore,wewouldexpecttheEffectstobe0tosupporttheHoTheredlineisaconfidencelimitbasedonourAlphalevelthatestablishesabasisforsayingAnythingbeyondthatlimitisdifferentthan0Thecalculationofthelineisbasedonafewfactors:ExperimentalerroralevelTotalnumberofrunsintheexperimentDegreesofFreedomAswereducethemodel,thepositionofthelinewillalsochange!,3.5、StatDOE,2KDOE-Analyze,71,去掉三因子的交互作用ABC进行重复分析将有足够的自由度来得到误差项并给出P值!,3.5、StatDOE,2KDOEReducedModel,72,Nowwecanreducethemodelmorebyremovingtheinteractionsthataresignificantlyaboveouravalueof0.05,Removetheseinteractions,3.5、StatDOE,2KDOEReducedModel,73,3.5、StatDOE,2KDOEReducedModel,74,3.5、StatDOE,2KDOEReducedModel,75,Identifytheresponsevariableandthetermstoincludeintheinteractionsplot,3.5、StatDO