英文版培訓(xùn)講義：Basic Statistics Use of Minitab

BasicStatistics&UseofMinitabBeltonGroupRexWong2StatisticsStatistics

isthebranchofsciencethatdealswiththecollection,presentation,analysis&interpretationofdataforthepurposeofdecision-makingandproblem-solving.Statisticsisacriticalskillinqualityimprovementasstatisticaltechniquescanbeusedtodescribeandtounderstandvariability.3VariabilityVariabilityistheresultofchangesintheconditionsunderwhichobservationsaremade.Variabilitycancomeaboutduetochangesinmaterialqualitymachinesettingsorconditionsmanpowerstandardsmethodsofprocessingmeasurementmilieu(environment)4Population&SamplePopulationtheentiresetofmeasurementsofinterestSampleasubsetofdatafromthepopulationParametersnumericalmeasuresofapopulationStatisticsnumericalmeasuresofasample5ParametervsStatistic

ParameterStatistic Mean Variance StandardDeviation6Typeofdata–

“Gappiness”Whethertherearegapsbetweensuccessivelyobservedvaluesofavariable.DiscreteVariablegapsexistbetweenobservationsobtainedbycountingContinuousVariablenogapsexistbetweenobservationsobtainedbymeasuring7Statistics-ObjectivesStatistics

isthebranchofsciencethatdealswiththecollection,presentation,analysis&interpretationofdataforthepurposeofdecision-makingandproblem-solving.ObjectivesofStatistics:datareduction — DescriptiveStatisticsinferentialmeasurement — InferentialStatisticsidentificationofrelationships — Regression,ANOVA8Statistics-Overview9Descriptive&InferentialStatisticsDescriptiveStatisticscomprisesthosemethodsconcernedwithcollectinganddescribingasetofdatasoastoyieldmeaninginformationInferentialStatisticscomprisesthosemethodsconcernedwiththeanalysisofasubsetofdataleadingtopredictionsorinferencesabouttheentiresetofdata10DescriptiveStatistics-Overview11NumericalMeasuresDescribesthecharacteristicsofthedataset.Keynumericalmeasures:measuresoflocation(centraltendency)measuresofdispersion(variation)measuresofshape(distribution)12MeasureofLocationMean(willnotbediscussed)Median(willnotbediscussed)Mode(willnotbediscussed)Quartiles13QuartilesWhenanorderedsetofdataisdividedintofourequalparts,thedivisionpointsarecalledquartiles.ThefirstorlowerquartileQ1isavaluethathasapproximately25%oftheobservationsbelowinvalue.ThesecondquartileQ2isavaluethathasapproximately50%oftheobservationsbelowinvalue.Itisalsocalledthemedian.ThethirdorupperquartileQ3isavaluethathasapproximately75%oftheobservationsbelowinvalue.14QuartilesTwentyorderedobservationsonthetimestofailure(inhours)ofelectricalinsulationmaterialareshownbelow. 204228252300324444624720816912 117612961392148815122520285631923528371015MeasureofDispersionRange(Willnotbediscussed)Variance(Willnotbediscussed)StandardDeviation(Willnotbediscussed)Inter-QuartileRange16Inter-quartilerangeTheinter-quartilerangeisanothermeasureofdispersion.

IQR=Q3-Q1Theinter-quartilerangeislesssensitivetoextremevaluesinasamplethantherange.Forthetwosamples(1,3,5,8,9and1,5,5,5,9),theirinter-quartilerangesare5and0respectively.17MeasureofShape-SkewnessSkewnessThedegreeofassymmetryofadistributionarounditsmeanisreferredtoasitsskewness.18MeasureofShape-KurtosisKurtosisKurtosischaracterizestherelativepeakednessorflatnessofadistributioncomparedtoanormal(mesokurtic)distribution.19MiniTab’sDescriptiveStatisticsStat

BasicStatisticsDisplayDescriptiveStatisticsproducesstatisticsforeachcolumnofdata(orsubsetswithinacolumn)anddisplaysthemintheSessionWindowandoptionallyinagraphtheuserhasnocontroloverwhichstatisticsarecomputed/displayedStat

BasicStatisticsStoreDescriptiveStatisticsdescriptivestatisticsforeachcolumn(orsubsetswithinacolumn)aredisplayedinadjacentcolumnswithintheWorksheettheusercanselectwhichstatisticsaretobecomputed/displayed,buthasnocontrolovertheorderinwhichtheyaredisplayedInstructorwillshowyouthemethodofusingMinitab.20GraphicalPresentationVisualinterpretationthethedataset.Commongraphicaltoolstoillustrateadataset:DotPlotBoxPlotHistogramStem&LeafDiagram21DotPlotThedotplotisusefulfordisplayingasmallbodyofdata.Thelocationorcentraltendencyinthedatasetanditsspreadordispersionareeasilyidentified.Itcanalsobeusedincomparingtwoormoredatasets.22DotPlotThepullstrengthofbondingwiresfromtwosuppliersareshownbelowA: 16.8516.4017.2116.3516.5217.0416.9617.1516.5916.57B: 17.5017.6318.2518.0017.8617.7518.2217.9017.9618.15TheDotPlotrevealsthatwiresfromsupplierAseemstoresultinlowerpullstrength,butthevariabilitywithinbothgroupsisaboutthesame.23Box&WhiskersPlot(BoxPlot)The“box”displaysthelowerquartile(Q1)themedian(Q2)theupperquartile(Q3)The“whiskers:extendtotheminimumthemaximumNottobeusedwhensamplesizeislessthan10units.

MedianMaximumMinimumQ1Q324ProcedureformakingBoxPlot1. Arrangethedatasetinascendingorder.2. Determinetheminimumandmaximum,thelowerandupperquartiles,themedian,andTukey’soutliers.3. Drawaboxthatextendsfromthelowerquartiletotheupperquartile;themedianisalinedrawnthroughthebox.4. Drawlines(orwhiskers)thatextendfromtheendsofthebox a)fromQ1toMax{Minimum,Q1-1.5IQR} b)fromQ3toMin{Maximum,Q3+1.5IQR}5. Outliersarerepresentedbyappropriatesymbols25HistogramThehistogram,agraphicalpresentationofthefrequencydistribution,providesavisualimpressionoftheshapeofthedistributionofmeasurements.X-axis :measurementscaleY-axis :frequency(orrelativefrequency)scaleAreaofeachclassinterval’srectangleisproportionaltothefrequencyforthatclassinterval.26HistogramExamplea)c)b)SampleSize=100unitsa)Bins=5 Width=40b)Bins=9 Width=20c)Bins=18 Width=1027MinitabforSixSigmaITiscaninstalledtheMinitabforyouonceyourrequestisapproved.Minitabisbasic&essentialtoolsforSixSigmaproject.Yourprojectcanbepresentedandcalculatedbyotherstatisticalsoftware(eg,Statistica,SigmaPlot,etc)butalltherestofcourseisdevelopedwithuseofMinitab.28MinitabWindowsMenuBarToolBarSessionWindow:commandsandresultsappearhere(Ctrl+S)DataWindow:worksheetsappearhere;darkbarindicatesthatthisistheselectedwindow(Ctrl+D)Data&SessionWindowsMenuBar29MinitabWindowsSessionWindows–provideresultoutputDataWindows–rawdatastorehereGraphWindows–GraphoutputafteranalysisInfoWindows–providesummaryofdatawindows,etc.HistoryWindows–provideactionsinfothatyouhavedone.Session(Project)Manager–Manageyouroutput(includinggraph)Worksheet(Project)Manager–Manageyourworksheetsuchasrename.Graph(Project)Manager–Manageyourgraphssuchas“tile”,“maximize”,etc30ToolBarToolBar(DataWindow)ShortcutsforfrequentlyusedcommandsThecenterbuttonofthetoolbarchangesastheactivewindowchangesPlacemouseonthebuttontodetermineuseofeachbuttonToolBar(SessionWindow)31WorksheetDataC1-T--RefertoText(Qualitative)VariableC3-D--RefertoDateVariableC2--Numeric(Quantitative)Variable32GraphEditingChangestoExistingFontsChangestoExistingLinesChangestoExistingFillChangestoExisting