常用质量统计方法Hypothesis Testing Methods

HypothesisTestingMethodsVariablesData2Attheendofthismodule,youwillbeableto:Understandtheapplicationofsingleandtwoparametermeantestingusing...•OnesampleZ-test•Onesamplet-test•Twosamplet-test•Pairedt-testUnderstandtheapplicationofvariancetestingEffectivelyconductandutilizethesetestsusingMinitabHypothesisTestingMethodObjectivesHypothesisTestingRoadmapHo:s1=s2=s3=...Ha:atleastoneisdifferentMinitab:Stat-Anova-HomogofVarianceForonlytwos‘sthisissimilartoanF-Test:F=(S1)2/(S2)2IfFcalcFtable,thenrejectnull.(UseChi-Squaredforonesample)Ho:M1=M2=M3=...Ha:atleastoneisdifferentMinitab:Stat-Nonparametric-Mann-Whitney(OR)Stat-Nonparametric-Kruskal-Wallis(OR)Stat-Nonparametric-Mood’sMedian(OR)Stat-Nonparametric-FriedmansM1=Medianofsample1,etc...Ho:m1=m2Ha:m1m2Minitab:Stat-BasicStats-2-SampleT(ComparesMeansusingpooledStdDev)CheckboxtoassumeequalvariancesHo:M1=MtargetHa:M1MtargetMinitab:Stat-Nonparametric-1Sample-Sign(OR)Stat-Nonparametric-1Sample-Wilcoxon(Thisisalsousedforpairedcomparisons:Ho:M1-M2=0)M1=Medianofsample1Mtarget=TargetMedianHo:m1=m2Ha:m1m2Minitab:Stat-BasicStats-2-SampleT(ComparesMeansusingunpooledStdDev)CheckboxtoassumeunequalvariancesQuantitativeY(onefactoronly)Levene’sTestBartlett’sTest/FTestNormalityTestOneWayAnovaQualitativeY(2factorsonly)ContingencyTableHo:TwofactorsareindependentHa:TwofactorsaredependentMinitab:Stat-Tables-Chi-squareTestHo:m1=m2=m3=...Ha:atleastoneisdifferentMinitab:Stat-Anova-One-way(BecarefulifBartlett’sp0.05)AssumesEqualVariancesHo:DataisNormalHa:DataisNOTNormalMinitab:Stat-BasicStat-NormalityTestUseAnderson-DarlingHo:s1=s2=s3=...Ha:atleastoneisdifferentMinitab:Stat-Anova-HomogofVariance(Requiresstackeddata)(Foronlytwos‘sthisisthesameasanF-Test:F=(S1)2/(S2)2IfFcalcFtable,thenrejectnull.Foralltests:p0.05FailtoRejectHo(null)p0.05RejectHoNonNormalNormalTwoorMoreSamplesChi-SquaredOneSampleHo:s1=stargetHa:s1stargetMinitab:Stat-BasicStatDisplayDescStatGraphsGraphicalSummaryIfstargetfallsbetweenCI,ThenfailtorejectHo.TwoorMoreSamples2Samplet-test(VariancesEqual)2Samplet-test(VariancesNotEqual)1Samplet-testHo:m1=mtargetHa:m1mtargetMinitab:Stat-BasicStats-1Sample-T(Thisisalsousedforpairedcomparisons:Ho:m1-m2=0)1Sample2orMoreSamplesTwoorMoreSamplesTwoSamplesProportionsTestingHo:P1=P2Ha:P1P2Minitab:Stat-BscStat-1or2ProportionsAlliedSignalBBs&GenCorpBBsweremajorcontributorstothischart.4Thez-testisusedinthefollowingapplications:Singlemeancomparedtoatargetvalue...whenthestandarddeviationisknownZ-test5Z-Distribution(StandardNormalDistribution)Howdoesz-actualcompare?•Comparez=tozcrit•Ifzzcrit,thenrejectequalityf(z)azcritz6ZStatisticxisthemeanofarandomsampleofsizentakenfromanormalpopulationhavingameanm,andastandarddeviations_n/xZsm-=Z-statistic7Thet-testisusedinthefollowingapplications:SinglemeancomparedtoatargetvalueComparisonoftwoindependentgroupmeansComparisonofpairedgroupmean...whenthestandarddeviationisunknownt-test8tDistributionHowdoest-actualcompare?•Comparet=totcrit•Ifttcrit,thenrejectequalityf(t)atcritt9sknownvssunknownZStatistictStatisticForthet-statistic,xisthemeanofarandomsampleofsizentakenfromanormalpopulationhavingameanm,andanestimatedstandarddeviations,withtheparameter=n-1nx/sm-nsx/m-___HowthetStatisticisDifferent10SingleParameterTestingStep1:StatethePracticalProblemStep2:Testfornormalityofthedata:Ho:DataisnormalHa:DataisnotnormalStep3:Determinetargetsformands(ors2)Step4:StatetheNullHypothesis:Fors:Form:Ho:spopulation=stargetHo:mpopulation=mtarget(or)Medianpopulation=MediantargetStatetheAlternativeHypothesis:Fors:Form:Ha:spopulationstargetHa:mpopulationmtarget(or)MedianpopulationMediantarget•Mean:1Samplet-test•(alsousedforpaireddata)•Sigma:ConfidenceInterval•Median:Non-parametrics•FailureRate:1Proportion11Step5:Determinetheappropriateteststatisticc2(calc)totestHo:spopulation=stargett(calc)totestHo:mpopulation=mtargetStep6:FindthecriticalvaluefromtheappropriatedistributionandaStep7:Ifcalculatedstatisticcriticalstatistic,thenREJECTHoOrIfP-Value0.05(P-Valuea),thenREJECTHoStep8:TranslatethestatisticalconclusionintoprocesstermsSingleParameterTesting(cont.)12Theexamplewillinclude10measurementsofarandomsample:»2661262426412670265026382645265226282675Thequestionis:Isthemeanofthesamplerepresentativeofatargetvalueof2650?TheHypotheses:Ho=2650Ha2650Hocanberejectedifp.05Example:SingleMeanComparedtoTarget13TheOldFashionedWayStatetheHypothesesCalculatethesamplemean(x)Calculatethesamplestandarddeviation(s)Determinethedegreesoffreedom(n-1)Lookupthet-statistic(tcrit)forthedfofthesample,Ha,&confidencelevelCalculatetheconfidencelimit(s)andcomparetothetargetAcceptorrejectHo_TheMinitabWayStatetheHypothesesEnterthedataforthesamplesetintotheMinitabworksheetRunthe“1-samplet-test”andpluginthetargetvaluewherepromptedChoosewhichalternativehypothesisyouwanttotestLetMinitabdothemathMakeadecisiononyourclaimusingthecalculatedpvalueRunningtheStatistics….14StatBasicStatistics1-SampletPutthedatamanuallyintoMinitabSingleMeantoaTarget-UsingMinitab15Nowwe’llcalculatetheconfidence