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1、TheTwo-Samplet-TestandRandomizationTestbyKeithM.Bower,M.S.ReprintedwithpermissionfromtheAmericanSocietyforQuality.ManySixSigmapractitionersuse“Student’s”independenttwo-samplet-testwheninvestigatingdifferencesinmeans.Thistypeoftestisbasedupondrawingrandomsamplesfromtwoindependen

2、tnormal(Gaussian)distributions.Often,however,theassumptionofnormalityand/orrandomsamplingisviolated.Thisarticlediscusseswhenandwhythetwo-samplet-testmaybeconsideredrobusttotheseassumptionsbycomparingt-testresultstorandomizationtestresults.AssumptionsofNormalityandRandomSampling

3、Thetwo-samplet-testiswidelyusedwhenaddressingqualityissuespertainingtobusiness,engineering,andelsewhere.Thetheoreticalfoundationforthistestincludesthefollowingassumptions:•Thetwosamplesareeachdrawnfromnormaldistributions.•Thetwosamplesaredrawnrandomlyfromtheirrespectivepopulati

4、ons.However,formanyinvestigations,oneorbothoftheseassumptionsmaybeunrealistic.1Forexample,considertheinvestigationbyAlfredHallstrometal.Theexperimenterswantedtoassesswhetherartificialrespiration(inadditiontochestcompressions)isnecessarybeforeanEmergencyMedicalServicesunitprovid

5、esexpertcare.Totestforadifferenceinsurvivalratesusingthetwomethods,telephonedispatchersrandomlyprovidedthecalleratthesceneinstructionsineither:•Chestcompressionsandmouth-to-mouthventilation.•Chestcompressionsonly.Inthissituation,itmaynotbereasonabletoassumethattheexperimentersh

6、aveobtaineda“representative”samplefromaspecificpopulationbecausethesubjectsinthisstudyarenotstrategicallydrawnfromalargerpopulationofinterest;theyareself-selecting.Importantly,however,thetwomethodsoftreatmentwereappliedrandomlytothesubjects.Thecallerhadanequalprobabilityofbeing

7、instructedtoperformeithermethodonthepatient.Thisconceptofapplyingtreatmentsatrandomistheassumptionbehindrandomizationtests,whichwerefirstdescribedbyRonaldA.Fisher.AnExampleComparingt-TestandRandomizationTestResultsConsidertwofertilizers(AandB)thatarerandomlyappliedtoatypeofsunf

8、lowerseed.Themaximumheightsreached(infeet)arerecordeda