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HypothesisTesting

LearningObjectives

Aftercompletingthismodule,thestudentwillbeableto

carryoutastatisticaltestofsignificance calculatetheacceptanceandrejectionregion calculateandinterpretthepvalueofastatistical

test

calculateandinterprettype1andtype2errors calculatethepowerofatest

KnowledgeandSkills

Concepts:nullhypothesis,alternative,teststatistic,rejectionregion,acceptanceregion,pvalue,significancelevel,type1error,type2error,falsepositive,falsenegative,powerofatest

Resamplingmethod Fishersexacttest

Prerequisites

binomialdistribution hypergeometricdistribution Normaldistribution Sampleaverage Samplestandarddeviation macrosinExcel

InclassActivity1

Ifthenewtreatmentwasnotbetterthanthecurrenttreatment,wewouldhypothesizethatthenewtreatmenthasprobability0.3ofbeingsuccessful.Alternatively,ifthenewtreatmentisbetterthanthecurrenttreatment,wewouldhypothesizethatthenewtreatmenthasprobabilitygreaterthan0.3ofbeingsuccessful.

Ifthenewtreatmenthasthesamelikelihoodofsuccessthanthecurrenttreatment,namelyprobability0.3,thenthenumberofpatientsinthesmallclinicaltrialwhoaretreatedsuccessfullyunderthenewtreatmentisbinomiallydistributedwith10trialsandsuccessprobability0.3.ThefollowingtablewascreatedinEXCELusingtheBINOMDISTfunctionandshowsthisprobabilitydistribution:

x P(X=x)

0 0.02821 0.12112 0.23353 0.26684 0.20015 0.10296 0.03687 0.00908 0.00149 0.0001

10 0.0000

Weseethattheprobabilityoffiveormoresuccesseswhenthesuccessprobabilityis0.3is

0.1029 0.0368 0.0090 0.0014 0.0000 0.1502+ + + + =

Thus,itisnotunlikelytosee5(ormore)outof10patientsrecoverwhenthesuccessprobabilityofrecoveryis0.3.Weconcludethatthereisnotenoughevidencetoconcludethatthenewtreatmentisbetter.

Discussinyourgroupthefollowingquestions:

InclassActivity2

Thehypothesisthecoinisfairiscalledthenullhypothesisandisdenotedby 0H .Thealternativethe

hypothesisandwhichisthealternativelater.)Wesummarizethisas

=

0

1

: 0.5

: 0.5

H p

H p