Statistical hypothesis testing with SAS and R PDF
Preview Statistical hypothesis testing with SAS and R
Statistical Hypothesis Testing with SAS and R Statistical Hypothesis Testing with SAS and R Dirk Taeger Institute forPreventionandOccupationalMedicineoftheGermanSocial AccidentInsurance,Institute oftheRuhr-UniversitätBochum(IPA) Bochum,Germany Sonja Kuhnt DepartmentofComputerScience,DortmundUniversityofAppliedSciences andArts,Dortmund,Germany Thiseditionfirstpublished2014 ©2014JohnWiley&Sons,Ltd Registeredoffice JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyforpermissionto reusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. TherightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththeCopyright,Designs andPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyform orbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbytheUKCopyright, DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbeavailablein electronicbooks. Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrandnamesandproduct namesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheirrespectiveowners.The publisherisnotassociatedwithanyproductorvendormentionedinthisbook. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsinpreparingthisbook, theymakenorepresentationsorwarrantieswithrespecttotheaccuracyorcompletenessofthecontentsofthisbookand specificallydisclaimanyimpliedwarrantiesofmerchantabilityorfitnessforaparticularpurpose.Itissoldontheunder- standingthatthepublisherisnotengagedinrenderingprofessionalservicesandneitherthepublishernortheauthorshallbe liablefordamagesarisingherefrom.Ifprofessionaladviceorotherexpertassistanceisrequired,theservicesofacompetent professionalshouldbesought. LibraryofCongressCataloging-in-PublicationData Taeger,Dirk,author. StatisticalhypothesistestingwithSASandR/DirkTaeger,SonjaKuhnt. pagescm Includesbibliographicalreferencesandindex. ISBN978-1-119-95021-9(hardback) 1. Statisticalhypothesistesting.2. SAS(Computerprogramlanguage)3. R(Computerprogramlanguage) I.Kuhnt,Sonja,author.II.Title. QA277.T342014 519.50285′5133–dc23 2013041089 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN:978-1-119-95021-9 Setin10/12ptTimesbyLaserwordsPrivateLimited,Chennai,India 1 2014 ToThomasandKatharina Contents Preface xiii PartI INTRODUCTION 1 1 Statisticalhypothesistesting 3 1.1 Theoryofstatisticalhypothesistesting 3 1.2 TestingstatisticalhypothesiswithSASandR 4 1.2.1 ProgrammingphilosophyofSASandR 5 1.2.2 TestinginSASandR–Anexample 6 1.2.3 Calculatingp-values 11 1.3 Presentationofthestatisticaltests 13 References 15 PartII NORMALDISTRIBUTION 17 2 Testsonthemean 19 2.1 One-sampletests 19 2.1.1 z-test 19 2.1.2 t-test 22 2.2 Two-sampletests 23 2.2.1 Two-samplez-test 23 2.2.2 Two-samplepooledt-test 26 2.2.3 Welchtest 28 2.2.4 Pairedz-test 31 2.2.5 Pairedt-test 33 References 35 3 Testsonthevariance 36 3.1 One-sampletests 36 3.1.1 𝜒2-testonthevariance(meanknown) 36 3.1.2 𝜒2-testonthevariance(meanunknown) 39 viii CONTENTS 3.2 Two-sampletests 41 3.2.1 Two-sampleF-testonvariancesoftwopopulations 41 3.2.2 t-testonvariancesoftwodependentpopulations 44 References 47 PartIII BINOMIALDISTRIBUTION 49 4 Testsonproportions 51 4.1 One-sampletests 51 4.1.1 Binomialtest 51 4.2 Two-sampletests 55 4.2.1 z-testforthedifferenceoftwoproportions(unpooledvariances) 55 4.2.2 z-testfortheequalitybetweentwoproportions(pooledvariances) 59 4.3 K-sampletests 62 4.3.1 K-samplebinomialtest 62 References 64 PartIV OTHERDISTRIBUTIONS 65 5 Poissondistribution 67 5.1 TestsonthePoissonparameter 67 5.1.1 z-testonthePoissonparameter 67 5.1.2 ExacttestonthePoissonparameter 70 5.1.3 z-testonthedifferencebetweentwoPoissonparameters 72 References 75 6 Exponentialdistribution 76 6.1 Testontheparameterofanexponentialdistribution 76 6.1.1 z-testontheparameterofanexponentialdistribution 76 Reference 78 PartV CORRELATION 79 7 Testsonassociation 81 7.1 One-sampletests 81 7.1.1 Pearson’sproductmomentcorrelationcoefficient 81 7.1.2 Spearman’srankcorrelationcoefficient 86 7.1.3 Partialcorrelation 91 7.2 Two-sampletests 94 7.2.1 z-testfortwocorrelationcoefficients(independentpopulations) 94 References 98
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