Table Of Content

OUPCORRECTEDPROOF–FINAL,16/5/2019,SPi Statistical Thinking from Scratch OUPCORRECTEDPROOF–FINAL,16/5/2019,SPi OUPCORRECTEDPROOF–FINAL,16/5/2019,SPi Statistical Thinking from Scratch A Primer for Scientists M. D. EDGE 1 OUPCORRECTEDPROOF–FINAL,16/5/2019,SPi 3 GreatClarendonStreet,Oxford,OX26DP, UnitedKingdom OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwide.Oxfordisaregisteredtrademarkof OxfordUniversityPressintheUKandincertainothercountries ©M.D.Edge2019 Themoralrightsoftheauthorhavebeenasserted FirstEditionpublishedin2019 Impression:1 Allrightsreserved.Nopartofthispublicationmaybereproduced,storedin aretrievalsystem,ortransmitted,inanyformorbyanymeans,withoutthe priorpermissioninwritingofOxfordUniversityPress,orasexpresslypermitted bylaw,bylicenceorundertermsagreedwiththeappropriatereprographics rightsorganization.Enquiriesconcerningreproductionoutsidethescopeofthe aboveshouldbesenttotheRightsDepartment,OxfordUniversityPress,atthe addressabove Youmustnotcirculatethisworkinanyotherform andyoumustimposethissameconditiononanyacquirer PublishedintheUnitedStatesofAmericabyOxfordUniversityPress 198MadisonAvenue,NewYork,NY10016,UnitedStatesofAmerica BritishLibraryCataloguinginPublicationData Dataavailable LibraryofCongressControlNumber:2019934651 ISBN978–0–19–882762–7(hbk.) ISBN978–0–19–882763–4(pbk.) DOI:10.1093/oso/9780198827627.001.0001 Printedandboundby CPIGroup(UK)Ltd,Croydon,CR04YY LinkstothirdpartywebsitesareprovidedbyOxfordingoodfaithand forinformationonly.Oxforddisclaimsanyresponsibilityforthematerials containedinanythirdpartywebsitereferencedinthiswork. OUPCORRECTEDPROOF–FINAL,16/5/2019,SPi forIsabel OUPCORRECTEDPROOF–FINAL,16/5/2019,SPi OUPCORRECTEDPROOF–FINAL,16/5/2019,SPi Contents Acknowledgments xi Prelude 1 1 Encountering data 5 1.1 Thingstocome 7 2 R and exploratory data analysis 11 2.1 InteractingwithR 13 2.2 Tutorial:theIrisdata 15 2.3 Chaptersummary 24 2.4 Furtherreading 25 3 The line of best fit 26 Box3-1: Mathematicsrequiredforthischapter 27 3.1 Definingthe“best”fit 28 3.2 Derivation:findingtheleast-squaresline 31 3.3 Conclusions 34 3.4 Chaptersummary 37 3.5 Furtherreading 37 4 Probability and random variables 38 Box4-1: Setsandsetnotation 40 4.1 [Optionalsection]Theaxiomsofprobability 41 4.2 Relationshipsbetweenevents:conditionalprobabilityandindependence 43 4.3 Bayes’theorem 45 Box4-2: Bayes’theoreminstatistics 47 4.4 Discreterandomvariablesanddistributions 48 4.5 Continuousrandomvariablesanddistributions 51 Box4-3: Integration 52 4.6 Probabilitydensityfunctions 53 4.7 Familiesofdistributions 55 4.8 Chaptersummary 58 4.9 Furtherreading 58 OUPCORRECTEDPROOF–FINAL,16/5/2019,SPi viii CONTENTS 5 Properties of random variables 60 5.1 Expectedvaluesandthelawoflargenumbers 60 Box5-1: Measuresoflocation 61 5.2 Varianceandstandarddeviation 65 5.3 Jointdistributions,covariance,andcorrelation 68 5.4 [Optionalsection]Conditionaldistribution,expectation,andvariance 72 5.5 Thecentrallimittheorem 74 5.6 Aprobabilisticmodelforsimplelinearregression 79 Box5-2: Assumptionsaboutthelinearmodelandclaimsthatfollow 80 5.7 Chaptersummary 86 5.8 Furtherreading 86 Interlude 88 6 Properties of point estimators 91 Box6-1: Processes,populations,andsamples 92 6.1 Bias 94 6.2 Variance 96 6.3 Meansquarederror 96 6.4 Consistency 97 6.5 Efficiency 99 6.6 [Optionalsection]Statisticaldecisiontheoryandrisk 100 6.7 Robustness 103 6.8 Estimatorsforsimplelinearregression 105 6.9 Conclusion 109 6.10 Chaptersummary 109 6.11 Furtherreading 109 7 Interval estimation and inference 111 7.1 Standarderror 111 7.2 Confidenceintervals 112 Box7-1: Athoughtexperimentaboutconfidenceintervals 114 7.3 FrequentistinferenceI:nullhypotheses,teststatistics,andpvalues 116 7.4 FrequentistinferenceII:alternativehypothesesandtherejection framework 121 7.5 [Optionalsection]Connectinghypothesistestsandconfidenceintervals 124 7.6 NHSTandtheabuseoftests 125 7.6.1 Lackofreplication 125 7.6.2 Ossificationofα=0.05 125 7.6.3 α=0.05asagatekeeper 126 7.6.4 Identificationofscientifichypothesiswithastatisticalhypothesis 126 7.6.5 Neglectofothergoals,suchasestimationandprediction 126 7.6.6 Adegradedintellectualculture 127 7.6.7 EvaluatingsignificancetestsinlightofNHST 129 OUPCORRECTEDPROOF–FINAL,16/5/2019,SPi CONTENTS ix 7.7 FrequentistinferenceIII:power 131 7.8 Puttingittogether:Whathappenswhenthesamplesizeincreases? 135 7.9 Chaptersummary 137 7.10 Furtherreading 137 8 Semiparametric estimation and inference 139 8.1 Semiparametricpointestimationusingthemethodofmoments 142 8.1.1 Plug-inestimators 143 8.1.2 Themethodofmoments 145 8.2 Semiparametricintervalestimationusingthebootstrap 149 Box8-1: Bootstrappivotalintervals 154 8.3 Semiparametrichypothesistestingusingpermutationtests 157 8.4 Conclusion 162 8.5 Chaptersummary 163 8.6 Furtherreading 163 9 Parametric estimation and inference 165 Box9-1: Logarithms 166 9.1 Parametricestimationusingmaximumlikelihood 168 9.1.1 Maximum-likelihoodestimationforsimplelinearregression 172 9.2 Parametricintervalestimation:thedirectapproachandFisher information 175 9.2.1 Thedirectapproach 175 9.2.2 [Optionalsubsection]TheFisherinformationapproach 177 9.3 ParametrichypothesistestingusingtheWaldtest 180 9.3.1 TheWaldtest 180 9.4 [Optionalsection]Parametrichypothesistestingusingthe likelihood-ratiotest 181 9.5 Chaptersummary 185 9.6 Furtherreading 185 10 Bayesian estimation and inference 186 10.1 Howtochooseapriordistribution? 187 10.2 Theunscaledposterior,conjugacy,andsamplingfromtheposterior 188 10.3 BayesianpointestimationusingBayesestimators 193 10.4 Bayesianintervalestimationusingcredibleintervals 196 10.5 [Optionalsection]Bayesian“hypothesistesting”usingBayesfactors 198 10.6 Conclusion:Bayesianvs.frequentistmethods 201 10.7 Chaptersummary 202 10.8 Furtherreading 202