Table Of ContentVisual Statistics
Use R!
Alexey Shipunov
TONGUE
PEAK EARLOBE
TOE PINKY
THUMB ARM
CHIN CHEEK
July27,2020version
Shipunov,Alexey(andmanyothers). Visualstatistics. UseR!
July27,2020version. 451pp.
URL:http://ashipunov.me/shipunov/school/biol_240/en/
Onthecover: Rplotillustratingcorrelationsbetweenhumanphenotypictraits. See
thepage255formoreexplanation.
Thisbookisdedicatedtothepublicdomain
Contents
Foreword 9
I One or two dimensions 13
1 Thedata 14
1.1 Originofthedata. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2 Populationandsample . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 Howtoobtainthedata . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4 Whattofindinthedata . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4.1 Whydoweneedthedataanalysis . . . . . . . . . . . . . . . . 17
1.4.2 Whatdataanalysiscando . . . . . . . . . . . . . . . . . . . . . 17
1.4.3 Whatdataanalysiscannotdo . . . . . . . . . . . . . . . . . . . 18
1.5 Answerstoexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Howtoprocessthedata 20
2.1 Generalpurposesoftware . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Statisticalsoftware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 Graphicalsystems . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Statisticalenvironments. . . . . . . . . . . . . . . . . . . . . . 21
2.3 TheveryshorthistoryoftheSandR . . . . . . . . . . . . . . . . . . . 22
2.4 Use,advantagesanddisadvantagesoftheR . . . . . . . . . . . . . . . 22
2.5 HowtodownloadandinstallR . . . . . . . . . . . . . . . . . . . . . . 23
2.6 HowtostartwithR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6.1 LaunchingR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6.2 Firststeps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6.3 Howtotype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6.4 Overgrowncalculator . . . . . . . . . . . . . . . . . . . . . . . 30
2.6.5 HowtoplaywithR . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.7 Randdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3
2.7.1 HowtoenterthedatafromwithinR . . . . . . . . . . . . . . . 34
2.7.2 Howtonameyourobjects . . . . . . . . . . . . . . . . . . . . . 34
2.7.3 Howtoloadthetextdata . . . . . . . . . . . . . . . . . . . . . 35
2.7.4 HowtoloaddatafromInternet . . . . . . . . . . . . . . . . . . 38
2.7.5 Howtouseread.table()properly . . . . . . . . . . . . . . . . 38
2.7.6 Howtoloadbinarydata . . . . . . . . . . . . . . . . . . . . . . 40
2.7.7 Howtoloaddatafromclipboard . . . . . . . . . . . . . . . . . 41
2.7.8 HowtoeditdatainR . . . . . . . . . . . . . . . . . . . . . . . . 42
2.7.9 Howtosavetheresults . . . . . . . . . . . . . . . . . . . . . . 43
2.7.10 Historyandscripts . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.8 Rgraphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.8.1 Graphicalsystems . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.8.2 Graphicaldevices. . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.8.3 Graphicaloptions . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.8.4 Interactivegraphics . . . . . . . . . . . . . . . . . . . . . . . . 56
2.9 Answerstoexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3 Typesofdata 62
3.1 Degrees,hoursandkilometers: measurementdata . . . . . . . . . . . 62
3.2 Gradesandt-shirts: rankeddata . . . . . . . . . . . . . . . . . . . . . 68
3.3 Colors,namesandsexes: nominaldata . . . . . . . . . . . . . . . . . 70
3.3.1 Charactervectors. . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3.2 Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3.3 Logicalvectorsandbinarydata . . . . . . . . . . . . . . . . . . 76
3.4 Fractions,countsandranks: secondarydata. . . . . . . . . . . . . . . 79
3.5 Missingdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.6 Outliers,andhowtofindthem . . . . . . . . . . . . . . . . . . . . . . 86
3.7 Changingdata: basicsoftransformations . . . . . . . . . . . . . . . . 87
3.7.1 Howtotellthekindofdata . . . . . . . . . . . . . . . . . . . . 89
3.8 InsideR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.8.1 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.8.2 Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.8.3 Dataframes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.8.4 Overviewofdatatypesandmodes . . . . . . . . . . . . . . . . 103
3.9 Answerstoexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4 One-dimensionaldata 111
4.1 Howtoestimategeneraltendencies . . . . . . . . . . . . . . . . . . . 111
4.1.1 Medianisthebest . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.1.2 Quartilesandquantiles . . . . . . . . . . . . . . . . . . . . . . 113
4.1.3 Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.2 1-dimensionalplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4
4.3 Confidenceintervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.4 Normality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.5 Howtocreateyourownfunctions . . . . . . . . . . . . . . . . . . . . 130
4.6 Howgoodistheproportion? . . . . . . . . . . . . . . . . . . . . . . . 132
4.7 Answerstoexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5 Two-dimensionaldata: differences 148
5.1 Whatisastatisticaltest? . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.1.1 Statisticalhypotheses . . . . . . . . . . . . . . . . . . . . . . . 149
5.1.2 Statisticalerrors . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.2 Isthereadifference? Comparingtwosamples . . . . . . . . . . . . . . 151
5.2.1 Twosampletests . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.2.2 Effectsizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
5.3 Iftherearemorethantwosamples: ANOVA . . . . . . . . . . . . . . . 169
5.3.1 Oneway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.3.2 Morethenoneway . . . . . . . . . . . . . . . . . . . . . . . . . 183
5.4 Isthereanassociation? Analysisoftables . . . . . . . . . . . . . . . . 184
5.4.1 Contingencytables . . . . . . . . . . . . . . . . . . . . . . . . . 184
5.4.2 Tabletests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
5.5 Answerstoexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
5.5.1 Exercisesontwosamples . . . . . . . . . . . . . . . . . . . . . 201
5.5.2 ExercisesonANOVA . . . . . . . . . . . . . . . . . . . . . . . . 208
5.5.3 Exercisesontables . . . . . . . . . . . . . . . . . . . . . . . . . 212
6 Two-dimensionaldata: models 221
6.1 Analysisofcorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
6.1.1 Plotitfirst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
6.1.2 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
6.2 Analysisofregression . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
6.2.1 Singleline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
6.2.2 Manylines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
6.2.3 Morethenoneway,again . . . . . . . . . . . . . . . . . . . . . 248
6.3 Probabilityofthesuccess: logisticregression . . . . . . . . . . . . . . 250
6.4 Answerstoexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
6.4.1 Correlationandlinearmodels. . . . . . . . . . . . . . . . . . . 254
6.4.2 Logisticregression . . . . . . . . . . . . . . . . . . . . . . . . . 266
6.5 Howtochoosetherightmethod . . . . . . . . . . . . . . . . . . . . . 271
II Many dimensions 274
7 Draw 275
5
7.1 Pictographs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
7.2 Groupedplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
7.3 3Dplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
8 Discover 289
8.1 Discoverywithprimarydata . . . . . . . . . . . . . . . . . . . . . . . . 290
8.1.1 Shadowsofhyperclouds: PCA . . . . . . . . . . . . . . . . . . 290
8.1.2 Correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . 298
8.1.3 Projections,unfolds,t-SNEandUMAP . . . . . . . . . . . . . . 300
8.1.4 Non-negativematrixfactorization . . . . . . . . . . . . . . . . 304
8.2 Discoverywithdistances . . . . . . . . . . . . . . . . . . . . . . . . . . 305
8.2.1 Distances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
8.2.2 Makingmaps: multidimensionalscaling . . . . . . . . . . . . . 308
8.2.3 Makingtrees: hierarchicalclustering . . . . . . . . . . . . . . 311
8.2.4 Howtoknowthebestclusteringmethod . . . . . . . . . . . . 316
8.2.5 Howtocompareclusterings . . . . . . . . . . . . . . . . . . . . 319
8.2.6 Howgoodareresultedclusters . . . . . . . . . . . . . . . . . . 322
8.2.7 Makinggroups: k-meansandfriends . . . . . . . . . . . . . . . 325
8.2.8 Howtoknowclusternumbers . . . . . . . . . . . . . . . . . . . 328
8.2.9 Useprojectionpursuitforclustering . . . . . . . . . . . . . . . 332
8.2.10 Howtocomparedifferentordinations . . . . . . . . . . . . . . 333
8.3 Answerstoexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
9 Learn 341
9.1 Learningwithregression . . . . . . . . . . . . . . . . . . . . . . . . . 342
9.1.1 Lineardiscriminantanalysis . . . . . . . . . . . . . . . . . . . 342
9.1.2 Recursivepartitioning . . . . . . . . . . . . . . . . . . . . . . . 347
9.2 Ensemblelearnig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
9.2.1 RandomForest . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
9.2.2 Gradientboosting . . . . . . . . . . . . . . . . . . . . . . . . . 352
9.3 Learningwithproximity . . . . . . . . . . . . . . . . . . . . . . . . . . 354
9.4 Learningwithrules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
9.5 Learningfromtheblackboxes . . . . . . . . . . . . . . . . . . . . . . 359
9.5.1 SupportVectorMachines . . . . . . . . . . . . . . . . . . . . . 359
9.5.2 NeuralNetworks . . . . . . . . . . . . . . . . . . . . . . . . . . 361
9.6 Semi-supervisedlearning . . . . . . . . . . . . . . . . . . . . . . . . . 366
9.7 Howtochoosetherightmethod . . . . . . . . . . . . . . . . . . . . . 370
9.8 Answerstoexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
6
Appendices 374
A Exampleof Rsession 375
A.1 Starting... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
A.2 Describing... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
A.3 Plotting... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
A.4 Testing... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
A.5 Finishing... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386
A.6 Answerstoexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
B TenYearsLater,oruseRscript 388
B.1 HowtomakeyourRscript . . . . . . . . . . . . . . . . . . . . . . . . . 389
B.2 MyRscriptdoesnotwork! . . . . . . . . . . . . . . . . . . . . . . . . . 391
B.3 CommonpitfallsinRscripting . . . . . . . . . . . . . . . . . . . . . . 395
B.3.1 Advices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
B.3.1.1 UsetheSource,Luke!.. . . . . . . . . . . . . . . . . . 395
B.3.1.2 Keepitsimple . . . . . . . . . . . . . . . . . . . . . . 395
B.3.1.3 Learntoloveerrorsandwarnings . . . . . . . . . . . 395
B.3.1.4 Subselectbynames,notnumbers . . . . . . . . . . . 396
B.3.1.5 Aboutreservedwords,again . . . . . . . . . . . . . . 397
B.3.2 TheCase-bookofAdvancedRuser . . . . . . . . . . . . . . . . 397
B.3.2.1 ACaseofWere-objects . . . . . . . . . . . . . . . . . 397
B.3.2.2 ACaseofMissingCompare . . . . . . . . . . . . . . . 398
B.3.2.3 ACaseofOutlawParameters . . . . . . . . . . . . . . 398
B.3.2.4 ACaseofIdentity . . . . . . . . . . . . . . . . . . . . 399
B.3.2.5 TheAdventureoftheFloatingPoint . . . . . . . . . . 400
B.3.2.6 ACaseofTwinFiles . . . . . . . . . . . . . . . . . . . 400
B.3.2.7 ACaseofBadGrammar . . . . . . . . . . . . . . . . . 401
B.3.2.8 ACaseofDoubleDipping . . . . . . . . . . . . . . . . 402
B.3.2.9 ACaseofFactorJoin . . . . . . . . . . . . . . . . . . 402
B.3.2.10 ACaseofBadFont. . . . . . . . . . . . . . . . . . . . 402
B.3.2.11 ACaseofDisproportionateCondition . . . . . . . . . 403
B.3.3 Good,Bad,andNot-too-bad . . . . . . . . . . . . . . . . . . . 403
B.3.3.1 Good . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
B.3.3.2 Bad . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404
B.3.3.3 Nottoobad . . . . . . . . . . . . . . . . . . . . . . . . 406
B.4 Answerstoexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
C Rfragments 409
C.1 Randdatabases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
C.2 Randtime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
C.3 Randbootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
7
C.4 Randshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
C.5 RandBayes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
C.6 R,DNAandevolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
C.7 Randreporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
C.8 Rwithoutgraphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
C.9 Answerstoexercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
D MostessentialRcommands 438
E TheshortRglossary 440
F References 448
G Referencecard 451
8
Foreword
Thisbookiswrittenforthosewhowanttolearnhowtoanalyzedata. Thischallenge
arisesfrequentlywhenyouneedtodetermineapreviouslyunknownfact. Forexam-
ple: doesthisnewmedicinehaveaneffectonapatient’ssymptoms? Or: Istherea
differencebetweenthepublic’sratingoftwopoliticians? Or: howwilltheoilprices
changeinthenextweek?
Youmightthinkthatyoucanfindtheanswertosuchaquestionsimplybylookingat
thenumbers. Unfortunatelythisisoftennotthecase. Forexample,aftersurveying
262 people exiting a polling site, it was found that 52% voted for candidate A and
48%forcandidateB.
DotheresultsofthisexitpolltellyouthatcandidateAwontheelection?
Thinking about it, many would say “yes,” and then, considering it for a moment,
“Well,Idon’tknow,maybe?” Butthereisasimple(fromthepointofviewofmodern
computerprograms)“proportiontest”thattellsyounotonlytheanswer(inthiscase,
“No,theresultsoftheexitpolldonotindicatethatCandidateAwontheelection”)
butalsoallowsyoutocalculatehowmanypeopleyouwouldneedtosurveytobeable
toanswerthatquestion. Inthiscase,theanswerwouldbe“about5,000people”—see
theexplanationattheendofthechapteraboutone-dimensionaldata.
The ignorance of the statistical methods can lead to mistakes and misinterpreta-
tions. Unfortunately, understanding of these methods is far from common. Many
collegemajorsrequireacourseinprobabilitytheoryandmathematicalstatistics,but
allmanyofusrememberfromthesecoursesishorrorand/orfrustrationatcomplex
mathematicalformulasfilledwithGreekletters,someofthemwearinghats.
Itistruethatprobabilitytheoryformsthebasisofmostdataanalysismethodsbuton
the other hand, most people use fridge without knowledge about thermodynamics
and Carnot cycle. For the practical purposes of analyzing data, you do not have to
befullyfluentinmathematicalstatisticsandprobabilitytheory.
9
Therefore, we tried to follow Steven Hawking who in the “A Brief History of Time”
stated that “... someone told me that each equation I included in the book would
halve the sales. I therefore resolved not to have any equations at all ..”. Conse-
quently, thereisonlyoneequationinthisbook. Bytheway, aninterestingexercise
isjusttofind1 it.
Evenbetter,almostidealapproachwouldbethebooksimilartoR.Munroe’s“Thing
Explainer”2 where complicated concepts are explained using dictionary of 1,000
mostfrequentEnglishwords.
Tomakealongstoryshort,thistextbookisthekindof“statisticwithoutmath”but
withR.
Somecautionisrequired,though,forreadersofsuchbooks: manymethodsofsta-
tisticalanalysishave,sotospeak,afalsebottom. Youcanapplythesemethodswith-
outdelvingtoodeeplyintotheunderlyingprinciples,getresults,anddiscussthese
results in your report. But you might find one day that a given method was totally
unsuitableforthedatayouhad,andthereforeyourconclusionsareinvalid. Youmust
becarefulandawareofthelimitationsofanymethodyoutrytouseanddetermine
whethertheyareapplicabletoyoursituation.
Thisbookdevotedmostlytobiometry,methodsofdataanalysisappliedtobiological
objects. AsFredBooksteinmentionedinhisbook(2018),biologicalobjectshaveat
leasttwoimportantfeatures: morphologicalintegration(substantialbutinconstant
correlation among most pairs of measurements), and the centrality of measures of
extent(lengths,areas,weights). Wewillusethesefeaturesinthebook.
***
On examples: This book is based on a software which runs data files, and we have
mademostofthedatafilesusedhereavailabletodownloadfrom
http://ashipunov.me/data
Werecommendtocopydatafilestothedatasubdirectoryofyourworkingdirectory;
oneofpossiblemethodsistoopenthisURLinbrowseranddownloadallfiles. Then
allcodeexamplesshouldworkwithoutInternetconnection.
However, youcanloaddatadirectlyfromtheURLabove. Ifyoudecidetoworkon-
line, then the convention is that when the books says "data/...", replace it with
"http://ashipunov.me/data/...".
1
Usually,small(running)exercisesareboldfaced.
2https://xkcd.com/thing-explainer/
10
