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simpleR{UsingRforIntroductoryStatistics

JohnVerzani

20000400006000080000120000160000

2e+054e+056e+058e+05

y pagei

Preface

arenottoshowallthefeaturesof illustratethefeaturesof

Thesenoteswerewrittentotakeadvantageof

RCMD

INSTALLpackagename.tar.gz

Rpackagefrom:

0.4.zipforWindowsusers.

0.4.tar.gzforUNIXusers.

Copyrightc

Contents

Introduction1

Whatis

Data1

Starting

Enteringdatawith

Dataisa

UnivariateData8

BivariateData19

MultivariateData32

Manipulatingdataframes:

Using The simpleR{Using

RforIntroductoryStatistics

pageii

RandomData41

Randomnumbergeneratorsin

Simulations47

Using

ExploratoryDataAnalysis54

CondenceIntervalEstimation59

HypothesisTesting66

Two-sampletests68

ChiSquareTests72

RegressionAnalysis77

MultipleLinearRegression84

AnalysisofVariance89

Appendix:InstallingR94

Appendix:ExternalPackages94

Appendix:AsampleRsession94

simpleR{Using

RforIntroductoryStatistics

pageiii

Appendix:WhathappenswhenRstarts?100

Appendix:UsingFunctions100

Appendix:EnteringDatainto

R103 Using using Using

Appendix:TeachingTricks106

Appendix:Sourcesofhelp,documentation107

simpleR{Using

RforIntroductoryStatistics

Datapage1

Section1:Introduction

WhatisR

Ratthisearlylevelwillbetter

\learningcurve".

Thebenetsof

Rforanintroductorystudentare

Rhasanexcellentbuilt-inhelpsystem.

Rhasexcellentgraphingcapabilities.

Whatis

RprojectwasstartedbyRobertGentlemanand

audience.Itiscurrentlymaintainedbythe developers.The

Rprojectwebpage

http://www.r-project.org isthemainsiteforinformationon andothersourcesofdocumentation.

Anoteonnotation

datasetnamesanddierenttypesettingfor longersequencesofRcommands. andfor

Datasets.

Section2:Data

toenterdatainto

Randhowtomanipulatethedataoncethere.

StartingR

simpleR{UsingRforIntroductoryStatistics

Datapage2

the ways.Once

R:Copyright2001,TheRDevelopmentCoreTeam

Version1.4.0(2001-12-19)

Type`contributors()'formoreinformation.

Type`q()'toquitR.

[Previouslysavedworkspacerestored] +isusedforthecontinuationprompt.

Enteringdatawithc

ofthesenotes:

23031001

ToenterthisintoanRsessionwedosowith

>typos=c(2,3,0,3,1,0,0,1) >typos [1]23031001

Noticeafewthings

Weassignedthevaluestoavariablecalled

typos

Thevalueofthe

inputlineindicates thatlater.

Typingless

Applyingafunction

simpleR{Using

RforIntroductoryStatistics

Datapage3

>mean(typos) [1]1.25 >median(typos) [1]1 >var(typos) [1]1.642857

Dataisavector

Oursimpledatavector

setagain. following: >typos.draft1=c(2,3,0,3,1,0,0,1) >typos.draft2=c(0,3,0,3,1,0,0,1)

Rtochangetherst

page?Theanswerofcourseis\yes".Hereishow >typos.draft1=c(2,3,0,3,1,0,0,1) >typos.draft2=typos.draft1#makeacopy commentcharacterisignored(by inthevector typos.draft2 >typos.draft2#printoutthevalue [1]03031001 >typos.draft2[2]#print2ndpages'value [1]3 >typos.draft2[4]#4thpage [1]3 >typos.draft2[-4]#allbutthe4thpage [1]0301001 [1]030 slicing. pages2and4areaproblem.Canwedothiswith

Rinamoresystematicmanner?

simpleR{Using

RforIntroductoryStatistics

Datapage4

>max(typos.draft2)#whatareworstpages? [1]3#3typosperpage >typos.draft2==3#Wherearethey?

The2ndand4thansweryes(

TRUE)theothersno.

Thinkofthisasasking

andFALSE's.

TRUEvalues?Let'srephrase,which

whichwillwork,youareonyourwaytoRmastery: >which(typos.draft2==3) [1]24

Thebasicideaistocreateanewvector

onesforwhich typos.draft2==3: >n=length(typos.draft2)#howmanypages >pages=1:n#howwegetthepagenumbers >pages#pagesissimply1tonumberofpages [1]12345678 [1]24 usefulthingtoknow.Thecommand ifnot.Amoregeneral abovetry seq(a,b,1).

TRUEsand

dataasyoudesire. [1]24

Ryouneedtounderstandhowonecomposes

have >sum(typos.draft2)#Howmanytypos? [1]8 [1]4 [1]20000000

45,43,46,48,51,46,50,47,46,45

>x=c(45,43,46,48,51,46,50,47,46,45) >mean(x)#themean [1]46.7 simpleR{UsingRforIntroductoryStatistics

Datapage5

>median(x)#themedian [1]46 >max(x)#themaximumorlargestvalue [1]51 >min(x)#theminimumvalue [1]43 addthenexttwoweeksworthofdatato x.Thiswas

48,49,51,50,49,41,40,38,35,40

Wecanaddthisseveralways.

>x=c(x,48,49,51,50,49)#appendvaluestox >length(x)#howlongisxnow(itwas10) [1]15 >x[16]=41#addtoaspecifiedindex operatortocombinethepreviousvalueof index.Atthetimeoftheassignment,

RBasics:GraphicalDataEntryInterfaces

students.Hereareexampleswithannotations >x=de(x)#sameonly,doesn'tsavechanges >x=edit(x)#useseditortoeditx. >data.entry(x)#fails.xnotdefined

Errorinde(...,Modes=Modes,Names=Names):

Object"x"notfound

20astheotherdaysdon'thaveenoughdata.

>day=5; >mean(x[day:(day+4)]) [1]48

Thetrickistheslicetakesoutdays5,6,7,8,9

>day:(day+4) [1]56789 andthemeantakesjustthosevaluesofx. max(x).However,youmaybeinterested

Rhadabuilt-infunctionto

handlethis.Itiscalled ofdataalongwiththesimilar cummin: >cummax(x)#runningmaximum >cummin(x)#runningminimum simpleR{UsingRforIntroductoryStatistics

Datapage6

Example:Workingwithmathematics

7412223511129211121113315679

>mean(whale) [1]152.4 >var(whale) [1]5113.378 >std(whale)

Error:couldn'tfindfunction"std"

>sqrt(var(whale)) [1]71.50789 [1]71.50789 that

SD(X)=v

u u t1 n1n X i=1(XiX)2:

Noticethesumisnow

itisdone: >std=function(x)sqrt(var(x)) >std(whale) [1]71.50789 sd()command.Whichgives >sd(whale) [1]71.50789

RBasics:AccessingData

alogicalvector.Suppose xisthedatavector,forexamplex=1:10. howmanyelements? length(x) ithelementx[2](i=2) allbutithelement x[-2](i=2) rstkelements x[1:5](k=5) lastkelements x[(length(x)-5):length(x)](k=5) specicelements. x[c(1,3,5)](First,3rdand5th) allgreaterthansomevalue x[x>3](thevalueis3) biggerthanorlessthansomevalues x[x<-2|x>2] whichindicesarelargestwhich(x==max(x)) simpleR{UsingRforIntroductoryStatistics

Datapage7

Problems

6531165624659086621966499668216714567447

>x=diff(miles) ll-ups,the

17162024221521151722

andthefunction mintondtheminimum. average. commutes) >sum(commutes>=20)

463339374630483249353048

(supposethecarsareallsimilar)

90009500940094001000095001030010200

Use

2.5Trytoguesstheresultsofthese

Supposeweassume

>x=c(1,3,5,7,9) >y=c(2,3,5,7,11,13) 1.x+1 2.y*2

3.length(x)andlength(y)

4.x+y

5.sum(x>5)andsum(x[x>5])

6.sum(x>5|x<3)#read|as'or',&and'and'

7.y[3]

8.y[-3]

simpleR{UsingRforIntroductoryStatistics

UnivariateDatapage8

9.y[x](WhatisNA?)

10. y[y>=7]

2.6Letthedataxbegivenby

>x=c(1,8,2,6,3,8,5,5,5,5)

1.(X1+X2++X10)=10(use

sum)

2.Findlog10(Xi)foreachi.(Usethe

logfunctionwhichbydefaultisbasee) x.(Thisistherange.Youcanusemaxand minorguessabuiltincommand.)

Section3:UnivariateData

dowithit. becontinuous.

Categoricaldata

charts.

Usingtables

variable.

Example:Smokingsurvey

Yes,No,No,Yes,Yes

>x=c("Yes","No","No","Yes","Yes") >table(x) simpleR{UsingRforIntroductoryStatistics

UnivariateDatapage9

x NoYes 23

Factors

occasionallyimportanttoknowas iseasywiththecommand >x=c("Yes","No","No","Yes","Yes") >x#printoutvaluesinxquotesdbs_dbs14.pdfusesText_20

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