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  • What are the topics in introductory statistics?

    Topics discussed include displaying and describing data, the normal curve, regression, probability, statistical inference, confidence intervals, and hypothesis tests with applications in the real world.

  • What is the introductory concept of statistics?

    Statistics is a study of data: describing properties of data (descriptive statistics) and drawing conclusions about a population based on information in a sample (inferential statistics).

  • How do I study for an introduction to statistics?

    Study Tips for the Student of Basic Statistics

    1Use distributive practice rather than massed practice. 2Study in triads or quads of students at least once every week. 3Don't try to memorize formulas (A good instructor will never ask you to do this). 4Work as many and varied problems and exercises as you possibly can.
  • It is like any other academic subject, hard for some easy for others. It also depends in what context you are studying. For example, I used to teach Quantative methods to business students. Quants is what they call statistics so that seeing it in the prospectus doesn't scare them away.
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#printoutvaluesinx [1]"Yes""No""No""Yes""Yes" >factor(x)#printoutvalueinfactor(x) [1]YesNoNoYesYes

Levels:NoYes#noticelevelsareprinted.

Barcharts

3411343313212123231111431

thenweplot(gure1) >beer=scan()

1:3411343313212123231111431

26:

Read25items

>barplot(beer)#thisisn'tcorrect 02

Oops, I want 4 categories, not 25

1234
06 barplot(table(beer)) -- frequencies 1234

0.00.3

barplot(table(beer)/length(beer)) -- proportions

Figure1:Samplebarplots

Noticeafewthings:

Weused

youenterablankrow. simpleR{Using

RforIntroductoryStatistics

UnivariateDatapage10

Thecolorschemeiskindaugly.

barplotwiththerawdata.

Thesecondshowstheuseofthe

Finally,thecommand

>table(beer)/length(beer) 1234

0.400.160.320.12

Piecharts

theusage(similarto barplot(),butwithsomeaddedfeatures. >pie(beer.counts)#firstpie--kindofdull "Microbrew","Import")#givenames >pie(beer.counts)#printsoutnames #nowwithcolors 1 2 3

4Simple

domestic can

Domestic

bottle

Microbrew

ImportWith names

domestic can

Domestic

bottle

Microbrew

ImportNames and colors

Figure2:Piechartexample

nameswhichallowsustospecifynames isdonebysettingthepiechartattribute our using rainbowandgray.

Numericaldata

?pietosee. simpleR{Using

RforIntroductoryStatistics

UnivariateDatapage11

andspread.

Numericmeasuresofcenterandspread

mary.The

Example:CEOsalaries

beingindictedforcookingthebooks.)

12.4525083140.25

>sals=scan()#readinwithscan

1:12.4525083140.25

11:

Read10items

>mean(sals)#theaverage [1]8.565 >var(sals)#thevariance [1]225.5145 >sd(sals)#thestandarddeviation [1]15.01714 >median(sals)#themedian [1]3.5 [1]0.251.003.508.0050.00 >summary(sals)

Min.1stQu.MedianMean3rdQu.Max.

0.2501.2503.5008.5657.25050.000

10,17,18,25,28

point:

10,17,18,25,28,28

numberwhichinthisexampleis17.25.quotesdbs_dbs12.pdfusesText_18
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