course book r intro yes

7/21/2019 Course Book R Intro yes

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R: An Introduction



TMMJ R: An Introduction

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How to Use this User Guide

This handbook accompanies the taught sessions for the course. Each sectioncontains a brief overview of a topic for your reference and then one or moreexercises.

Exercises are arranged as follows:

A title and brief overview of the tasks to be carried out;

A numbered set of tasks, together with a brief description of each;

A numbered set of detailed steps that will achieve each task.

Some exercises, particularly those within the same section, assume that you havecompleted earlier exercises. Your teacher will direct you to the location of filesthat are needed for the exercises. If you have any problems with the text or theexercises, please ask the teacher or one of the demonstrators for help.

This book includes plenty of exercise activities – more than can usually be

completed during the hands-on sessions of the course. You should select some totry during the course, while the teacher and demonstrator(s) are around to guide you. Later, you may attend follow-up sessions at IT Services called Computer8, where you can continue work on the exercises, with some support from ITteachers. Other exercises are for you to try on your own, as a reminder or anextension of the work done during the course.

Text Conventions

A number of conventions are used to help you to be clear about what you need todo in each step of a task.

In general, the word press indicates you need to press a key on thekeyboard. Click , choose or select refer to using the mouse and clickingon items on the screen. If you have more than one mouse button, clickusually refers to the left button unless stated otherwise.

Labels and titles on the screen are shown l ike th is .

Drop-down menu options are indicated by the name of the optionsseparated by a vertical bar, for example i le |Pr int . In this example youneed to select the option Print from the i le menu or tab. To do this, click when the mouse pointer is on the i le menu or tab name; move thepointer to Print; when Print is highlighted, click the mouse button again.

A button to be clicked will lookl ike th is

.

The names of software packages are identified like this, and the names offiles to be used l ike th is .

Boxes with the broken borders have examples contained within.

Boxes with double borders have cautionary exposition within.

Software Used

R 2.14.0 or later versions

Files Usedtext_sample.Rd, age_weight.txt, district.txt, expenditure.txt, expenditure.csv



R: An Introduction TMMJ

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The other datasets used have been preloaded in the R package ‘datasets’. To list all thedatasets available, use the command

> data()

This will bring up a window listing the datasets and providing a short description of each. Toobtain a more detailed description, use the command help(). For example, the line below

brings up a html file describing the ‘Biochemical Oxygen Demand’ experiment in greaterdetail.

> help(“BOD”)

Revision Information

Version Date Author Changes made

2.0 Jan 2013 Esther Ng Created

Copyright

Esther Ng makes this document available under a Creative Commons licence: Attribution,Non-Commercial, No Derivatives. Individual resources are subject to their own licencingconditions as listed below.

Acknowledgements

David Baker, Denise Cattell and Kathryn Wenczek for their help in organising the course andputting the course notes together




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Contents

1 Introduction ............................................................................. 7

1.1. What you should already know .......................................................... 7

1.2. What will you learn?........................................................................... 7

2 Getting Started ......................................................................... 8

2.1. What is R? .......................................................................................... 8

2.1.1. Advantages ............................................................................................ 8

2.1.2. Disadvantages ...................................................................................... 8

2.2. Download and Installation ................................................................ 8

2.3. R and other tools/languages .............................................................. 8

2.3.1. Matlab ................................................................................................... 8

2.3.2. SPSS/SAS ............................................................................................. 8

2.3.3. C++....................................................................................................... 8

2.4. R on different platforms .................................................................... 9

2.5. Commands ......................................................................................... 9

2.6. Getting Help ....................................................................................... 9

Exercise 1 Getting Started ....................................................... 12

3 Basic Data Structures ............................................................. 13

3.1. Vectors ............................................................................................... 13

3.1.1. Creating numerical vectors .................................................................. 13

3.1.2. Accessing elements of numerical vectors ............................................14

3.1.3. Arithmetic operations on numerical vectors ....................................... 15

3.1.4. Useful vector commands ..................................................................... 15

3.2. Lists ...................................................................................................16

3.3. Matrices.............................................................................................16

3.3.1. Creating matrices ................................................................................16

3.3.2. Accessing elements of a matrix .......................................................... 18

3.3.3. Useful matrix commands ....................................................................19

3.4. Data frames ....................................................................................... 21

3.5. Factors ............................................................................................... 21

Exercise 2 Vectors and Matrices ............................................. 22

4 Reading and Writing data ...................................................... 24

4.1. Reading Text Files ............................................................................ 24

4.2. Reading built-in data ....................................................................... 24




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4.3. Editing Data in Spreadsheet style ................................................... 24

4.4. Writing out data ............................................................................... 25

Exercise 3 Reading and Writing Files ..................................... 25

5 Scripts, Objects and the Workspace ....................................... 27

5.1. Objects and the Workspace .............................................................. 27

5.2. Directories ........................................................................................ 28

5.3. Running scripts ................................................................................ 28

Exercise 4 Scripts, Objects and Workspaces .......................... 29

6 Control Statements and Loops .............................................. 31

6.1. If/Else and Ifelse ............................................................................... 31

6.2. Loops ................................................................................................. 31

Exercise 5 Loops and If/Else statements ................................ 33

7 Working with text in R ........................................................... 34

7.1. Characters and Strings ..................................................................... 34

7.2. Useful commands ............................................................................ 35

7.2.1. Count number of characters in the string .......................................... 35

7.2.2. Split the string .................................................................................... 35

7.2.3. Search text strings for a word ............................................................ 36

Exercise 6

Text Manipulations in R ........................................ 36

8 Graphs and Charts ................................................................. 37

8.1. High level plotting commands ......................................................... 37

8.1.1. Generic plot() command ..................................................................... 37

8.1.2. Boxplot ............................................................................................... 38

8.1.3. Histogram ........................................................................................... 38

8.1.4. Options ............................................................................................... 39

8.2. Low Level Plotting Functions .......................................................... 42

Exercise 7

Plotting functions in R ........................................... 43

9 Statistics with R ..................................................................... 45

9.1. Measures of Central Tendency and Spread ..................................... 45

9.2. Tests for continuous vs discrete variables ....................................... 45

9.2.1. 2 groups .............................................................................................. 45

9.2.2. 3 or more groups ................................................................................ 45

9.3. Tests for discrete vs discrete variables ............................................ 48

9.3.1. Chi Square Test .................................................................................. 48

9.3.2. Fisher’s Exact Test ............................................................................. 48




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9.4. Tests for continuous vs continuous variables ................................. 49

9.4.1. Pearson Correlation ........................................................................... 49

9.4.2. Spearman Correlation ........................................................................ 49

9.5. Regression ......................................................................................... 51

9.6. Probability Distributions ................................................................. 52

9.7. Other Statistical Features ................................................................ 52

9.8. Packages ........................................................................................... 53

Exercise 8 Statistics in R ......................................................... 53

10 Writing your own functions ................................................. 54

11 References ............................................................................. 55




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1 Introduction Welcome to Introduction to R!

This booklet accompanies the course delivered by Oxford University IT services,IT Learning Programme. Although the exercises are clearly explained so that youcan work through them independently, you will find that it will help if you alsoattend the taught session where you can get advice from the teacher,demonstrator(s) and even each other!

If at any time you are not clear about any aspect of the course, please make sure you ask your teacher or demonstrator for some help. If you are away from theclass, you can get help by email from your teacher or from [email protected].

1.1. What you should already know

While basic knowledge of programming would be helpful, it is not essential.Knowledge of statistics would be helpful in understanding the later chapters.

1.2. What will you learn?

This course will teach basic R programming for data analysis and presentation. While it provides a framework of tools, please remember that data is highlyindividualised from study to study, hence methods which seem applicable to onestudy are not necessarily generalizable to another study. R has an active networkof users who are constantly developing packages for various disciplines. Thesepackages are open-source and can be freely downloaded from

http://cran.r-project.org/







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2 Getting Started

2.1. What is R?

R is a collection of software tools for data manipulation, analysis andpresentation. It is an implementation of the S language. There are severaladvantages and disadvantages

2.1.1. Advantages

Extensive collection of statistical functions and operators for matrix calculations

Effective data handling and storage

Simple syntax

Good graphical facilities for data display

2.1.2.

DisadvantagesSteeper learning curve compared to SPSS or SAS for users with no background inprogramming

Slow performance compared to languages like C/C++

Larger room for error as R tends to make assumptions rather than produce errormessages when commands are unclear

2.2. Download and Installation

Detailed instructions can be found at http://cran.r-project.org/ for Windows,Unix and Mac. For certain packages, previous versions for R may be needed due

to various dependencies. These previously versions can also be downloaded fromthe website mentioned above.

2.3. R and other tools/languages

2.3.1. Matlab

For those with a background in engineering and a knowledge of Matlab, this documentfacilitates the translation of Matlab syntax into R syntax as there are functions which are verysimilar in both environments http://cran.r-project.org/doc/contrib/Hiebeler-matlabR.pdf

2.3.2. SPSS/SAS

For those who have mainly used SPSS/SAS for their statistical needs, R may seem confusingat first due to the command line interface. However, this documenthttp://www.et.bs.ehu.es/~etptupaf/pub/R/RforSAS&SPSSusers.pdf provides moreinformation to smoothen the transition between the different environments

2.3.3. C++

C++ code is often used to speed up calculations in R. The 2 languages can be interfaced moreeasily using this package. http://cran.r-project.org/web/packages/Rcpp/vignettes/Rcpp-introduction.pdf




http://cran.r-project.org/doc/contrib/Hiebeler-matlabR.pdf



http://www.et.bs.ehu.es/~etptupaf/pub/R/RforSAS&SPSSusers.pdf


http://cran.r-project.org/web/packages/Rcpp/vignettes/Rcpp-introduction.pdf












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2.4. R on different platforms

Most functions in R are common to all platforms. On a unix platform, the graphical devicemay need to be setup with a command such as

$ sys.putenv(“DISPLAY”=”:0.0”)

This may not work on all machines, and other settings may need to be adjusted.

When executing a script file from the command line in unix, the following can be used

$ R CMD BATCH my_script_file.R

Other details on differences between platforms can be found on http://www.r-project.org/user-2006/Slides/IacusEtAl.pdf

2.5. Commands

In R, the command prompt is ‘>’. If you see ‘+’ instead of ‘>’, it means that the command isincomplete. For example, if there are unpaired brackets or inverted commas, ‘+’ will be seeninstead of ‘>’. Commands can either run by typing them directly into the console or by typingthem into the R editor then highlighting, right-clicking and selecting the option ‘runselection’.

The output of a command can either be immediately printed to the screen or it can be storedin a variable.

For example, the output of a command ‘mean’ can either be immediately printed to thescreen (in which case it is not stored) or it can be stored in a variable (in this case the variablenamed ‘answer’) and later accessed by typing the variable name at the command prompt.

> mean(5,6,7)

[1] 5

> mean(5,6,7)->answer

> answer

[1] 5

In R, the output of a command can be assigned to a variable with ‘->’ or ‘=’. Direction ofassignment does not matter, hence ‘a<-5’ is equivalent to ‘5->a’, both assign the value of 5 tothe variable ‘a’.

Of note, all alphanumeric symbols are allowed in variable names, in addition to ‘.’ And ‘_’.However, variable names cannot start with a number eg. ‘a2’ is allowed but not ‘2a’

Commands can be separated by a new line or by a semi-colon(;). They can be commented out

with a hashmark(#).R has a command history function, in which previously issued commands can be recalled with the 2 vertical keys.

2.6. Getting Help

To get help on any specific function, use the command ‘help’ or ‘?’. For example, to search for help on the command ‘sum’, at the command line, type

> help(sum) or

> ?sumThis will bring up the help page http://127.0.0.1:26807/library/base/html/sum.html

http://www.r-project.org/user-2006/Slides/IacusEtAl.pdf




http://127.0.0.1:26807/library/base/html/sum.html









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This page contains several sections

sum {base} R Documentation

Sum of Vector Elements

Description

sum returns the sum of all the values present in its arguments.

Usagesum(..., na.rm = FALSE)

Arguments... numeric or complex or logical vectors.

na.rm logical. Should missing values (including NaN) be removed?

Details

This is a generic function: methods can be defined for it directly or viathe Summary group generic. For this to work properly, the arguments ... should beunnamed, and dispatch is on the first argument.

If na.rm is FALSE an NA or NaN value in any of the arguments will cause a valueof NA or NaN to be returned, otherwise NA and NaN values are ignored.

Logical true values are regarded as one, false values as zero. For historical

reasons, NULL is accepted and treated as if it were integer(0).

Value

The sum. If all of ... are of type integer or logical, then the sum is integer, and in

that case the result will be NA (with a warning) if integer overflow occurs.Otherwise it is a length-one numeric or complex vector.

NB: the sum of an empty set is zero, by definition.

This refers to the packagefrom which the function

comes

This shows how the function is used, together with the default

settings. In this case, NAs are not removed by default. Ifremoval is wished, use ‘na.rm=TRUE’

This refers to input

arguments of the function

This refers to output of the function

This provides further details on the function, including

appropriate usage and meaning of default settings

This refers to the class of the function. This information is

not usually needed by the general user.

http://127.0.0.1:26807/library/base/help/S3groupGeneric







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S4 methods

This is part of the S4 Summary group generic. Methods for it must use the

signature x, ..., na.rm.

‘ plotmath’ for the use of sum in plot annotation.

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language.Wadsworth & Brooks/Cole.

See Also

colSums for row and column sums.

[Package base version 2.14.2 Index]

This section contains related functions and isoften useful to explore as there may be

combined functions that save you writing code

This section references, and is especially useful for recently

developed statistical tools




http://127.0.0.1:26807/library/base/help/plotmath



http://127.0.0.1:26807/library/base/help/colSums


http://127.0.0.1:26807/library/base/html/00Index.html










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Exercise 1 Getting Started

In this exercise, we will explore the graphical user interface in R and the help functions

Task 1

Open the R console;

Learn how to use thehelp facility

Step 1

Open R. Click on theStart

button on the Task Bar then click on R.

This will bring up the R console.

Step 2 At the console, type

> help.start()

This will bring up a html page from the official CRAN website

http://127.0.0.1:31317/doc/html/index.html

Navigate to the link ‘An Introduction to R’. This link contains animmense amount of helpful information, inaddition to a SampleSession in Appendix A which should be worked through when youhave the time.

Step 3

We will be using the save() command later. In the R console, type>?save()

to bring up the html page on save(). What are the differences betweenthe save.image() and save() commands?







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3 Basic Data Structures

3.1. Vectors

3.1.1.

Creating numerical vectors

The simplest data structure in R is the numerical vector. This can be created with the c()command or with the assign command. The statements below are equivalent.

> x <- c(5,4,3,2,1)

> assign("x", c(5,4,3,2,1))

Sequences or repeats of numbers can be generated in R. To generate a sequence ofconsecutive numbers, either the colon operator or the function seq() can be used. If thesequence has steps of greater than 1, the seq() command can be used with a third argument.

> a<-c(1:10) ## this produces a sequence of 1 to 10 in steps of 1

> a

[1] 1 2 3 4 5 6 7 8 9 10

> a<-seq(1,10) ## this achieves the same effect as the command above

> a

[1] 1 2 3 4 5 6 7 8 9 10

> b<-seq(1,10,2) ## this produces a sequence of 1 to 10 in steps of 2

> b

[1] 1 3 5 7 9

> d<-rep(1,10) ## this produces a vector of 10 ‘ones’

> d

[1] 1 1 1 1 1 1 1 1 1 1

Vectors or parts of vectors can be concatenated together, with the c() command

> c(y,y,5)->y2

> y2

[1] 5 4 3 2 1 5 4 3 2 1 5

An empty vector can also be created and populated with numbers. This is useful when writingloops in which the result of repeated calculations are used to populate a vector.

> my_vector <- vector() ## creates empty vector

> my_vector[1] <- 42 ## inserts the value of 42 into the first slot of thevector

> my_vector[2] <- 43 ## inserts the value of 43 into the second slot of thevector

> length(my_vector) ## checks the length of the vector

[1] 2




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3.1.2. Accessing elements of numerical vectors

To access each element of the vector, square brackets are used. To access a few elements ofthe vector, a colon can be used.

> y <- x[5] ## this assigns the value of 1 to y since the fifth element ofx is 1

> z <- x[1:3] ## this creates a new vector z with 3 numbers – 5,4,3

Index vectors can be created to select specific elements within a vector. There are differenttypes of index vectors.

a) Logical index vectors

A logical index vector is comprised of a series of ‘TRUE’ and ‘FALSE’ elements.

> a<-seq(1,10) ## produces sequence of numbers from 1 to 10

> a<7 -> b ## creates a logical vector based on the conditions provided

> b[1] TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE

> a[b]

> [1] 1 2 3 4 5 6

> a[a<7] ## combines the above steps

[1] 1 2 3 4 5 6

b) Vector of positive integers

In this case, the values in the index vector must be smaller than the length of the vector being

indexed. The elements that correspond to the elements of the index vector are concatenatedinto a new vector

> primary.vector <- seq(1,10,2)

> index.vector <- c(1,3,5)

> primary.vector

[1] 1 3 5 7 9

> primary.vector[index.vector]

[1] 1 5 9

c) Vector of negative integers

This specifies the values to be excluded.

> index.vector <- c(-1,-3,-5)

> primary.vector[index.vector]

[1] 3 7




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3.1.3. Arithmetic operations on numerical vectors

Arithmetic operations can be performed on vectors. These are performed on each number within the vector. In the example below, 1 is subtracted from each number within the vector y2.

> y2-1

[1] 4 3 2 1 0 4 3 2 1 0 4

Caution: When shorter vectors are used in the expression, they are recycled. In the example below, the numbers in y are added individually to the numbers in y2, with the first number of y added to the first number of y2, the second number of y added to the second number of y2etc, until the fifth number of y is reached. After that, the first number of y is added to thesixth number of y2. While other environments may generate a warning message when vectors

of different lengths are added together, R will not generate such warnings. As such, users aremore prone to errors since it is more likely that one has wrongly tried to added 2 vectors ofdifferent lengths rather than wanting one vector to be fractionally recycled to be added toanother vector.

The use of the term ‘vector’ and later ‘matrix’ in this context does not pertain to linearalgebra. The vector operations performed with the commands detailed above are strictly forelement-wise operations. Linear algebra commands are different. For example, the symbolfor matrix multiplication is %*%. While linear algebra is beyond the scope of this course, anexcellent guide to Linear Algebra in R can be found in the link below.

http://bendixcarstensen.com/APC/linalg-notes-BxC.pdf

3.1.4. Useful vector commands

The length() command will find the length of the vector

> length(y2)

> [1] 11

The max() command will find the largest element of the vector

> max(y2)

> [1] 5

The min() command will find the smallest element of the vector

> min(y2)

> [1] 1

The sum() command will find the sum of all elements in the vector

> sum(y2)

> [1] 35

The mean() command will find the average of all elements in the vector

> mean(y2)

[1] 3

The sd() command will find the standard deviation of all elements in the vector

> sd(y2)







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[1] 1.490712

The sort() command returns vector sorted in numerical order

> sort(y2)

[1] 1 1 2 2 3 3 4 4 5 5 5

3.2.

Lists

A list is an ordered collection of objects known as components. Lists are like vectors exceptfor a few differences…

a) Different types of objects can be concatenated into lists eg. a list can consist of anumeric vector, a matrix and a character string. The components of a vector all haveto be of the same type eg. all numbers, all characters etc.

b) The components of a list are accessed by double square brackets ([[ ]]) whereas thecomponents of a vector are accessed with single square brackets ([ ])

c) Linear algebra can be performed on vectors of numbers but not lists of numbers

d)

Lists are recursive, meaning that one can create a list of lists of lists. This is notpossible with vectors.

e) Components of lists can be accessed by name through the $ operator. This is notpossible with a vector

> list() -> my_list ## creates an empty list

> 42 -> my_list[[1]] ## populates the list with numbers

> 43 -> my_list[[2]]

> names(my_list) <- c("first_entry","second_entry") ## assigns names to the

list components> my_list$first_entry ## accesses components of the list using the name

[1] 42

Caution: When to use lists and when to use vectors?

When performing mathematical or statistical calculations, it is easier to use vectors becauseone will be sure that all components of the vector will be of the numerical type and one canperform linear algebra with them. Lists are useful when manipulating data that includesdifferent types of information eg. databases of names, addresses, ages etc.

3.3. Matrices

An array is a subscripted collection of data elements. A matrix is a 2 dimensional array. Sincematrices are the most commonly used form of array, we will describe matrices in detail.

3.3.1. Creating matrices

Arrays and matrices can be created with the array and matrix commands respectively. Note

that the if byrow=TRUE for the matrix() function, the data will be entered by row, if byrow=FALSE, it will be entered by column, like the array() function.




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> my_matrix <- matrix(c(1,2,3, 7,8,9), nrow = 2, ncol=3, byrow=TRUE)

> my_matrix

[,1] [,2] [,3]

[1,] 1 2 3

[2,] 7 8 9> my_array <- array(c(1,7,2,8,3,9), c(2,3))

>my_array

[,1] [,2] [,3]

[1,] 1 2 3

[2,] 7 8 9

An empty matrix can be created and populated with data

> my_matrix <- matrix(nrow=3,ncol=3)

> my_matrix[2,2] <- 42

> my_matrix

[,1] [,2] [,3]

[1,] NA NA NA

[2,] NA 42 NA

[3,] NA NA NA

R inserts NA for any unpopulated elements in a matrix or vector

A matrix can also be created by binding vectors or matrices together using the cbind() orrbind() functions which binds vectors in terms of columns and rows respectively.

> rbind(my_matrix,my_matrix) ->combined_matrix

> combined_matrix

[,1] [,2] [,3]

[1,] 1 2 3

[2,] 7 8 9

[3,] 1 2 3

[4,] 7 8 9

Names can be assigned to the rows and columns of a matrix with the commands rownames()and colnames().

> rbind(my_matrix,my_matrix) ->combined_matrix

> rownames(combined_matrix) <-c("basket_1","basket_2","basket_3","basket_4")

> colnames(combined_matrix) <-c("number_of_apples","number_of_oranges","number_of_pears")




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> combined_matrix

number_of_apples number_of_oranges number_of_pears

basket_1 1 2 3

basket_2 7 8 9

basket_3 1 2 3 basket_4 7 8 9

3.3.2. Accessing elements of a matrix

The elements of a matrix can be accessed with 2 numbers separated in a square bracketseparated by a comma, with the first number being the row and the second number being thecolumn.

> combined_matrix[2,1]

[1] 7

Similar, several entries can be accessed at once with a colon, in the same way as a vector

> combined_matrix[2,1:3]

[1] 7 8 9

Elements can be accessed conditionally too.

For example, if one wanted to replace all numbers smaller than 3 with 0, this can be done

> combined_matrix[combined_matrix<3] <-0

> combined_matrix

[,1] [,2] [,3]

[1,] 0 0 3

[2,] 7 8 9

[3,] 0 0 3

[4,] 7 8 9

R does this by creating an index matrix of TRUE and FALSE depending on the conditionimposed.

> combined_matrix<3

[,1] [,2] [,3]

[1,] TRUE TRUE FALSE

[2,] FALSE FALSE FALSE

[3,] TRUE TRUE FALSE

[4,] FALSE FALSE FALSE

This can also be performed on selected rows or columns. The example below uses the original

object ‘combined_matrix’ and replaces numbers less than 3 with 0 only in the first row.




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> combined_matrix[1,which(combined_matrix[1,]<3)] <-0

> combined_matrix

[,1] [,2] [,3]

[1,] 0 0 3

[2,] 7 8 9[3,] 1 2 3

[4,] 7 8 9

In this way, matrix elements can be accessed or modified according to conditions in othermatrices. For example, if one had a matrix of gene expression values as well as a separatematrix of ‘YES’ and ‘NO’ to indicate whether a particular measurement is valid or not, onecould insert a number representing an invalid measurement eg. ‘-999’ into the matrix of geneexpression values depending on whether the corresponding word was ‘YES’ or ‘NO’ in the validity matrix.

An example is given below

> validity_matrix

[,1] [,2] [,3]

[1,] "YES" "YES" "NO"

[2,] "NO" "YES" "YES"

> measurement_matrix

[,1] [,2] [,3]

[1,] 4 4 3

[2,] 6 6 7

> measurement_matrix[validity_matrix=="NO"] <- -999 ## this inserts the value ‘-999’ intothe measurement matrix to represent entries that correspond to ‘NO’ in the validity matrix.Note that the conditional operator for equals to is ‘==’, like in most other environments.

> measurement_matrix

[,1] [,2] [,3]

[1,] 4 4 -999

[2,] -999 6 7

3.3.3. Useful matrix commands

The dim() command outputs the dimensions of the matrix, just as the ‘length’ commandoutputs the length of the matrix.

> dim(measurement_matrix)

[1] 2 3

The order() command returns an index of the numerical order. This is especially useful as thematrix can be sorted in ascending or descending or of a particular column (or row). Forexample, if one took example of fruits in a basket in section 3.3.1, one could order the basketsin terms of the number of oranges in them




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> combined_matrix


basket_1 1 2 3

basket_2 7 8 9

basket_3 1 2 3 basket_4 7 8 9

> combined_matrix[order(combined_matrix[,2]),]->combined_matrix_orange_ordered

> combined_matrix_orange_ordered


basket_1 1 2 3

basket_3 1 2 3

basket_2 7 8 9

basket_4 7 8 9

The functions rowMeans, colMeans, colSums and rowSums are usefully in finding theaverage of rows/columns and the sums of rows/columns respectively

> colMeans(combined_matrix_orange_ordered)


4 5 6

> rowMeans(combined_matrix_orange_ordered)

basket_1 basket_3 basket_2 basket_4

2 2 8 8

> colSums(combined_matrix_orange_ordered)


16 20 24

> rowSums(combined_matrix_orange_ordered)


6 6 24 24

The function t() is useful in transposing the matrix so that the rows become columns and thecolumns become rows.

> t(combined_matrix_orange_ordered) ->combined_matrix_orange_ordered_transposed

> combined_matrix_orange_ordered_transposed


number_of_apples 1 1 7 7

number_of_oranges 2 2 8 8number_of_pears 3 3 9 9




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Caution: All components of a matrix have to be of the same type. If a character is insertedinto a matrix of numbers, all components of the matrix will be coerced into a character type.

The type of object can be checked with the following commands – is.numeric, is.character,is.matrix, is.list, is.vector.

> is.numeric(combined_matrix_orange_ordered[1,3]) ## this checks the typeof element in the matrix at index [1,3]

[1] TRUE

> combined_matrix_orange_ordered[1,1] <- "unknown" ## this inserts thecharacter string into the matrix at index[1,1], hence coercing all otherelements of the index into character type

> combined_matrix_orange_ordered


basket_1 "unknown" "2" "3"

basket_3 "1" "2" "3" basket_2 "7" "8" "9"

basket_4 "7" "8" "9"

> is.numeric(combined_matrix_orange_ordered[1,3]) ## this demonstrates thatthe elements in the matrix are now no longer numeric type, but arecharacter type

[1] FALSE

> is.character(combined_matrix_orange_ordered[1,3])

[1] TRUE

The command typeof() can be used to find the type an object is. However, it may not give fullinformation eg. in the case of a character matrix, it will just report ‘character’.

3.4. Data frames

A data frame is like a matrix that may contain elements of different types.

Data frames can be constructed with the function data.frame(). Alternatively, a list can becoerced into a data frame using the function as.data.frame()

Data can be read into R to form a data frame using the read.table() function (discussed later).

When dealing with data frames (unlike matrices), the attach() and detach() functions allowfor a database to be loaded into R as a copy and modified temporarily without changing theoriginal database.

3.5. Factors

A factor is a vector object used to specify grouping of the components of other vectors. Anexample is given below

> c("chocolate","vanilla","chocolate","strawberry","vanilla","vanilla","chocolate") -> flavours

> factor(flavours) -> fflavours

> fflavours




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[1] chocolate vanilla chocolate strawberry vanilla vanillachocolate

Levels: chocolate strawberry vanilla

Factors can also be constructed from a vector of numbers eg.

> y<-c(3,3,5,6,6) ## creates a vector of numbers

> y

[1] 3 3 5 6 6

> as.factor(y) -> y.f ## converts these numbers to factors

> y.f

[1] 3 3 5 6 6

Levels: 3 5 6

Caution: as.numeric will convert factors in a different way compared to characters. This issomething that one has to beware of because data is sometimes read in terms of factors andother times in terms of characters (depending on the settings). Applying ‘as.numeric’ to astring of factors believed to be characters will provide an unexpected result. The exampleshown below is based on the vector ‘y.f’ created above.

> as.numeric(y.f) ## converts these factors back to numbers (a different set of numbers willresult)

[1] 1 1 2 3 3

> as.numeric(as.character(y.f)) ## converts these factors back to numbers (original set ofnumbers will result)

[1] 3 3 5 6 6

Exercise 2 Vectors and Matrices

In this exercise, we will explore vector and matrix manipulations in R

Task 1

Explore the properties ofa vector

Step 1

The ‘WWWusage’ dataset provides a time series of the number of usersconnected to the internet through a server each minute. Find out howmany entries there are in this vector with the command ________________

Step 2

Find the average of all the entries with the command

________________

Step 3

Extract the 40th to 60th entry in the vector and find that median ofthose 21 entries with the command

________________




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Task 2

Explore the properties ofa matrix

Step 1

The WorldPhones dataset describes the number of telephones in eachregion of the world (in the thousands). Find the dimensions of thedataset with the command

________________

Step 2

Find the difference between the number of phones in the two regions with the highest and lowest number of phones respectively in 1957

________________

Step 3

In which year did Africa have 1411 thousand phones?

________________

Step 4

Which area had 45939 thousand phones in 1951?

________________

Step 5

Find the total number of phones in all areas in 1959

_________________




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4 Reading and Writing data

4.1. Reading Text Files

Text files can be read into R with the read.table() command. There are several options thatcan be supplied with this command

a) skip – this refers to the number of lines in the file that should be skipped before theactual data is input (default is zero)

b) header – this refers to whether the first line should be read in as column names (R will count the number of entries in the first and second row, setting this to true ifthere are 1 fewer entries in the first row than the subsequent rows)

c) fill – this refers to whether rows which have fewer entries than others are filled with blank fields (if this is not explicitly stated and there are rows with fewer fields thanothers, R will produce a warning message)

d)

na.strings – this refers to the character string that symbolises ‘not applicable’. Thedefault setting is “NA”.

e) sep – this is the field separator. The default setting is whitespace ie. “ “

The file is read into R and a dataframe is created. This can be converted to a matrix with theas.matrix() command. This is useful when mathematical operations are performed on thedata.

When reading tab delimited text files rather than white-space delimited text files, thecommand read.delim() can be used. In read.delim(), the default setting for sep is “\t”. Whenreading a file with comma-separated values, the command read.csv() can be used.

Caution: It is always a good idea to check whether your file has been read in correctly using

command such as thesehead(x,n=yL) – prints first y lines of x

head(x,n=yL) – prints last y lines of x

summary(x) – this provides further information about the objects depending on its class. Inthe case of a numerical matrix, it supplies information on the measures of central tendencyand spread

4.2. Reading built-in data

There are several datasets automatically supplied with R, for testing purposes. These datasetscan be accessed with the command ‘data().’ The specific dataset can be loaded into R as

follows… > data(AirPassengers)

This creates an object called AirPassengers containing the built-in data.

Some R packages also contain built in data. This can be viewed using thedata(package=”package_name”) command. The data can then be loaded in using thedata(dataset_name, package=”package_name”) command.

4.3. Editing Data in Spreadsheet style

Data can be edited in a spreadsheet-like environment with the command

>edit(data_old) -> data_new




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In this way, the final object is assigned to data_new. If the objective is to alter the originaldataset, the command fix(data_old), which is equivalent to

>edit(data_old) -> data_old

4.4. Writing out data

Data can be written out into a text file using the write.table() command. Like the read.table()command, there are several options that can be used.

Append – if true, the output is appended to the file of the same name. If false, the existing fileis destroyed and replaced by the new file (default is false)

Quote – This determines whether characters are surrounded by double quotes (default istrue)

Sep – This determines what the field separator string is (default is whitespace “”)

Eol – This determines the character to be printed at the end of each line (default is “\n”)

Row.names – this determines whether the row names of x are to be written out

Col.names = this determine s whether the column names are to be written out

Write.csv() can be used to create a comma-separated-value file that is readable by MicrosoftExcel.

Exercise 3 Reading and Writing Files

In this exercise, we will explore reading and writing data into R

Task 1

Reading data

Step 1

The text file ‘expenditure.txt’ contains the personal expenditure of UScitizens in the 1940s to 1960s.

Open the file in Microsoft notepad to check the format, in particular whether it has a header row.

Step 2

In R, read the file into an object called ‘x’ with the command

_______________

Step 3

In R, find the standard deviation of Health and Medical Expenditurethrough all the years represented in the data with the command

________________

Step 4

Open the csv file ‘expenditure.csv’ in Microsoft Excel. Read it into R with the read.csv() command. Check that the resulting object is similarto the object read in from the text file.

Task 2

Writing data

Step 1

The Puromycin data frame has 23 rows and 3 columns of the reaction velocity versus substrate concentration in an enzymatic reactioninvolving untreated cells or cells treated with Puromycin. There are 3columns – substrate concentration, rate and state (treated vsuntreated). Explore the structure of this dataset with the head() andsummary() commands




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Step 2

Create a matrix with the rows of the puromycin dataframe that have‘treated’ in the third column with the following command.

________________

Step 3

Write out this matrix into a text file with the following command

________________

Open this text file in Microsoft Notepad and check that it contains what you expected.

Step 4

Create a matrix with the rows of the puromycin dataframe that have arate of greater than 100 counts/min/min with the following command

________________

Step 5

Write out this matrix into a csv file with the following command

________________

Open this csv file in Microsoft Excel and check that it contains what you expected.




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5 Scripts, Objects and the Workspace

5.1. Objects and the Workspace

The basic unit that is manipulated in R is an object. An object can be a variable, a function, orgeneral structure built from different components. In an R session, objects are created andstored. They can be accessed with the ls() command.

To remove an object, the command rm() can be used. To clear the workspace of all objects,the command rm(list=ls()) can be used.

The objects used in a session (and the command history) can be stored in a file with thecommand save.image(). The objects can be reloaded to the workspace with the commandload(). If one wishes to save specific objects, this can be performed with the save() commandand a list of objects as the argument.

An example is given below.

> a<-1> b<-2> c<-3> d<-4> ls()[1] "a" "b" "c" "d" ## this lists the objects in the current workspace > save.image("my_workspace.RData") ## this saves all the objects in thecurrent workspace> rm(list=ls()) ## this clears the workspace of all objects > ls() ## this lists the objects in the workspace (none at present) character(0)

> load("my_workspace.RData") ## this loads up the stored workspace file > ls() ## the objects stored within the workspace file are loaded into thecurrent workspace[1] "a" "b" "c" "d"> rm(d) ## this removes the object ‘d’ > ls()[1] "a" "b" "c"> save("a","b",file="my_objects.Rd") ## this selectively stores 2 objects – a and b> rm(list=ls())> load("my_objects.Rd") ## this loads up the 2 objects stored in the Rdfile> ls()

[1] "a" "b"

The R workspace has memory limits (dependent on the machine it is run on), which meansthat extremely large datasets may have to be analysed in chunks. The commandmemory.size() provides the total amount of memory used by R while the commandmemory.limit() provides the memory limit for the workspace. The memory limit can bealtered by providing the command memory.limit () with an argument eg.

> memory.size() ## this reports the memory currently used

[1] 14.81> memory.limit() ## this reports the memory limit of the workspace




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[1] 3583

> memory.limit(3600) ## this changes the limit to the value of the argumentsupplied

[1] 3600

> memory.limit() ## this reports the new memory limit

[1] 3600

To end the session, the command q() is used. At this point, you will be prompted with aquestion ‘Save Workspace Image?’ If you click on yes, all objects in the workspace are writtento a file called ‘.RData’ and the command lines are written to a file called ‘.Rhistory’. When Ris started from the same directory, both files are automatically loaded.

Caution: It is a good idea to store your workspaces separately according to project rather than‘.Rhistory’ or ‘.Rdata’ since variables with common names eg. ‘x’ or ‘foo’ may take on different

values for different projects, leading to mistaken identities. When saving a script file, the ‘.R’extension has to be added explicitly as R will not add it for you, unlike the addition of ‘.doc’ by Microsoft word or ‘.xls’ by Microsoft Excel.

5.2. Directories

When loading workspace files or script files, R has to be started within the directory that thefiles are stored. To check which directory R is in, one can use the command getwd(). Tochange directory within R, one can use the command setwd().

If one does not wish to change directory, an alternative is to use the full path to the file whenloading it into R.


> getwd() ## this prints the current directory that R is in

[1] "C:/Me/u0302066/Documents"

> setwd("C:/You/u0302066/Documents") ## this changes the directory

> getwd()

[1] "C:/You/u0302066/Documents"

> load(“C:/Me/u0302066/Documents/my_workspace.RData”) ## this loads a workspace located in a different directory by stating the full path to the workspace

> ls()[1] "a" "b" "c" "d"

5.3. Running scripts

So far, we have been running commands by typing them into the R editor and clicking on ‘runselection’ or by typing them directly in the console. Commands typed into the R editor canalso be stored in a file, with the extension ‘.R’ and run at the console with the command‘source’. For example

> source(“my_commands.R”)




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will run all commands in the file ‘my_commands.R’

The function ‘sink’ can be used to divert all output from the console into a file. For example,

> sink(“my_record.lis”)

will divert all subsequent output to an external file ‘my_record.lis’ and the command sink()

will restore it to the console again.

Exercise 4 Scripts, Objects and Workspaces

In this exercise, we will explore scripts, objects and workspaces in R

Task 1

Writing and executingscripts

Step 1

Click on File|New script. This opens up a box titled ‘Untitled – Reditor’.

Step 2

Type into the box

rm(list=ls())

a<-1

b<-2

ls()

Step 3

Execute the command by highlighting it then right click | run line orselection. What output do you get? ___________________

Step 4

In the R editor, type in a command that creates a new variable‘sum_of_a_and_b’ by adding a and b together ____________________

Step 5

Remove all objects in the workspace with the command _____________________

Step 6

Save the script file as ‘my_script_file.R’ by doing File|Save as. Makesure that your cursor is in the R editor and not in the R console when you do this.

Step 7Execute the script file by typing source(“my_script_file.R”) in the Rconsole

Task 2

Saving and loading objects

Step 1

Create a 2 new variables – ‘difference_of_a_and_b’,’product_of_a_and_b’.

Step 2

Save these 2 objects in a file called ‘my_objects.Rd’ with the followingcommand ________________

Step 3

Quit R without saving the workspace.




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Step 4

Open a new session of R and load these 2 objects into the workspace with the following command ___________________




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6 Control Statements and Loops

6.1. If/Else and Ifelse

The if/else syntax is as follows

> if (condition) expr_1 else expr_2


> y<-1

> if(y>2) x<-3 else x <-4

> x

[1] 4

The conditional expression often contains the ‘and’ or ‘or’ operators, which are represented by ‘&&’ and ‘||’ (or ‘&’ and ‘|’ described later). Here is an example of how to use them.

> z<-1

> y<-1

> if(y<2&&z<2) x<-3 else x <-4

> x

[1] 3

The above statement can also be written in the ifelse syntax as follows

> ifelse(y<2&&z<2,3,4)->x

> x

[1] 3

Caution: The ‘and’ and ‘or’ operators can take 2 forms. ‘ And’ can be represented by ‘&’ or

‘&&’. ‘Or’ can be represented by ‘|’ or ‘||’. The ‘short circuit’ form of the operators are ‘&&’ and‘||’ respectively. These only evaluate the second argument if necessary, unlike ‘&’ and ‘|’, which evaluate both arguments. Additionally, if the arguments are vectors, ‘&’ and ‘|’ returnsa vector of ‘TRUE’ and ‘FALSE’ while ‘&&’ and ‘||’ return a single output based on the firstelement of the vector (in addition to a warning). With that in mind, how should we decide which to use? For most conditional testing, the arguments are single elements rather than vectors, hence && can be used safely. The warning would come in useful in case you haveunintentionally included a vector as an argument.

6.2. Loops

This can be achieved with ‘for’ or ‘while’.




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The syntax is as follows…

> for (i in n:m){expr} where n is the first value and m is the last value of i for which theexpression within curly brackets should be evaluated

An example is given below

> my_results <- vector() ## this creates an empty vector to store results

> my_matrix <- matrix(c(1,2,3, 7,8,9), nrow = 2, ncol=3, byrow=TRUE)

> my_matrix ## this generates a matrix for testing purposes

[,1] [,2] [,3]

[1,] 1 2 3

[2,] 7 8 9

> for(i in 1:3){ ##this loops through the numbers 1 to 3

+ mean(my_matrix[,i])->my_results[i] ## this finds the mean of each columnin the matrix

+ print(i)} ## this prints the counter so that we know which column we areup to

[1] 1

[1] 2

[1] 3

> my_results

[1] 4 5 6

Printing the counter is useful especially when running very long loops, so that we are able tomonitor and make sure that the loop is still running and has not hanged itself.

The while syntax for the above statement is as follows

> i<-1

> while(i<4){

+ mean(my_matrix[,i])->my_results[i]

+ print(i)

+ i<-i+1}

[1] 1

[1] 2

[1] 3

> my_results

[1] 4 5 6

As you might have realised by now, both loops basically perform the same function as the

colMeans() command. In R, there are many built-in functions that perform complicatedoperations. It is always good to do a search using the help function and look at relatedcommands on the help page to see if you can avoid writing your own functions or loops.




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An alternative to writing loops is to use the ‘apply’ command as it runs faster than loops.

The syntax for the apply() command is

apply(X,margin,fun) where the function ‘fun’ is applied to the matrix ‘X’ either row -wise (in

which case margin=1) or column-wise (in which case margin=2)The syntax for the above loops would be

apply(my_matrix,2,mean) -> my_result

Exercise 5 Loops and If/Else statements

In this exercise, we will explore loops and if/else statements in R

Task 1

Loops

Step 1

The dataset ‘airquality’ contains daily airquality measurements in New York in 1973. It is a dataframe with observation of 6 variables – meanozone in parts perbillion, solar radiation, wind in miles perhour,temperature in degrees fahrenhait, month and day of month. View thefirst few lines of the dataset with the command head().

Step 2

For each day, we would like to create a hypothetical ‘wind-temperature’ score calculated by

Wind *2 + temperature of that day – temperature of the next day

Write a loop to create this score for each day and store it in a vector. Itis not necessary to calculate this value for the last day in the dataset. You should end up with a vector the length of the number of rows inthe data frame minus one.

Hint – Let the loop variable i be the row-number

Task 2

If else statements

Step 1

For each day, we would like to create a conditional score based ontemperature and solar radiation. If the solar radiation is higher than150 units and the temperature is higher than 60 degrees fahrenhait,the score should be 1. If not, it should be 0. Write an ifelse statement tocalculate this score for the all days in the dataset. You should end up with a vector of zeros and ones. The vector should be the same lengthas the number of rows in the dataset.




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7 Working with text in R

7.1. Characters and Strings

So far the functions that we have described mainly discuss numerical types. In this chapter, we will discuss several common and useful functions for working with text in R. This will beuseful for working with charts and graphs as described in the next chapter.

A character is the single unit of text. Characters can be joined together to form text strings eg.“This is a text string”

Text string can be joined together to form vectors of text strings. Of course, characters canalso be joined together to form vectors of characters. However, joining characters to form a vector is not equivalent to joining characters together to form a text string. To do the latter,one needs the ‘paste’ command (described later).

> "I am a text string" -> text_string_1> "I am another text string" -> text_string_2 ## creates 2 text strings> c(text_string_1,text_string_2)->text_string_vector ## joins 2 textstrings into a vector > text_string_vector ## prints out the vector [1] "I am a text string" "I am another text string"> text_string_vector[2] ## accesses the second element of the vector[1] "I am another text string"> c(text_string_vector,"I am yet another text string") ->text_string_vector ## adds a third text string element to the text_stringvector> text_string_vector[1] "I am a text string" "I am another text string"

[3] "I am yet another text string"

As can be seen above, adding another text string to the vector of text string does not join textstrings together. To do that, we need the paste command. An example is given below.

> paste(text_string_1,text_string_2,sep=" ") -> text_string_3> text_string_3[1] "I am a text string I am another text string"

The separator can be changed with the ‘sep’ option.

> paste(text_string_1,text_string_2,sep=" and ") -> text_string_3> text_string_3[1] "I am a text string and I am another text string"

Like text strings, characters can either be pasted together or joined together to form a vector

> paste("t","e","x","t","s","t","r","i","n","g",sep="") -> my_text_string> c("t","e","x","t","s","t","r","i","n","g") -> my_text_vector> my_text_string[1] "textstring"> my_text_vector[1] "t" "e" "x" "t" "s" "t" "r" "i" "n" "g"




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When files are read into R, numbers are sometimes read in as characters. These can beconverted into numbers with the as.numeric() command. If there are any characters in the vector, they will be converted to “NA”.

7.2. Useful commands

7.2.1. Count number of characters in the string

nchar() reports how many characters there are in the string

> my_text_string[1] "textstring"

> nchar(my_text_string)[1] 10

7.2.2. Split the string

The substr() command splits the text string with the following syntax substr(text,start,stop)

> substr(my_text_string,1,4)[1] "text"

The strsplit() command splits the text string at a delimiter with the following syntaxstrsplit(text,delimiter).

> strsplit("why is are there so many ones at the end of this line","")[[1]][1][1] "why"

This begs the question – why is there are need for the [[1]]?

This is because strsplit() operates on vectors and splits each element of the vector along thedelimiter, then creates a list with each element of the vector being each element of the list.Hence, if there were a vector of text strings, it would be split into a list of text strings asfollows

> text_vector<-(c("I bet R","is having a laugh"))> strsplit(text_vector," ")[[1]][1] "I" "bet" "R"

[[2]][1] "is" "having" "a" "laugh"

To access the word “laugh”, we would do

> strsplit(text_vector," ")[[2]][4]

[1] "laugh"




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7.2.3. Search text strings for a word

Vectors of text strings can be searched for a word. The syntax is as followsgrep(“search_term”,text).

> grep("laugh",text_vector) [1] 2

This reports that the word laugh is in the second text string of the vector of text strings

Exercise 6 Text Manipulations in R

In this exercise, we will practise manipulating text in R

Task 1

Working with text vectors and text strings

Step 1

The file ‘text_sample.Rd’ contains 2 objects, ‘txt1’ and ‘txt2’. Load thefile into R with the command load().

Step 2

Create a new vector by concatenating elements of each vector together.The new vector should read “my” “dog” “loves” “my” “cat”

Step 3

Paste the elements of this new vector together to create a text stringthat reads “my dog loves my cat”

Task 2

Splitting text

Step 1

Split the new string “my dog loves my cat” w ith the whitespacedelimiter “ “

Step 2

Extract the second word “dog” from the output of step 1

Step 3

Extract the word ‘do’ from the word ‘dog’ with the substr() command




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8 Graphs and ChartsThere are 2 different types of plotting commands – high level and low level.High level commands create a new plot on the graphics device, low level commands addinformation to an existing plot.

8.1. High level plotting commands

These always start a new plot, erasing anything already on the graphics device. Axes, labelsand titles are created with the automatic default settings.

8.1.1. Generic plot() command

The plot() function is the most commonly used graphical function in R. The type of plot thatresults depends on the arguments supplied.

If plot(x,y) is typed in, a scatterplot of y against x is produced if both are vectors.

If plot (x) is typed in and x is a vector, the values of x will be plotted against their index. If x isa matrix with 2 columns, the first column will be plotted against the second column.

Other formats include plot(x~y), plot(f,y) where f is a factor object and plot(~expr) etc. Thesecan detailed in the help pages on plot.

The women dataset gives the average heights and weights for American women aged 30–39.It consists of a matrix with the first column being height and the second column being weight.

To produce a scatterplot representing the relationship between height and weight, we can usethe following command

> plot(women)




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8.1.2. Boxplot

These can be performed with the boxplot() command

The OrchardSprays dataset in R contains information on a study on the effect of differentconcentrations of lime sulphur in repelling honey bee. There are 64 observations on 4 variables – treatment groups (these different groups are represented by alphabets, with A being the highest concentration of lime sulphur, G being the lowest concentration of limesulphur, H being no lime sulphur at all), response (as measured by decrease in concentrationof sugar solution that the lime sulphur is dissolved in), row position and column position(latin square design)

Boxplots express the relationship between 2 variables, one continuous and one discrete. Theyrepresent a five point summary - the smallest observation (sample minimum), lower quartile(Q1), median (Q2), upper quartile (Q3), and largest observation (sample maximum).

In this example, we can represent the relationship between response and treatment group by

> boxplot(decrease~treatment,data=OrchardSprays)

The resultant boxplot shows a clear relationship between response to treatment andconcentration of lime sulphur in the sugar solution, which differs between the groups.

8.1.3. Histogram

A histogram groups continuous variables into categories and plots them in terms offrequency. The bins of a histogram can be adjusted according to the distribution of data withthe ‘breaks’ option. In this example, we can plot a histogram of the treatment response




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> hist(OrchardSprays$decrease)

There are many other plotting functions eg.

qqplot() – does a quantile-quantile plot

persp(x,y,z) – draws a 3D contour surface representing the relationship between 3 variables

These different plot functions are detailed in the document http://cran.r-project.org/doc/manuals/R-intro.pdf

8.1.4. Options

Various additional details can be added to the plot

To add a title, use the ‘main’ option

To change the axis labels, use the ‘xlab’ and ‘ylab’ options

To change the axis margins, use the ‘xlim’ and ‘ylim’ options

For example, the plot above can be modified with the following command

http://cran.r-project.org/doc/manuals/R-intro.pdf









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> hist(OrchardSprays$decrease, main="Histogram of Treatment Response",xlab="Treatment response")

The option ‘type’ can be used to modify the type of graph produced. Type=”p” is the defaultand results in individual points. Type=”l” plots lines and type=”b” plots points connected by

lines. For example, in the case of women’s height and weight, the resultant plots are asfollows

> plot(women,type="l")




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> plot(women,type="b")

The option ‘col’ can be used to change the colour of the graph.

For example, this command colours all the points blue.

> plot(women,type="b",col=”blue”)




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The points can also be selectively coloured by making the colour argument a vector as follows

> plot(women,type="b",col=c(rep("black",7),rep("blue",8)))

8.2.

Low Level Plotting Functions

To add additional features to plots, these commands can be used. They do not erase thecurrent plot.

Points(x,y) adds points to the plot. lines(x,y) adds lines to the plot

For example, the command below adds the point with the corresponding coordinates to theplot




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> points(64,140)

Some other options for modifying the graph include

Text() – adds text to the graph

Legend() – adds a legend to the graph

Abline() – adds a line in the format y=ax+b

Polygon() – adds a polygon

A full list can be found in the ‘Introduction to R’ manual on the R website.

Exercise 7 Plotting functions in R

In this exercise, we will explore plotting functions in R

Task 1

Drawing line graphs

Step 1

The dataset ‘longley’ contains economic variables that observed yearlyfrom 1947 to 1962. Plot the GNP on the y axis and the year on the xaxis. Use type=”b” to create a plot with both the points and a line

joining them. Label the axes accordingly. Give your plot an appropriatetitle.

Step 2

Using the command points(), add the figures for ‘Unemployed’ to theplot. Use type=”b” to create a plot with both points and lines joiningthem. Colour the points blue with the option ‘col’.

Step 3

What problem do you notice? Modify the graph limits with the ‘ylim’optionand replot both lines.

Task 2

Drawing histograms

Step 1

Draw a histogram of the variable ‘Employed’. Give it an appropriatetitle and axes labels. Does it follow a Gaussian distribution?




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45 IT Services

9 Statistics with R

9.1. Measures of Central Tendency and Spread

These can be obtained with the following commands, which calculate the required measurefrom the vector argument supplied

> test_vector <- seq(10)> test_vector[1] 1 2 3 4 5 6 7 8 9 10> mean(test_vector)[1] 5.5> median(test_vector)[1] 5.5> sd(test_vector)

[1] 3.02765> max(test_vector)[1] 10> min(test_vector)[1] 1> summary(test_vector)

Min. 1st Qu. Median Mean 3rd Qu. Max.1.00 3.25 5.50 5.50 7.75 10.00

9.2. Tests for continuous vs discrete variables

9.2.1. 2 groups

With normally distributed measurements in 2 groups, one can measure the relationship between continuous and discrete variables with a parametric paired or unpaired t test withthe command t.test().

This test has a few options. The default setting is an unpaired test but this can be changed with the option (paired=FALSE). The default setting is a 2 tailed test but this can be altered with the option (alternative=LESS or alternative=GREATER).

When the data is not normally distributed, one would use the non-parametric Wilcoxon test with the commandwilcox.test, with the options paired=TRUE(Wilcoxon signed rank test), orpaired=FALSE(Wilcoxon rank sum test, otherwise known as Mann Whitney U test).

9.2.2. 3 or more groups

When the data is distributed normally, one can use the parametric Analysis of Variance test with the command aov(). When the data is not normally distributed, one can use the non-parametric Kruskal-Wallis test with the command kruskal.test().

The following example is from the dataset called ‘chickwts’. This describes an experiment tocompare the effectiveness of different types of feed supplements on the growth rate ofchickens. This dataset consists of 71 observations on 2 variables. The first variable is chick weight after 6 weeks and the second variable is the grouping based on the type of feed. There

are 6 types of feeds, which can be accessed with the following command.




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> summary(chickwts)

weight feed

Min. :108.0 casein :12

1st Qu.:204.5 horsebean:10

Median :258.0 linseed :12 Mean :261.3 meatmeal :11

3rd Qu.:323.5 soybean :14

Max. :423.0 sunflower:12

Let’s say we wish to find out how feed affects chick weight, one quick way to do this is to visualise the data with a boxplot.

> boxplot(weight~feed,data=chickwts,las=2) ## las=2 turns the x labshorizontally

Let’s say we wish to find out whether chicks fed with casein have a significantly higher weightthan chicks fed with horsebean.

The first step is to check whether the data is normally distributed. This can be done byplotting a histogram of the weights.




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> hist(chickwts$weight)

Since the data is normally distributed, we can use the unpaired t test as follows

>t.test(chickwts$weight[which(chickwts$feed=="casein")],chickwts$weight[which(chickwts$feed=="horsebean")])

Welch Two Sample t-test

data: chickwts$weight[which(chickwts$feed == "casein")] andchickwts$weight[which(chickwts$feed == "horsebean")]

t = 7.3423, df = 18.36, p-value = 7.21e-07

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

116.6982 210.0685

sample estimates:

mean of x mean of y

323.5833 160.2000

The output provides more information about the results of the t test. The t statistic is shown,together with the degrees of freedom, 95% confidence interval and p value. The means ofeach of group are shown. When var.equal = FALSE (by default), the welch 2 sample test is




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used, which is an adaptation of the Student’s t test adapted for unequal variances. If var.equal=TRUE, the variances are pooled.

If we wish to conduct an analysis of variance amongst all the feed groups, we can use thefollowing

> summary(aov(chickwts$weight~chickwts$feed))

Df Sum Sq Mean Sq F value Pr(>F)

chickwts$feed 5 231129 46226 15.37 5.94e-10 ***

Residuals 65 195556 3009

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

This tells us that there are significant differences between at least 2 groups. However, we donot know which pairs of groups have differences and which do not. To do this, we canperform posthoc tests.

>pairwise.t.test(chickwts$weight,chickwts$feed,p.adjust.method="none",pool.sd=FALSE,var.equal=FALSE)

Pairwise comparisons using t tests with non-pooled SD

data: chickwts$weight and chickwts$feed

casein horsebean linseed meatmeal soybean

horsebean 7.2e-07 - - - -

linseed 0.00026 0.00687 - - -

meatmeal 0.09866 0.00011 0.02933 - -

soybean 0.00352 0.00016 0.19799 0.22523 -

sunflower 0.82151 1.7e-08 2.4e-05 0.04441 0.00043

9.3. Tests for discrete vs discrete variables

9.3.1. Chi Square Test

This is used when comparing 2 discrete variables to measure whether the observedproportions are significantly different from the null hypothesis. There should be more than 5observations for each cell. The R command is chisq.test().

9.3.2. Fisher’s Exact Test

This is used when there are fewer than 5 observations for each cell. The command isfisher.test()




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In this example, we create a 2x2 matrix of the number of male and female students in a 2classes – physics and biology. We would like to find out whether there is a statisticaldifference in the proportion of males compared to females in each subject class. Since thereare more than 5 subjects in each category, we should use the chi square test.

> gender_subject <- matrix(c(23,45, 25,57), nrow = 2, ncol=2, byrow=TRUE)

> rownames(gender_subject) <- c("males","females")

> colnames(gender_subject) <- c("physics","biology")

> gender_subject

physics biology

males 23 45

females 25 57

> chisq.test(gender_subject)

Pearson's Chi-squared test with Yates' continuity correction

data: gender_subject

X-squared = 0.0677, df = 1, p-value = 0.7947

9.4. Tests for continuous vs continuous variables

9.4.1. Pearson Correlation

This is used when both variables are normally distributed. The R command is

cor.test(x,y,method=”pearson”)

9.4.2. Spearman Correlation

This is used when one or both variables are not normally distributed. The R command iscor.test(x,y,method=”spearman”)

The example below comes from the ‘women’ dataset, which documents the heights and weights of a sample of American women.

The first step is to check whether both height and weight variables are normally distributed.This can be performed as follows either with a histogram (previous example) or with the

Shapiro wilk test.

> shapiro.test(women[,1])

Shapiro-Wilk normality test

data: women[, 1]

W = 0.9636, p-value = 0.7545





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Shapiro-Wilk normality test

data: women[, 2]

W = 0.9604, p-value = 0.6986

Since both height and weight do not show significant deviation from normality, Pearsoncorrelation can be used.

> cor.test(women[,1],women[,2],method="pearson")

Pearson's product-moment correlation

data: women[, 1] and women[, 2]

t = 37.8553, df = 13, p-value = 1.088e-14

alternative hypothesis: true correlation is not equal to 0


0.9860970 0.9985447

sample estimates:

cor

0.9954948

The relevant statistics can be extracted as follows

> cor.test(women[,1],women[,2],method="pearson")$p.value

[1] 1.088019e-14

> cor.test(women[,1],women[,2],method="pearson")$estimate

cor

0.9954948

Caution: Correlation coefficient of zero does not necessarily mean that there is no

relationship between the 2 variables. The scatterplots below demonstrate non-linear

relationships between 2 variables




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Pearson correlation = -0.09 Pearson correlation = -0.08

9.5. Regression

Fitting linear models can be performed with the command lm(). The example belowexamines regression of weight on height for the R dataset ‘women’ described above.

> summary(lm(women[,1]~women[,2]))

Call:

lm(formula = women[, 1] ~ women[, 2])

Residuals:

Min 1Q Median 3Q Max

-0.83233 -0.26249 0.08314 0.34353 0.49790

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 25.723456 1.043746 24.64 2.68e-12 ***

women[, 2] 0.287249 0.007588 37.85 1.09e-14 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.44 on 13 degrees of freedom

Multiple R-squared: 0.991, Adjusted R-squared: 0.9903

F-statistic: 1433 on 1 and 13 DF, p-value: 1.091e-14

The relevant values can be extracted as follows




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P value : summary(lm(women[,1]~women[,2]))$coeff[2,4]

Regression coefficient: summary(lm(women[,1]~women[,2]))$coeff[2,1]

Residuals: summary(lm(women[,1]~women[,2]))$residuals

Other regression models can be fitted with the glm function using the ‘link’ option. The

various options are given below. They can also be found on the glm function help page. binomial(link = "logit")gaussian(link = "identity")Gamma(link = "inverse")inverse.gaussian(link = "1/mu^2") poisson(link = "log")quasi(link = "identity", variance = "constant")quasibinomial(link = "logit")quasipoisson(link = "log")

9.6. Probability Distributions

R has a set of built-in functions related to probability distributions.

These functions can evaluate the

- probability density function (prefix the name with ‘d’)

- cumulative distribution function (prefix the name with ‘p’)

- quantile function (prefix the name with ‘q’)

- simulate from the distribution (prefix the name with ‘r’)

where the name refers to a set of R names eg. ‘binom’ (binomial), ‘chisq’ (chi square), ‘hyper’(hypergeometric) etc. The full list can be found on the official R manual accessible here


9.7. Other Statistical Features

R has a large compendium of statistical features, which are constantly being added by usersin the form of new packages (later chapter).

Some of the commonly used statistical features include

Maximum likelihood models – commands depend on the model being fitted. Moreinformation can be found here http://www.stat.umn.edu/geyer/5931/mle/mle.pdf

Mixed models – the nlme package is recommended, with the functions lme() andnlme()

Local approximating regression – the loess() function performs a non-parametricregression

Principal Components Analysis/Singular Value Decomposition – The former can beperformed with the prcomp() or princomp() function. The latter can be performed with the svd() function. Be careful of whether rows/columns are standardised orcentred

Robust regression – Many functions are contained in the MASS package

Clustering – various types of clustering functions exist eg. hclust() does hierarchicalclustering

Tree-based models – these can be found in packages rpart and tree



http://www.stat.umn.edu/geyer/5931/mle/mle.pdf








53 IT Services

Machine learning – various unsupervised learning algorithms can be easilyimplemented in R eg. support vector machines with the function svm(), neuralnetworks with the package nnet(), random forests with the package randomForest

9.8. Packages

Many of these statistical features are found in packages developed by users. These packagescan be installed within the R environment with the command

> install.packages(“package_name”)

Packages have been developed for statistical analysis in different disciplines:

1. Bioinformatics

Many of the packages for bioinformatics are embedded with the ‘bioconductor’ environment.Bioconductor can be downloaded from http://www.bioconductor.org/

2. Social Sciences

Most of the functions needed for social sciences can be found in the base packages. Further

details are here http://cran.r-project.org/web/views/SocialSciences.html

3. Financial Engineering

Many of the functions can be found in this suite of packages ‘R/Rmetrics’

These are but a few examples. The CRAN repository contains a full list of packages that can be downloaded. Packages that not within that repository have to be downloaded and installedmanually with by clicking on Packages| Insta l l packages f rom l ocal z ip f i le

Exercise 8 Statistics in R

In this exercise, we will explore statistics in RTask 1

Comparing 2 groups

Step 1

The text file ‘district.txt’ contains the ages of residents in 2 differentdistricts. Plot the ages as a histogram to asses normality.

Step 2

Use the appropriate test to check whether there is a statisticallysignificant difference between the ages of residents in the 2 districts.

Task 2

Correlation

Step 1

The file ‘ageweight.txt’ contains information about the age and weightsof participants in a clinical study. There are 2 groups of participants –

healthy controls and patients with carpal tunnel syndrome. Plot theage variable vs the weight variable on a graph to assess if therelationship is linear.

Step 2

Create histograms of ages and weights to assess whether these variables have a normal distribution. What correlation test isappropriate for this situation?

Step 3

Perform the correlation test on the whole dataset

Step 4

Perform the correlation test separately on patients and on controls

http://www.bioconductor.org/



http://cran.r-project.org/web/views/SocialSciences.html








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10 Writing your own functions

When you need to perform a repeated function in R, a function can be written to performthis. The syntax to write a function is

my_function <- functionx(x){

commands(x) -> y

return(y)}

Taking the example in the ‘loops’ exercise

The dataset in question is ‘airquality’

> head(airquality)

Ozone Solar.R Wind Temp Month Day

1 41 190 7.4 67 5 1

2 36 118 8.0 72 5 2

3 12 149 12.6 74 5 3

4 18 313 11.5 62 5 4

5 NA NA 14.3 56 5 5

6 28 NA 14.9 66 5 6

For each day, we would like to create a conditional score based on temperature and solarradiation. If the solar radiation is higher than 150 units and the temperature is higher than60 degrees fahrenhait, the score should be 1. If not, it should be 0. Write an ifelse statementto calculate this score for the all days in the dataset. You should end up with a vector of zerosand ones. The vector should be the same length as the number of rows in the dataset.

Instead of writing a loop, we can write a function and apply it to the matrix. The argument tothe function would be row of the matrix

The function would be written as follows

calc_score <- function(x){

ifelse(x[2]>150|x[4]>60,1,0) -> y

return(y)}

The function can then be applied to the matrix as follows

apply(airquality, 1, calc_score) -> result




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11 References

The manual titled “An Introduction to R” located on the official R website at http://cran.r-

project.org/doc/manuals/R-intro.pdf is the main reference used in the creation of thisdocument. Other references, with hyperlinks, are documented in the relevant text passages.









06/02/2013

1

R: An introduction

Esther Ng – [email protected]

What is R?

• Suite of software facilities for

‐ data manipulation and storage

‐ calculation on arrays/matrices

‐ graphical display

• Implementation of the S language

Course Book Page 8



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2

Pros and

Cons

Pros

• Open source and cross platform

• Very well suited for statistical analysis

• Active user development in the form of packages

• Active user group list/form

Cons

• Learning curve

•

Computationally slow

(compared

to

languages

like

C/Fortran)

• Minimal graphic user interface

• Workspace memory limitations

Course Book Page 8

Other Languages

Matlab

• this document facilitates the translation of Matlab syntax into R

syntax http://cran.r‐project.org/doc/contrib/Hiebeler‐matlabR.pdf

SPSS/SAS

• For those who have mainly used SPSS/SAS for their statistical needs,

this document

http://www.et.bs.ehu.es/~etptupaf/pub/R/RforSAS&SPSSusers.pdf facilitates the translation of SPSS/SAS syntax into R

C/C++

• C++ code is often used to speed up calculations in R. The 2

languages can be interfaced more easily using this package. http://cran.r‐project.org/web/packages/Rcpp/vignettes/Rcpp‐

introduction.pdf

Course Book Page 8



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3

BasicsCommand Prompt

• The default command prompt is >

• If you see + appearing, it means that the

command is incomplete eg. unpaired bracket

Getting Help

• The ?() or help() function brings up a html page

describing the

argument

• For example, if we want to find out how to use

the command ‘svd’, type in help(svd)

Course Book Page 9

Vectors and

Matrices



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4

VectorsThe simplest data structure in R is the vector.

How to create vectors?

> x <‐ c(5,4,3,2,1)

Alternatively, an empty vector can be created

then populated with elements

> x <‐ vector()

> x[2] <‐ 3 ## this inserts the value 3 into the

second element of the vector x

Course Book Page 13

In R, words after the ## sign are ignored as they are comments

Vectors

How to access elements of vectors?

As implied in the example above, elements of a

vector can be accessed by their index, with square

brackets. A few elements can be accessed with a

colon

> x[3] ## this accesses the third element

[1] 3

> x[3:5] ## this accesses the third to fifth element

[1] 3 2 1

Course Book Page 14



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5

VectorsHow to access elements conditionally?

> x[x<3] ## selects elements with a value < 3

[1] 2 1

What are some common vectors?

> b<‐seq(1,10,2) ## sequence of 1 to 10 in steps of 2

> b

[1] 1 3 5 7 9

> d<

‐rep(1,10)

##

repetition

of

10

‘ones’

> d

[1] 1 1 1 1 1 1 1 1 1 1

Course Book Page 14

Vectors

Common vector commands

• length() finds the length of the vector

• max() finds the largest element of the vector

• min() finds

the

smallest

element

of

the

vector

• sum() finds the sum of all elements

• mean() finds the average of all elements

• sd() finds the standard deviation of all elements

Course Book Page 15



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6

VectorsHow to perform arithmetic on vectors?

> x*2 ## this multiplies each element by 2

[1] 10 8 6 4 2

> x+x ## this adds the vectors element‐wise

[1] 10 8 6 4 2

> x*x ## this multiplies vectors element‐wise

[1] 25

16

9

4

1

Linear algebra uses a different set of operations eg. %*% stands for matrix multiplication

Course Book Page 15

Matrices

A matrix is a 2 dimensional frame of numbers. It can

be thought of as vectors lined up in rows/columns

How to create a matrix?

This is one way…

> my_matrix <

‐ matrix(c(1,2,3,7,8,9),

nrow =

2,

ncol=3, byrow=TRUE)

> my_matrix

[,1] [,2] [,3]

[1,] 1 2 3

[2,] 7 8 9

Course Book Page 16



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7

MatricesA second way is by creating an empty matrix and

subsequently populating it with data

> my_matrix <‐ matrix(nrow=3,ncol=3)

> my_matrix[2,2] <‐ 42

> my_matrix

[,1] [,2] [,3]

[1,]

NA

NA NA[2,] NA 42 NA

[3,] NA NA NA

Course Book Page 17

Matrices

A third way of creating matrices to bind vectors or matrices together

> rbind(my_matrix,my_matrix) ‐>combined_matrix

>

combined_matrix[,1] [,2] [,3]

[1,] 1 2 3

[2,] 7 8 9

[3,] 1 2 3

[4,] 7 8 9

Course Book Page 17



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8

MatricesHow to access elements of a matrix?

The matrix can be accessed with square brackets

matrix[rowindex, columnindex]

> combined_matrix[2,1]

[1] 7

Several entries can be accessed with a colon

> combined_matrix[2,1:3]

[1] 7 8 9

Course Book Page 18

Matrices

Common matrix commands

• dim() returns the dimensions of the matrix

• t() transposes the matrix

• rowSums, colSums, rowMeans, colMeans

return the sums and means of rows and

columns respectively

• Names can be assigned to rows/columns with

the command rownames() and colnames()

Course Book Page 19



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9

Lists and

Data

frames

• Matrices and vectors can be made of numbers,

characters or factors, but not a combination of

different types

• Lists are similar to vectors and data frames are

similar to matrices except lists and data frames

can comprise of different types of objects

• There are

some

other

differences

(see

notes)

• In this course we will focus on matrices/vectors

Course Book Page 21

To Exercise 2 ‐>

Exercise 2

Before you start exercise 2…

Look up the ‘which’ command with the help() or

?() function

The datasets

that

are

required

eg.

WWWusage

are all preloaded into the R by default. To find

out more details about how the data was

collected, use the help() function eg.

help(WWWusage)

Course Book Page 21

To Exercise 2 ‐>



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10

Reading in Data

Reading Data

What format of data can R read?

• Text files

• Excel files (store them as .csv)

• Preloaded datasets (from R packages)

Data from

other

software

eg.

SPSS,

SAS

should

be

converted to text files to be read into R

It is a good idea to open the file before reading it in so

that one can check whether there are header lines etc.

as this will affect the command options

Course Book Page 28



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11

Reading Data

read.table() has the following options

• header – does the first line consist of column

names?

• skip – are there a few lines at the start of the file

that should not be read in? eg. file description

• sep – what separates the fields? eg. tab, space

• fill – do all the rows in the file have the same

number of columns?

read.delim() and

read.csv()

are

similar

to

read.table()

except for the option defaults

After reading a file in, it is always a good idea to check

the object with a head() command

Course Book Page 28

Example

Step 1 Open the file and have a look

Course Book Page 28



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12

Example

Step 2 Read in the file with the appropriate

options> read.table(“class.txt”,header=TRUE,skip=4,sep=“ “) ‐>

my_class

Step 3 Check the object> head(my_class)

Names Ages Gender

1 Mary 8 Female

2

Tom

9

Male3 Tim 12 Male

4 Sally 13 Female

Course Book Page 28

Writing Data

write.table() has the following options

• row.names – should the row names be written?

• col.names – should the col names be written?

• quote – should characters be enclosed in quotes?

• sep – what is

the

field

separator

string?

write.csv() can be used to create a comma‐separated‐

value file that is readable by Microsoft Excel

After writing a file out, it is always a good idea to open

the file and make sure that the format is correct

Course Book Page 29



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13

QuestionnairePreparing file in excel

‐ Enter data with first line as variable name

‐ Save as tab delimited file

‐ If working in older versions of excel, can save as

comma separated value (.csv) file

‐ Do not use variable names (or string variables)

that have

spaces.

Instead,

fill

the

spaces

with

an

underscore

‐ Open up the text file to check that it looks right

Questionnaire

> read.table(“H://class_sample.txt",header=TRUE) ‐>

class_sample

> head(class_sample)

Gender Age Height Weight Car Income

1 Male 23 165 65 yes 1400

2 Female

35

155

54

no

2444

3 Male 42 176 65 yes 2144

4 Male 32 155 45 no 2111

5 Female 23 165 56 yes 1111

6 Male 35 155 65 no 2333

What happens if you do read.table(“H://class_sample.txt") ‐>

class_sample



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14

Questionnaire> read.table(“H://class_sample.txt",header=TRUE) ‐>

class_sample



1 Male 23 165 65 yes 1400

2 Female 35 155 54 no 2444

3 Male 42 176 65 yes 2144

4 Male 32 155 45 no 2111

5

Female

23

165

56

yes

11116 Male 35 155 65 no 2333

What happens if you do read.table(“H://class_sample.txt") ‐>

class_sample

Questionnaire

Explore the following

1. Find the average age of all the participants

2. Find the average weight of the male participants

3. Find the standard deviation of the heights of female

participants

4. How many

females

own

cars?



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15

Questionnaire1. mean(class_sample[,2])

2. mean(class_sample[class_sample[,1]=="Male",4])

3. sd(class_sample[class_sample[,1]=="Female",3])

4. table(class_sample[class_sample[,1]=="Female",5])

Objects and

Workspaces



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16

Basics ‐ Objects

The basic unit in R is the object. An object can be a

number, vector, matrix, function etc.

Creating objects

• Various ways eg. list ()‐>my_list creates an empty

list, seq(5) ‐> my_vector creates a vector sequence

of 1 to 5

Removing objects

• rm(object1,object2)

Saving objects

• save(object1,object2…, file=“my_objects.Rd”) or

write it out at text file (later)

Course Book Page 24

Basics ‐ Workspace

• The workspace is the collection of objects in the

current R session

Listing objects in the workspace

• ls()

Saving the workspace

• save.image(“my_workspace.RData”)Loading workspaces or objects

• load(“my_workspace.RData”)

At the end of the session, R will ask if you wish to save

the current workspace. If you save it, it will be

automatically reloaded next session

Course Book Page 24



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17

Basics ‐ Directories

Directories in R

• To check which directory R is in, one can use the

command getwd()

• To change directory within R, one can use the

command setwd()

• This is important when running scripts, saving

objects/workspaces and writing out data as R will

not give a warning when files are overwritten

Course Book Page 25

Basics ‐ Scripts

3 ways to run commands

1. Type them directly into the console

2. Type them into the R editor then right click | run

selection

3. Save them as a script file with ‘.R’ extension and use

the command

> source (“my_script_file.R”)

Course Book Page 26

To Exercise 3 ‐>



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18

Questionnaire

Write a script that will

‐ calculate BMI of participants

‐ Insert it into a new column to the right hand side

of the data

‐ Write out a new file with the BMI in it

Questionnaire

Step 1: Go to File > New script

Step 2: Enter read.table(“class_sample.txt”,header=TRUE)‐

>class_sample

Step3: Highlight and right click then select ‘run line or

selection’

Step4: Check

it

is

read

in

correctly

with

‘head’

command



1 Male 23 165 65 yes 1400

2 Female 35 155 54 no 2444

3 Male 42 176 65 yes 2144

4 Male 32 155 45 no 2111

5 Female 23 165 56 yes 1111

6 Male 35 155 65 no 2333



06/02/2013

19

Questionnaire

Step 5: Enter

(class_sample[,4]/(class_sample[,3])^2)*10000‐>class_sample[,7]

Step 6: Check output


Gender Age Height Weight Car Income V7

1 Male 23 165 65 yes 1400 23.87511

2 Female 35 155 54 no 2444 22.47659

3 Male 42 176 65 yes 2144 20.98399

Step 7: Assign column name

"BMI" ‐

> colnames(class_sample)[7]

Step 8: Write out file

write.table(class_sample,file="class_sample_with_BMI.txt",row.na

mes=FALSE,col.names=TRUE,quote=FALSE)

Questionnaire

Step 5: Open text file to check that it looks correct

Step 6: Save script file with a .R extension

Go to File>save as>”calculate_BMI.R”

Step 7: Test out script on a different file

Change “class_sample.txt” to “my_class.txt”

Change “class_sample_with_BMI.txt”

to

“my_class_with_BMI.txt”

Step 8: Save file

Step 9: In the R console, type in source(“calculate_BMI.R”)

Step 10: Check the output file called “my_class_with_BMI.txt”

To Exercise 3 ‐>



06/02/2013

20

Loops and Conditional Statements

Conditional Statements

R can perform conditional operations with the if/else

or ifelse command

The syntax

for

an

if/else

statement

is

> if (condition) expr_1 else expr_2

Alternatively

> ifelse(condition, expr_1, expr_2)

Course Book Page 31



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21

Example> y<‐1 ## sets the value of y to 1

> if(y>2) x<‐3 else x <‐4 ## assigns 3 to x if y is greater than 2 and 4 to x if y is

less than 2

> x

[1] 4

And (&&) and If (||) statements can also be included

> z<‐1; y<‐1 ## sets the value of z and y both to 1

> if(y<2&&z<2) x<‐3 else x <‐4 ## assigns 3 to x if both y and z are less than 2

> x

[1] 3

Alternatively

> ifelse(y<2&&z<2,3,4) ‐>x

> x

[1] 3

Course Book Page 31

Loops

The syntax for a loop is

> for (i in n:m){expr} where n is the first value and m is

the last value of i for which the expression within curly

brackets should be evaluated

Course Book Page 32



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22

Example

> my_results <‐ vector() ## this creates an empty vector to store results

> my_matrix <‐ matrix(c(1,2,3, 7,8,9), nrow = 2, ncol=3, byrow=TRUE)

> my_matrix ## this generates a matrix for testing purposes

[,1] [,2] [,3]

[1,] 1 2 3

[2,] 7 8 9

> for(i in 1:3){ ##this loops through the numbers 1 to 3

+ mean(my_matrix[,i])‐>my_results[i] ## this finds the mean of each column

+ print(i)} ## this prints the counter so that we know which column we are

[1] 1

[1] 2

[1] 3

> my_results

[1] 4 5 6

Course Book Page 32

Questionnaire

Read the file “my_class_with_BMI.txt” into R and create a

column that states ‘yes’ if the person’s BMI is above 20 and ‘no’

if it isn’t

read.table(“my_class_with_BMI.txt”,header=TRUE)‐>my_class

for(i in 1:nrow(my_class)){

ifelse(my_class[i,7]>20,”yes”,”no”) ‐> my_class[i,8]}

check result with the head command

To Exercise 5 ‐>



06/02/2013

23

Working with Characters

Working with characters

• Besides numbers, characters can also be

manipulated in R

• Characters are enclosed in “ “

•

Characters

can

be

joined

together

to

form

text

strings with the paste() command

> paste("t","e","x","t",sep="") ‐> text_string

> text_string

[1] "text"

Course Book Page 34



06/02/2013

24

Useful character

operations

1.The substr() command splits the text string with the following

syntax substr(text,start,stop)

> substr(“new_text_string”,1,3)

[1] “new"

2. The strsplit() command splits the text string at a delimiter with

the following syntax strsplit(text,delimiter).

3. The nchar() command counts the number of characters in the

text string with the syntax nchar(text)

4. The

grep()

command

searches

for

a matching

string

Course Book Page 35

Questionnaire

Use the ‘grep’ command to extract the rows

containing female participants

my_class[grep(“female”,my_class[,1]),]‐>

my_class_femalescheck result with the head command

To Exercise 6 ‐>



06/02/2013

25

Working with Graphs

Graphs in R

There are 2 different types of plotting commands – high level

and low level.

High level commands create a new plot on the graphics device,

low level commands add information to an existing plot.

The plot() function is the most commonly used graphical

function in R. The type of plot that results depends on the

arguments supplied.

If plot(x,y) is typed in, a scatterplot of y against x is produced if

both are vectors.

If plot (x) is typed in and x is a vector, the values of x will be

plotted against their index. If x is a matrix with 2 columns, the

first column will be plotted against the second column.

Plot Function

Course Book Page 37



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26

ExampleThe women dataset gives the average heights and weights for American

women aged 30–39. It consists of a matrix with the first column being height

and the second column being weight.

To produce a scatterplot representing the relationship between height and

weight, we can use the following command

> plot(women)

Course Book Page 37

ExampleThe option ‘type’ can be used to modify the type of graph produced.

Type=”p” is the default and results in individual points. Type=”l” plots lines

and type=”b” plots points connected by lines.

> plot(women, type=“l”)

Course Book Page 37



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ExampleThe option ‘col’ can be used to change the colour of the graph.

For example, this command colours all the points blue.

> plot(women,type="b",col=”blue”)

Alternatively, points can be made different colours by creating a vector of

colours

Course Book Page 37

Boxplots express the relationship between 2 variables, one

continuous and one discrete

Five point summary ‐ sample minimum, lower quartile, median,

upper quartile, and sample maximum

The OrchardSprays dataset contains information on the effect of

different concentrations of pesticide dissolved in sugar solution

(treatment groups represented by different alphabets) on their effects on repelling honey bees (measured by uptake of sugar

solution)

Boxplot Function Course Book Page 38



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28

Questionnaire

Do a boxplot of income for each gender

boxplot(my_class[,6]~my_class[,1],main="Income of male and

female participants",ylab="Income")

Course Book Page 32

To Exercise 6 ‐>

ExampleIn this example, we can represent the relationship between response and

treatment group by

> boxplot(decrease~treatment,data=OrchardSprays)

The resultant boxplot shows a clear relationship between response to

treatment and concentration of pesticide in the sugar solution, which differs

between the groups.

Course Book Page 38



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29

Questionnaire

Plot a graph of height vs weight of participants

plot(my_class[,3],my_class[,4],main=“Weight vs Height of

Participants”,xlab=“Height in cm”,ylab=“Weight in kg”)

To save graph as pdf ###

pdf(“height_vs_weight.pdf”)

plot(my_class[,3],my_class[,4],main=“Weight

vs Height

of

Participants”,xlab=“Height in cm”,ylab=“Weight in kg”)

dev.off()

To Exercise 6 ‐>

Histogram Function

A histogram groups continuous variables into categories and plots them in

terms of frequency. In this example, we can plot a histogram of the treatment

response

> hist(OrchardSprays$decrease)

Course Book Page 38



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30

Title and Labels

• To add a title, use the ‘main’ option

• To change the axis labels, use the ‘xlab’ and ‘ylab’ options

• To change the axis margins, use the ‘xlim’ and ‘ylim’ options

> hist(OrchardSprays$decrease, main="Histogram of Treatment Response",

xlab="Treatment response")

Course Book Page 38

Questionnaire

Draw a histogram of participants’ heights

hist(my_class[,3],main="Histogram of participants'

heights",xlab="Height “)

To Exercise 6 ‐>



06/02/2013

31

Low Level Commands

To add additional features to plots, ‘low level’ commands can be used. They

do not erase the current plot.

Points() adds points to the plot

Lines() adds lines to the plot

Text() – adds text to the graph

Legend() – adds a legend to the graph

> plot(women,type="b")

> points(64,140)

produces the graph below with the

additional point at the coordinates

(64,140)

Course Book Page 42

To Exercise 7 ‐>

Statistics in

R



06/02/2013

32

Central tendency

and

spread

> test_vector <‐ seq(10)

> test_vector

[1] 1 2 3 4 5 6 7 8 9 10

> mean(test_vector)

[1] 5.5

> median(test_vector)

[1] 5.5

> sd(test_vector)

[1] 3.02765

> max(test_vector)

[1] 10

> min(test_vector)

[1] 1

> summary(test_vector)

Min. 1st Qu. Median Mean 3rd

Qu. Max.

1.00 3.25 5.50 5.50 7.75

10.00

Course Book Page 45

Comparing Measures of Centrality1. 2 groups

a) Parametric – Paired and Unpaired T test – t.test

(paired=FALSE or paired=TRUE)

b)Non‐parametric – Wilcoxon Signed Rank Test, Wilcoxon

Rank Sum

Test

– wilcox.test(paired=FALSE

or

paired=TRUE)

2. 3 or more groups

a) Parametric – ANOVA – aov()

b)Non‐parametric – Kruskal Wallis Test – kruskal.test()

Course Book Page 45



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33

Assessing normality

1. Histogram

2. QQ plot – qqplot()

3. Shapiro Wilk Test – shapiro.test()

Course Book Page 45

Example

The following example is from the dataset called

‘chickwts’. This describes an experiment to compare the

effectiveness of different types of feed supplements on

the growth rate of chickens. This dataset consists of 71

observations on

2 variables.

The

first

variable

is

chick

weight after 6 weeks and the second variable is the

grouping based on the type of feed.

Course Book Page 46



06/02/2013

34

Example

Let’s say we wish to find out how feed affects chick weight, one

quick way to do this is to visualise the data with a boxplot.

> boxplot(weight~feed,data=chickwts,las=2) ## las=2 turns the x

labs horizontally

Course Book Page 46

Example

Based on the boxplot, let us test the hypothesis that chicks fed with

casein have a significantly higher weight than chicks fed with

horsebean.

The first step is to check whether the data is normally distributed.

This can be done by plotting a histogram of the weights.

> hist(chickwts$weight)

Course Book Page 47



06/02/2013

35

Example

>t.test(chickwts$weight[which(chickwts$feed=="casein")],chickwts$

weight[which(chickwts$feed=="horsebean")])

t = 7.3423, df = 18.36, p‐value = 7.21e‐07



116.6982 210.0685

sample estimates:

mean of x mean of y

323.5833 160.2000

Course Book Page 47

Example

> summary(aov(chickwts$weight~chickwts$feed))

Df Sum Sq Mean Sq F value Pr(>F)

chickwts$feed 5 231129 46226 15.37 5.94e‐10 ***

Residuals 65 195556 3009

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Posthoc Testing

>pairwise.t.test(chickwts$weight,chickwts$feed,p.adjust.method="none",pool.sd=FALSE,var.equal=FALSE)

casein horsebean linseed meatmeal soybean

horsebean 7.2e‐07 ‐ ‐ ‐ ‐

linseed 0.00026 0.00687 ‐ ‐ ‐

meatmeal 0.09866 0.00011 0.02933 ‐ ‐

soybean 0.00352 0.00016 0.19799 0.22523 ‐

sunflower 0.82151 1.7e‐08 2.4e‐05 0.04441 0.00043

Course Book Page 47



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36

QuestionnaireIs there a significant difference between the

heights of males and females?

shapiro.test(my_class[,3])

t.test(my_class[,3]~my_class[,1])

wilcox.test(my_class[,3]~my_class[,1])

Comparing 2 discrete variables

Chi Square Test

This is used when comparing 2 discrete variables to

measure whether the observed proportions are

significantly different

from

the

null

hypothesis.

There

should be more than 5 observations for each cell. The R

command is chisq.test().

Fisher’s Exact Test

This is used when there are fewer than 5 observations for

each cell. The command is fisher.test()

Course Book Page 48



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37

Example

In this example, we create a 2x2 matrix of the number of male and

female students in a 2 classes – physics and biology. We would like

to find out whether there is a statistical difference in the proportion

of males compared to females in each subject class. Since there are

more than 5 subjects in each category, we should use the chi square

test.

> gender_subject <‐ matrix(c(23,45, 25,57), nrow = 2, ncol=2, byrow=TRUE)

> rownames(gender_subject) <‐ c("males","females")

> colnames(gender_subject) <‐ c("physics","biology")

> gender_subject

physics biology

males

23

45

females 25 57

> chisq.test(gender_subject)

X‐squared = 0.0677, df = 1, p‐value = 0.7947

Course Book Page 49

Questionnaire

Are males and females equally likely to own a

car?

table(my_class[,1],my_class[,5])

fisher.test(my_class[,1],my_class[,5])

chisq.test(my_class[,1],my_class[,5])



06/02/2013

38

Comparing 2 continuous variables

Pearson Correlation

This is used when both variables are normally distributed. The R

command is cor.test(x,y,method=”pearson”)

Spearman Correlation

This is used when one or both variables are not normally

distributed. The R command is cor.test(x,y,method=”spearman”)

The example below comes from the ‘women’ dataset, which

documents the heights and weights of a sample of American

women

Course Book Page 50

Comparing 2 continuous variables

Step 1: Check whether both height and weight variables are

normally distributed. This can be performed as follows either with a

histogram or a shapiro‐wilk test


W = 0.9636, p‐value = 0.7545


W = 0.9604, p‐value = 0.6986

Step 2: Plot a graph and check if they are linearly related

Since both height and weight do not show significant deviation from

normality and they are linearly related, Pearson correlation can be

used.

Course Book Page 50



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Comparing 2 continuous

variables> cor.test(women[,1],women[,2],method="pearson")

t = 37.8553, df = 13, p‐value = 1.088e‐14



0.9860970 0.9985447

sample estimates:

cor

0.9954948

The relevant statistics can be extracted as follows

>

cor.test(women[,1],women[,2],method="pearson")$p.value[1] 1.088019e‐14

> cor.test(women[,1],women[,2],method="pearson")$estimate

cor

0.9954948

Course Book Page 50

Caution – the importance of plotting

Spearman Correlation more

appropriate than Pearson

Correlation

Neither spearman nor pearson

correlation are appropriate

Course Book Page 51



06/02/2013

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QuestionnaireIs height correlated with weight?



cor.test(my_class[,3],my_class[,4],method=“pearson”)

cor.test(my_class[,3],my_class[,4],method=“spearman”)

Linear RegressionLinear Regression can be performed with the lm() command

> summary(lm(women[,1]~women[,2]))

Residuals:

Min 1Q Median 3Q Max

‐0.83233 ‐0.26249 0.08314 0.34353 0.49790

Coefficients:Estimate Std. Error t value Pr(>|t|)

(Intercept) 25.723456 1.043746 24.64 2.68e‐12 ***

women[, 2] 0.287249 0.007588 37.85 1.09e‐14 ***

‐‐‐

Residual standard error: 0.44 on 13 degrees of freedom

Multiple R‐squared: 0.991, Adjusted R‐squared: 0.9903

F‐statistic: 1433 on 1 and 13 DF, p‐value: 1.091e‐14

Course Book Page 51



06/02/2013

41

Linear Regression

To obtain individual statistics …

P value : summary(lm(women[,1]~women[,2]))$coeff[2,4]

Regression coefficient:

summary(lm(women[,1]~women[,2]))$coeff[2,1]

Residuals: summary(lm(women[,1]~women[,2]))$residuals

Other regression models can be fitted with the glm() function using

the ‘link’ option eg.

‐ Binomial(link = "logit")

‐

Gamma(link

=

"inverse")‐ Poisson(link = "log") etc…

Course Book Page 51

To Exercise 8 ‐>

Other statisticsMaximum likelihood models

Mixed models

Local approximating regression

Principal Components Analysis/Singular Value Decomposition

Robust regression

ClusteringTree‐based models

Machine learning

…and much more…

Course Book Page 52



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PackagesMany of these statistical features are found in packages developed

by users. These packages can be installed within the R environment

with the command

> install.packages(“package_name”)

Packages have been developed for statistical analysis in different

disciplines

Bioinformatics: Bioconductor

Social Sciences: variety of packages http://cran.r‐

project.org/web/views/SocialSciences.htmlFinancial Engineering: R/Rmetrics

Many more…

Course Book Page 53



06/02/2013

1

Exercise 2

WWWusage Dataset – use the help() command to find out details

Exercise 2

Task 1 Step 1

The ‘WWWusage’ dataset provides a time series of the number of users

connected to the internet through a server each minute. Find out how many

entries there are in this vector

> length(WWWusage)

[1] 100

Task 1 Step 2

Find the average of all the entries with the command

> mean(WWWusage)

[1] 137.08

> summary(WWWusage)

Min. 1st Qu. Median Mean 3rd Qu. Max.

83.0 99.0 138.5 137.1 167.5 228.0

Task 1 Step 3

Extract the 40th to 60th entry (inclusive) in the vector and find that median of

those 21 entries with the command

> median(WWWusage[40:60])

[1] 169



06/02/2013

2

Exercise 2

Task 2 Step

1

The WorldPhones dataset describes the number of telephones in each region

of the world (in the thousands). Find the dimensions of the dataset.

> dim(WorldPhones)

[1] 7 7

Task 2 Step 2

Find the difference between the number of phones in the two regions with

the highest and lowest number of phones respectively in 1957

> head(WorldPhones) ## checks the data format

N.Amer Europe Asia S.Amer Oceania Africa Mid.Amer

1951 45939 21574 2876 1815 1646 89 555

1956 60423 29990 4708 2568 2366 1411 733

1957 64721 32510 5230 2695 2526 1546 773

1958

68484

35218 6662

2845

2691

1663

836

1959 71799 37598 6856 3000 2868 1769 911

1960 76036 40341 8220 3145 3054 1905 1008

> WorldPhones[which(rownames(WorldPhones)==1957),] ‐> phones_1957

## assigns the row representing 1957 to a new vector

> max(phones_1957)‐min(phones_1957)

[1] 63948

Exercise 2

Task 2 Step 3

In which year did Africa have 1411 thousand phones?

> which(WorldPhones[,6]==1411)

1956 ## this is the row name

2 ## this is the row index

Task 2 Step 4

Which area had 45939 thousand phones in 1951?

> which(WorldPhones[1,]==45939)

N.Amer ## this

is

the

column

name

1 ## this is the column index

Task 2 Step 5

Find the total number of phones in all areas in 1959

> WorldPhones[which(rownames(WorldPhones)==1959),] ‐> phones_1959

> sum(phones_1959)

[1] 124801



06/02/2013

3

Exercise 3

Task 1 Step

3

Execute the command by highlighting it then right click | run line or selection. What

output do you get?

[1] "a" "b“

Task 1 Step 4

In the R editor, type in a command that creates a new variable ‘sum_of_a_and_b’ by

adding a and b together

sum_of_a_and_b <‐ a+b

Task 1 Step 5

Remove all objects in the workspace with the command

rm(list=ls())

Exercise 3

Task 2 Step 1

Create a 2 new variables – ‘difference_of_a_and_b’, ’product_of_a_and_b’.

difference_of_a_and_b <‐ a – b

product_of_a_and_b <‐ a * b

Task 2 Step 2

Save these 2 objects in a file called ‘my_objects.Rd’

save(difference_of_a_and_b, product_of_a_and_b, file=“my_objects.Rd”)

Task 2 Step 4

Open a new session of R and load these 2 objects into the workspace

load(“my_objects.Rd”)



06/02/2013

4

Exercise 4

Task 1 Step

1

The text file ‘expenditure.txt’ contains the personal expenditure of US citizens in the

1940s to 1960s.

Open the file in Microsoft notepad to check the format, in particular whether it has

a header row.

Task 1 Step

2

In R, read the file into an object called ‘x’

read.table(“expenditure.txt”, header=TRUE) ‐> x

Exercise 4

Task 1 Step 3

In R, find the standard deviation of Health and Medical expenditure through all the

years represented in the data

> head(x) ## checks that the data is read in correctly

y1940 y1945 y1950 y1955 y1960

Food_and_Tobacco 22.200 44.500 59.60 73.2 86.80

Household_Operation 10.500 15.500 29.00 36.5 46.20

Medical_and_Health 3.530

5.760

9.71

14.0 21.10

Personal_Care 1.040 1.980 2.45 3.4 5.40

Private_Education 0.341 0.974 1.80 2.6 3.64

> as.matrix(x)‐>x.m ## converts from data frame to matrix

> sd(x.m[3,]) ## since health and medical is the 3rd row

[1] 6.995902



06/02/2013

5

Exercise 4

Task 1 Step

4

Open the csv file ‘expenditure.csv’ in Microsoft Excel. Read it into R with the

read.csv() command. Check that the resulting object is similar to the object read in

from the text file.

Exercise 4

Task 1 Step 4

> read.csv("expenditure.csv", header=TRUE) ‐> y

> head(y)

X y1940 y1945 y1950 y1955 y1960

1 Food_and_Tobacco 22.200 44.500 59.60 73.2 86.80

2 Household_Operation 10.500 15.500 29.00 36.5 46.20

3 Medical_and_Health 3.530 5.760 9.71 14.0 21.10

4 Personal_Care 1.040 1.980 2.45 3.4 5.40

5

Private_Education 0.341

0.974

1.80

2.6

3.64

Do note that the row names have become the first column. Hence, if we want to

calculate the SD of the third row, we would have to do this

> as.matrix(y) ‐> y.m

> sd(y.m[3,‐1])

[1] 6.995902



06/02/2013

6

Exercise 4

Task 2 Step

1

> head(Puromycin)

conc rate state

1 0.02 76 treated

2 0.02 47 treated

3 0.06 97 treated

4 0.06 107 treated

5 0.11 123 treated

> summary(Puromycin)

conc rate state

Min. :0.0200 Min. : 47.0 treated :12

1st Qu.:0.0600 1st Qu.: 91.5 untreated:11

Median :0.1100

Median

:124.0

Mean :0.3122 Mean :126.8

3rd Qu.:0.5600 3rd Qu.:158.5

Max. :1.1000 Max. :207.0

Exercise 4

Task 2 Step 2

Create a matrix with the rows of the puromycin dataframe that have ‘treated’ in the

third column

> Puromycin[Puromycin$state=="treated",] ‐> puromycin_treated

Task 2 Step 3

Write out this matrix into a text file

write.table(puromycin_treated,file="puromycin_treated.txt",row.names=FALSE,col.names=TRUE,quote=FALSE)

Open this text file in Microsoft Notepad and check that it contains what you

expected.



06/02/2013

7

Exercise 4

Task 2 Step

2

Create a matrix with the rows of the puromycin dataframe that have a rate of

greater than 100 counts/min/min

> Puromycin[Puromycin$rate>100,] ‐> puromycin_rate_100

Task 2 Step 3

Write out this matrix into a csv file.

> write.csv(puromycin_rate_100,file=“puromycin_rate_100.csv”)

Exercise 4

Task 2 Step 2

Create a matrix with the rows of the puromycin dataframe that have a rate of

greater than 100 counts/min/min

> Puromycin[Puromycin$rate>100,] ‐> puromycin_rate_100

Task 2 Step 3

Write out this matrix into a csv file.

> write.csv(puromycin_rate_100,file=“puromycin_rate_100.csv”)



06/02/2013

8

Exercise 5

Task 1 Step

1

The dataset ‘airquality’ contains daily airquality measurements in New York in 1973.

It is a dataframe with observation of 6 variables – mean ozone in parts per billion,

solar radiation, wind in miles per hour, temperature in degrees fahrenhait, month

and day of month.

> head(airquality)

Ozone Solar.R Wind Temp Month Day

1 41 190 7.4 67 5 1

2 36 118 8.0 72 5 2

3 12 149 12.6 74 5 3

4 18 313 11.5 62 5 4

5 NA NA 14.3 56 5 5

6

28

NA 14.9

66

5

6

Exercise 5

Task 1 Step 2

For each day, we would like to create a hypothetical ‘wind‐temperature’ score

calculated by

Wind *2 + temperature of that day – temperature of the next day

Write a loop to create this score for each day and store it in a vector. It is not

necessary to calculate this value for the last day in the dataset. You should end up

with a vector the length of the number of rows in the data frame minus one.

Hint – Let the loop variable i be the row‐number

wt_score <‐ vector()

as.matrix(airquality)‐>airquality.m

for(i in 1:nrow(airquality.m) ‐1){

2*airquality.m[i,3]+airquality.m[i,4]+airquality.m[(i+1),4] ‐>wt_score[i]

print(i)}



06/02/2013

9

When the

loop

is

executed,

this

is

what

you

get…

…..

[1] 147

[1] 148

[1] 149

[1] 150

[1] 151

[1] 152

> wt_score

[1] 153.8 162.0 161.2 141.0 150.6 160.8 141.2 147.6 170.2 160.2 156.8 154.4

[13] 152.4 147.8 148.4 153.0 147.0 161.8 153.0 140.4 151.4 167.2 141.4 142.0

[25] 148.2 144.8 140.0 172.0 189.8 166.4 168.8 169.2 160.4 183.2 187.4 181.2

[37] 189.6 188.4 190.8 204.6 203.0 206.8 192.4 178.0 186.6 179.0 178.8 178.4

…..

When the loop is executed, this is what you get…

…..

[1] 146

[1] 147

[1] 148

[1] 149

[1] 150

[1] 151

[1] 152

[1] 153

> ts_score

[1] 1 1 1 1 NA 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0

[26] 1 NA 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

[51] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

[76] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

[101] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

…..



06/02/2013

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How to

deal

with

NAs…

1. Leave them as NAs

2. Exclude the whole row

3. Recode them into a different value

Depends on how you intend to analyse the data subsequently…

Exercise 6

Task 1 Step 1

The file ‘text_sample.Rd’ contains 2 objects, ‘txt1’ and ‘txt2’. Load the file into R with

the command load()

> load(“text_sample.Rd”)

> txt1

[1] "my" "dog" "loves" "to" "eat" "green"

[7] "raincoats" "not" "yellow" "ones"

> txt2

[1] "my" "cat" "loves" "to" "eat" "blue"

[7] "raincoats"

"not"

"green"

"ones"

Task 1 Step 1

Create a new vector by concatenating elements of each vector together. The new

vector should read “my” “dog” “loves” “my” “cat”

> c(txt1[1:3],txt2[1:2])‐>combined_txt

> combined_txt

[1] "my" "dog" "loves" "my" "cat"



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11

Exercise 6

Task 1 Step

3

Paste the elements of this new vector together to create a text string that reads “my

dog loves my cat”

Option 1

> paste(“my”, ”dog”, ”loves”, “my”, “cat”, sep=“ “) ‐> combined_txt_string

> combined_txt_string

[1] "my dog loves my cat"

Option 2 (more generalisable)

> combined_txt[1] ‐> y

> for (i in 2:length(combined_txt)){

+ combined_txt[i]‐> x

+ paste(y,x,sep="

")

‐>y}

> y ‐> combined_txt_string

> combined_txt_string

[1] "my dog loves my cat"

Exercise 6

Task 2 Step 1

Split the new string “my dog loves my cat” with the whitespace delimiter “ “

strsplit(combined_txt_string, “ “)[[1]] ‐> split_text

> split_text

[1] "my" "dog" "loves" "my" "cat"

Task 2 Step

2

Extract the second word “dog” from the output of step 1

> split_text[2]‐>x

> x

[1] "dog”

Task 2 Step 3

Extract the word ‘do’ from the word ‘dog’ with the substr() command

> substr(x,1,2)‐> y

> y

[1] "do"



06/02/2013

12

Exercise 7

The dataset ‘longley’ contains economic variables that observed yearly from 1947 to

1962. Plot the unemployed figure on the y axis and the year on the x axis. Use

type=”b” to create a plot with both the points and a line joining them. Label the axes

accordingly. Give your plot an appropriate title.

> head(longley)

GNP.deflator GNP Unemployed Armed.Forces Population Year Employed

1947 83.0 234.289 235.6 159.0 107.608 1947 60.323

1948 88.5 259.426 232.5 145.6 108.632 1948 61.122

1949 88.2 258.054 368.2 161.6 109.773 1949 60.171

1950 89.5 284.599 335.1 165.0 110.929 1950 61.187

1951 96.2 328.975 209.9 309.9 112.075 1951 63.221

1952 98.1 346.999 193.2 359.4 113.270 1952 63.639

Exercise 7

> plot(longley[,2]~longley[,6],type="b",main="Gross National Product by

Year",xlab="year",ylab="Gross National Product")



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13

Exercise 7

Using the

command

points(),

add

the

figures

for

‘Unemployed’

to

the

plot.

Use

type=”b” to create a plot with both points and lines joining them. Colour the points

blue with the option ‘col’.

> points(longley[,3]~longley[,6],type="b",col="blue")

What problem do you

notice? Modify the graph

limits with the ‘ylim’

optionand replot both

lines.

Exercise 7

> plot(longley[,2]~longley[,6],type="b",main="GNP and Employment Figures by

Year",xlab="year",ylab="",ylim=c(150,550))

> points(longley[,3]~longley[,6],type="b",col="blue")

Blue – Unemployment

Figures

Black ‐

GNP



06/02/2013

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Exercise 7

Draw a histogram

of

the

variable

‘Employed’.

Give

it

an

appropriate

title

and

axes

labels. Does it follow a Gaussian distribution?

> hist(longley$Employed,main="Histogram of Employment Figures",xlab="Number

of Employed Individuals")

Bimodal Distribution

Exercise 8

The text file ‘district.txt’ contains the ages of residents in 2 different districts. Plot

the ages as a histogram to assess normality.

> read.table("district.txt",header=TRUE)‐>district_ages

> head(district_ages)

ages district

1 40.07498 1

2 38.97194 1

3 41.53431 1

4 40.50542 1

5 40.44160

1

6 38.47041 1

> hist(district$ages)



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Exercise 8

Since the

distribution

is

approximately

gaussian,

we

can

use

the

T test.

> table(district_ages$district) ## this checks how the districts are labelled

1 2 ## in this case, the districts are labelled 1 and 2

100 100

> t.test(district_ages[district_ages$district==1,1],district_ages[district_ages$district==2,1])

t = ‐12.2399, df = 196.978, p‐value < 2.2e‐16



‐1.935837 ‐1.398598

sample estimates:

mean of

x mean

of

y 40.13208 41.79930

Exercise 8

The file ‘age_weight.txt’ contains information about the age and weights of

participants in a clinical study. There are 2 groups of participants – healthy controls

and patients with carpal tunnel syndrome. Plot the age variable vs the weight

variable on a graph to assess if the relationship is linear.

> read.table("age_weight.txt",header=TRUE)‐> aw

> head(aw)

Age Weight Status

1 28 47 control

2 40

45 control

3 26 50 control



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16

Exercise 8

> plot(aw$Weight~aw$Age,main="Graph

of

weight

vs age

of

participants",xlab="age",ylab="weight")

Exercise 8

Create histograms of ages and weights to assess whether these variables have a

normal distribution. What correlation test is appropriate for this situation?

> hist(aw$Weight,main="histogram of participants' weights",xlab="weights in kilograms")



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Exercise 8

> hist(aw$Age,main="histogram

of

participants'

ages",xlab="age

in

years")

Exercise 8

Perform the correlation test on the whole dataset

> cor.test(aw$Weight,aw$Age)

t = 31.9103, df = 198, p‐value < 2.2e‐16



0.8891198 0.9350319

sample estimates:

cor

0.9149901



06/02/2013

Exercise 8

Perform the

correlation

test

separately

on

patients

and

on

controls

> cor.test(aw$Weight[aw$Status=="control"],aw$Age[aw$Status=="control"])

t = ‐0.5959, df = 98, p‐value = 0.5526



‐0.2535143 0.1379581

sample estimates:

cor

‐0.06008829

> cor.test(aw$Weight[aw$Status=="CTS"],aw$Age[aw$Status=="CTS"])

t = 18.5412, df = 98, p‐value < 2.2e‐16


95 percent confidence

interval:

0.8294343 0.9192753

sample estimates:

cor

0.8821381