Chapter 1 Practice with basic R

The main purpose of this session is to give participants who have not had much (or any) experience with using R a chance to practice the basics and to ask questions. For others, it should serve as a reminder of some of the basic features of the language.

R can be installed on all major platforms (i.e. Windows, macOS, Linux). We do not assume in this exercise that you are using any particular platform. Many people like to use the RStudio graphical user interface (GUI), which gives the same look and feel across all platforms.

1.1 The working directory

A key concept in R is the working directory (or folder in the terminology of Windows). The working directory is where R looks for data files that you may want to read in and where R will write out any files you create. It is a good idea to keep separate working directories for different projects. In this course we recommend that you keep a separate working directory for each exercise.

If you are working on the command line in a terminal, then you can change to the correct working directory and then launch R by typing R.

If you are using a GUI then you will typically need to change to the correct working directory after starting R. In RStudio, you can change directory from the Session menu. However it is much more useful to create a new project to keep your source files and data. When you open a project in the RStudio GUI, your working directory is automatically changed to the directory associated with the project.

You can display the current working directory with the getwd() (get working directory) function and set it with the setwd() (set working directory) function. The function dir() can be used to see what files you have in the working directory.

1.2 The workspace

You can quit R by typing

q()

at the R command prompt. You will be asked if you want to save your workspace. We strongly recommend that you answer no to this question. If you answer yes then R will write a file named .RData into the working directory containing all the objects you created during your session. This file will be automatically loaded the next time you start R and this will restore all the objects in your workspace.

It may seem convenient to keep your R objects from one session to another. But this has many disadvantages.

You may not remember how an object was created. This becomes a problem if you need to redo your analysis after the data has been changed or updated, or if you accidentally delete the object.
An object might be modified or overwritten. In this case your analysis will give you a different answer but you will not know why. You may not even notice that the answer has changed.
It becomes impossible to clean your workspace if you cannot remember which objects are required by which analyses. As a result, your workspace will become cluttered with old objects.

We strongly recommend that you follow some basic principles of reproducible research.

Always start with a clean (empty) workspace.
Read in the data you need from a pristine source.
Put your R commands in a script file so that they can be run again in a future session.
All modifications to the data that you need to make should be done in R using a script and not by editing the data source. This way, if the original data is modified or updated then you can run the script again on the updated data.

1.3 Using R as a calculator

Try using R as an interactive calculator by typing different arithmetic expressions on the command line. Pressing the return key on the command line finishes the expression. R will then evaluate the expression and print out the result.

Note that R allows you to recall previous commands using the vertical arrow key. You can edit a recalled command and then resubmit it by pressing the return key. Keeping that in mind, try the following:

12 + 16
(12 + 16) * 5
sqrt((12 + 16) * 5) # square root
round(sqrt((12 + 16) * 5), 2) # round to two decimal places

The hash symbol # denotes the start of a comment. Anything after the hash is ignored by R.

Round braces are used a lot in R. In the above expressions, they are used in two different ways. Firstly, they can be used to establish the order of operations. In the example

(12 + 16) * 5

## [1] 140

they ensure that 12 is added to 16 before the result is multiplied by 5. If you omit the braces then you get a different answer

12 + 16 * 5

## [1] 92

because multiplication has higher precedence than addition. The second use of round braces is in a function call (e.g. sqrt, round). To call a function in R, type the name followed by the arguments inside round braces. Some functions take multiple arguments, and in this case they are separated by commas.

You can see that complicated expressions in R can have several levels of nested braces. To keep track of these, it helps to use a syntax-highlighting editor. For example, in RStudio, when you type an opening bracket (, RStudio will automatically add a closing bracket ), and when the cursor moves past a closing bracket, RStudio will automatically highlight the corresponding opening bracket. Features like this can make it much easier to write R code free from syntax errors.

Instead of printing the result to the screen, you can store it in an object, say

a <- round(sqrt((12 + 16) * 5), 2)

In this case R does not print anything to the screen. You can see the results of the calculation, stored in the object a, by typing a and also use a for further calculations, e.g:

exp(a)
log(a) # natural logarithm
log10(a) # log to the base 10

The left arrow expression <-, pronounced gets, is called the assignment operator, and is obtained by typing < followed by - (with no space in between). It is also possible to use the equals sign = for assignment.

Note that object names in R are case sensitive. So you can assign different values to objects named A and a.

1.4 Vectors

All commands in R are functions which act on objects. One important kind of object is a vector, which is an ordered collection of numbers, or character strings (e.g. Charles Darwin), or logical values (TRUE or FALSE). The components of a vector must be of the same type (numeric, character, or logical). The combine function c(), together with the assignment operator, is used to create vectors. Thus

v <- c(4, 6, 1, 2.2)

creates a vector v with components 4, 6, 1, 2.2 and assigns the result to the vector v.

A key feature of the R language is that many operations are vectorized, meaning that you can carry out the same operation on each element of a vector in a single operation. Try

## [1] 4.0 6.0 1.0 2.2

3 + v

## [1] 7.0 9.0 4.0 5.2

3 * v

## [1] 12.0 18.0  3.0  6.6

and you will see that R understands what to do in each case.

R extends ordinary arithmetic with the concept of a missing value represented by the symbol NA (Not Available). Any operation on a missing value creates another missing value. You can see this by repeating the same operations on a vector containing a missing value:

v <- c(4, 6, NA)
3 + v

## [1]  7  9 NA

3 * v

## [1] 12 18 NA

The fact that every operation on a missing value produces a missing value can be a nuisance when you want to create a summary statistic for a vector:

mean(v)

## [1] NA

While it is true that the mean of v is unknown because the value of the third element is missing, we normally want the mean of the non-missing elements. Fortunately the mean function has an optional argument called na.rm which can be used for this.

mean(v, na.rm = TRUE)

## [1] 5

Many functions in R have optional arguments that can be omitted, in which case they take their default value (For example, the mean function has default na.rm=FALSE). You can explicitly values to optional arguments in the function call to override the default behaviour.

You can get a description of the structure of any object using the function str(). For example, str(v) shows that v is numeric with 4 components. If you just want to know the length of a vector then it is much easier to use the length function.

length(v)

## [1] 3

1.5 Sequences

There are short-cut functions for creating vectors with a regular structure. For example, if you want a vector containing the sequence of integers from 1 to 10, you can use

1:10

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

The seq() function allows the creation of more general sequences. For example, the vector (15, 20, 25, … ,85) can be created with

seq(from = 15, to = 85, by = 5)

##  [1] 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

The objects created by the : operator and the seq() function are ordinary vectors, and can be combined with other vectors using the combine function:

c(5, seq(from = 20, to = 85, by = 5))

##  [1]  5 20 25 30 35 40 45 50 55 60 65 70 75 80 85

You can learn more about functions by typing ? followed by the function name. For example ?seq gives information about the syntax and usage of the function seq().

Create a vector w with components 1, -1, 2, -2
Display this vector

## [1]  1 -1  2 -2

Obtain a description of w using str()

##  num [1:4] 1 -1 2 -2

Create the vector w+1, and display it.

## [1]  2  0  3 -1

Create the vector v with components (5, 10, 15, … , 75) using seq().

##  [1]  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Now add the components 0 and 1 to the beginning of v using c().

##  [1]  0  1  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Find the length of this vector.

## [1] 17

1.6 Displaying and changing parts of a vector (indexing)

Square brackets in R are used to extract parts of vectors. So x[1] gives the first element of vector x. Since R is vectorized you can also supply a vector of integer index values inside the square brackets. Any expression that creates an integer vector will work.

Try the following commands:

x <- c(2, 7, 0, 9, 10, 23, 11, 4, 7, 8, 6, 0)
x[4]

## [1] 9

x[3:5]

## [1]  0  9 10

x[c(1, 5, 8)]

## [1]  2 10  4

Trying to extract an element that is beyond the end of the vector is, surprisingly, not an error. Instead, this returns a missing value

N <- length(x)
x[N + 1]

## [1] NA

There is a reason for this behaviour, which we will discuss in the recap.

R also allows logical subscripting. Try the following

x > 10

##  [1] FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE

x[x > 10]

## [1] 23 11

The first expression creates a logical vector of the same length as x, where each element has the value TRUE or FALSE depending on whether or not the corresponding element of x is greater than 10. If you supply a logical vector as an index, R selects only those elements for which the conditions is TRUE.

You can combine two logical vectors with the operators & (logical and) and | (logical or). For example, to select elements of x that are between 10 and 20 we combine two one-sided logical conditions for $x \geq 10$ and $x \leq 20$:

x[x >= 10 & x <= 20]

## [1] 10 11

The remaining elements of x that are either less than 10 or greater than 20 are selected with

x[x < 10 | x > 20]

##  [1]  2  7  0  9 23  4  7  8  6  0

Indexing can also be used to replace parts of a vector:

x[1] <- 1000
x

##  [1] 1000    7    0    9   10   23   11    4    7    8    6    0

This replaces the first element of x. Logical subscripting is useful for replacing parts of a vector that satisfy a certain condition. For example to replace all elements that take the value 0 with the value 1:

x[x == 0] <- 1
x

##  [1] 1000    7    1    9   10   23   11    4    7    8    6    1

If you want to replace parts of a vector then you need to make sure that the replacement value is either a single value, as in the example above, or a vector equal in length to the number of elements to be replaced. For example, to replace elements 2, 3, and 4 we need to supply a vector of replacement values of length 3.

x[2:4] <- c(0, 8, 1)
x

##  [1] 1000    0    8    1   10   23   11    4    7    8    6    1

It is important to remember this when you are using logical subscripting because the number of elements to be replaced is not given explicitly in the R code, and it is easy to get confused about how many values need to be replaced. If we want to add 3 to every element that is less than 3 then we can break the operation down into 3 steps:

y <- x[x < 3]
y <- y + 3
x[x < 3] <- y
x

##  [1] 1000    3    8    4   10   23   11    4    7    8    6    4

First we extract the values to be modified, then we modify them, then we write back the modified values to the original positions. R experts will normally do this in a single expression.

x[x < 3] <- x[x < 3] + 3

Remember, if you are confused by a complicated expression you can usually break it down into simpler steps.

If you want to create an entirely new vector based on some logical condition then use the ifelse() function. This function takes three arguments: the first is a logical vector; the second is the value taken by elements of the logical vector that are TRUE; and the third is the value taken by elements that are FALSE.

In this example, we use the remainder operator %% to identify elements of x that have value 0 when divided by 2 (i.e. the even numbers) and then create a new character vector with the labels even and odd:

x %% 2

##  [1] 0 1 0 0 0 1 1 0 1 0 0 0

ifelse(x %% 2 == 0, "even", "odd")

##  [1] "even" "odd"  "even" "even" "even" "odd"  "odd"  "even" "odd"  "even"
## [11] "even" "even"

Now try the following:

Display elements that are less than 10, but greater than 4
Modify the vector x, replacing by 10 all values that are greater than 10
Modify the vector x, multiplying by 2 all elements that are smaller than 5 (Remember you can do this in steps).

1.7 Lists

Collections of components of different types are called lists, and are created with the list() function. Thus

m <- list(4, TRUE, "name of company")
m

## [[1]]
## [1] 4
## 
## [[2]]
## [1] TRUE
## 
## [[3]]
## [1] "name of company"

creates a list with 3 components: the first is numeric, the second is logical and the third is character. A list element can be any object, including another list. This flexibility means that functions that need to return a lot of complex information, such as statistical modelling functions, often return a list.

As with vectors, single square brackets are used to take a subset of a list, but the result will always be another list, even if you select only one element

m[1:2] # A list containing first two elements of m

## [[1]]
## [1] 4
## 
## [[2]]
## [1] TRUE

m[3] # A list containing the third element of m

## [[1]]
## [1] "name of company"

If you just want to extract a single element of a list then you must use double square braces:

m[[3]] # Extract third element

## [1] "name of company"

Lists are more useful when their elements are named. You can name an element by using the syntax name=value in the call to the list function:

mylist <- list(
  name = c("Joe", "Ann", "Jack", "Tom"),
  age = c(34, 50, 27, 42)
)
mylist

## $name
## [1] "Joe"  "Ann"  "Jack" "Tom" 
## 
## $age
## [1] 34 50 27 42

This creates a new list with the elements name, a character vector of names, and age a numeric vector of ages. The components of the list can be extracted with a dollar sign $

mylist$name

## [1] "Joe"  "Ann"  "Jack" "Tom"

mylist$age

## [1] 34 50 27 42

1.8 Data frames

Data frames are a special structure used when we want to store several vectors of the same length, and corresponding elements of each vector refer to the same record. For example, here we create a simple data frame containing the names of some individuals along with their age in years, their sex (coded 1 or 2) and their height in cm.

mydata <- data.frame(
  name = c("Joe", "Ann", "Jack", "Tom"),
  age = c(34, 50, 27, 42), 
  sex = c(1, 2, 1, 1),
  height = c(185, 170, 175, 182)
)

The construction of a data frame is just like a named list (except that we use the constructor function data.frame instead of list). In fact data frames are also lists so, for example, you can extract vectors using the dollar sign:

mydata$height

## [1] 185 170 175 182

On the other hand, data frames are also two dimensional objects:

mydata

##   name age sex height
## 1  Joe  34   1    185
## 2  Ann  50   2    170
## 3 Jack  27   1    175
## 4  Tom  42   1    182

When you print a data frame, each variable appears in a separate column. You can use square brackets with two comma-separated arguments to take subsets of rows or columns.

mydata[1, ]

##   name age sex height
## 1  Joe  34   1    185

mydata[, c("age", "height")]

##   age height
## 1  34    185
## 2  50    170
## 3  27    175
## 4  42    182

mydata[2, 4]

## [1] 170

We will look into indexing of data frames in more detail below.

Now let’s create another data frame with more individuals than the first one:

yourdata <- data.frame(
  name = c("Ann", "Peter", "Sue", "Jack", "Tom", "Joe", "Jane"),
  weight = c(67, 81, 56, 90, 72, 79, 69)
)

This new data frame contains the weights of the individuals. The two data sets can be joined together with the merge function.

newdata <- merge(mydata, yourdata)
newdata

##   name age sex height weight
## 1  Ann  50   2    170     67
## 2 Jack  27   1    175     90
## 3  Joe  34   1    185     79
## 4  Tom  42   1    182     72

The merge function uses the variables common to both data frames – in this case the variable name – to uniquely identify each row. By default, only rows that are in both data frames are preserved, the rest are discarded. In the above example, the records for Peter, Sue, and Jane, which are not in mydata are discarded. If you want to keep them, use the optional argument all=TRUE.

newdata <- merge(mydata, yourdata, all = TRUE)
newdata

##    name age sex height weight
## 1   Ann  50   2    170     67
## 2  Jack  27   1    175     90
## 3  Jane  NA  NA     NA     69
## 4   Joe  34   1    185     79
## 5 Peter  NA  NA     NA     81
## 6   Sue  NA  NA     NA     56
## 7   Tom  42   1    182     72

This keeps a row for all individuals but since Peter, Sue and Jane have no recorded age, height, or sex these are missing values.

1.9 Working with built-in data frames

We shall use the births data which concern 500 mothers who had singleton births (i.e. no twins) in a large London hospital. The outcome of interest is the birth weight of the baby, also dichotomised as normal or low birth weight. These data are available in the Epi package:

library(Epi)
data(births)
objects()

##  [1] "births"   "m"        "mydata"   "mylist"   "N"        "newdata" 
##  [7] "v"        "w"        "x"        "y"        "yourdata"

The function objects() shows what is in your workspace. To find out a bit more about births try

help(births)

The dataframe "diet" in the Epi package contains data from a follow-up study with coronary heart disease as the end-point.

Load these data with

data(diet)

and print the contents of the data frame to the screen.. 2. Check that you now have two objects, births, and diet in your workspace. 3. Get help on the object diet. 4. Remove the object diet with the command

remove(diet)

Check that the object diet is no longer in your workspace.

1.10 Referencing parts of the data frame (indexing)

Typing births will list the entire data frame – not usually very helpful. You can use the head function to see just the first few rows of a data frame

head(births)

##   id bweight lowbw gestwks preterm matage hyp sex
## 1  1    2974     0   38.52       0     34   0   2
## 2  2    3270     0      NA      NA     30   0   1
## 3  3    2620     0   38.15       0     35   0   2
## 4  4    3751     0   39.80       0     31   0   1
## 5  5    3200     0   38.89       0     33   1   1
## 6  6    3673     0   40.97       0     33   0   2

Now try

births[1, ]

##   id bweight lowbw gestwks preterm matage hyp sex
## 1  1    2974     0   38.52       0     34   0   2

This will list all the values for the first row. Similarly,

births[2, ]

##   id bweight lowbw gestwks preterm matage hyp sex
## 2  2    3270     0      NA      NA     30   0   1

will list the value taken by the second row, and so on. To list the data for the first 10 subjects, try

births[1:10, ]

##    id bweight lowbw gestwks preterm matage hyp sex
## 1   1    2974     0   38.52       0     34   0   2
## 2   2    3270     0      NA      NA     30   0   1
## 3   3    2620     0   38.15       0     35   0   2
## 4   4    3751     0   39.80       0     31   0   1
## 5   5    3200     0   38.89       0     33   1   1
## 6   6    3673     0   40.97       0     33   0   2
## 7   7    3628     0   42.14       0     29   0   2
## 8   8    3773     0   40.21       0     37   0   1
## 9   9    3960     0   42.03       0     36   0   2
## 10 10    3405     0   39.33       0     39   0   1

Often we want to extract rows of a data frame based on a condition. To select all subjects with height less than 180 cm from the data frame mydata we can use the subset() function.

subset(mydata, height < 180)

##   name age sex height
## 2  Ann  50   2    170
## 3 Jack  27   1    175

1.11 Summaries

A good way to start an analysis is to ask for a summary of the data by typing

summary(births)

##        id           bweight         lowbw         gestwks         preterm      
##  Min.   :  1.0   Min.   : 628   Min.   :0.00   Min.   :24.69   Min.   :0.0000  
##  1st Qu.:125.8   1st Qu.:2862   1st Qu.:0.00   1st Qu.:37.94   1st Qu.:0.0000  
##  Median :250.5   Median :3188   Median :0.00   Median :39.12   Median :0.0000  
##  Mean   :250.5   Mean   :3137   Mean   :0.12   Mean   :38.72   Mean   :0.1286  
##  3rd Qu.:375.2   3rd Qu.:3551   3rd Qu.:0.00   3rd Qu.:40.09   3rd Qu.:0.0000  
##  Max.   :500.0   Max.   :4553   Max.   :1.00   Max.   :43.16   Max.   :1.0000  
##                                                NA's   :10      NA's   :10      
##      matage           hyp             sex       
##  Min.   :23.00   Min.   :0.000   Min.   :1.000  
##  1st Qu.:31.00   1st Qu.:0.000   1st Qu.:1.000  
##  Median :34.00   Median :0.000   Median :1.000  
##  Mean   :34.03   Mean   :0.144   Mean   :1.472  
##  3rd Qu.:37.00   3rd Qu.:0.000   3rd Qu.:2.000  
##  Max.   :43.00   Max.   :1.000   Max.   :2.000  
##

This prints some summary statistics (minimum, lower quartile, mean, median, upper quartile, maximum). For variables with missing values, the number of NAs is also printed.

To see the names of the variables in the data frame try

names(births)

## [1] "id"      "bweight" "lowbw"   "gestwks" "preterm" "matage"  "hyp"    
## [8] "sex"

Variables in a data frame can be referred to by name, but to do so it is necessary also to specify the name of the data frame. Thus births$hyp refers to the variable hyp in the births data frame, and typing births$hyp will print the data on this variable. To summarize the variable hyp try

summary(births$hyp)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   0.000   0.000   0.144   0.000   1.000

Alternatively you can use

with(births, summary(hyp))

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   0.000   0.000   0.144   0.000   1.000

1.12 Generating new variables

New variables can be produced using assignment together with the usual mathematical operations and functions. For example

logbw <- log(births$bweight)

produces the variable logbw in your workspace, while

births$logbw <- log(births$bweight)

produces the variable logbw in the births data frame.

You can also replace existing variables. For example bweight measures birth weight in grams. To convert the units to kilograms we replace the original variable with a new one:

births$bweight <- births$bweight / 1000

1.13 Turning a variable into a factor

In R categorical variables are known as factors, and the different categories are called the levels of the factor. Variables such as hyp and sex are originally coded using integer codes, and by default R will interpret these codes as numeric values taken by the variables. Factors will become very important later in the course when we study modelling functions, where factors and numeric variables are treated very differently. For the moment, you can think of factors as value labels that are more informative than numeric codes.

For R to recognize that the codes refer to categories it is necessary to convert the variables to be factors, and to label the levels. To convert the variable hyp to be a factor, try

births$hyp <- factor(births$hyp, labels = c("normal", "hyper"))

This takes the original numeric codes (0, 1) and replaces them with informative labels normal’’ and ``hyper for normal blood pressure and hypertension, respectively.

Convert the variable sex into a factor with labels "M" and "F" for values 1 and 2, respectively

1.14 Frequency tables

When starting to look at any new data frame the first step is to check that the values of the variables make sense and correspond to the codes defined in the coding schedule. For categorical variables (factors) this can be done by looking at one-way frequency tables and checking that only the specified codes (levels) occur. The most useful function for making simple frequency tables is table. The distribution of the factor hyp can be viewed using

with(births, table(hyp))

## hyp
## normal  hyper 
##    428     72

or by specifying the data frame as in

table(births$hyp)

## 
## normal  hyper 
##    428     72

For simple expressions the choice is a matter of taste, but with is shorter for more complicated expressions.

Find the frequency distribution of sex.

## 
##   M   F 
## 264 236

## sex
##   M   F 
## 264 236

If you give two or more arguments to the table function then it produces cross-tabulations. Find the two-way frequency distribution of sex and hyp.

##    hyp
## sex normal hyper
##   M    221    43
##   F    207    29

Create a logical variable called early according to whether gestwks is less than 30 or not. Make a frequency table of early.

## early
## FALSE  TRUE 
##   485     5

1.15 Grouping the values of a numeric variable

For a numeric variable like matage it is often useful to group the values and to create a new factor which codes the groups. For example we might cut the values taken by matage into the groups 20–29, 30–34, 35–39, 40–44, and then create a factor called agegrp with 4 levels corresponding to the four groups. The best way of doing this is with the function cut. Try

births$agegrp <- 
  cut(
    births$matage, 
    breaks = c(20, 30, 35, 40, 45), 
    right = FALSE
  )
with(births, table(agegrp))

## agegrp
## [20,30) [30,35) [35,40) [40,45) 
##      70     200     194      36

By default the factor levels are labelled [20-25), [25-30), etc., where [20-25) refers to the interval which includes the left hand end (20) but not the right hand end (25). This is the reason for right=FALSE. When right=TRUE (which is the default) the intervals include the right hand end but not the left hand.

Observations which are not inside the range specified by the breaks argument result in missing values for the new factor. Hence it is important that the first element in breaks is smaller than the smallest value in your data, and the last element is larger than the largest value.

Summarize the numeric variable gestwks, which records the length of gestation for the baby, and make a note of the range of values.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   24.69   37.94   39.12   38.72   40.09   43.16      10

Create a new factor gest4 which cuts gestwks at 20, 35, 37, 39, and 45 weeks, including the left hand end, but not the right hand. Make a table of the frequencies for the four levels of gest4.