3 Transforming, summarising, and analysing data

Most datasets are stored as tables, with rows and columns. In this chapter we’ll see how you can import and export such data, and how it is stored in R. We’ll also discuss how you can transform, summarise, and analyse your data.

After working with the material in this chapter, you will be able to use R to:

  • Distinguish between different data types,
  • Import data from Excel spreadsheets and csv text files,
  • Compute descriptive statistics for subgroups in your data,
  • Find interesting points in your data,
  • Add new variables to your data,
  • Modify variables in your data,
  • Remove variables from your data,
  • Save and export your data,
  • Work with RStudio projects,
  • Run t-tests and fit linear models,
  • Use %>% pipes to chain functions together.

The chapter ends with a discussion of ethical guidelines for statistical work.

3.1 Data frames and data types

3.1.1 Types and structures

We have already seen that different kinds of data require different kinds of statistical methods. For numeric data we create boxplots and compute means, but for categorical data we don’t. Instead we produce bar charts and display the data in tables. It is no surprise then, that what R also treats different kinds of data differently.

In programming, a variable’s_data type_ describes what kind of object is assigned to it. We can assign many different types of objects to the variable a: it could for instance contain a number, text, or a data frame. In order to treat a correctly, R needs to know what data type its assigned object has. In some programming languages, you have to explicitly state what data type a variable has, but not in R. This makes programming R simpler and faster, but can cause problems if a variable turns out to have a different data type than what you thought14.

R has six basic data types. For most people, it suffices to know about the first three in the list below:

  • numeric: numbers like 1 and 16.823 (sometimes also called double).
  • logical: true/false values (boolean): either TRUE or FALSE.
  • character: text, e.g. "a", "Hello! I'm Ada." and "name@domain.com".
  • integer: integer numbers, denoted in R by the letter L: 1L, 55L.
  • complex: complex numbers, like 2+3i. Rarely used in statistical work.
  • raw: used to hold raw bytes. Don’t fret if you don’t know what that means. You can have a long and meaningful career in statistics, data science, or pretty much any other field without ever having to worry about raw bytes. We won’t discuss raw objects again in this book.

In addition, these can be combined into special data types sometimes called data structures, examples of which include vectors and data frames. Important data structures include factor, which is used to store categorical data, and the awkwardly named POSIXct which is used to store date and time data.

To check what type of object a variable is, you can use the class function:

x <- 6
y <- "Scotland"
z <- TRUE


What happens if we use class on a vector?

numbers <- c(6, 9, 12)

class returns the data type of the elements of the vector. So what happens if we put objects of different type together in a vector?

all_together <- c(x, y, z)

In this case, R has coerced the objects in the vector to all be of the same type. Sometimes that is desirable, and sometimes it is not. The lesson here is to be careful when you create a vector from different objects. We’ll learn more about coercion and how to change data types in Section 5.1.

3.1.2 Types of tables

The basis for most data analyses in R are data frames: spreadsheet-like tables with rows and columns containing data. You encountered some data frames in the previous chapter. Have a quick look at them to remind yourself of what they look like:

# Bookstore example
age <- c(28, 48, 47, 71, 22, 80, 48, 30, 31)
purchase <- c(20, 59, 2, 12, 22, 160, 34, 34, 29)
bookstore <- data.frame(age, purchase)

# Animal sleep data

# Diamonds data

Notice that all three data frames follow the same format: each column represents a variable (e.g. age) and each row represents an observation (e.g. an individual). This is the standard way to store data in R (as well as the standard format in statistics in general). In what follows, we will use the terms column and variable interchangeably, to describe the columns/variables in a data frame.

This kind of table can be stored in R as different types of objects - that is, in several different ways. As you’d expect, the different types of objects have different properties and can be used with different functions. Here’s the run-down of four common types:

  • matrix: a table where all columns must contain objects of the same type (e.g. all numeric or all character). Uses less memory than other types and allows for much faster computations, but is difficult to use for certain types of data manipulation, plotting and analyses.
  • data.frame: the most common type, where different columns can contain different types (e.g. one numeric column, one character column).
  • data.table: an enhanced version of data.frame.
  • tbl_df (“tibble”): another enhanced version of data.frame.

First of all, in most cases it doesn’t matter which of these four that you use to store your data. In fact, they all look similar to the user. Have a look at the following datasets (WorldPhones and airquality come with base R):

# First, an example of data stored in a matrix:

# Next, an example of data stored in a data frame:

# Finally, an example of data stored in a tibble:

That being said, in some cases it really matters which one you use. Some functions require that you input a matrix, while others may break or work differently from what was intended if you input a tibble instead of an ordinary data frame. Luckily, you can convert objects into other types:

WorldPhonesDF <- as.data.frame(WorldPhones)

airqualityMatrix <- as.matrix(airquality)


Exercise 3.1 The following tasks are all related to data types and data structures:

  1. Create a text variable using e.g. a <- "A rainy day in Edinburgh". Check that it gets the correct type. What happens if you use single quotes marks instead of double quotes when you create the variable?

  2. What data types are the sums 1 + 2, 1L + 2 and 1L + 2L?

  3. What happens if you add a numeric to a character, e.g. "Hello" + 1?

  4. What happens if you perform mathematical operations involving a numeric and a logical, e.g. FALSE * 2 or TRUE + 1?

(Click here to go to the solution.)

Exercise 3.2 What do the functions ncol, nrow, dim, names, and row.names return when applied to a data frame?

(Click here to go to the solution.)

Exercise 3.3 matrix tables can be created from vectors using the function of the same name. Using the vector x <- 1:6 use matrix to create the following matrices:

\[\begin{pmatrix} 1 & 2 & 3\\ 4 & 5 & 6 \end{pmatrix}\]


\[\begin{pmatrix} 1 & 4\\ 2 & 5\\ 3 & 6 \end{pmatrix}.\]

Remember to check ?matrix to find out how to set the dimensions of the matrix, and how it is filled with the numbers from the vector!

(Click here to go to the solution.)

3.2 Vectors in data frames

In the next few sections, we will explore the airquality dataset. It contains daily air quality measurements from New York during a period of five months:

  • Ozone: mean ozone concentration (ppb),
  • Solar.R: solar radiation (Langley),
  • Wind: average wind speed (mph),
  • Temp: maximum daily temperature in degrees Fahrenheit,
  • Month: numeric month (May=5, June=6, and so on),
  • Day: numeric day of the month (1-31).

There are lots of things that would be interesting to look at in this dataset. What was the mean temperature during the period? Which day was the hottest? Which was the windiest? What days were the temperature more than 90 degrees Fahrenheit? To answer these questions, we need to be able to access the vectors inside the data frame. We also need to be able to quickly and automatically screen the data in order to find interesting observations (e.g. the hottest day)

3.2.1 Accessing vectors and elements

In Section 2.6, we learned how to compute the mean of a vector. We also learned that to compute the mean of a vector that is stored inside a data frame15 we could use a dollar sign: data_frame_name$vector_name. Here is an example with the airquality data:

# Extract the Temp vector:

# Compute the mean temperature:

If we want to grab a particular element from a vector, we must use its index within square brackets: [index]. The first element in the vector has index 1, the second has index 2, the third index 3, and so on. To access the fifth element in the Temp vector in the airquality data frame, we can use:


The square brackets can also be applied directly to the data frame. The syntax for this follows that used for matrices in mathematics: airquality[i, j] means the element at the i:th row and j:th column of airquality. We can also leave out either i or j to extract an entire row or column from the data frame. Here are some examples:

# First, we check the order of the columns:
# We see that Temp is the 4th column.

airquality[5, 4]    # The 5th element from the 4th column,
                    # i.e. the same as airquality$Temp[5]
airquality[5,]      # The 5th row of the data
airquality[, 4]     # The 4th column of the data, like airquality$Temp
airquality[[4]]     # The 4th column of the data, like airquality$Temp
airquality[, c(2, 4, 6)] # The 2nd, 4th and 6th columns of the data
airquality[, -2]    # All columns except the 2nd one
airquality[, c("Temp", "Wind")] # The Temp and Wind columns


Exercise 3.4 The following tasks all involve using the the [i, j] notation for extracting data from data frames:

  1. Why does airquality[, 3] not return the third row of airquality?

  2. Extract the first five rows from airquality. Hint: a fast way of creating the vector c(1, 2, 3, 4, 5) is to write 1:5.

  3. Compute the correlation between the Temp and Wind vectors of airquality without refering to them using $.

  4. Extract all columns from airquality except Temp and Wind.

(Click here to go to the solution.)

3.2.2 Use your dollars

The $ operator can be used not just to extract data from a data frame, but also to manipulate it. Let’s return to our bookstore data frame, and see how we can make changes to it using the dollar sign.

age <- c(28, 48, 47, 71, 22, 80, 48, 30, 31)
purchase <- c(20, 59, 2, 12, 22, 160, 34, 34, 29)
bookstore <- data.frame(age, purchase)

Perhaps there was a data entry error - the second customer was actually 18 years old and not 48. We can assign a new value to that element by referring to it in either of two ways:

bookstore$age[2] <- 18
# or
bookstore[2, 1] <- 18

We could also change an entire column if we like. For instance, if we wish to change the age vector to months instead of years, we could use

bookstore$age <- bookstore$age * 12

What if we want to add another variable to the data, for instance the length of the customers’ visits in minutes? There are several ways to accomplish this, one of which involves the dollar sign:

bookstore$visit_length <- c(5, 2, 20, 22, 12, 31, 9, 10, 11)

As you see, the new data has now been added to a new column in the data frame.


Exercise 3.5 Use the bookstore data frame to do the following:

  1. Add a new variable rev_per_minute which is the ratio between purchase and the visit length.

  2. Oh no, there’s been an error in the data entry! Replace the purchase amount for the 80-year old customer with 16.

(Click here to go to the solution.)

3.2.3 Using conditions

A few paragraphs ago, we were asking which was the hottest day in the airquality data. Let’s find out! We already know how to find the maximum value in the Temp vector:


But can we find out which day this corresponds to? We could of course manually go through all 153 days e.g. by using View(airquality), but that seems tiresome and wouldn’t even be possible in the first place if we’d had more observations. A better option is therefore to use the function which.max:


which.max returns the index of the observation with the maximum value. If there is more than one observation attaining this value, it only returns the first of these.

We’ve just used which.max to find out that day 120 was the hottest during the period. If we want to have a look at the entire row for that day, we can use


Alternatively, we could place the call to which.max inside the brackets. Because which.max(airquality$Temp) returns the number 120, this yields the same result as the previous line:


Were we looking for the day with the lowest temperature, we’d use which.min analogously. In fact, we could use any function or computation that returns an index in the same way, placing it inside the brackets to get the corresponding rows or columns. This is extremely useful if we want to extract observations with certain properties, for instance all days where the temperature was above 90 degrees. We do this using conditions, i.e. by giving statements that we wish to be fulfilled.

As a first example of a condition, we use the following, which checks if the temperature exceeds 90 degrees:

airquality$Temp > 90

For each element in airquality$Temp this returns either TRUE (if the condition is fulfilled, i.e. when the temperature is greater than 90) or FALSE (if the conditions isn’t fulfilled, i.e. when the temperature is 90 or lower). If we place the condition inside brackets following the name of the data frame, we will extract only the rows corresponding to those elements which were marked with TRUE:

airquality[airquality$Temp > 90, ]

If you prefer, you can also store the TRUE or FALSE values in a new variable:

airquality$Hot <- airquality$Temp > 90

There are several logical operators and functions which are useful when stating conditions in R. Here are some examples:

a <- 3
b <- 8

a == b     # Check if a equals b
a > b      # Check if a is greater than b
a < b      # Check if a is less than b
a >= b     # Check if a is equal to or greater than b
a <= b     # Check if a is equal to or less than b
a != b     # Check if a is not equal to b
is.na(a)   # Check if a is NA
a %in% c(1, 4, 9) # Check if a equals at least one of 1, 4, 9

When checking a conditions for all elements in a vector, we can use which to get the indices of the elements that fulfill the condition:

which(airquality$Temp > 90)

If we want to know if all elements in a vector fulfill the condition, we can use all:

all(airquality$Temp > 90)

In this case, it returns FALSE, meaning that not all days had a temperature above 90 (phew!). Similarly, if we wish to know whether at least one day had a temperature above 90, we can use any:

any(airquality$Temp > 90)

To find how many elements that fulfill a condition, we can use sum:

sum(airquality$Temp > 90)

Why does this work? Remember that sum computes the sum of the elements in a vector, and that when logical values are used in computations, they are treated as 0 (FALSE) or 1 (TRUE). Because the condition returns a vector of logical values, the sum of them becomes the number of 1’s - the number of TRUE values - i.e. the number of elements that fulfill the condition.

To find the proportion of elements that fulfill a condition, we can count how many elements fulfill it and then divide by how many elements are in the vector. This is exactly what happens if we use mean:

mean(airquality$Temp > 90)

Finally, we can combine conditions by using the logical operators & (AND), | (OR), and, less frequently, xor (exclusive or, XOR). Here are some examples:

a <- 3
b <- 8

# Is a less than b and greater than 1?
a < b & a > 1

# Is a less than b and equal to 4?
a < b & a == 4

# Is a less than b and/or equal to 4?
a < b | a == 4

# Is a equal to 4 and/or equal to 5?
a == 4 | a == 5

# Is a less than b XOR equal to 4?
# I.e. is one and only one of these satisfied?
xor(a < b, a == 4)


Exercise 3.6 The following tasks all involve checking conditions for the airquality data:

  1. Which was the coldest day during the period?

  2. How many days was the wind speed greater than 17 mph?

  3. How many missing values are there in the Ozone vector?

  4. How many days are there for which the temperature was below 70 and the wind speed was above 10?

(Click here to go to the solution.)

Exercise 3.7 The function cut can be used to create a categorical variable from a numerical variable, by dividing it into categories corresponding to different intervals. Reads its documentation and then create a new categorical variable in the airquality data, TempCat, which divides Temp into the three intervals (50, 70], (70, 90], (90, 110]16.

(Click here to go to the solution.)

3.3 Importing data

So far, we’ve looked at examples of data they either came shipped with base R or ggplot2, or simple toy examples that we created ourselves, like bookstore. While you can do all your data entry work in R, bookstore style, it is much more common to load data from other sources. Two important types of files are comma-separated value files, .csv, and Excel spreadsheets, .xlsx. .csv files are spreadsheets stored as text files - basically Excel files stripped down to the bare minimum - no formatting, no formulas, no macros. You can open and edit them in spreadsheet software like LibreOffice Calc, Google Sheets or Microsoft Excel. Many devices and databases can export data in .csv format, making it a commonly used file format that you are likely to encounter sooner rather than later.

3.3.1 Importing csv files

In order to load data from a file into R, you need its path - that is, you need to tell R where to find the file. Unless you specify otherwise, R will look for files in its current working directory. To see what your current working directory is, run the following code in the Console panel:


In RStudio, your working directory will usually be shown in the Files panel. If you have opened RStudio by opening a .R file, the working directory will be the directory in which the file is stored. You can change the working directory by using the function setwd or selecting Session > Set Working Directory > Choose Directory in the RStudio menu.

Before we discuss paths further, let’s look at how you can import data from a file that is in your working directory. The data files that we’ll use in examples in this book can be downloaded from the book’s web page. They are stored in a zip file (data.zip) - open it an copy/extract the files to the folder that is your current working directory. Open philosophers.csv with a spreadsheet software to have a quick look at it. Then open it in a text editor (for instance Notepad for Windows, TextEdit for Mac or Gedit for Linux). Note how commas are used to separate the columns of the data:

"Aristotle","Pretty influential, as philosophers go.",-384,"322 BC",
"Basilides","Denied the existence of incorporeal entities.",-175,
"125 BC",4
"Cercops","An Orphic poet",,,"3.2"
"Dexippus","Neoplatonic!",235,"375 AD","2.7"
"Epictetus","A stoic philosopher",50,"135 AD",5
"Favorinus","Sceptic",80,"160 AD","4.7"

Then run the following code to import the data using the read.csv function and store it in a variable named imported_data:

imported_data <- read.csv("philosophers.csv")

If you get an error message that says:

Error in file(file, "rt") : cannot open the connection
In addition: Warning message:
In file(file, "rt") :
  cannot open file 'philosophers.csv': No such file or directory

…it means that philosophers.csv is not in your working directory. Either move the file to the right directory (remember, you can use run getwd() to see what your working directory is) or change your working directory, as described above.

Now, let’s have a look at imported_data:


The columns Name and Description both contain text, and have been imported as character vectors17. The Rating column contains numbers with decimals and has been imported as a numeric vector. The column Born only contain integer values, and has been imported as an integer vector. The missing value is represented by an NA. The Deceased column contains years formatted like 125 BC and 135 AD. These have been imported into a character vector - because numbers and letters are mixed in this column, R treats is as a text string (in Chapter 5 we will see how we can convert it to numbers or proper dates). In this case, the missing value is represented by an empty string, "", rather than by NA.

So, what can you do in case you need to import data from a file that is not in your working directory? This is a common problem, as many of us store script files and data files in separate folders (or even on separate drives). One option is to use file.choose, which opens a pop-up window that lets you choose which file to open using a graphical interface:

imported_data2 <- read.csv(file.choose())

A third option is not to write any code at all. Instead, you can import the data using RStudio’s graphical interface by choosing File > Import dataset > From Text (base) and then choosing philosophers.csv. This will generate the code needed to import the data (using read.csv) and run it in the Console window.

The latter two solutions work just fine if you just want to open a single file once. But if you want to reuse your code or run it multiple times, you probably don’t want to have to click and select your file each time. Instead, you can specify the path to your file in the call to read.csv.

3.3.2 File paths

File paths look different in different operating systems. If the user Mans has a file named philosophers.csv stored in a folder called MyData on his desktop, its path on an English-language Windows system would be:


On a Mac it would be:


And on Linux:


You can copy the path of the file from your file browser: Explorer18 (Windows), Finder19 (Mac) or Nautilus/similar20 (Linux). Once you have copied the path, you can store it in R as a character string.

Here’s how to do this on Mac and Linux:

file_path <- "/Users/Mans/Desktop/MyData/philosophers.csv" # Mac
file_path <- "/home/Mans/Desktop/MyData/philosophers.csv"  # Linux

If you’re working on a Windows system, file paths are written using backslashes, \, like so:


You have to be careful when using backslashes in character strings in R, because they are used to create special characters (see Section 5.5). If we place the above path in a string, R won’t recognise it as a path. Instead we have to reformat it into one of the following two formats:

# Windows example 1:
file_path <- "C:/Users/Mans/Desktop/MyData/philosophers.csv"
# Windows example 2:
file_path <- "C:\\Users\\Mans\\Desktop\\MyData\\philosophers.csv"

If you’ve copied the path to your clipboard, you can also get the path in the second of the formats above by using

file_path <- readClipboard()   # Windows example 3

Once the path is stored in file_path, you can then make a call to read.csv to import the data:

imported_data <- read.csv(file_path)

Try this with your philosophers.csv file, to make sure that you know how it works.

Finally, you can read a file directly from a URL, by giving the URL as the file path. Here is an example with data from the WHO Global Tuberculosis Report:

# Download WHO tuberculosis burden data:
tb_data <- read.csv("https://tinyurl.com/whotbdata")

.csv files can differ slightly in how they are formatted - for instance, different symbols can be used to delimit the columns. You will learn how to handle this in the exercises below.

A downside to read.csv is that it is very slow when reading large (50 MB or more) csv files. Faster functions are available in add-on packages; see Section 5.7.1. In addition, it is also possible to import data from other statistical software packages such as SAS and SPSS, from other file formats like JSON, and from databases. We’ll discuss most of these in Section 5.14

3.3.3 Importing Excel files

One common file format we will discuss right away though - .xlsx - Excel spreadsheet files. There are several packages that can be used to import Excel files to R. I like the openxlsx package, so let’s install that:


Now, download the philosophers.xlsx file from the book’s web page and save it in a folder of your choice. Then set file_path to the path of the file, just as you did for the .csv file. To import data from the Excel file, you can then use:

imported_from_Excel <- read.xlsx(file_path)


As with read.csv, you can replace the file path with file.choose() in order to select the file manually.


Exercise 3.8 The abbreviation CSV stands for Comma Separated Values, i.e. that commas , are used to separate the data columns. Unfortunately, the .csv format is not standardised, and .csv files can use different characters to delimit the columns. Examples include semicolons (;) and tabs (multiple spaces, denoted \t in strings in R). Moreover, decimal points can be given either as points (.) or as commas (,). Download the vas.csv file from the book’s web page. In this dataset, a number of patients with chronic pain have recorded how much pain they experience each day during a period, using the Visual Analogue Scale (VAS, ranging from 0 - no pain - to 10 - worst imaginable pain). Inspect the file in a spreadsheet software and a text editor - check which symbol is used to separate the columns and whether a decimal point or a decimal comma is used. Then set file_path to its path and import the data from it using the code below:

vas <- read.csv(file_path, sep = ";", dec = ",", skip = 4)

  1. Why are there two variables named X and X.1 in the data frame?

  2. What happens if you remove the sep = ";" argument?

  3. What happens if you instead remove the dec = "," argument?

  4. What happens if you instead remove the skip = 4 argument?

  5. What happens if you change skip = 4 to skip = 5?

(Click here to go to the solution.)

Exercise 3.9 Download the projects-email.xlsx file from the book’s web page and have a look at it in a spreadsheet software. Note that it has three sheet: Projects, Email, and Contact.

  1. Read the documentation for read.xlsx. How can you import the data from the second sheet, Email?

  2. Some email addresses are repeated more than once. Read the documentation for unique. How can you use it to obtain a vector containing the email addresses without any duplicates?

(Click here to go to the solution.)

Exercise 3.10 Download the vas-transposed.csv file from the book’s web page and have a look at it in a spreadsheet software. It is a transposed version of vas.csv, where rows represent variables and columns represent observations (instead of the other way around, as is the case in data frames in R). How can we import this data into R?

  1. Import the data using read.csv. What does the resulting data frame look like?

  2. Read the documentation for read.csv. How can you make it read the row names that can be found in the first column of the .csv file?

  3. The function t can be applied to transpose (i.e. rotate) your data frame. Try it out on your imported data. Is the resulting object what you were looking for? What happens if you make a call to as.data.frame with your data after transposing it?

(Click here to go to the solution.)

3.4 Saving and exporting your data

In many a case, data manipulation is a huge part of statistical work, and of course you want to be able to save a data frame after manipulating it. There are two options for doing this in R - you can either export the data as e.g. a .csv or a .xlsx file, or save it in R format as an .RData file.

3.4.1 Exporting data

Just as we used the functions read.csv and read.xlsx to import data, we can use write.csv and write.xlsx to export it. The code below saves the bookstore data frame as a .csv file and an .xlsx file. Both files will be created in the current working directory. If you wish to store them somewhere else, you can replace the "bookstore.csv" bit with a full path, e.g. "/home/mans/my-business/bookstore.csv".

# Bookstore example
age <- c(28, 48, 47, 71, 22, 80, 48, 30, 31)
purchase <- c(20, 59, 2, 12, 22, 160, 34, 34, 29)
bookstore <- data.frame(age, purchase)

# Export to .csv:
write.csv(bookstore, "bookstore.csv")

# Export to .xlsx (Excel):
write.xlsx(bookstore, "bookstore.xlsx")

3.4.2 Saving and loading R data

Being able to export to different spreadsheet formats is very useful, but sometimes you want to save an object that can’t be saved in a spreadsheet format. For instance, you may wish to save a machine learning model that you’ve created. .RData files can be used to store one or more R objects.

To save the objects bookstore and age in a .Rdata file, we can use the save function:

save(bookstore, age, file = "myData.RData")

To save all objects in your environment, you can use save.image:

save.image(file = "allMyData.RData")

When we wish to load the stored objects, we use the load function:

load(file = "myData.RData")

3.5 RStudio projects

It is good practice to create a new folder for each new data analysis project that you are working on, where you store code, data and the output from the analysis. In RStudio you can associate a folder with a Project, which lets you start RStudio with that folder as your working directory. Moreover, by opening another Project you can have several RStudio sessions, each with their separate variables and working directories, running simultaneously.

To create a new Project, click File > New Project in the RStudio menu. You then get to choose whether to create a Project associated with a folder that already exists, or to create a Project in a new folder. After you’ve created the Project, it will be saved as an .Rproj file. You can launch RStudio with the Project folder as the working directory by double-clicking the .Rproj file. If you already have an active RStudio session, this will open another session in a separate window.

When working in a Project, I recommend that you store your data in a subfolder of the Project folder. You can the use relative paths to access your data files, i.e. paths that are relative to you working directory. For instance, if the file bookstore.csv is in a folder in your working directory called Data, it’s relative path is:

file_path <- "Data/bookstore.csv"

Much simpler that having to write the entire path, isn’t it?

If instead your working directory is contained inside the folder where bookstore.csv is stored, its relative path would be

file_path <- "../bookstore.csv"

The beauty of using relative paths is that they are simpler to write, and if you transfer the entire project folder to another computer, your code will still run, because the relative paths will stay the same.

3.6 Running a t-test

R has thousands of functions for running different statistical hypothesis tests. We’ll delve deeper into that in Chapter 7, but we’ll have a look at one of them right away: t.test, which (yes, you guessed it!) can be used to run Student’s t-test, which can be used to test whether the mean of two populations are equal.

Let’s say that we want to compare the mean sleeping times of carnivores and herbivores, using the msleep data. t.test takes two vectors as input, corresponding to the measurements from the two groups:

carnivores <- msleep[msleep$vore == "carni",]
herbivores <- msleep[msleep$vore == "herbi",]
t.test(carnivores$sleep_total, herbivores$sleep_total)

The output contains a lot of useful information, including the p-value (\(0.53\)) and a 95 % confidence interval. t.test contains a number of useful arguments that we can use to tailor the test to our taste. For instance, we can change the confidence level of the confidence interval (to 90 %, say), use a one-sided alternative hypothesis (“carnivores sleep more than herbivores,” i.e. the mean of the first group is greater than that of the second group) and perform the test under the assumption of equal variances in the two samples:

t.test(carnivores$sleep_total, herbivores$sleep_total,
       conf.level = 0.90,
       alternative = "greater",
       var.equal = TRUE)

We’ll explore t.test and related functions further in Section 7.2.

3.7 Fitting a linear regression model

The mtcars data from Henderson and Velleman (1981) has become one of the classic datasets in R, and a part of the initiation rite for new R users is to use the mtcars data to fit a linear regression model. The data describes fuel consumption, number of cylinders and other information about cars from the 1970’s:


Let’s have a look at the relationship between gross horsepower (hp) and fuel consumption (mpg):

ggplot(mtcars, aes(hp, mpg)) +

The relationship doesn’t appear to be perfectly linear, but nevertheless, we can try fitting a linear regression model to the data. This can be done using lm. We fit a model with mpg as the response variable and hp as the explanatory variable:

m <- lm(mpg ~ hp, data = mtcars)

The first argument is a formula, saying that mpg is a function of hp, i.e.

\[mpg=\beta_0 +\beta_1 \cdot hp.\]

A summary of the model is obtained using summary. Among other things, it includes the estimated parameters, p-values and the coefficient of determination \(R^2\).


We can add the fitted line to the scatterplot by using geom_abline, which lets us add a straight line with a given intercept and slope - we take these to be the coefficients from the fitted model, given by coef:

# Check model coefficients:

# Add regression line to plot:
ggplot(mtcars, aes(hp, mpg)) +
      geom_point() + 
      geom_abline(aes(intercept = coef(m)[1], slope = coef(m)[2]),
                colour = "red")

Diagnostic plots for the residuals are obtained using plot:


If we wish to add further variables to the model, we simply add them to the right-hand-side of the formula in the function call:

m2 <- lm(mpg ~ hp + wt, data = mtcars)

In this case, the model becomes

\[mpg=\beta_0 +\beta_1 \cdot hp + \beta_2\cdot wt.\]

There is much more to be said about linear models in R. We’ll return to them in Section 8.1.


Exercise 3.11 Fit a linear regression model to the mtcars data, using mpg as the response variable and hp, wt, cyl, and am as explanatory variables. Are all four explanatory variables significant?

(Click here to go to the solution.)

3.8 Grouped summaries

Being able to compute the mean temperature for the airquality data during the entire period is great, but it would be even better if we also had a way to compute it for each month. The aggregate function can be used to create that kind of grouped summary.

To begin with, let’s compute the mean temperature for each month. Using aggregate, we do this as follows:

aggregate(Temp ~ Month, data = airquality, FUN = mean)

The first argument is a formula, similar to what we used for lm, saying that we want a summary of Temp grouped by Month. Similar formulas are used also in other R functions, for instance when building regression models. In the second argument, data, we specify in which data frame the variables are found, and in the third, FUN, we specify which function should be used to compute the summary.

By default, mean returns NA if there are missing values. In airquality, Ozone contains missing values, but when we compute the grouped means the results are not NA:

aggregate(Ozone ~ Month, data = airquality, FUN = mean)

By default, aggregate removes NA values before computing the grouped summaries.

It is also possible to compute summaries for multiple variables at the same time. For instance, we can compute the standard deviations (using sd) of Temp and Wind, grouped by Month:

aggregate(cbind(Temp, Wind) ~ Month, data = airquality, FUN = sd)

aggregate can also be used to count the number of observations in the groups. For instance, we can count the number of days in each month. In order to do so, we put a variable with no NA values on the left-hand side in the formula, and use length, which returns the length of a vector:

aggregate(Temp ~ Month, data = airquality, FUN = length)

Another function that can be used to compute grouped summaries is by. The results are the same, but the output is not as nicely formatted. Here’s how to use it to compute the mean temperature grouped by month:

by(airquality$Temp, airquality$Month, mean)

What makes by useful is that unlike aggregate it is easy to use with functions that take more than one variable as input. If we want to compute the correlation between Wind and Temp grouped by month, we can do that as follows:

names(airquality)  # Check that Wind and Temp are in columns 3 and 4
by(airquality[, 3:4], airquality$Month, cor)

For each month, this outputs a correlation matrix, which shows both the correlation between Wind and Temp and the correlation of the variables with themselves (which always is 1).


Exercise 3.12 Load the VAS pain data vas.csv from Exercise 3.8. Then do the following:

  1. Compute the mean VAS for each patient.

  2. Compute the lowest and highest VAS recorded for each patient.

  3. Compute the number of high-VAS days, defined as days where the VAS was at least 7, for each patient.

(Click here to go to the solution.)

Exercise 3.13 Install the datasauRus package using install.packages("datasauRus") (note the capital R!). It contains the dataset datasaurus_dozen. Check its structure and then do the following:

  1. Compute the mean of x, mean of y, standard deviation of x, standard deviation of y, and correlation between x and y, grouped by dataset. Are there any differences between the 12 datasets?

  2. Make a scatterplot of x against y for each dataset (use facetting!). Are there any differences between the 12 datasets?

(Click here to go to the solution.)

3.9 Using %>% pipes

Consider the code you used to solve part 1 of Exercise 3.5:

bookstore$rev_per_minute <- bookstore$purchase / bookstore$visit_length

Wouldn’t it be more convenient if you didn’t have to write the bookstore$ part each time? To just say once that you are manipulating bookstore, and have R implicitly understand that all the variables involved reside in that data frame? Yes. Yes, it would. Fortunately, R has tools that will let you do just that.

3.9.1 Ceci n’est pas une pipe

The magrittr package21 adds a set of tools called pipes to R. Pipes are operators that let you improve your code’s readability and restructure your code so that it is read from the left to the right instead of from the inside out. Let’s start by installing the package:


Now, let’s say that we are interested in finding out what the mean wind speed (in m/s rather than mph) on hot days (temperature above 80, say) in the airquality data is, aggregated by month. We could do something like this:

# Extract hot days:
airquality2 <- airquality[airquality$Temp > 80, ]
# Convert wind speed to m/s:
airquality2$Wind <- airquality2$Wind * 0.44704
# Compute mean wind speed for each month:
hot_wind_means <- aggregate(Wind ~ Month, data = airquality2,
                            FUN = mean)

There is nothing wrong with this code per se. We create a copy of airquality (because we don’t want to change the original data), change the units of the wind speed, and then compute the grouped means. A downside is that we end up with a copy of airquality that we maybe won’t need again. We could avoid that by putting all the operations inside of aggregate:

# More compact:
hot_wind_means <-  aggregate(Wind*0.44704 ~ Month,
                            data = airquality[airquality$Temp > 80, ],
                            FUN = mean)

The problem with this is that it is a little difficult to follow because we have to read the code from the inside out. When we run the code, R will first extract the hot days, then convert the wind speed to m/s, and then compute the grouped means - so the operations happen in an order that is the opposite of the order in which we wrote them.

magrittr introduces a new operator, %>%, called a pipe, which can be used to chain functions together. Calls that you would otherwise write as

new_variable <- function_2(function_1(your_data))

can be written as

your_data %>% function_1 %>% function_2 -> new_variable

so that the operations are written in the order they are performed. Some prefer the former style, which is more like mathematics, but many prefer the latter, which is more like natural language (particularly for those of us who are used to reading from left to right).

Three operations are required to solve the airquality wind speed problem:

  1. Extract the hot days,
  2. Convert the wind speed to m/s,
  3. Compute the grouped means.

Where before we used function-less operations like airquality2$Wind <- airquality2$Wind * 0.44704, we would now require functions that carried out the same operations if we wanted to solve this problem using pipes.

A function that lets us extract the hot days is subset:

subset(airquality, Temp > 80)

The magrittr function inset lets us convert the wind speed:

inset(airquality, "Wind", value = airquality$Wind * 0.44704)

And finally, aggregate can be used to compute the grouped means. We could use these functions step-by-step:

# Extract hot days:
airquality2 <- subset(airquality, Temp > 80)
# Convert wind speed to m/s:
airquality2 <- inset(airquality2, "Wind",
                     value = airquality2$Wind * 0.44704)
# Compute mean wind speed for each month:
hot_wind_means <- aggregate(Wind ~ Month, data = airquality2,
                            FUN = mean)

But, because we have functions to perform the operations, we can instead use %>% pipes to chain them together in a pipeline. Pipes automatically send the output from the previous function as the first argument to the next, so that the data flows from left to right, which make the code more concise. They also let us refer to the output from the previous function as ., which saves even more space. The resulting code is:

airquality %>%
      subset(Temp > 80) %>% 
      inset("Wind", value = .$Wind * 0.44704) %>%
      aggregate(Wind ~ Month, data = ., FUN = mean) ->

You can read the %>% operator as then: take the airquality data, then subset it, then convert the Wind variable, then compute the grouped means. Once you wrap your head around the idea of reading the operations from left to right, this code is arguably clearer and easier to read. Note that we used the right-assignment operator -> to assign the result to hot_wind_means, to keep in line with the idea that the data flows from the left to the right.

3.9.2 Aliases and placeholders

In the remainder of the book, we will use pipes in some situations where they make the code easier to write or read. Pipes don’t always make code easier to read though, as can be seen if we use them to compute \(\exp(\log(2))\):

# Standard solution:
# magrittr solution:
2 %>% log %>% exp

If you need to use binary operators like +, ^ and <, magrittr has a number of aliases that you can use. For instance, add works as an alias for +:

x <- 2
exp(x + 2)
x %>% add(2) %>% exp

Here are a few more examples:

x <- 2
# Base solution;          magrittr solution
exp(x - 2);               x %>% subtract(2) %>% exp
exp(x * 2);               x %>% multiply_by(2) %>% exp
exp(x / 2);               x %>% divide_by(2) %>% exp
exp(x^2);                 x %>% raise_to_power(2) %>% exp
head(airquality[,1:4]);   airquality %>% extract(,1:4) %>% head
airquality$Temp[1:5];     airquality %>%
                            use_series(Temp) %>% extract(1:5)

In simple cases like these it is usually preferable to use the base R solution - the point here is that if you need to perform this kind of operation inside a pipeline, the aliases make it easy to do so. For a complete list of aliases, see ?extract.

If the function does not take the output from the previous function as its first argument, you can use . as a placeholder, just as we did in the airquality problem. Here is another example:

cat(paste("The current time is ", Sys.time())))
Sys.time() %>% paste("The current time is", .) %>% cat

If the data only appears inside parentheses, you need to wrap the function in curly brackets {}, or otherwise %>% will try to pass it as the first argument to the function:

airquality %>% cat("Number of rows in data:", nrow(.)) # Doesn't work
airquality %>% {cat("Number of rows in data:", nrow(.))} # Works!

In addition to the magrittr pipes, from version 4.1 R also offers a native pipe, |>, which can be used in lieu of %>% without loading any packages. Nevertheless, we’ll use %>% pipes in the remainder of the book, partially because they are more commonly used (meaning that you are more likely to encounter them when looking at other people’s code), and partially because magrittr also offers some other useful pipe operators. You’ll see plenty of examples of how pipes can be used in Chapters 5-9, and learn about other pipe operators in Section 6.2.


Exercise 3.14 Rewrite the following function calls using pipes, with x <- 1:8:

  1. sqrt(mean(x))

  2. mean(sqrt(x))

  3. sort(x^2-5)[1:2]

(Click here to go to the solution.)

Exercise 3.15 Using the bookstore data:
age <- c(28, 48, 47, 71, 22, 80, 48, 30, 31)
purchase <- c(20, 59, 2, 12, 22, 160, 34, 34, 29)
visit_length <- c(5, 2, 20, 22, 12, 31, 9, 10, 11)
bookstore <- data.frame(age, purchase, visit_length)

Add a new variable rev_per_minute which is the ratio between purchase and the visit length, using a pipe.

(Click here to go to the solution.)

3.10 Flavours of R: base and tidyverse

R is a programming language, and just like any language, it has different dialects. When you read about R online, you’ll frequently see people mentioning the words “base” and “tidyverse.” These are the two most common dialects of R. Base R is just that, R in its purest form. The tidyverse is a collection of add-on packages for working with different types of data. The two are fully compatible, and you can mix and match as much as you like. Both ggplot2 and magrittr are part of the tidyverse.

In recent years, the tidyverse has been heavily promoted as being “modern” R which “makes data science faster, easier and more fun.” You should believe the hype. The tidyverse is marvellous. But if you only learn tidyverse R, you will miss out on much of what R has to offer. Base R is just as marvellous, and can definitely make data science as fast, easy and fun as the tidyverse. Besides, nobody uses just base R anyway - there are a ton of non-tidyverse packages that extend and enrich R in exciting new ways. Perhaps “extended R” or “superpowered R” would be better names for the non-tidyverse dialect.

Anyone who tells you to just learn one of these dialects is wrong. Both are great, they work extremely well together, and they are similar enough that you shouldn’t limit yourself to just mastering one of them. This book will show you both base R and tidyverse solutions to problems, so that you can decide for yourself which is faster, easier, and more fun.

A defining property of the tidyverse is that there are separate functions for everything, which is perfect for code that relies on pipes. In contrast, base R uses fewer functions, but with more parameters, to perform the same tasks. If you use tidyverse solutions there is a good chance that there exists a function which performs exactly the task you’re going to do with its default settings. This is great (once again, especially if you want to use pipes), but it means that there are many more functions to master for tidyverse users, whereas you can make do with much fewer in base R. You will spend more time looking up function arguments when working with base R (which fortunately is fairly straightforward using the ? documentation), but on the other hand, looking up arguments for a function that you know the name of is easier than finding a function that does something very specific that you don’t know the name of. There are advantages and disadvantages to both approaches.

3.11 Ethics and good statistical practice

Throughout this book, there will be sections devoted to ethics. Good statistical practice is intertwined with good ethical practice. Both require transparent assumptions, reproducible results, and valid interpretations.

One of the most commonly cited ethical guidelines for statistical work is The American Statistical Association’s Ethical Guidelines for Statistical Practice (Committee on Professional Ethics of the American Statistical Association, 2018), a shortened version of which is presented below22. The full ethical guidelines are available at https://www.amstat.org/ASA/Your-Career/Ethical-Guidelines-for-Statistical-Practice.aspx

  • Professional Integrity and Accountability. The ethical statistician uses methodology and data that are relevant and appropriate; without favoritism or prejudice; and in a manner intended to produce valid, interpretable, and reproducible results. The ethical statistician does not knowingly accept work for which he/she is not sufficiently qualified, is honest with the client about any limitation of expertise, and consults other statisticians when necessary or in doubt. It is essential that statisticians treat others with respect.
  • Integrity of data and methods. The ethical statistician is candid about any known or suspected limitations, defects, or biases in the data that may affect the integrity or reliability of the statistical analysis. Objective and valid interpretation of the results requires that the underlying analysis recognizes and acknowledges the degree of reliability and integrity of the data.
  • Responsibilities to Science/Public/Funder/Client. The ethical statistician supports valid inferences, transparency, and good science in general, keeping the interests of the public, funder, client, or customer in mind (as well as professional colleagues, patients, the public, and the scientific community).
  • Responsibilities to Research Subjects. The ethical statistician protects and respects the rights and interests of human and animal subjects at all stages of their involvement in a project. This includes respondents to the census or to surveys, those whose data are contained in administrative records, and subjects of physically or psychologically invasive research.
  • Responsibilities to Research Team Colleagues. Science and statistical practice are often conducted in teams made up of professionals with different professional standards. The statistician must know how to work ethically in this environment.
  • Responsibilities to Other Statisticians or Statistics Practitioners. The practice of statistics requires consideration of the entire range of possible explanations for observed phenomena, and distinct observers drawing on their own unique sets of experiences can arrive at different and potentially diverging judgments about the plausibility of different explanations. Even in adversarial settings, discourse tends to be most successful when statisticians treat one another with mutual respect and focus on scientific principles, methodology, and the substance of data interpretations.
  • Responsibilities Regarding Allegations of Misconduct. The ethical statistician understands the differences between questionable statistical, scientific, or professional practices and practices that constitute misconduct. The ethical statistician avoids all of the above and knows how each should be handled.
  • Responsibilities of Employers, Including Organizations, Individuals, Attorneys, or Other Clients Employing Statistical Practitioners. Those employing any person to analyze data are implicitly relying on the profession’s reputation for objectivity. However, this creates an obligation on the part of the employer to understand and respect statisticians’ obligation of objectivity.

Similar ethical guidelines for statisticians have been put forward by the International Statistical Institute (https://www.isi-web.org/about-isi/policies/professional-ethics), the United Nations Statistics Division (https://unstats.un.org/unsd/dnss/gp/fundprinciples.aspx), and the Data Science Association (http://www.datascienceassn.org/code-of-conduct.html). For further reading on ethics in statistics, see Franks (2020) and Fleming & Bruce (2021).


Exercise 3.16 Discuss the following. In the introduction to American Statistical Association’s Ethical Guidelines for Statistical Practice, it is stated that “using statistics in pursuit of unethical ends is inherently unethical.” What is considered unethical depends on social, moral, political, and religious values, and ultimately you must decide for yourself what you consider to be unethical ends. Which (if any) of the following do you consider to be unethical?

  1. Using statistical analysis to help a company that harm the environment through their production processes. Does it matter to you what the purpose of the analysis is?
  2. Using statistical analysis to help a tobacco or liquor manufacturing company. Does it matter to you what the purpose of the analysis is?
  3. Using statistical analysis to help a bank identify which loan applicants that are likely to default on their loans.
  4. Using statistical analysis of social media profiles to identify terrorists.
  5. Using statistical analysis of social media profiles to identify people likely to protest against the government.
  6. Using statistical analysis of social media profiles to identify people to target with political adverts.
  7. Using statistical analysis of social media profiles to target ads at people likely to buy a bicycle.
  8. Using statistical analysis of social media profiles to target ads at people likely to gamble at a new online casino. Does it matter to you if it’s an ad for the casino or for help for gambling addiction?

  1. And the subsequent troubleshooting makes programming R more difficult and slower.↩︎

  2. This works regardless of whether this is a regular data.frame, a data.table or a tibble.↩︎

  3. In interval notation, (50, 70] means that the interval contains all values between 50 and 70, excluding 50 but including 70; the intervals is open on the left but closed to the right.↩︎

  4. If you are running an older version of R (specifically, a version older than the 4.0.0 version released in April 2020), the character vectors will have been imported as factor vectors instead. You can change that behaviour by adding a stringsAsFactors = FALSE argument to read.csv.↩︎

  5. To copy the path, navigate to the file in Explorer. Hold down the Shift key and right-click the file, selecting Copy as path.↩︎

  6. To copy the path, navigate to the file in Finder and right-click/Control+click/two-finger click on the file. Hold down the Option key, and then select Copy “file name” as Pathname.↩︎

  7. To copy the path from Nautilus, navigate to the file and press Ctrl+L to show the path, then copy it. If you are using some other file browser or the terminal, my guess is that you’re tech-savvy enough that you don’t need me to tell you how to find the path of a file.↩︎

  8. Arguably the best-named R package.↩︎

  9. The excerpt is from the version of the guidelines dated April 2018, and presented here with permission from the ASA.↩︎