Data Types and Structures
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Overview
Questions
 What are the different data types in R?
 What are the different data structures in R?
 How do I access data within the various data structures?
Objectives
 Expose learners to the different data types in R and show how these data types are used in data structures.
 Learn how to create vectors of different types.
 Be able to check the type of vector.
 Learn about missing data and other special values.
 Get familiar with the different data structures (lists, matrices, data frames).
Understanding Basic Data Types and Data Structures in R
To make the best of the R language, you’ll need a strong understanding of the basic data types and data structures and how to operate on them.
Data structures are very important to understand because these are the objects you will manipulate on a daytoday basis in R. Dealing with object conversions is one of the most common sources of frustration for beginners.
Everything in R is an object.
R has 6 basic data types. (In addition to the five listed below, there is also raw which will not be discussed in this workshop.)
 character
 numeric (real or decimal)
 integer
 logical
 complex
Elements of these data types may be combined to form data structures, such as atomic vectors. When we call a vector atomic, we mean that the vector only holds data of a single data type. Below are examples of atomic character vectors, numeric vectors, integer vectors, etc.

character:
"a"
,"swc"

numeric:
2
,15.5

integer:
2L
(theL
tells R to store this as an integer) 
logical:
TRUE
,FALSE

complex:
1+4i
(complex numbers with real and imaginary parts)
R provides many functions to examine features of vectors and other objects, for example

class()
 what kind of object is it (highlevel)? 
typeof()
 what is the object’s data type (lowlevel)? 
length()
 how long is it? What about two dimensional objects? 
attributes()
 does it have any metadata?
R
# Example
x < "dataset"
typeof(x)
OUTPUT
[1] "character"
R
attributes(x)
OUTPUT
NULL
R
y < 1:10
y
OUTPUT
[1] 1 2 3 4 5 6 7 8 9 10
R
typeof(y)
OUTPUT
[1] "integer"
R
length(y)
OUTPUT
[1] 10
R
z < as.numeric(y)
z
OUTPUT
[1] 1 2 3 4 5 6 7 8 9 10
R
typeof(z)
OUTPUT
[1] "double"
R has many data structures. These include
 atomic vector
 list
 matrix
 data frame
 factors
Vectors
A vector is the most common and basic data structure in R and is pretty much the workhorse of R. Technically, vectors can be one of two types:
 atomic vectors
 lists
although the term “vector” most commonly refers to the atomic types not to lists.
The Different Vector Modes
A vector is a collection of elements that are most commonly of mode
character
, logical
, integer
or
numeric
.
You can create an empty vector with vector()
. (By
default the mode is logical
. You can be more explicit as
shown in the examples below.) It is more common to use direct
constructors such as character()
, numeric()
,
etc.
R
vector() # an empty 'logical' (the default) vector
OUTPUT
logical(0)
R
vector("character", length = 5) # a vector of mode 'character' with 5 elements
OUTPUT
[1] "" "" "" "" ""
R
character(5) # the same thing, but using the constructor directly
OUTPUT
[1] "" "" "" "" ""
R
numeric(5) # a numeric vector with 5 elements
OUTPUT
[1] 0 0 0 0 0
R
logical(5) # a logical vector with 5 elements
OUTPUT
[1] FALSE FALSE FALSE FALSE FALSE
You can also create vectors by directly specifying their content. R will then guess the appropriate mode of storage for the vector. For instance:
R
x < c(1, 2, 3)
will create a vector x
of mode numeric
.
These are the most common kind, and are treated as double precision real
numbers. If you wanted to explicitly create integers, you need to add an
L
to each element (or coerce to the integer type
using as.integer()
).
R
x1 < c(1L, 2L, 3L)
Using TRUE
and FALSE
will create a vector
of mode logical
:
R
y < c(TRUE, TRUE, FALSE, FALSE)
While using quoted text will create a vector of mode
character
:
R
z < c("Sarah", "Tracy", "Jon")
Examining Vectors
The functions typeof()
, length()
,
class()
and str()
provide useful information
about your vectors and R objects in general.
R
typeof(z)
OUTPUT
[1] "character"
R
length(z)
OUTPUT
[1] 3
R
class(z)
OUTPUT
[1] "character"
R
str(z)
OUTPUT
chr [1:3] "Sarah" "Tracy" "Jon"
Adding Elements
The function c()
(for combine) can also be used to add
elements to a vector.
R
z < c(z, "Annette")
z
OUTPUT
[1] "Sarah" "Tracy" "Jon" "Annette"
R
z < c("Greg", z)
z
OUTPUT
[1] "Greg" "Sarah" "Tracy" "Jon" "Annette"
Vectors from a Sequence of Numbers
You can create vectors as a sequence of numbers.
R
series < 1:10
seq(10)
OUTPUT
[1] 1 2 3 4 5 6 7 8 9 10
R
seq(from = 1, to = 10, by = 0.1)
OUTPUT
[1] 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4
[16] 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9
[31] 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4
[46] 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9
[61] 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4
[76] 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9
[91] 10.0
Missing Data
R supports missing data in vectors. They are represented as
NA
(Not Available) and can be used for all the vector types
covered in this lesson:
R
x < c(0.5, NA, 0.7)
x < c(TRUE, FALSE, NA)
x < c("a", NA, "c", "d", "e")
x < c(1+5i, 23i, NA)
The function is.na()
indicates the elements of the
vectors that represent missing data, and the function
anyNA()
returns TRUE
if the vector contains
any missing values:
R
x < c("a", NA, "c", "d", NA)
y < c("a", "b", "c", "d", "e")
is.na(x)
OUTPUT
[1] FALSE TRUE FALSE FALSE TRUE
R
is.na(y)
OUTPUT
[1] FALSE FALSE FALSE FALSE FALSE
R
anyNA(x)
OUTPUT
[1] TRUE
R
anyNA(y)
OUTPUT
[1] FALSE
Other Special Values
Inf
is infinity. You can have either positive or
negative infinity.
R
1/0
OUTPUT
[1] Inf
NaN
means Not a Number. It’s an undefined value.
R
0/0
OUTPUT
[1] NaN
What Happens When You Mix Types Inside a Vector?
R will create a resulting vector with a mode that can most easily accommodate all the elements it contains. This conversion between modes of storage is called “coercion”. When R converts the mode of storage based on its content, it is referred to as “implicit coercion”. For instance, can you guess what the following do (without running them first)?
R
xx < c(1.7, "a")
xx < c(TRUE, 2)
xx < c("a", TRUE)
You can also control how vectors are coerced explicitly using the
as.<class_name>()
functions:
R
as.numeric("1")
OUTPUT
[1] 1
R
as.character(1:2)
OUTPUT
[1] "1" "2"
Finding Commonalities
Do you see a property that’s common to all these vectors above?
All vectors are onedimensional and each element is of the same type.
Objects Attributes
Objects can have attributes. Attributes are part of the object. These include:
 names
 dimnames
 dim
 class
 attributes (contain metadata)
You can also glean other attributelike information such as length (works on vectors and lists) or number of characters (for character strings).
R
length(1:10)
OUTPUT
[1] 10
R
nchar("Software Carpentry")
OUTPUT
[1] 18
Matrix
In R matrices are an extension of the numeric or character vectors. They are not a separate type of object but simply an atomic vector with dimensions; the number of rows and columns. As with atomic vectors, the elements of a matrix must be of the same data type.
R
m < matrix(nrow = 2, ncol = 2)
m
OUTPUT
[,1] [,2]
[1,] NA NA
[2,] NA NA
R
dim(m)
OUTPUT
[1] 2 2
You can check that matrices are vectors with a class attribute of
matrix
by using class()
and
typeof()
.
R
m < matrix(c(1:3))
class(m)
OUTPUT
[1] "matrix" "array"
R
typeof(m)
OUTPUT
[1] "integer"
While class()
shows that m is a matrix,
typeof()
shows that fundamentally the matrix is an integer
vector.
Data types of matrix elements
Consider the following matrix:
R
FOURS < matrix(
c(4, 4, 4, 4),
nrow = 2,
ncol = 2
)
Given that typeof(FOURS[1])
returns
"double"
, what would you expect typeof(FOURS)
to return? How do you know this is the case even without running this
code?
Hint Can matrices be composed of elements of different data types?
We know that typeof(FOURS)
will also return
"double"
since matrices are made of elements of the same
data type. Note that you could do something like
as.character(FOURS)
if you needed the elements of
FOURS
as characters.
Matrices in R are filled columnwise.
R
m < matrix(1:6, nrow = 2, ncol = 3)
Other ways to construct a matrix
R
m < 1:10
dim(m) < c(2, 5)
This takes a vector and transforms it into a matrix with 2 rows and 5 columns.
Another way is to bind columns or rows using rbind()
and
cbind()
(“row bind” and “column bind”, respectively).
R
x < 1:3
y < 10:12
cbind(x, y)
OUTPUT
x y
[1,] 1 10
[2,] 2 11
[3,] 3 12
R
rbind(x, y)
OUTPUT
[,1] [,2] [,3]
x 1 2 3
y 10 11 12
You can also use the byrow
argument to specify how the
matrix is filled. From R’s own documentation:
R
mdat < matrix(c(1, 2, 3, 11, 12, 13),
nrow = 2,
ncol = 3,
byrow = TRUE)
mdat
OUTPUT
[,1] [,2] [,3]
[1,] 1 2 3
[2,] 11 12 13
Elements of a matrix can be referenced by specifying the index along each dimension (e.g. “row” and “column”) in single square brackets.
R
mdat[2, 3]
OUTPUT
[1] 13
List
In R lists act as containers. Unlike atomic vectors, the contents of a list are not restricted to a single mode and can encompass any mixture of data types. Lists are sometimes called generic vectors, because the elements of a list can by of any type of R object, even lists containing further lists. This property makes them fundamentally different from atomic vectors.
A list is a special type of vector. Each element can be a different type.
Create lists using list()
or coerce other objects using
as.list()
. An empty list of the required length can be
created using vector()
R
x < list(1, "a", TRUE, 1+4i)
x
OUTPUT
[[1]]
[1] 1
[[2]]
[1] "a"
[[3]]
[1] TRUE
[[4]]
[1] 1+4i
R
x < vector("list", length = 5) # empty list
length(x)
OUTPUT
[1] 5
The content of elements of a list can be retrieved by using double square brackets.
R
x[[1]]
OUTPUT
NULL
Vectors can be coerced to lists as follows:
R
x < 1:10
x < as.list(x)
length(x)
OUTPUT
[1] 10
Examining Lists
 What is the class of
x[1]
?  What is the class of
x[[1]]
?

R
class(x[1])
OUTPUT
[1] "list"

R
class(x[[1]])
OUTPUT
[1] "integer"
Elements of a list can be named (i.e. lists can have the
names
attribute)
R
xlist < list(a = "Karthik Ram", b = 1:10, data = head(mtcars))
xlist
OUTPUT
$a
[1] "Karthik Ram"
$b
[1] 1 2 3 4 5 6 7 8 9 10
$data
mpg cyl disp hp drat wt qsec vs am gear carb
Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1
R
names(xlist)
OUTPUT
[1] "a" "b" "data"
Examining Named Lists
 What is the length of this object?
 What is its structure?
R
length(xlist)
OUTPUT
[1] 3

R
str(xlist)
OUTPUT
List of 3 $ a : chr "Karthik Ram" $ b : int [1:10] 1 2 3 4 5 6 7 8 9 10 $ data:'data.frame': 6 obs. of 11 variables: ..$ mpg : num [1:6] 21 21 22.8 21.4 18.7 18.1 ..$ cyl : num [1:6] 6 6 4 6 8 6 ..$ disp: num [1:6] 160 160 108 258 360 225 ..$ hp : num [1:6] 110 110 93 110 175 105 ..$ drat: num [1:6] 3.9 3.9 3.85 3.08 3.15 2.76 ..$ wt : num [1:6] 2.62 2.88 2.32 3.21 3.44 ... ..$ qsec: num [1:6] 16.5 17 18.6 19.4 17 ... ..$ vs : num [1:6] 0 0 1 1 0 1 ..$ am : num [1:6] 1 1 1 0 0 0 ..$ gear: num [1:6] 4 4 4 3 3 3 ..$ carb: num [1:6] 4 4 1 1 2 1
Lists can be extremely useful inside functions. Because the functions in R are able to return only a single object, you can “staple” together lots of different kinds of results into a single object that a function can return.
A list does not print to the console like a vector. Instead, each element of the list starts on a new line.
Elements are indexed by double brackets. Single brackets will still
return a(nother) list. If the elements of a list are named, they can be
referenced by the $
notation
(i.e. xlist$data
).
Data Frame
A data frame is a very important data type in R. It’s pretty much the de facto data structure for most tabular data and what we use for statistics.
A data frame is a special type of list where every element of the list has same length (i.e. data frame is a “rectangular” list).
Data frames can have additional attributes such as
rownames()
, which can be useful for annotating data, like
subject_id
or sample_id
. But most of the time
they are not used.
Some additional information on data frames:
 Usually created by
read.csv()
andread.table()
, i.e. when importing the data into R.  Assuming all columns in a data frame are of same type, data frame can be converted to a matrix with data.matrix() (preferred) or as.matrix(). Otherwise type coercion will be enforced and the results may not always be what you expect.
 Can also create a new data frame with
data.frame()
function.  Find the number of rows and columns with
nrow(dat)
andncol(dat)
, respectively.  Rownames are often automatically generated and look like 1, 2, …, n. Consistency in numbering of rownames may not be honored when rows are reshuffled or subset.
Creating Data Frames by Hand
To create data frames by hand:
R
dat < data.frame(id = letters[1:10], x = 1:10, y = 11:20)
dat
OUTPUT
id x y
1 a 1 11
2 b 2 12
3 c 3 13
4 d 4 14
5 e 5 15
6 f 6 16
7 g 7 17
8 h 8 18
9 i 9 19
10 j 10 20
Useful Data Frame Functions

head()
 shows first 6 rows 
tail()
 shows last 6 rows 
dim()
 returns the dimensions of data frame (i.e. number of rows and number of columns) 
nrow()
 number of rows 
ncol()
 number of columns 
str()
 structure of data frame  name, type and preview of data in each column 
names()
orcolnames()
 both show thenames
attribute for a data frame 
sapply(dataframe, class)
 shows the class of each column in the data frame
See that it is actually a special list:
R
is.list(dat)
OUTPUT
[1] TRUE
R
class(dat)
OUTPUT
[1] "data.frame"
Because data frames are rectangular, elements of data frame can be referenced by specifying the row and the column index in single square brackets (similar to matrix).
R
dat[1, 3]
OUTPUT
[1] 11
As data frames are also lists, it is possible to refer to columns
(which are elements of such list) using the list notation, i.e. either
double square brackets or a $
.
R
dat[["y"]]
OUTPUT
[1] 11 12 13 14 15 16 17 18 19 20
R
dat$y
OUTPUT
[1] 11 12 13 14 15 16 17 18 19 20
The following table summarizes the onedimensional and twodimensional data structures in R in relation to diversity of data types they can contain.
Dimensions  Homogenous  Heterogeneous 

1D  atomic vector  list 
2D  matrix  data frame 
Callout
Lists can contain elements that are themselves mutidimensional (e.g. a lists can contain data frames or another type of objects). Lists can also contain elements of any length, therefore list do not necessarily have to be “rectangular”. However in order for the list to qualify as a data frame, the length of each element has to be the same.
Column Types in Data Frames
Knowing that data frames are lists, can columns be of different type?
What type of structure do you expect to see when you explore the
structure of the PlantGrowth
data frame? Hint: Use
str()
.
The weight column is numeric while group is a factor. Lists can have elements of different types. Since a Data Frame is just a special type of list, it can have columns of differing type (although, remember that type must be consistent within each column!).
R
str(PlantGrowth)
OUTPUT
'data.frame': 30 obs. of 2 variables:
$ weight: num 4.17 5.58 5.18 6.11 4.5 4.61 5.17 4.53 5.33 5.14 ...
$ group : Factor w/ 3 levels "ctrl","trt1",..: 1 1 1 1 1 1 1 1 1 1 ...
Key Points
 R’s basic data types are character, numeric, integer, complex, and logical.
 R’s basic data structures include the vector, list, matrix, data frame, and factors. Some of these structures require that all members be of the same data type (e.g. vectors, matrices) while others permit multiple data types (e.g. lists, data frames).
 Objects may have attributes, such as name, dimension, and class.