# 9  V is for vector

## 9.1 The Vector

A vector is an object that contains one or several values of the same data type. For example, the object `vec.char` described below is a vector that contains 3 data elements of the type character.

``````vec.char <- c("one", "two", "three")
vec.char``````
`` "one"   "two"   "three"``

When conducting a statistical analysis, a vector is possibly the simplest object in which you may store entries for a single variable. In the following example, 24 data points corresponding to the temperature for a specific location registered over a period of 24 hours have been stored in the vector `temperature`:

``temperature <- c(8.7, 9.2, 9.4, 9.5, 9.7, 10.1, 10.3, 10.6, 10.7, 10.8, 11.3, 11.9, 12.2, 12.3, 11.7, 10.2, 10.3, 10.3, 10.4, 10.3, 10.1, 9.7, 9.5, 9.4)``
``temperature``
``````   8.7  9.2  9.4  9.5  9.7 10.1 10.3 10.6 10.7 10.8 11.3 11.9 12.2 12.3 11.7
 10.2 10.3 10.3 10.4 10.3 10.1  9.7  9.5  9.4``````

Note that the data type of the whole vector is determined by the type of the elements it contains, as shown here:

``class(temperature)``
`` "numeric"``

### 9.1.1 Combining with c

Perhaps the simplest way to make a vector is with the function `c()` which combines the elements given between parentheses.

The data elements to concatenate must be separated with a comma `,`.

``````results <- c(42, sqrt(42), 42 ^ 2)
results``````
``   42.000000    6.480741 1764.000000``

This may be applied not only to numerical values, but also to characters. When storing characters, you must use quotation marks `"` `"` around the elements.

``````one_two_three <- c("one", "two", "three")
one_two_three``````
`` "one"   "two"   "three"``

Note that you may combine data elements of various natures. Here we combine and store both numbers and characters, but everything becomes a character:

``````one_2_three_4 <- c("one", 2, "three", 4)
one_2_three_4``````
`` "one"   "2"     "three" "4"    ``

### 9.1.2 Coercion

If one tries to store data elements of different types in a single vector, all the elements in this vector will be coerced into the type that is the most general.
The ranking from the most specific to the most general is as follows: logical < integer < numeric < character.
Let’s take the following example where we store a numeric, a character and an integer together:

``````coercion <- c(15, "fifteen", 15L)
class(coercion)``````
`` "character"``

As you see here the type of `coercion` is character, in other words the type of the most general data element.

### 9.1.3 Accessing data elements

It is possible to extract specific data elements from a vector based on their position. To do so, we use square brackets `[` `]`. Indicate first the vector name and then the element position(s) between the brackets:

``temperature[c(2, 6)] ``
``  9.2 10.1``

Use negative indices to remove an element.

Exercise

From the vector `month.name`

• select the eighth element
• select the third and ninth elements
• drop the second and fifth elements

## 9.2 Data types for vectors

Here we will first review the primitive data types, then see a few useful data classes.

### 9.2.1 Primitive data types

R lets you manipulate 6 primitive data types: numeric, integer, character, logical (also called Boolean), complex and raw. Only the first four types are relevant to the scope of this website.

In the following sections, we will use the function `class()` to identify the nature of the data stored in objects (`mode()` and `typeof()` give related information).

#### 9.2.1.1 numeric

Any number with a decimal value, whether positive or negative, is of type numeric. The object `num` created below contains a single decimal value and is thus also numeric.

``````num <- -35.2
class(num)``````
`` "numeric"``

#### 9.2.1.2 integer

Integers are positive or negative numbers that do not contain a decimal value. The object `int` below contains a single integer and is thus of type integer.

``````int <- 35L
class(int)``````
`` "integer"``

Note that `int` was assigned the number 35L. The “L” that follows the number forces the object to store it as an integer. If we write 35 instead of 35L, the object is just numeric as shown below.

``````not_int <- 35
class(not_int)``````
`` "numeric"``

#### 9.2.1.3 character

An object containing a string of letters combined (or not) with numbers, or even a single letter, is of type character. The letters may be upper and/or lower case. The object `char` below contains a single word and is thus defined as character.

``````char <- "Letters"
class(char)``````
`` "character"``

Note that the strings of characters must be stored in objects using `"` `"`.

#### 9.2.1.4 logical

Logical (or boolean) defines binary objects which contain `TRUE` or `FALSE`. This is the case of the object `logic` below.

``````logic <- TRUE
class(logic)``````
`` "logical"``

Note that `TRUE` and `FALSE` are sometimes replaced with “T” or “F”. This is bad coding practice, which may result in weird errors that may compromise your work and the validity of its output.

### 9.2.2 Modifying data types

It is possible to modify the type of an existing object with a series of simple functions like `as.numeric()`, `as.integer()`, `as.character()`, etc.

Let’s consider the object `integ` created below.

``````integ <- 35L
integ``````
`` 35``

`integ` contains a single data element (`35L`) which is defined as an integer:

``class(integ)``
`` "integer"``

`integ` may be transformed into a simple numerical value by using the function `as.numeric()`:

``````integ_num <- as.numeric(integ)
class(integ_num)``````
`` "numeric"``

And it is possible to reverse this action with `as.integer()`:

``````integ_int <- as.integer(integ_num)
class(integ_int)``````
`` "integer"``

It is also possible to transform it into a string of characters with `as.character()`:

``````integ_char <- as.character(integ)
class(integ_char)``````
`` "character"``
Exercise

Make a vector that contains a word, a number and a logical value

• what class is it
• coerce it to a numeric vector. What happens. Why?

R allows to transform the format of an object from something simple like a number or a string of characters to something more advanced like a date or a factor. Date and factor are not data types per se, but data classes.

#### 9.2.3.1 Dates

The data element `1980-02-08` stored in the object `birthdate` below is nothing more than a string of characters.

``````birthday <- "1980-02-08"
birthday``````
`` "1980-02-08"``
``class(birthday)``
`` "character"``

To make it a date object, one must use the function `as.Date()`:

``````birthdate <- as.Date(birthday)
birthdate``````
`` "1980-02-08"``
``class(birthdate)``
`` "Date"``

Even though this does not seem to affect the way the data element is displayed, such a conversion is determining with regard to how th element is going to be handled in calculations. The calculation below displays the date that occurs 10 days before `birthdate`:

``````ten_days_before_my_birthdate <- birthdate - 10
ten_days_before_my_birthdate``````
`` "1980-01-29"``

Such a calculation would not have been possible without the conversion from character to date, as demonstrated by this error message:

``ten_days_before_my_birthday <- birthday - 10``
``Error in birthday - 10: non-numeric argument to binary operator``
Exercise

There is a tutorial for handling dates with the `lubridate` package in `biostats.tutorials`.

#### 9.2.3.2 Factors

A factor is an object that only contains predefined values. These predefined values are called the levels of the factor. Factors are especially useful in the context of statistical analysis where categorical data are involved (like ANOVA, etc), and for forcing the order of categories on a plot. Categories often appear as “text labels”, and may thus look like simple strings of characters.

In the following example, the object `scandinavian_countries` is a factor that contains 7 elements and three levels: `Norway`, `Sweden` and `Denmark`.

``scandinavian_countries ``
`````` Norway  Denmark Sweden  Denmark Sweden  Norway  Denmark
Levels: Norway Denmark Sweden``````
``class(scandinavian_countries)``
`` "factor"``

One way to build such a factor consists in converting a character object such as `scandinavia` with the function `factor()`. However, one must not forget to set the levels correctly with the argument `levels =`.

``````scandinavia <- c("Norway", "Denmark", "Sweden", "Denmark", "Sweden", "Norway", "Denmark")
scandinavian_kingdoms <- factor(scandinavia, levels = c("Norway", "Denmark", "Sweden"))
scandinavian_kingdoms``````
`````` Norway  Denmark Sweden  Denmark Sweden  Norway  Denmark
Levels: Norway Denmark Sweden``````

## 9.3 Creating sequences and series

Throughout this website, we will use examples that include random series of numbers, sequences of characters or numbers, etc. These sequences and series are often created by a bunch of functions or expressions, some of which are described below.

### 9.3.1 Repetitions

The function `rep()` comes handy when you wish to repeat data elements `n` times in a row, or to repeat a sequence of elements `n` times. Using various arguments, you can decide how many times and/or in which manner the elements or sequences have to be repeated.

The simplest form of usage of `rep()` is `rep(x, times = n)` where `x` is what you want to repeat (string, number(s), etc) and `n` the number of iterations.

``rep(c(1, 2, 3), times = 3)``
`` 1 2 3 1 2 3 1 2 3``
``rep(c("One", "Two", "Three"), times = 3)``
`` "One"   "Two"   "Three" "One"   "Two"   "Three" "One"   "Two"   "Three"``

The argument `each = n` allows for repeating `n` times each element at a time.

``rep(c(1, 2, 3), each = 3)``
`` 1 1 1 2 2 2 3 3 3``
``rep(c("One", "Two", "Three"), each = 3)``
`` "One"   "One"   "One"   "Two"   "Two"   "Two"   "Three" "Three" "Three"``
Exercise

Write code that will

• repeat the letters A – C three times so the output is A B C A…
• repeat the letters A – C three times so the output is A A A B…

### 9.3.2 Sequences

The following section provides you with expressions or functions that build sequences of numerical or text values.

#### 9.3.2.1 Using the colon operator

The colon separator `:` used in the expression `a:b` creates a series of consecutive numbers ranging from `a` to `b` with an increment of 1.

``14:24``
``  14 15 16 17 18 19 20 21 22 23 24``

Note that `b` is not necessarily the last element of the series.

``14:24.5``
``  14 15 16 17 18 19 20 21 22 23 24``
``14.5:24``
``  14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5``

#### 9.3.2.2 The function seq()

Similar to `a:b`, `seq(a, b)` creates a series of consecutive numbers ranging from `a` to `b` with an increment of 1.

``seq(14, 24)``
``  14 15 16 17 18 19 20 21 22 23 24``

Again, `b` is not necessarily the last element of the series.

``seq(14, 24.5)``
``  14 15 16 17 18 19 20 21 22 23 24``
``seq(14.5, 24)``
``  14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5``

You can use a set of additional arguments in `seq()` to adjust the output. Adding `by =` allows to tune the incrementation to any value you want (including decimal values). `length.out =` adjusts the incrementation to provide the desired number of elements ranging precisely from `a` to `b`.

``seq(14, 24, by = 2.5)``
`` 14.0 16.5 19.0 21.5 24.0``
``seq(14, 24, length.out = 7)``
`` 14.00000 15.66667 17.33333 19.00000 20.66667 22.33333 24.00000``
Exercise
• Make a sequence of integers between -5 and 10
• Make a sequence of between 0 and 10 that increment by 1.7
• Make a sequence between 4 and 34 that is 10 elements long

### 9.3.3 Random series

The following section provides you with functions that build series of random, numerical values. It demonstrates functions to make sequences from uniform and normal distributions, but there are many more distributions available in R.

#### 9.3.3.1 The function runif()

`runif(n)` returns a series of `n` random numbers from a uniform distribution between 0 and 1.

``runif(n = 7)``
`` 0.77754622 0.09860594 0.48448292 0.70357260 0.04673104 0.13528951 0.39894030``

`runif(n, min = a, max = b)` returns a series of `n` random numbers in the range from `a` to `b`:

``runif(n = 7, min = 10, max = 100)``
`` 73.45378 48.30441 80.75696 93.66836 27.05938 45.53991 40.23410``

#### 9.3.3.2 The function rnorm()

`rnorm(n)` creates a series of `n` numbers taken from a normal distribution.

``rnorm(n = 10)``
``````  -0.9080117 -0.7332665 -0.4944632  0.9108703  0.1242632 -0.1930169
 -0.7077276  1.1407162 -0.9652213  2.3968283``````

By default, the normally distributed population is set up with a mean of 0 and a standard deviation of 1, but this may be adjusted with `mean =` and `sd =`.

``rnorm(n = 10, mean = 50, sd = 3)``
``````  48.00924 51.61782 49.75104 49.19227 45.62999 50.24278 47.50642 47.36313
 50.50498 50.13968``````

#### 9.3.3.3 The function sample()

`sample(x, size, replace = TRUE/FALSE)` returns a sample of `n` values randomly taken in the object `x` (which may be a vector, a series such as `1:100`, etc). `replace =` followed by either TRUE or FALSE defines whether or not a data element can appear repeatedly in the sample.

``sample(x = 1:100, size = 10, replace = FALSE)``
``  62 47  6 48 63 33  8 64 66 86``
``sample(x = 20:30, size = 7, replace = TRUE)``
`` 24 30 23 30 20 30 22``

An interesting property of the function `sample()` is that it can be used to shuffle the result of an expression or the content of a vector, something which is useful for randomization of data elements. In the following example, `sample()` shuffles and returns all the values in `1:10`:

``sample(1:10)``
``   6  7  3  9  4  2 10  1  5  8``

#### 9.3.3.4`set.seed()`

The sequence of “random” numbers that R generates are not strictly random but pseudo-random. The sequence repeats with a very long period (219937 - 1 for the default Mersenne-Twister algorithm). If you want to get exactly the same sequence again (for reproducibility), you can set the seed for the random numbers with `set.seed()`.

``````set.seed(300)
rnorm(n = 5)``````
``  1.37379088  0.86210687  0.47348910  0.70126281 -0.08505527``
``````set.seed(300)
rnorm(n = 5)``````
``  1.37379088  0.86210687  0.47348910  0.70126281 -0.08505527``
Exercise
• Generate 10 random numbers from a uniform distribution between 10 and 20
• Generate 10 random numbers from a normal distribution with a mean of 4 and a standard deviation of 2
• sample 10 values from the sequence 1:10 with replacement