2 - Vectors in R

#statistics #R

Class: STAT-211

Notes:

Creating a Vector in R

In R, you create a vector with the combine function c(). You place the vector elements separated by a comma between the parentheses. For example:

# Poker winnings from Monday to Friday
poker_vector <- c(140, -50, 20, -120, 240)

# Roulette winnings from Monday to Friday
roulette_vector <- c(-24, -50, 100, -350, 10)

# Other examples of vectors
numeric_vector <- c(1, 10, 49)
character_vector <- c("a", "b", "c")
boolean_vector <- c(TRUE, FALSE, TRUE)

Once you have created these vectors in R, you can use them to do calculations.

Naming a vector

As a data analyst, it is important to have a clear view on the data that you are using. Understanding what each element refers to is therefore essential.

You can give a name to the elements of a vector with the names() function. Have a look at this example:

some_vector <- c("John Doe", "poker player")
names(some_vector) <- c("Name", "Profession")

This code first creates a vector some_vector and then gives the two elements a name. The first element is assigned the name Name, while the second element is labeled Profession. Printing the contents to the console yields following output:

          Name     Profession 
    "John Doe" "poker player"

Example:

# Poker winnings from Monday to Friday
poker_vector <- c(140, -50, 20, -120, 240)

# Roulette winnings from Monday to Friday
roulette_vector <- c(-24, -50, 100, -350, 10)

# Assign days as names of poker_vector
names(poker_vector) <- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday")

# Assign days as names of roulette_vector
names(roulette_vector) <- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday")

# Show
poker_vector
roulette_vector

Output:

poker_vector
   Monday   Tuesday Wednesday  Thursday    Friday 
      140       -50        20      -120       240 
roulette_vector
   Monday   Tuesday Wednesday  Thursday    Friday 
      -24       -50       100      -350        10

Use variables for efficiency, for example:

# Poker winnings from Monday to Friday
poker_vector <- c(140, -50, 20, -120, 240)

# Roulette winnings from Monday to Friday
roulette_vector <- c(-24, -50, 100, -350, 10)

# The variable days_vector
days_vector <- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday")
 
# Assign the names of the day to roulette_vector and poker_vector
names(poker_vector) <- days_vector  
names(roulette_vector) <- days_vector

Output:

poker_vector
   Monday   Tuesday Wednesday  Thursday    Friday 
      140       -50        20      -120       240 
roulette_vector
   Monday   Tuesday Wednesday  Thursday    Friday 
      -24       -50       100      -350        10

Sum two vectors

It is important to know that if you sum two vectors in R, it takes the element-wise sum. For example, the following three statements are completely equivalent:

c(1, 2, 3) + c(4, 5, 6)
c(1 + 4, 2 + 5, 3 + 6)
c(5, 7, 9)

You can also do the calculations with variables that represent vectors:

a <- c(1, 2, 3) 
b <- c(4, 5, 6)
c <- a + b

A function that helps you perform addition with vectors is sum(). It calculates the sum of all elements of a vector. For example, to calculate the total amount of money you have lost/won with poker you do:

total_poker <- sum(poker_vector)

Comparisons in R

Use the > to perform a "greater than comparison"

total_poker > total_roulette

Output:

total_poker > total_roulette
[1] TRUE

Accessing elements of a vector

Suppose you only want to focus on a selection of the total_vector. In other words, our goal is to select specific elements of the vector. To select elements of a vector (and later matrices, data frames, …), you can use square brackets. Between the square brackets, you indicate what elements to select. For example, to select the first element of the vector, you type poker_vector[1]. To select the second element of the vector, you type poker_vector[2], etc. Notice that the first element in a vector has index 1, not 0 as in many other programming languages.

# Poker and roulette winnings from Monday to Friday:
poker_vector <- c(140, -50, 20, -120, 240)
roulette_vector <- c(-24, -50, 100, -350, 10)
days_vector <- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday")
names(poker_vector) <- days_vector
names(roulette_vector) <- days_vector

# Define a new variable based on a selection
poker_wednesday <- poker_vector[3]
poker_wednesday

Output:

poker_wednesday
Wednesday 
       20

To select multiple elements from a vector, you can add square brackets at the end of it. You can indicate between the brackets what elements should be selected. For example: suppose you want to select the first and the fifth day of the week: use the vector c(1, 5) between the square brackets. For example, the code below selects the first and fifth element of poker_vector:

poker_vector[c(1, 5)]

Example:

# Poker and roulette winnings from Monday to Friday:
poker_vector <- c(140, -50, 20, -120, 240)
roulette_vector <- c(-24, -50, 100, -350, 10)
days_vector <- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday")
names(poker_vector) <- days_vector
names(roulette_vector) <- days_vector

# Define a new variable based on a selection
poker_midweek <- poker_vector[c(2, 3, 4)]
poker_midweek

Output:

poker_midweek
  Tuesday Wednesday  Thursday 
      -50        20      -120

Selecting multiple elements of poker_vector with c(2, 3, 4) is not very convenient. Statisticians created an easier way to do this: c(2, 3, 4) can be abbreviated to2:4, which generates a vector with all natural numbers from 2 up to 4.

So, another way to find the mid-week results is poker_vector[2:4]. Notice how the vector 2:4 is placed between the square brackets to select element 2 up to 4.

Example:

# Define a new variable based on a selection
roulette_selection_vector <- roulette_vector[2:5]
roulette_selection_vector

Output:

roulette_selection_vector
  Tuesday Wednesday  Thursday    Friday 
      -50       100      -350        10

Accessing elements using names

Another way to tackle the previous exercise is by using the names of the vector elements (Monday, Tuesday, …) instead of their numeric positions. For example,

poker_vector["Monday"]

will select the first element of poker_vector since "Monday" is the name of that first element.

Just like you did in the previous exercise with numerics, you can also use the element names to select multiple elements, for example:

poker_vector[c("Monday","Tuesday")]

Calculating the mean of a vector

Calculate the average of the values in poker_start with the mean() function

# Select poker results for Monday, Tuesday and Wednesday
poker_start <- poker_vector[c("Monday", "Tuesday", "Wednesday")]

# Calculate the average of the elements in poker_start
mean(poker_start)

Output:

mean(poker_start)
[1] 36.66667

Selection by comparison

The (logical) comparison operators known to R are:

The nice thing about R is that you can use these comparison operators also on vectors. For example:

c(4, 5, 6) > 5
[1] FALSE FALSE TRUE

This command tests for every element of the vector if the condition stated by the comparison operator is TRUE or FALSE.

Example:

# Which days did you make money on poker?
selection_vector <- poker_vector > 0
selection_vector
   Monday   Tuesday Wednesday  Thursday    Friday 
     TRUE     FALSE      TRUE     FALSE      TRUE

In the previous example you used selection_vector <- poker_vector > 0 to find the days on which you had a positive poker return. Now, you would like to know not only the days on which you won, but also how much you won on those days.

You can select the desired elements, by putting selection_vector between the square brackets that follow poker_vector:

# Which days did you make money on poker?
selection_vector <- poker_vector > 0

# Select from poker_vector these days
poker_winning_days <- poker_vector[selection_vector]
poker_winning_days
   Monday Wednesday    Friday 
      140        20       240

R knows what to do when you pass a logical vector in square brackets: it will only select the elements that correspond to TRUE in selection_vector.