What's a factor and why would you use it?

In this chapter you dive into the wonderful world of factors.

The term factor refers to a statistical data type used to store categorical variables. The difference between a categorical variable and a continuous variable is that a categorical variable can belong to a limited number of categories. A continuous variable, on the other hand, can correspond to an infinite number of values.

It is important that R knows whether it is dealing with a continuous or a categorical variable, as the statistical models you will develop in the future treat both types differently. (You will see later why this is the case.)

A good example of a categorical variable is sex. In many circumstances you can limit the sex categories to "Male" or "Female". (Sometimes you may need different categories. For example, you may need to consider chromosomal variation, hermaphroditic animals, or different cultural norms, but you will always have a finite number of categories.)

Instructions

Assign to variable theory the value "factors".

# Assign to the variable theory what this chapter is about!
theory <- "factors"

What's a factor and why would you use it? (2)

To create factors in R, you make use of the function factor(). First thing that you have to do is create a vector that contains all the observations that belong to a limited number of categories. For example, sex_vector contains the sex of 5 different individuals:

sex_vector <- c("Male","Female","Female","Male","Male")

It is clear that there are two categories, or in R-terms 'factor levels', at work here: "Male" and "Female".

The function factor() will encode the vector as a factor:

factor_sex_vector <- factor(sex_vector)

Instructions

Convert the character vector sex_vector to a factor with factor() and assign the result to factor_sex_vector
Print out factor_sex_vector and assert that R prints out the factor levels below the actual values.

# Sex vector
sex_vector <- c("Male", "Female", "Female", "Male", "Male")

# Convert sex_vector to a factor
factor_sex_vector <- factor(sex_vector)

# Print out factor_sex_vector
factor_sex_vector

Output after running code:

# Convert sex_vector to a factor
factor_sex_vector <- factor(sex_vector)
# Print out factor_sex_vector
factor_sex_vector
[1] Male   Female Female Male   Male  
Levels: Female Male

What's a factor and why would you use it? (3)

There are two types of categorical variables: a nominal categorical variable and an ordinal categorical variable.

A nominal variable is a categorical variable without an implied order. This means that it is impossible to say that 'one is worth more than the other'. For example, think of the categorical variable animals_vector with the categories "Elephant", "Giraffe", "Donkey" and "Horse". Here, it is impossible to say that one stands above or below the other. (Note that some of you might disagree ;-) ).

In contrast, ordinal variables do have a natural ordering. Consider for example the categorical variable temperature_vector with the categories: "Low", "Medium" and "High". Here it is obvious that "Medium" stands above "Low", and "High" stands above "Medium".

Instructions

Submit the answer to check how R constructs and prints nominal and ordinal variables. Do not worry if you do not understand all the code just yet, we will get to that.

# Animals
animals_vector <- c("Elephant", "Giraffe", "Donkey", "Horse")
factor_animals_vector <- factor(animals_vector)
factor_animals_vector

# Temperature
temperature_vector <- c("High", "Low", "High","Low", "Medium")
factor_temperature_vector <- factor(temperature_vector, order = TRUE, levels = c("Low", "Medium", "High"))
factor_temperature_vector

Output after running code:

# Animals
animals_vector <- c("Elephant", "Giraffe", "Donkey", "Horse")
factor_animals_vector <- factor(animals_vector)
factor_animals_vector

[1] Elephant Giraffe  Donkey   Horse   
Levels: Donkey Elephant Giraffe Horse

# Temperature
temperature_vector <- c("High", "Low", "High","Low", "Medium")
factor_temperature_vector <- factor(temperature_vector, order = TRUE, levels = c("Low", "Medium", "High"))
factor_temperature_vector

[1] High   Low    High   Low    Medium
Levels: Low < Medium < High

Factor levels

When you first get a dataset, you will often notice that it contains factors with specific factor levels. However, sometimes you will want to change the names of these levels for clarity or other reasons. R allows you to do this with the function levels():

levels(factor_vector) <- c("name1", "name2",...)

A good illustration is the raw data that is provided to you by a survey. A common question for every questionnaire is the sex of the respondent. Here, for simplicity, just two categories were recorded, "M" and "F". (You usually need more categories for survey data; either way, you use a factor to store the categorical data.)

survey_vector <- c("M", "F", "F", "M", "M")

Recording the sex with the abbreviations "M" and "F" can be convenient if you are collecting data with pen and paper, but it can introduce confusion when analyzing the data. At that point, you will often want to change the factor levels to "Male" and "Female" instead of "M" and "F" for clarity.

Watch out: the order with which you assign the levels is important. If you type levels(factor_survey_vector), you'll see that it outputs [1] "F" "M". If you don't specify the levels of the factor when creating the vector, R will automatically assign them alphabetically. To correctly map "F" to "Female" and "M" to "Male", the levels should be set to c("Female", "Male"), in this order.

Instructions

Check out the code that builds a factor vector from survey_vector. You should use factor_survey_vector in the next instruction.
Change the factor levels of factor_survey_vector to c("Female", "Male"). Mind the order of the vector elements here.

# Code to build factor_survey_vector
survey_vector <- c("M", "F", "F", "M", "M")
factor_survey_vector <- factor(survey_vector)

# Specify the levels of factor_survey_vector
levels(factor_survey_vector) <- c("Female", "Male")

factor_survey_vector

Output after running code:

# Code to build factor_survey_vector
survey_vector <- c("M", "F", "F", "M", "M")
factor_survey_vector <- factor(survey_vector)

# Specify the levels of factor_survey_vector
levels(factor_survey_vector) <- c("Female", "Male")
factor_survey_vector

[1] Male   Female Female Male   Male  
Levels: Female Male

Summarizing a factor

After finishing this course, one of your favorite functions in R will be summary(). This will give you a quick overview of the contents of a variable:

summary(my_var)

Going back to our survey, you would like to know how many "Male" responses you have in your study, and how many "Female" responses. The summary() function gives you the answer to this question.

Instructions

Ask a summary() of the survey_vector and factor_survey_vector. Interpret the results of both vectors. Are they both equally useful in this case?

# Build factor_survey_vector with clean levels
survey_vector <- c("M", "F", "F", "M", "M")
factor_survey_vector <- factor(survey_vector)
levels(factor_survey_vector) <- c("Female", "Male")
factor_survey_vector

# Generate summary for survey_vector
summary(survey_vector)

# Generate summary for factor_survey_vector
summary(factor_survey_vector)

Output after running code:

# Build factor_survey_vector with clean levels
survey_vector <- c("M", "F", "F", "M", "M")
factor_survey_vector <- factor(survey_vector)
levels(factor_survey_vector) <- c("Female", "Male")
factor_survey_vector

[1] Male   Female Female Male   Male  
Levels: Female Male

# Generate summary for survey_vector
summary(survey_vector)

   Length     Class      Mode 
        5 character character 

# Generate summary for factor_survey_vector
summary(factor_survey_vector)

Female   Male 
     2      3

Battle of the sexes

You might wonder what happens when you try to compare elements of a factor. In factor_survey_vector you have a factor with two levels: "Male" and "Female". But how does R value these relative to each other?

Instructions

Read the code in the editor and submit the answer to test if male is greater than (>) female.

# Build factor_survey_vector with clean levels
survey_vector <- c("M", "F", "F", "M", "M")
factor_survey_vector <- factor(survey_vector)
levels(factor_survey_vector) <- c("Female", "Male")

# Male
male <- factor_survey_vector[1]

# Female
female <- factor_survey_vector[2]

# Battle of the sexes: Male 'larger' than female?
male > female

Output after running code:

# Build factor_survey_vector with clean levels
survey_vector <- c("M", "F", "F", "M", "M")
factor_survey_vector <- factor(survey_vector)
levels(factor_survey_vector) <- c("Female", "Male")

# Male
male <- factor_survey_vector[1]

# Female
female <- factor_survey_vector[2]

# Battle of the sexes: Male 'larger' than female?
male > female
Warning message: ‘>’ not meaningful for factors
[1] NA

Ordered factors

Since "Male" and "Female" are unordered (or nominal) factor levels, R returns a warning message, telling you that the greater than operator is not meaningful. As seen before, R attaches an equal value to the levels for such factors.

But this is not always the case! Sometimes you will also deal with factors that do have a natural ordering between its categories. If this is the case, we have to make sure that we pass this information to R…

Let us say that you are leading a research team of five data analysts and that you want to evaluate their performance. To do this, you track their speed, evaluate each analyst as "slow", "medium" or "fast", and save the results in speed_vector.

Instructions

As a first step, assign speed_vector a vector with 5 entries, one for each analyst. Each entry should be either "slow", "medium", or "fast". Use the list below:

Analyst 1 is medium,
Analyst 2 is slow,
Analyst 3 is slow,
Analyst 4 is medium and
Analyst 5 is fast. No need to specify these are factors yet.

# Create speed_vector
speed_vector <- c("medium", "slow", "slow", "medium", "fast")

Output after running code:

# Create speed_vector
speed_vector <- c("medium", "slow", "slow", "medium", "fast")

Ordered factors (2)

speed_vector should be converted to an ordinal factor since its categories have a natural ordering. By default, the function factor() transforms speed_vector into an unordered factor. To create an ordered factor, you have to add two additional arguments: ordered and levels.

factor(some_vector,
       ordered = TRUE,
       levels = c("lev1", "lev2" ...))

By setting the argument ordered to TRUE in the function factor(), you indicate that the factor is ordered. With the argument levels you give the values of the factor in the correct order.

Instructions

From speed_vector, create an ordered factor vector: factor_speed_vector. Set ordered to TRUE, and set levels to c("slow", "medium", "fast").

# Create speed_vector
speed_vector <- c("medium", "slow", "slow", "medium", "fast")

# Convert speed_vector to ordered factor vector
factor_speed_vector <- factor(speed_vector, ordered = TRUE, levels = c("slow", "medium", "fast"))

# Print factor_speed_vector
factor_speed_vector
summary(factor_speed_vector)

Output after running code:

# Create speed_vector
speed_vector <- c("medium", "slow", "slow", "medium", "fast")

# Convert speed_vector to ordered factor vector
factor_speed_vector <- factor(speed_vector, ordered = TRUE, levels = c("slow", "medium", "fast"))

# Print factor_speed_vector

factor_speed_vector
[1] medium slow   slow   medium fast  
Levels: slow < medium < fast

summary(factor_speed_vector)
  slow medium   fast 
     2      2      1

Comparing ordered factors

Having a bad day at work, 'data analyst number two' enters your office and starts complaining that 'data analyst number five' is slowing down the entire project. Since you know that 'data analyst number two' has the reputation of being a smarty-pants, you first decide to check if his statement is true.

The fact that factor_speed_vector is now ordered enables us to compare different elements (the data analysts in this case). You can simply do this by using the well-known operators.

Instructions

Use [2] to select from factor_speed_vector the factor value for the second data analyst. Store it as da2.
Use [5] to select the factor_speed_vector factor value for the fifth data analyst. Store it as da5.
Check if da2 is greater than da5; simply print out the result. Remember that you can use the > operator to check whether one element is larger than the other.

# Create factor_speed_vector
speed_vector <- c("medium", "slow", "slow", "medium", "fast")
factor_speed_vector <- factor(speed_vector, ordered = TRUE, levels = c("slow", "medium", "fast"))

# Factor value for second data analyst
da2 <- factor_speed_vector[2]

# Factor value for fifth data analyst
da5 <-factor_speed_vector[5]

# Is data analyst 2 faster than data analyst 5?
da2 > da5

Output after running code:

# Is data analyst 2 faster than data analyst 5?
da2 > da5
[1] FALSE

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factors.md

factors.md

What's a factor and why would you use it?

Instructions

What's a factor and why would you use it? (2)

Instructions

What's a factor and why would you use it? (3)

Instructions

Factor levels

Instructions

Summarizing a factor

Instructions

Battle of the sexes

Instructions

Ordered factors

Instructions

Ordered factors (2)

Instructions

Comparing ordered factors

Instructions

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What's a factor and why would you use it?

Instructions

What's a factor and why would you use it? (2)

Instructions

What's a factor and why would you use it? (3)

Instructions

Factor levels

Instructions

Summarizing a factor

Instructions

Battle of the sexes

Instructions

Ordered factors

Instructions

Ordered factors (2)

Instructions

Comparing ordered factors

Instructions