How to Create a Three Way Table in R

A three-way table, also known as a three-dimensional contingency table, is a tabular representation of the joint frequencies of three categorical variables. It provides a way to analyze the relationships between three categorical variables simultaneously. In this article, we will study different approaches by which we can create a three-way table in R Programming Language.

Ways to Create a Three-Way Table in R

Below are some of the ways by which we can create a three-way table in R

1. Using the ftable() Function
2. Using the xtabs() Function
3. Using the table() Using table() with Array Indexing
4. Using Nested for Loops

Create Three-Way Tables in R using ftable()

Syntax

In R, We can create a three-way table by using the ftable() function:

three_way_ftable <- ftable(three_way)

# Generate example data
set.seed(123)  # for reproducibility

# Create a data frame with sample data
data <- data.frame(
  Subject = sample(c("Math", "Science", "English"), 100, replace = TRUE),
  Gender = sample(c("Male", "Female"), 100, replace = TRUE),
  Performance = sample(c("High", "Medium", "Low"), 100, replace = TRUE)
)
head(data)
# Create a three-way table using the table() function
three_way_table <- ftable(data$Subject, data$Gender, data$Performance)

# Display the table
print(three_way_table)

Output:

  Subject Gender Performance
1 English   Male      Medium
2 English Female        High
3 English Female        High
4 Science   Male      Medium
5 English   Male         Low
6 Science   Male        High                High Low Medium
                               
English Female    11   5      2
        Male       6   6      5
Math    Female     8   3      6
        Male       9   2      5
Science Female    10   2      9
        Male       3   2      6

In this method, we utilize the ftable() function in R to create a three-way table. We start by passing the variables of interest (e.g., Subject, Gender, Performance) into the ftable() function. Internally, the function identifies unique combinations of levels for each variable and computes the frequencies of these combinations.Finally ,the resulting table displays the frequencies of occurrences for each combination of categories.

Create Three-Way Tables in R using xstabs()

In R,we can create a three-way table by using the xtabs() function

Syntax

three_way <- xtabs(~ var1 + var2 + var3, data=df) 

# Generate example data
set.seed(123)  # for reproducibility

# Create a data frame with sample data
exam_data <- data.frame(
  Year = sample(c("Freshman", "Sophomore", "Junior"), 200, replace = TRUE),
  Study_Method = sample(c("Self-Study", "Group Study"), 200, replace = TRUE),
  Result = sample(c("Pass", "Fail"), 200, replace = TRUE)
)
head(exam_data)
# Create a three-way contingency table using xtabs()
three_way_table_xtabs <- xtabs(~ Year + Study_Method + Result, data = exam_data)

# Display the table
print(three_way_table_xtabs)

Output:

       Year Study_Method Result
1    Junior  Group Study   Fail
2    Junior   Self-Study   Pass
3    Junior  Group Study   Pass
4 Sophomore   Self-Study   Fail
5    Junior  Group Study   Fail
6 Sophomore   Self-Study   Pass, , Result = Fail           Study_Method
Year        Group Study Self-Study
  Freshman           15         19
  Junior             17         21
  Sophomore          17         20, , Result = Pass           Study_Method
Year        Group Study Self-Study
  Freshman           15         14
  Junior              8         21
  Sophomore          15         18

In this method, we use the xtabs() function to construct a three-way table. We specify the formula ~ var1 + var2 + var3 to indicate the three categorical variables of interest (e.g., Year, Study_Method, Result). The xtabs() function then cross-tabulates these variables to generate a contingency table, where the rows and columns correspond to the levels of each variable. The resulting table displays the frequencies of occurrences for each combination of categories.

Create Three-Way Tables in R using table() with Array Indexing

In R,we can create a three-way table by using table() with Array Indexing

Syntax

three_way_table <- table(var1, var2, var3, data = your_data_frame)

# Example data
data <- data.frame(
  Gender = c("Male", "Female", "Male", "Male", "Female", "Female"),
  AgeGroup = c("Young", "Young", "Old", "Old", "Young", "Old"),
  Region = c("East", "West", "West", "East", "East", "West")
)
data
# Creating a three-way table
three_way_table <- table(data$Gender, data$AgeGroup, data$Region)

# Print the table
print(three_way_table)

Output:

  Gender AgeGroup Region
1   Male    Young   East
2 Female    Young   West
3   Male      Old   West
4   Male      Old   East
5 Female    Young   East
6 Female      Old   West, ,  = East        
         Old Young
  Female   0     1
  Male     1     1, ,  = West        
         Old Young
  Female   1     1
  Male     1     0

In this method, we use the table() function with array indexing to create a three-way table. The table() function computes the frequency of each combination of levels from the three categorical variables: Gender, AgeGroup, and Region. By specifying the three variables as arguments to the table() function, we obtain a three-dimensional array representing the joint frequencies. Each dimension of the array corresponds to a variable, and the entries in the array represent the frequency of each combination of levels.

Create Three-Way Tables in R using Nested for Loops

# Example data
data <- data.frame(
  Gender = c("Male", "Female", "Male", "Male", "Female", "Female"),
  AgeGroup = c("Young", "Young", "Old", "Old", "Young", "Old"),
  Region = c("East", "West", "West", "East", "East", "West")
)
data 
# Unique levels of variables
genders <- unique(data$Gender)
age_groups <- unique(data$AgeGroup)
regions <- unique(data$Region)

# Initialize an empty table
three_way_table <- array(0, dim = c(length(genders),length(age_groups),length(regions)))

# Fill in the table
for (i in 1:length(genders)) {
  for (j in 1:length(age_groups)) {
    for (k in 1:length(regions)) {
      three_way_table[i, j, k] <- sum(data$Gender == genders[i] & 
                                      data$AgeGroup == age_groups[j] & 
                                      data$Region == regions[k])
    }
  }
}

# Print the table
print(three_way_table)

Output:

  Gender AgeGroup Region
1   Male    Young   East
2 Female    Young   West
3   Male      Old   West
4   Male      Old   East
5 Female    Young   East
6 Female      Old   West, , 1     [,1] [,2]
[1,]    1    1
[2,]    1    0, , 2     [,1] [,2]
[1,]    0    1
[2,]    1    1

In this method, we create a three-way table using nested for loops. We first identify the unique levels of each categorical variable (Gender, AgeGroup, Region). Then, we initialize an empty three-dimensional array to store the frequencies of each combination of levels. We iterate over each combination of levels using nested loops and calculate the frequency of each combination by counting the occurrences in the original data frame (data). Finally, we populate the three-way table with the calculated frequencies.

Conclusion

In this article we understood that creating a three-way table in R is a straightforward process that allows for the comprehensive analysis of relationships between three categorical variables. Through the utilization of functions like table() or xtabs(), R enables users to efficiently generate contingency tables summarizing the joint distribution of these variables.