Introduction

Working with frequency tables is a common task in data analysis, and R provides several ways to create them. The xtabs() function stands out as a powerful tool that uses a formula interface to create contingency tables from your data. Whether you’re counting occurrences of categories or creating complex cross-tabulations, xtabs() makes the process straightforward and flexible.

In this guide, we’ll explore how to use xtabs() effectively, starting with basic syntax and moving through practical examples. You’ll learn how to create simple frequency tables, handle multiple variables, work with weighted data, and solve common problems that R programmers encounter.

What is xtabs()?

The xtabs() function creates contingency tables (also called cross-tabulation tables or crosstabs) by counting combinations of factor levels in your data . Think of it as a way to summarize how often different combinations of categories appear together.

What makes xtabs() special is its formula interface. Instead of passing individual vectors like you would with table(), you can work directly with data frames using a simple formula notation .

Basic Syntax

Here’s the basic syntax for xtabs():

xtabs(formula, data, subset, na.action, exclude, drop.unused.levels, sparse = FALSE)

Let’s break down the main parameters:

formula: A formula like ~ var1 + var2 that describes which variables to cross-tabulate
data: Your data frame containing the variables
subset: Optional - select specific rows to include
na.action: How to handle missing values (NA)
exclude: Values to exclude from the table
drop.unused.levels: Whether to remove unused factor levels
sparse: Return a sparse matrix (useful for large tables)

Simple Examples

Single Variable Frequency Table

Let’s start with the simplest case - counting frequencies for one variable:

# Create sample data
survey_data <- data.frame(
  Product = c("A", "B", "A", "C", "B", "A", "B", "C", "A", "A")
)

# Create frequency table
product_freq <- xtabs(~ Product, data = survey_data)
print(product_freq)

Product
A B C 
5 3 2

Two-Variable Cross-Tabulation

Now let’s look at relationships between two variables:

# Sample data with two variables
survey_data <- data.frame(
  Gender = c("Male", "Female", "Male", "Female", "Male", 
             "Female", "Male", "Female", "Male", "Female"),
  Product = c("A", "B", "A", "B", "C", "A", "B", "C", "A", "B")
)

# Create cross-tabulation
gender_product <- xtabs(~ Gender + Product, data = survey_data)
print(gender_product)

        Product
Gender   A B C
  Female 1 3 1
  Male   3 1 1

Working with Data Frames

One of the biggest advantages of xtabs() over table() is how well it works with data frames . You don’t need to extract individual columns:

# More complex data frame
sales_data <- data.frame(
  Region = c("North", "South", "North", "South", "North", 
             "South", "North", "South", "North", "South"),
  Device = c("Mobile", "Desktop", "Mobile", "Mobile", "Desktop",
             "Mobile", "Desktop", "Desktop", "Mobile", "Mobile"),
  Sales = c(100, 150, 200, 120, 180, 90, 220, 160, 140, 110)
)

# Count by Region and Device
device_region <- xtabs(~ Device + Region, data = sales_data)
print(device_region)

         Region
Device    North South
  Desktop     2     2
  Mobile      3     3

Weighted Frequency Tables

Sometimes you need to sum values instead of just counting rows. xtabs() handles this by putting a variable on the left side of the formula:

# Sum sales by device type
sales_by_device <- xtabs(Sales ~ Device, data = sales_data)
print(sales_by_device)

Device
Desktop  Mobile 
    710     760

This sums the Sales values for each device type instead of just counting occurrences.

For a two-way weighted table:

# Sum sales by device and region
sales_summary <- xtabs(Sales ~ Device + Region, data = sales_data)
print(sales_summary)

         Region
Device    North South
  Desktop   400   310
  Mobile    440   320

Three-Way Tables

xtabs() can handle multiple dimensions easily:

# Add a time period variable
sales_data$Period = c("Q1", "Q2", "Q1", "Q2", "Q1", 
                      "Q2", "Q1", "Q2", "Q1", "Q2")

# Three-way table
three_way <- xtabs(~ Device + Region + Period, data = sales_data)
print(three_way)

, , Period = Q1

         Region
Device    North South
  Desktop     2     0
  Mobile      3     0

, , Period = Q2

         Region
Device    North South
  Desktop     0     2
  Mobile      0     3

# Use ftable() for better display
print(ftable(three_way))

               Period Q1 Q2
Device  Region             
Desktop North          2  0
        South          0  2
Mobile  North          3  0
        South          0  3

The ftable() function creates a “flat” table that’s easier to read when you have three or more variables .

Including NA Values

By default, xtabs() might exclude rows with missing values. To include them:

# Data with NA values
data_with_na <- data.frame(
  Category = c("A", "B", NA, "A", "B", "C", NA, "A"),
  Group = c("X", "Y", "X", "Y", "X", "Y", "X", "Y")
)

# Include NA as a category
with_na <- xtabs(~ Category + Group, data = data_with_na, 
                 na.action = na.pass)
print(with_na)

        Group
Category X Y
       A 1 2
       B 1 1
       C 0 1

Setting na.action = na.pass ensures that NA values appear in your table .

Dynamic Column Selection

When you need to select columns programmatically, use as.formula():

# Function to create frequency table for any column
create_freq_table <- function(data, col_name) {
  formula_str <- paste("~", col_name)
  xtabs(as.formula(formula_str), data = data)
}

# Use the function
my_col <- "Product"
result <- create_freq_table(survey_data, my_col)
print(result)

Product
A B C 
4 4 2

This technique is useful when building interactive applications or processing multiple columns.

Converting Output to Data Frame

The output of xtabs() is a special table object. To convert it for further analysis:

# Create a frequency table
freq_table <- xtabs(~ Gender + Product, data = survey_data)

# Convert to data frame
freq_df <- as.data.frame(freq_table)
print(freq_df)

  Gender Product Freq
1 Female       A    1
2   Male       A    3
3 Female       B    3
4   Male       B    1
5 Female       C    1
6   Male       C    1

Common Problems and Solutions

1. Calculating Means Instead of Sums

xtabs() only sums values, not averages them . To get means:

# Get sums and counts
sum_table <- xtabs(Sales ~ Device, data = sales_data)
count_table <- xtabs(~ Device, data = sales_data)

# Calculate means
mean_table <- sum_table / count_table
print(mean_table)

Device
 Desktop   Mobile 
177.5000 126.6667

2. Removing Unused Factor Levels

If your factors have levels with no data:

# Remove unused levels before creating table
# sales_data$Device <- droplevels(sales_data$Device)
clean_table <- xtabs(~ Device, data = sales_data)
clean_table

Device
Desktop  Mobile 
      4       6

3. Group-wise Tables

To create separate tables for each group:

# Split by region and create tables
by(sales_data, sales_data$Region, function(subset) {
  xtabs(~ Device, data = subset)
})

sales_data$Region: North
Device
Desktop  Mobile 
      2       3 
------------------------------------------------------------ 
sales_data$Region: South
Device
Desktop  Mobile 
      2       3

Your Turn!

Here’s a practice problem to test your understanding:

Problem: Given the following data frame, create a weighted frequency table showing total scores by student grade and subject. Then, calculate the average score for each grade-subject combination.

student_data <- data.frame(
  Grade = c("A", "B", "A", "B", "C", "A", "B", "C", "A", "B"),
  Subject = c("Math", "Math", "Science", "Science", "Math", 
              "Science", "Math", "Science", "Math", "Science"),
  Score = c(85, 78, 92, 88, 75, 95, 82, 79, 88, 85)
)

# Your code here

Click here for Solution!

# Step 1: Create weighted frequency table (sum of scores)
score_sums <- xtabs(Score ~ Grade + Subject, data = student_data)
print("Sum of scores:")

[1] "Sum of scores:"

print(score_sums)

     Subject
Grade Math Science
    A  173     187
    B  160     173
    C   75      79

# Step 2: Create count table
count_table <- xtabs(~ Grade + Subject, data = student_data)
print("\nCount of students:")

[1] "\nCount of students:"

print(count_table)

     Subject
Grade Math Science
    A    2       2
    B    2       2
    C    1       1

# Step 3: Calculate averages
avg_scores <- score_sums / count_table
print("\nAverage scores:")

[1] "\nAverage scores:"

print(avg_scores)

     Subject
Grade Math Science
    A 86.5    93.5
    B 80.0    86.5
    C 75.0    79.0

# Bonus: Convert to data frame for easier viewing
avg_df <- as.data.frame(avg_scores)
names(avg_df)[3] <- "AvgScore"
print("\nAs data frame:")

[1] "\nAs data frame:"

print(avg_df)

  Grade Subject AvgScore
1     A    Math     86.5
2     B    Math     80.0
3     C    Math     75.0
4     A Science     93.5
5     B Science     86.5
6     C Science     79.0

Quick Takeaways

Key Points to Remember:

xtabs() uses formula notation (~) to specify variables
Put variables on the right side of ~ to count frequencies
Put a numeric variable on the left side to sum values
Use data = parameter to work directly with data frames
Add na.action = na.pass to include NA values in tables
Use as.formula() for dynamic column selection
Convert to data frame with as.data.frame() for further processing
For means, divide sum tables by count tables
Use ftable() to display multi-dimensional tables clearly

Conclusion

The xtabs() function provides a flexible and powerful way to create frequency tables in R. Its formula interface makes it particularly convenient when working with data frames, and its ability to handle weighted frequencies and multiple dimensions makes it suitable for a wide range of data analysis tasks.

Remember that while xtabs() excels at creating frequency and sum tables, you’ll need to combine it with other functions for more complex aggregations like means or medians. By mastering xtabs() alongside complementary functions like ftable() and data frame conversions, you’ll be well-equipped to handle any frequency analysis task in R.

Ready to put xtabs() to work? Start by applying it to your own datasets, experiment with different formula combinations, and don’t forget to explore how it integrates with your broader data analysis workflow!

FAQs

Q1: What’s the difference between xtabs() and table()?
A: The main difference is that xtabs() uses a formula interface and works directly with data frames using the data = parameter, while table() requires you to pass individual vectors. xtabs() is generally more convenient for data frame operations.

Q2: Can xtabs() calculate percentages directly?
A: No, xtabs() creates count or sum tables. To get percentages, use prop.table() on the result: prop.table(xtabs(~ var1 + var2, data = mydata)).

Q3: How do I handle very large tables with xtabs()?
A: For large tables, set sparse = TRUE to return a sparse matrix, which uses less memory. This is especially useful when many combinations have zero counts.

Q4: Can I use xtabs() with continuous variables?
A: Yes, but you should first convert continuous variables to categories using cut() or similar functions. Otherwise, you’ll get a separate count for each unique value.

Q5: How do I save xtabs() output to a CSV file?
A: First convert to a data frame, then use write.csv(): write.csv(as.data.frame(my_xtabs), "output.csv").

Engage!

Did this guide help you understand xtabs() better? We’d love to hear about your experiences using it in your R projects! Share your favorite use cases or any creative applications you’ve discovered in the comments below, or connect with us on social media to join the conversation with other R programmers.

References

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