R prop.table() Function

The prop.table() function in R calculates the proportion or relative frequency of values in a contingency table. It calculates the value of each cell in a table as a proportion of all values.

For example, let’s say you have a table with a total of 5 elements like this: table(c(“A”, “B”, “C”, “D”, “E”)).

Each value occurs only once, so for each value, the count is 1, and the total count is 5.

Now, the prop.table() function divides each cell by the total. So, each element’s count is proportional to the total count: 1/5 = 0.2. 

When you use this function, the sum of all proportions = 1 because it rescales counts into weights (probabilities).

This function transforms the absolute frequencies (counts) into relative proportions.

Here is another code example with a figure:

data <- c("mercedez", "bmw", "jaguar", "land rover", "audi")

# Creating a table from the data
table <- table(data)

# Calculating the proportions of the table
proportions <- prop.table(table)

print(proportions)

# Output:
# data
#  audi  bmw   jaguar  land rover  mercedez
#  0.2   0.2    0.2       0.2        0.2

In this code, each cell is divided by the total number of elements, which is 5. Divide each element 1 by 5 = 0.2, and hence each got the frequency of 0.2.

Syntax

prop.table(input, margin = NULL)

Parameters

mat <- matrix(1:9, 3)

print(mat)

# Output:
#      [,1]  [,2]   [,3]
# [1,]   1     4      7
# [2,]   2     5      8
# [3,]   3     6      9

pt <- prop.table(mat, 1)

print(pt)

# Output:
#           [,1]        [,2]       [,3]
# [1,]   0.08333333  0.3333333   0.5833333
# [2,]   0.13333333  0.3333333   0.5333333
# [3,]   0.16666667  0.3333333   0.5000000

mat <- matrix(1:9, 3)

pt <- prop.table(mat, 2)

print(pt)

# Output:
#        [,1]        [,2]       [,3]
# [1,]  0.1666667  0.2666667   0.2916667
# [2,]  0.3333333  0.3333333   0.3333333
# [3,]  0.5000000  0.4000000   0.3750000

Empty table

If you have an empty table, it handles a zero-length table gracefully without any error, but returns useless empty output.

empty_table <- table(numeric(0))

prop.table(empty_table)

# Output: numeric(0)

Empty 2D Table (Matrix)

If you pass an empty matrix, it returns an empty matrix because there is nothing to proportionate.

empty_table <- table(numeric(0), numeric(0))

prop.table(empty_table)

# Output: <0 x 0 matrix>

As you can see, the prop.table() preserves the structure and returns another empty matrix.

Zero-only tables

There is a difference between a zero-only table and an empty table. Empty means nothing in the table and zero-only table contains value 0. Every count is 0.

When prop.table() attempts to normalize such a table, it ends up dividing by 0 (since the total is 0). For truly zero-sum structures (e.g., all-zero matrices or empty tables): NaN or empty output.

zero_mat <- matrix(0, nrow = 1, ncol = 1)

prop.table(zero_mat)

# Output:
#        [,1]
# [1,]   NaN

Always check sum(x) > 0 before applying prop.table() to avoid undefined results.

That’s it!