R prop.table() Function

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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:

Usage of a prop.table() function

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

Argument Description
input It represents an object of class “table”, an array, or a matrix containing numeric values.
margin It represents an integer vector specifying the dimensions (margins) over which to compute the proportions.

Row-wise proportions

You can use the “margin” argument to specify the dimensions.

There are two types of margins.

  1. row-wise
  2. column-wise
margin = 1(row-wise):  It sums across rows. Each row sums to 1.

margin = 2(column-wise): It sums down columns. Each column sums to 1.

If we want row-wise proportions, we can pass 1 as a second argument to the prop.table() method.

Using a prop.table with margin = 1

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

 

Column-wise proportions

For getting column-wise proportions, you can pass 2 as a second argument to this method.

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

Ensure that you interpret the proportions in the context of how they were calculated (overall, row-wise, or column-wise) to draw meaningful conclusions from your data.

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!

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