The prop.table() function in R can be used to calculate the value of each cell in a table as a proportion of all values.

This function uses the following basic syntax:

prop.table(x, margin = NULL)

where:

• x: Name of the table
• margin: The margin to divide by (1 = row, 2 = column, default is NULL)

The following examples show how to use this function in practice with the following matrix in R:

#create matrix
x <- matrix(1:6, nrow=2)

#view matrix
x

     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6

Example 1: Use prop.table with margin = NULL

The following code shows how to use prop.table() without specifying a margin to divide by:

prop.table(x)

           [,1]      [,2]      [,3]
[1,] 0.04761905 0.1428571 0.2380952
[2,] 0.09523810 0.1904762 0.2857143

The sum of all of the values in the original table is: 1 + 3 + 5 + 2 + 4 + 6 = 21.

The prop.table() function shows each individual value as a proportion of the whole.

For example:

• Cell [1, 1] = 1/21 = .0476
• Cell [1, 2] = 3/21 = .1428
• Cell [1, 3] = 5/21 = .2380
• Cell [2, 1] = 2/21 = .0952
• Cell [2, 2] = 4/21 = .1904
• Cell [3, 2] = 6/21 = .2857

Note that all of the values in the prop.table() output add up to 1.

Example 2: Use prop.table with margin = 1

The following code shows how to use prop.table() with margin=1, which divides each individual value by the row sums: 

prop.table(x, margin = 1)

          [,1]      [,2]      [,3]
[1,] 0.1111111 0.3333333 0.5555556
[2,] 0.1666667 0.3333333 0.5000000

The sum of all of the values in the first row of the original table is: 1 + 3 + 5 = 9.

The sum of all of the values in the second row of the original table is: 2 + 4 + 6 = 12.

Thus, the output shows each individual value as a proportion of the row sum.

For example:

• Cell [1, 1] = 1/9 = .1111
• Cell [1, 2] = 3/9 = .3333
• Cell [1, 3] = 5/9 = .5555
• Cell [2, 1] = 2/12 = .1667
• Cell [2, 2] = 4/12 = .3333
• Cell [3, 2] = 6/12 = .5000

Note that the values in each row of the prop.table() output add up to 1.

Example 3: Use prop.table with margin = 2

The following code shows how to use prop.table() with margin=2, which divides each individual value by the column sums: 

prop.table(x, margin = 2)

          [,1]      [,2]      [,3]
[1,] 0.3333333 0.4285714 0.4545455
[2,] 0.6666667 0.5714286 0.5454545

The sum of the values in the first column of the original table is: 1 + 2 = 3.

The sum of the values in the second column of the original table is: 3 + 4 = 7.

The sum of the values in the third column of the original table is: 5 + 6 = 11.

Thus, the output shows each individual value as a proportion of the column sum.

For example:

• Cell [1, 1] = 1/3 = .3333
• Cell [2, 1] = 2/3 = .6667
• Cell [1, 2] = 3/7 = .4285
• Cell [2, 2] = 4/7 = .5714
• Cell [1, 3] = 5/11 = .4545
• Cell [3, 3] = 6/11 = .5454

Note that the values in each column of the prop.table() output add up to 1.

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