The R Book

Calculating tables of proportions

The margins of a table (the row totals or the column totals) are often useful for calculating proportions instead of counts. Here is a data matrix called counts:

counts<-matrix(c(2,2,4,3,1,4,2,0,1,5,3,3),nrow=4)
counts

      [,1]   [,2]   [,3]
[1,]     2      1      1
[2,]     2      4      5
[3,]     4      2      3
[4,]     3      0      3

The proportions will be different when they are expressed as a fraction of the row totals or as a fraction of the column totals. You need to remember that the row subscripts come first, which is why margin number 1 refers to the row totals:

prop.table(counts,1)

          [,1]      [,2]      [,3]
[1,] 0.5000000 0.2500000 0.2500000
[2,] 0.1818182 0.3636364 0.4545455
[3,] 0.4444444 0.2222222 0.3333333
[4,] 0.5000000 0.0000000 0.5000000

The column totals are the second margin, so to express the counts as proportions of the relevant column total use:

prop.table(counts,2)
          [,1]      [,2]       [,3]
[1,] 0.1818182 0.1428571 0.08333333
[2,] 0.1818182 0.5714286 0.41666667
[3,] 0.3636364 0.2857143 0.25000000
[4,] 0.2727273 0.0000000 0.25000000

To check that the column proportions sum to one, use colSums like this:

colSums(prop.table(counts,2))
[1]   1   1   1

If you want the proportions expressed as a fraction of the grand total sum(counts), then simply omit the margin number:

prop.table(counts)

           [,1]       [,2]       [,3]
[1,] 0.06666667 0.03333333 0.03333333
[2,] 0.06666667 0.13333333 0.16666667
[3,] 0.13333333 0.06666667 0.10000000
[4,] 0.10000000 0.00000000 0.10000000
sum(prop.table(counts))

[1] 1

In any particular case, ...