Spliting into groups

If the values of X are used to split the individuals into groups, the conditional distributions of Y given X are the distributions within each of these groups. They are found by dividing the cell counts by the totals for each such group. The columns of the table below show the conditional distributions for a contingency table, expressed as percentages.

Conditional percentages for Y, given X
    Variable X
Variable Y         X1           X2           X3           X4     
  Y1 000.5 000.8 017.8 018.2
Y2 012.1 044.6 050.9 051.5
Y3 036.3 032.8 019.1 018.2
Y4 051.2 021.8 012.2 012.1
Total 100.0 100.0 100.0 100.0

The conditional distributions of X given Y are similarly found by using Y to create the groups of individuals. They are found by dividing the cell counts by the totals in the other margin of the original contingency table.

Conditional percentages for X, given Y
    Variable X
Variable Y       X1       X2       X3       X4     Total 
  Y1 02.9 04.4 83.8 8.8 100.0 
Y2 12.9 42.3 40.5 4.2 100.0 
Y3 44.8 35.9 17.5 1.7 100.0 
Y4 63.6 24.0 11.3 1.2 100.0 

Both tables of conditional proportions (or percentages) are often informative.