Examining the variables separately

Although our main interest is usually on the relationship between two categorical variables, it can also be of interest to examine the overall distribution of each variable separately. These are called the marginal distributions of the two variables.

The marginal distributions are determined by the row and column totals of a contingency table.

Rank and age in a university

In a similar way, the marginal proportions for the variables are obtained by adding the joint proportions across rows and down columns. Writing the joint proportion for row-category x and column-category y as pxy, the marginal proportions are:

Marginal proportion for:
x y

Rank and age in a university

    Rank
Age Full
professor
Associate
professor
Assistant
professor
Instructor Total
  Under 30 2/1164 3/1164 57/1164 6/1164 68/1164
30 to 39 52/1164 170/1164 163/1164 17/1164 402/1164
40 to 49 156/1164 125/1164 61/1164 6/1164 348/1164
50 and over 220/1164 83/1164 39/1164 4/1164 346/1164
Total 430/1164 381/1164 320/1164 33/1164

The highlighted values are the overall proportions for each age (yellow) and rank (green) category in the university — i.e. the marginal distributions of these two variables.