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 |
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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.