Proportions within groups

To compare the distributions of a categorical variable in different groups, it is best to examine the proportions within the groups — the cell frequencies divided by their group totals.

In a study of racial differences in blood types, 145,057 blood specimens from the Blood Bank of Hawaii were tested.

  Blood type  
Ethnic group      O           A           B           AB         Total   
Hawaiian   01,903 02,490 00,178 0,099   4,670
Hawaiian-white 04,469 04,671 00,606 0,236   9,982
Hawaiian-chinese 02,206 02,368 00,568 0,243   5,385
White 53,759 50,008 16,252 5,001 125,020

From the table of within-group percentages below, it is clearer that blood groups B and AB are rarer for Hawaiians and Hawaiian-whites than for the other ethnic groups.

  Blood type  
Ethnic group     O         A         B         AB       Total  
Hawaiian   40.7 53.3 03.8 02.1 100.0
Hawaiian-white 44.8 46.8 06.1 02.4 100.0
Hawaiian-chinese 41.0 44.0 10.5 04.5 100.0
White 43.0 40.0 13.0 04.0 100.0

Bar charts of proportions

Bar charts can be used to graphically compare groups and it is again best to use proportions within groups rather than raw frequencies, especially if the groups are of different sizes.

Clustering the bars

Each cluster of bars above is a valid bar chart for one group. Alternatively, the same bars can be clustered by the variable of interest:

This makes it easier to make comparisons between the groups.