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.