There are several measures by which to judge the coherence between variables in a crosstab.
In a 2 x 2 table these are the relative risk and the percentage difference.
For these and larger tables there is the Chi-square, similar to the square of the standard deviation.
The relative risk
A disaster scenario gives the following cross table.
.
|
Survival |
||
Gender |
Survived |
Died |
Total |
Male |
10 |
35 |
45 |
Female |
50 |
55 |
105 |
Total |
60 |
90 |
150 |
You see that more women than men died, however relatively speaking this is not the case.
The absolute risk of dying in the disaster was within the group of men:
35/45 = 0.78 or 78%
The absolute risk of dying in the disaster was within the group of women:
55/105 = 0.52 or 52%
The relative risk of dying in the disaster is the ratio of these two risks:
0.78 / 0.52 = 1.5
This relative risk indicates that the risk for men is one and a half times that for women.
In a situation where the variables are independent, the relative risk is equal to 1. Explain.
The percentage difference
The cross table with the rows in percentage.
|
Survival |
||
Gender |
Survived |
Died |
Total |
Male |
22 % |
78 % |
100 % |
Female |
48 % |
52 % |
100 % |
|
|
|
|
The percentage difference between men and women who died is 26%.
In a situation where the variables are independent, the percentage difference is equal to 0. Explain.
| 4.2a | Calculate the absolute and relative risk and the percentage difference between the group of men and the group of women for the category "Died". |
