Question

When X and Y are conditionally dependent at each level of Z yet marginally independent, Z is called a suppressor variable. Specify joint probabilities for a 2×2×2 table to show that this can happen (a) when there is homogeneous association, and (b) when the association has opposite direction in the partial tables.

Answer 1

To show that Z can be a suppressor variable, a 2x2x2 table can be created with joint probabilities. In a) homogeneous association, and b) opposite direction association in the partial tables.

Step-by-step explanation:

To show that Z can be a suppressor variable when X and Y are conditionally dependent at each level of Z yet marginally independent, we can create a 2x2x2 table with joint probabilities.

a) In the case of homogeneous association, where the association between X and Y is the same at each level of Z, we can have the following joint probabilities:

| X\Y | 0 | 1 |
|----|----|----|
| 0 | 1/8| 1/8|
| 1 | 1/4| 1/4|

b) In the case of opposite direction association in the partial tables, we can have the following joint probabilities:

| X\Y | 0 | 1 |
|----|----|----|
| 0 | 1/4| 1/8|
| 1 | 1/8| 1/4|