Question

Marginal totals aren’t the whole storyHere are the row and column totals for a two-way table with two rows and two columns:

Find two different sets of counts a, b, c, and dfor the body of the table that give these same totals. This shows that the relationship between two variables cannot be obtained from the two individual distributions of the variables.

Short answer

$$\begin{gathered} a=30,b=20,c=30,d=20 \\ a=40,b=10,c=20,d=30 \end{gathered}$$

Step-by-step solution

Step 1. Given information.

The given table is:

Step 2. For the body of the table, find two different sets of counts a, b, c, and d that provide the same totals.

We can see that the rows' total of the table is 50 and its column total are 60 and 40 respectively.

it means we need to satisfy the following equations:

$$\begin{gathered} a+b=50,c+d=50 \\ a+c=60,b+d=40 \end{gathered}$$

one set of possible values of terms a, b, c,and dare $a=30,b=20,c=30,d=20$

Another set is:

$a=40,b=10,c=20,d=30$