605 Here are the row and column totals for a twoway table wi

(6.05) Here 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 d for 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.

Solution

From the given, we have, 6+b= 50=> b= 44

And b+d= 40=> d= 40-44=-4

Also, c+d=50

(ans)

Given d=39.

As b+d=40=> b=40-39=1

As, a+b=50=> a= 50-1=49

As c+d=50=> c= 50-39= 11

(ans)

This shows that the relationship between two variables can not be obtained from the individual distributions of the variables.