Question

Find the association between intelligence of fathers and the intelligence of sons from the following data:
Intelligent fathers with intelligent sons: $50$
Dull fathers with intelligent sons: $100$
Dull fathers with dull sons: $300$
Intelligent fathers with dull sons: $200$

Answer 1

Let A denote the intelligence of father’s and B denote the intelligence of Son’s

Then, we know that

Yules’s co-efficient of association is

$Q=\frac{\left(AB\right).\left(\alpha \beta \right)-\left(A\beta \right).\left(\alpha \beta \right)}{\left(AB\right).\left(\alpha \beta \right)+\left(A\beta \right).\left(\alpha \beta \right)}$

$=\frac{50\times 300-200\times 100}{50\times 300+200\times 100}$

$=\frac{15000-20000}{15000+20000}$

$=\frac{-5000}{35000}$

$=-\frac{1}{7}$

$=-0.428$

There is a negative association between the intelligence of father’s and son’s