What will be the Yule’s Coefficient of Association?

Question

This might be a very basic question but I am not so familiar with Yule's Coefficient of Association. The below question appeared in a test which is as under

I have tried to solve the problem after reading some notes from various sites and came up with the below solution

Total adults(N) = 10000 Literate (A) = 1290 Unemployed (B) = 1390 Literate and unemployed(AB) = 820

Let X = Illiterate, Y = Employeed

The 2 X 2 contingency table will be

          A      X       Total
B        820    570      1390
Y        470    8140     8610
Total   1290    8710     10000

Yule's Coefficient of Association ( (AB)(XY) – (AY)(XB) ) / ( (AB)(XY) + (AY)(XB) )

= ( (820 * 8140) – (470 * 570 ) / (820 * 8140) + (470 * 570 ) )
= ( 6674800 – 267900 ) / ( 6674800 + 267900 )
= 6406900 / 6942700
=+ 0.9228

Comment : The association is positive between Literacy and UnEmployment

Is it correct?

Please assist.

Answer 1

Your contingency table looks sensible based on the information you have

Looking at that, your comment that the association is positive between Literacy and Unemployment looks correct

Wikipedia's article on Yule’s Y, also known as the coefficient of colligation gives a slightly different expression $$Y = \frac{\sqrt{ad}-\sqrt{bc}}{\sqrt{ad}+\sqrt{bc}}$$ which may give about $0.6662$ with your data

but I think your value of 0.9228 is Yule's Q as a Yule coefficient of association and looks sensible