yules coefficient of association | Theory of attributes | Explained .

 Yule's coefficient of association

            This measurement is used to determine the existence of a relation between two qualities A and B (binary complementary variables). Examples of attributes are drinking, smoking, blindness, honesty and so on.

            Udny Yule (1871-1951) was a British Statistican.He was educated at Winchester college and university college London. After a year of research in experimental physics, he returned to university in 1893 to work as a demonstrator for karl Pearson. Pearson begin working in statistics and Yule followed the Pearson’s research.Yule was a prolific writer who was engaged in the royal statistical society receiving the Guy medal in gold in 1911 and serving as president of the royal statistical society in 1924-26. He was responsible for the concept of association

 Coefficient of association

 Coefficient of  association determines the strength and direction of an ,association The term association refers to the  degree of agreement between qualities.

           Prof. Yule has given a formula; In this formula the coefficient of association is denoted by 'Q' which ranges between 1 to -l is defined as follows:

\[Q = \frac{{(AB)(\alpha \beta ) - (A\beta )(\alpha B)}}{{(AB)(\alpha \beta ) + (A\beta )(\alpha B)}}\]

 

if Q=0, A and B are independent.

if Q=+1, A and B are perfect positive associated.

if Q=-1  A and B have perfect negative association.

-1≤ Q≤+1

Below are the solved examples;

Here the attribute A and B are positively associated.

From the above Q=-0.606 ,there is a negative association between A and B.

        

    From the above it is clear that Q=+1, there is perfect positive association between two attributes, A and B.

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