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# How to find the extent or degree of association in theory of attributes?

## Question:

Find the extent of association between intelligence of husband and the intelligence of wife when

• Intelligent husbands with intelligent wives = 50

• Intelligent husbands with dull wives = 200

• Dull husbands with intelligent wives = 100

• Dull husbands with dull wives = 300

## Solution:

Step 1: Define the attributes

• A : intelligent husband

• α : dull husband

• B : intelligent wife

• β : dull wife

Step 2: Based on given data, note the frequencies

• (AB) = 50

• (Aβ) = 200

• (αB) = 100

• (αβ) = 300

Step 3: Find the Yule's Coefficient of Association

Q = [(AB)(α​β) - (A​β)(αB)] / [(AB)(α​β) + (A​β)(αB)]

∴ Q = [(50) x (300) - (200) x (100)] / [(50) x (300) + (200) x (100)]

∴ Q = [15000 - 20000] / [15000 + 20000]

∴ Q = -5000 / 35000

∴ Q = -1/7

∴ Q = -0.1428

## Concept Recap:

• The value of Yule's Coefficient of Association lies between -1 and 1.

• If the value of Yule's Coefficient is 0, the attributes are independent.

• If the value of Yule's Coefficient lies between 0 and 1, the attributes are positively associated.

• If the value of Yule's Coefficient lies between 0 and 0.5, the attributes are weakly positively associated.

• If the value of Yule's Coefficient lies between 0.5 and 1, the attributes are strongly positively associated.

• If the value of Yule's Coefficient lies between -1 and 0, the attributes are negatively associated.

• If the value of Yule's Coefficient lies between 0 and -0.5, the attributes are weakly negatively associated.

• If the value of Yule's Coefficient lies between -0.5 and -1, the attributes are strongly negatively associated.

• If the value of Yule's Coefficient is 1, the attributes are completely associated.

• If the value of Yule's Coefficient is -1, the attributes are completely dissassociated.