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.


Answer:

Since the value of Yule's Coefficient lies between 0 and -0.5, there is weak negative association between the intelligence of husband and intelligence of wife.


Video Solution:


How to find the extent or degree of association in theory of attributes with a solved example from Theory of Attributes