Independence and Association of Attributes

Learning Objective:

• What is Independence of Attributes?

• What is Association of Attributes?

• What are methods to study Independence and Association of Attributes?

Concepts

• Two attributes are said to be independent if there does not exist any kind of relation between them.

• Two attributes are said to be associated if they are not independent i.e. they are related in some way or another.

• Association of Attributes can be Positive or Negative.

• When two attributes are present or absent together in the data then the attributes are positively associated.

• When the presence of one attribute is associated with the absence of the other attribute then the attributes are negatively associated.

Video: Independence and Association of Attributes.

Formulas to Study Independence and Association of Attributes

• Proportion Method

1. Attributes are independent when (AB)/(B) = (Aβ)/(β)

2. Attributes are positively associated when (AB)/(B) > (Aβ)/(β)

3. Attributes are negatively associated when (AB)/(B) < (Aβ)/(β)

4. If A and B are independent then (A and β), (α and B) and (α and β) are also independent.

• Comparison Method

1. Attributes are independent when (AB) = (A) x (B) / N

2. Attributes are positively associated when (AB) > (A) x (B) / N

3. Attributes are negatively associated when (AB) < (A) x (B) / N

• Yule's Coefficient of Association

1. Q🇦​​​​​🇧​​​​​ = [(AB) (αβ) - (Aβ) (αB)] / [(AB) (αβ) + (Aβ) (αB)]

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

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

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

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

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

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

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

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

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

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