**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**

**Attributes are independent when (AB)/(B) = (Aβ)/(β)****Attributes are positively associated when (AB)/(B) > (Aβ)/(β)****Attributes are negatively associated when (AB)/(B) < (Aβ)/(β)****If A and B are independent then (A and β), (α and B) and (α and β) are also independent.**

**Comparison Method**

**Attributes are independent when (AB) = (A) x (B) / N****Attributes are positively associated when (AB) > (A) x (B) / N****Attributes are negatively associated when (AB) < (A) x (B) / N**

**Yule's Coefficient of Association**

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