association and attributes and its techniques

1. ASSOCIATION 0F
ATTRIBUTES
Presented by :-
Ojas Maheshwari
Sonam Jain

2. THEORY AND ASSOCIATION
OF ATTRIBUTES
Attributes are studied under the following two categories
A) Theory of Attributes
B) Association of Attributes

3. ASSOCIATION OF ATTRIBUTES
•According to statistics two attributes A and B are associated only if they appear
together in a greater number of cases than is to be expected if they are independent.
EX: Two attributes A and B are associated:
If (AB) ≠ (A) ×(B)
N
i.e. (AB) ˃ (A) ×(B) ( Positive association)
N
Or (AB) ˂ (A) ×(B) ( Negative association)
N
If (AB) = (A) ×(B) Then the two attributes A and B are independent.
N

4. TYPES OF ASSOCIATION
1) Positive Association
2) Negative Association
3) Independence
4) Complete Association & Disassociation

5. 1) POSITIVE ASSOCIATION
Two attributes are said to be positive when they are present or absent
together.
EX: In a college the introduction of extra coaching leads to good results and
this happens for number of years. Thus we can say extra coaching and
good results have a positive association.
2) NEGATIVE ASSOCIATION
When the two attributes are present alternatively, that is, if one is present
the other is absent and if the other is present the former is absent.

6. 3) INDEPENDENCE
Absence of association means Independence. When two attributes
do not have the tendency to be present together ,they are called
Independence.
4) COMPLETE ASSOCIATION & DISASSOCIATION
For finding out the association of two attributes as complete, two
courses are open to us . Either we may say that for complete
association all A’s must be all B’s and all B’s must be A’s . i.e. they
both should be appear in equal numbers.
Similarly complete Disassociation may take place when no A’s are
B’s and no α’s are β ’s or when either of these statements is true.

7. METHODS OF STUDYING ASSOCIATION
Association refers to the relationship between two attributes.
whether the two attributes are associated or not can be
determined by the following methods:
PROBABILI
TY
METHOD
PROPORTI
ON
METHOD
YULE’S
COEFFICIENT
OF
ASSOCIATION
COEFFICIE
NT OF
COLLIGATI
ON
COEFFICIE
NT OF
CONTIGEN
CY

8. PROBABILITY METHOD
This method is based on the theory of probability for calculating
the expected Frequencies of the attributes.
Ex: Expected frequency of (AB) = (A) ×(B)
N
In this method actually observed frequencies of attributes are
compared with their expected frequencies.
Q1 Find if A & B are independent ,positively associated or
negatively associated from data given as (A)=470, (B)=620,
(AB)=320,N=1000 ?

9. PROPORTION METHOD
If there is no relationship of any kind between two attributes A &
B we expect to find the same proportion of A’s among the B’s , as
amongst no B’s i.e. β ’s , then these two attributes may be termed
as independent.
• If the proportion of A’s amongst the B’s is greater than among
the not B’s ( or β ’s ) the two attributes A& B are positively
associated.
• If the proportion of A’s among B’s is less than the among not
B’s ( or β ’s ) then the two attributes A and B are negatively
associated.

10. YULE’S COEFFICIENT OF ASSOCIATION:
•Its most popular method of association because here we can
determine nature of association as well as degree /extent to which
the attributes are associated.
•The degree of association is measured by the coefficient of
association given by Prof. YULE is as follows:
Q = (AB) × (αβ) – ( Aβ) × (αβ)
(AB) × (αβ) + (Aβ) × (αβ)
Where : Q is coefficient of Association. Generally Q lies between
+1 and -1.

11. Q2.Investigate association between eye color of husbands & eye color of
wives from data given below:
Husband with light eyes & wives with light eyes =309
Husband with light eyes & wives with not light eyes =214
Husband with not light eyes & wives with light eyes =132
Husband with not light eyes & wives with not light eyes =119

12. THANK
YOU