association of attributes
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This document discusses association and attributes in statistics. It provides three methods for determining the association between two attributes/variables: the frequency method, proportion method, and Yule's coefficient of association. The frequency method compares observed and expected values, the proportion method compares ratios, and Yule's coefficient ranges from -1 to 1 to measure the intensity of association. Formulas are provided for the proportion method and Yule's coefficient to calculate the nature and strength of association between two attributes.
association of attributes
- 1. Association of Attribute Presented by – Abhishek Goyal Archana Kajal Shrivastav Ritu Mittal Simran Gupta
- 2. Association Attribute In statistics, association tells you whether two variables are related. An attribute refers to the quality of a characteristic. Association of Attribute
- 3. • There are certain representations that are made in the theory of attributes. The population in the theory of attributes is divided into two classes, namely the negative class and the positive class. The positive class is represented as A, B, C, etc. The negative class is represented as α, β, etc.
- 4. FREQUENCY METHOD Under this method the actual number of observations are required with the expected ones. Expected value= Row total Column total grand total Positively associated if expected value is less than observed value. Negatively associated if expected value is more than observed value.
- 6. Proportion Method Symbolically, two attributes may be termed as: i. Independent if (𝑨𝑩) (𝑩) = (𝑨𝜷) (𝜷) ii Positively associated if (𝑨𝑩) (𝑩) > (𝑨𝜷) (𝜷) iii. Negatively associated if (𝑨𝑩) (𝑩) < (𝑨𝜷) 𝜷
- 7. • Use proportion method to determine the nature of association between A and B: B β Total A 30 50 80 α 20 100 120 Total 50 150 200
- 8. Yule’s coefficient of association To measure the intensity of association between two attributes A and B, Andrew Yule has given the formula of coefficient of association denoted by the symbol Q, as follows: Q= 𝑨𝑩 𝜶𝜷 −(𝑨𝜷)(𝜶𝑩) 𝑨𝑩 𝜶𝜷 +(𝑨𝜷)(𝜶𝑩)
- 9. For two attributes A and B we have (AB)=8, (A) =18, (αβ) =5 and N =35 calculated the coefficient of association ?
- 10. COEFFICIENT OF COLLIGATION Yule has computed another coefficient called the coefficient of colligation (Aβ) × (αB) 1- (AB) × ( α β) ϒ = (A β) × (αB) 1 + (AB) × ( αβ) From this coefficient we can obtain Yule’s coefficient of association ,i.e.,Q as follows:
- 11. • From the given data compute coefficient of colligation and coefficient of association AB = 30, αβ = 5, Aβ = 10, αB= 5
Editor's Notes
- #3: The theory of attributes deals with qualitative types of characteristics that are calculated by using quantitative measurements.
- #4: There are certain representations that are made in the theory of attributes. The population in the theory of attributes is divided into two classes, namely the negative class and the positive class. The positive class signifies that the attribute is present in that particular item under study, and this class in the theory of attributes is represented as A, B, C, etc. The negative class signifies that the attribute is not present in that particular item under study, and this class in the theory of attributes is represented as α, β, etc
- #8: Under this method the ratios or proportions of the concerned variables are compared. If there exists no relationship between two attributes A and B, there would be the same proportion od A’s amongst B’s and the proportion of B’s amongst A’s.
- #10: The Yule’s coefficient of association ‘Q’ varies between ±1, and is interpreted like Pearson’s coefficient of correlation. If Q is zero, there is no association between the attributes, if the value of Q is +1, there is a perfect positive association and if Q is -1, the attributes have perfect negative association.