Learning Objective:
What are characteristics in Theory of Attributes?
What are the types of Dichotomous Classification in Theory of Attributes?
What are Attribute Classes?
What are Attribute Frequencies?
What are Contingency Table?
Using Contingency Table.
Consistency of Data.
What is Independence of Attributes?
What is Association of Attributes?
What are methods to study Independence and Association of Attributes?
How to construct Contingency Table for 3 Attributes?
What is Coefficient of Colligation?
Concepts
Measurable characteristics can be termed as Quantitative Characteristics.
Quantitative Characteristics are called as Variables.
Non-Measurable characteristics can be termed as Qualitative Characteristics.
Qualitative Characteristics can be called as Attributes.
Attributes types can be Positive or Negative.
Positive Attributes are denoted as "A", "B", "C"....
Negative Attributes are denoted as "α", "β", "γ"....
Attributes themselves represent a Group. Such groups can be termed as "Classes"
Positive Attributes can have Positive Frequencies and Negative Attributes can have Negative Frequencies.
Invalid classes can be "A" and "α"; "B" and "β"; "C" and "γ"
Relationship of Frequency can be studied in the Contingency Table.
Contingency Table can be for 2 OR 3 Attributes.
Contingency Table for 2 Attributes is also termed as 9 Square Table or 2 x 2 Table.
Any class frequencies cannot be greater than total population. Hence each class frequency must be less than or equal to "N"
Any class frequencies cannot be negative. Hence each class frequency must be greater than or equal to 0.
9 square table can be used to check consistency of data for 2 attributes.
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.
Yule computed another coefficient called coefficient of colligation (γ)
Yule's coefficient of colligation is generally restricted to 2 x 2 tables.