Attribute
An attribute refers to the quality of a characteristic. The theory of attributes analyzes qualitative characteristics using quantitative measurements. Therefore, the attribute needs slightly different kinds of statistical treatments, which the variables do not get. Attributes refer to the characteristics of the item under study, like the habit of smoking, or drinking. So ‘smoking’ and ‘drinking’ both refer to the example of an attribute.
Researchers widely use these techniques in the theory of attributes, relying on statistical knowledge.
In the theory of attributes, the researcher puts more emphasis on quality (rather than on quantity). Since statistical techniques deal with quantitative measurements, researchers convert qualitative data into quantitative data in the theory of attributes.
The theory makes certain representations. This theory divides the population into two classes: the negative class and the positive class. The positive class indicates that the it is present in the particular item under study, and researchers represent this class as A, B, C, etc. The negative class indicates that it is not present in the particular item under study, and researchers represent this class as α, β, etc.
The assembling of the two attributes, i.e. by combining the letters under consideration (such as AB), denotes the assembling of these two.
This assembling is termed dichotomous classification. The class frequencies refer to the number of observations allocated to it. These class frequencies are symbolically denoted by bracketing the terminologies. (B), for example, stands for the class frequency of the attribute B. The frequencies of the class also have some levels in it. For example, the class represented by the ‘n’ attribute refers to the class with the nth order. For example, (B) refers to the class of 2nd order in this theory.
These symbols also play the role of an operator. For example, A.N=(A) means that the operation of dichotomizing N according to the attribute A gives the class frequency equal to (A).
There is also independence nature in this theory. These two remain independent only if they do not correlate with each other.
In this theory, A and B associate only if they are not independent and relate to each other in some way.
The positive association in the two attributes exists under the following condition:
(AB) > (A) (B)/ N.
The negative association in the two attributes exists under the following condition:
(AB) < (A) (B) /N.
The situation of complete association in the two attributes arises when the occurrence of A is completely dependent upon the occurrence of B. However, B may occur without A, and the same thing holds true if A is the independent one.
Ordinarily, these are said to be associated if the two occur together in a number of cases.
The consistency between the two attributes (A)=20 and (AB)=25 is not present as the (AB) cannot be greater than (A) if they have been observed from the same population.