An attribute refers to the quality of a characteristic. The theory of attributes deals with qualitative types of characteristics that are calculated by 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.
The researcher should note that the techniques involve statistical knowledge and are used at a wider extent in the theory of attributes.
In the theory of attributes, the researcher puts more emphasis on quality (rather than on quantity). Since the statistical techniques deal with quantitative measurements, qualitative data is converted into quantitative data in the theory of attributes.
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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.
The assembling of the two attributes, i.e. by combining the letters under consideration (such as AB), denotes the assembling of the two attributes.
This assembling of the two attributes is termed dichotomous classification. The number of the observations that have been allocated in the attributes is known as the class frequencies. These class frequencies are symbolically denoted by bracketing the attribute terminologies. (B), for example, stands for the class frequency of the attribute B. The frequencies of the class also have some levels in the attribute. For example, the class that is represented by the ‘n’ attribute refers to the class that has the nth order. For example, (B) refers to the class of 2nd order in the theory of attributes.
These attribute 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 the theory of attributes. The two attributes are said to be independent only if the two attributes are absolutely uncorrelated to each other.
In the theory of attributes, the attributes A and B are said to be associated with each other only if the two attributes are not independent, but are related to each other in some way or another.
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 attribute A is completely dependent upon the occurrence of attribute B. However, attribute B may occur without attribute A, and the same thing holds true if attribute A is the independent one.
Ordinarily, the two attributes 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 attribute (AB) cannot be greater than attribute (A) if they have been observed from the same population.