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An attribute can be noticed by its presence or absence. It should be known that the methods of statistical techniques that are used in the study of the variables can also be used at a much wider extent in the theory of the attribute and vice versa.
There are certain notations used in the theory of attribute.
- A population is divided into two classes, namely the negative and the positive class according to the presence or absence of an attribute.
- The positive class, which indicates the presence of the attribute, is generally denoted by capital roman letters like A, B, C, etc. The negative class, which indicates the absence of the attribute, is generally denoted by Greek letters like α, β, etc.
- The combination of the two attributes are denoted by grouping the letters together. In other words, AB is the combination of the two attributes A and B.
- If the population is divided into two subclasses with respect to each of the attributes, then that classification is termed a dichotomous classification.
The number of observations assigned to the attribute is termed as the class frequencies which are denoted by bracketing the attribute symbols. For example, (A) stands for the frequency of the attribute A. A class represented by ‘n’ attribute is called a class of nth order and the corresponding frequency of that attribute is the frequency of the nth order. For example, (A) is a class frequency of first order.
These class symbols of the attribute also work as 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).
The two attributes A and B are said to be independent only if there exists no relationship of any kind between those two attributes. If the two attributes are independent, then one can expect that the same proportion of A attribute amongst B attribute is the same as that amongst the β attribute, and the proportion of B attribute amongst A attribute is the same as that amongst the α attribute.
The two attribute A and B are said to be associated if the two attributes are not independent but are related in some way or another. The two attributes are said to be positively associated if (AB) > (A) (B)/ N, and are said to be negatively associated if (AB) < (A) (B) /N.
The two attributes A and B are said to be completely associated if the attribute A cannot occur without the attribute B, though the attribute B may occur without the attribute A, and vice versa.
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 the attribute (A) if they have been observed from the same population.
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