Different attributes in themselves are called different classes and the number of observations assigned to them are called frequencies which are denoted by bracketing the class symbols. Thus (A) stands for the frequency of A and (AB) for the number of objects possessing the attribute AB.
a class represented by n attributes is called a class of nth order and the corresponding g=frequency as the frequency of the nth order. Thus (A) is a class frequency of order1; (AB), (AC), (βγ) etc., are class frequencies of second order; (ABC), (A βγ), (αβC) etc. are frequencies of third order and so on. N, the total number of members of the population, without any specification of attributes, is reckoned as a frequency of zero-order.
Thus in a dichotomous classification with respect to n attributes, the number of class frequencies of order ‘r’ is (nCr)*2r, since r attributes out of n can be selected in(nCr) ways and each of the r attributes contributes two symbols, one representing the positive part (eg., A) and the other the negative part (e.g., α). Thus the total number of class frequencies of all orders, for n attributes is:
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