Research Methodology - Dr. Krishan K. Pandey

146 Research Methodology
some attribute, say C with which attributes A and B are associated (but in reality there is no association
between A and B). Such association may also be the result of the fact that the attributes A and B
might not have been properly defined or might not have been correctly recorded. Researcher must
remain alert and must not conclude association between A and B when in fact there is no such
association in reality.
In order to judge the significance of association between two attributes, we make use of Chisquare
test * by finding the value of Chi-square ( χ2 ) and using Chi-square distribution the value of
χ2 can be worked out as under:
χ 2
2
dOij −Eiji
=∑
i = 1, 2, 3 …
E
where j = 1, 2, 3 …
O ij = observed frequencies
E ij = expected frequencies.
Association between two attributes in case of manifold classification and the resulting contingency
table can be studied as explained below:
We can have manifold classification of the two attributes in which case each of the two attributes
are first observed and then each one is classified into two or more subclasses, resulting into what is
called as contingency table. The following is an example of 4 × 4 contingency table with two attributes
A and B, each one of which has been further classified into four sub-categories.
Table 7.2: 4 × 4 Contingency Table
Attribute A
ij
A 1 A 2 A 3 A 4 Total
B 1 (A 1 B 1 ) (A 2 B 1 ) (A 3 B 1 ) (A 4 B 1 ) (B 1 )
Attribute B B 2 (A 1 B 2 ) (A 2 B 2 ) (A 3 B 2 ) (A 4 B 2 ) (B 2 )
B 3 (A 1 B 3 ) (A 2 B 3 ) (A 3 B 3 ) (A 4 B 3 ) (B 3 )
B 4 (A 1 B 4 ) (A 2 B 4 ) (A 3 B 4 ) (A 4 B 4 ) (B 4 )
Total (A 1 ) (A 2 ) (A 3 ) (A 4 ) N
Association can be studied in a contingency table through Yule’s coefficient of association as
stated above, but for this purpose we have to reduce the contingency table into 2 × 2 table by
combining some classes. For instance, if we combine (A 1 ) + (A 2 ) to form (A) and (A 3 ) + (A 4 ) to form
(a) and similarly if we combine (B 1 ) + (B 2 ) to form (B) and (B 3 ) + (B 4 ) to form (b) in the above
contingency table, then we can write the table in the form of a 2 × 2 table as shown in Table 4.3
* See Chapter “Chi-square test” for all details.