Statistical Methods

7.4. X2- test for independence of attributes in 2 x 2 contingency table

Unit 7 - Chi-square distribution

7.4. - test for independence of attributes in 2 x 2 contingency table

Suppose that an attribute data of size n is classified according to two attributes, say, A and B and the attribute A is further subdivided into two classes A₁ and A₂ and the attribute B into B₁, and B₂. Such attribute data can be presented in the form of a table called 2 x 2 contingency table as shown below:
Table 2: 2x2 contingency table

B\A	A1	A2	Total
B1	a	b	a+b
B2	c	d	c+d
Total	a+c	b+d	N= a+b+c+d

It may be of interest to test the independence of attributes A and B.
H0 : The two attributes A and B are independent.
H1 : The two attributes A and B are dependent.
It is tested by the test. A simple formula for computing of a 2 x 2 contingency table is given by,