Research Methodology - Dr. Krishan K. Pandey

Chi-square Test 247
c h
χ 2
N ⋅ ad − bc −05
. N
(corrected) =
ba + bgbc + dgba + cgbb + dg
In case we use the usual formula for calculating the value of chi-square viz.,
χ 2
2
dOij −Eiji
=∑
,
E
then Yates’ correction can be applied as under:
(corrected) =
χ 2 1 1
1
2
ij
O − E −05
. O2 − E2
−05
.
+
E
E
2
2
2
+ ...
It may again be emphasised that Yates’ correction is made only in case of (2 × 2) table and that
too when cell frequencies are small.
Illustration 9
The following information is obtained concerning an investigation of 50 ordinary shops of small size:
Shops Total
In towns In villages
Run by men 17 18 35
Run by women 3 12 15
Total 20 30 50
Can it be inferred that shops run by women are relatively more in villages than in towns? Use
χ 2 test.
Solution: Take the hypothesis that there is no difference so far as shops run by men and women in
towns and villages. With this hypothesis the expectation of shops run by men in towns would be:
( A) × ( B)
Expectation of ( AB)
=
N
where A = shops run by men
B = shops in towns
(A) = 35; (B) = 20 and N = 50
35 × 20
Thus, expectation of ( AB)
= = 14
50
Hence, table of expected frequencies would be