Test of homogeneity
This is concerned along with the proposition that several populations are homogenous along with respect to some characteristic of interest for example; one may be interested in knowing if raw material available from various retailers is homogenous. A random sample is drawn from each of the population and the number in each of sample falling into every category is determined. The sample data is shown in a contingency table
The analytical procedure is the similar as that discussed for the test of independence
Illustration
A random sample of 400 persons was selected from each of three age groups and every person was asked to specify which types of TV programs are preferred. The results are displayed in the given table
Kind of program
|
Age group
|
A
|
B
|
C
|
Total
|
|
Under 30
|
120
|
30
|
50
|
200
|
|
30 - 44
|
10
|
75
|
15
|
100
|
|
45 and above
|
10
|
30
|
60
|
100
|
|
Total
|
140
|
135
|
125
|
400
|
Test the hypothesis that populations are homogenous along with respect to the types of television program they prefer, at 5 percent level of significance.
Solution
Assume that take hypothesis that the populations are homogenous with respect to different forms of television programs they prefer
Applying χ2 test
|
O
|
E
|
(O - E) 2
|
(O - E) 2 /E
|
|
120
|
70.00
|
2500.00
|
35.7143
|
|
10
|
35.00
|
625.00
|
17.8571
|
|
10
|
35.00
|
625.00
|
17.8571
|
|
30
|
67.50
|
1406.25
|
20.8333
|
|
75
|
33.75
|
1701.56
|
50.4166
|
|
30
|
33.75
|
14.06
|
0.4166
|
|
50
|
62.50
|
156.25
|
2.500
|
|
15
|
31.25
|
264.06
|
8.4499
|
|
60
|
31.25
|
826.56
|
26.449
|
|
|
|
|
Σ(O - E) 2 /E = 180.4948
|
χ2 = Σ(O - E)2/E
The table value of χ2 for 4d.f. at 5 percent level of significance is 9.488
The calculated value of χ2 is greater than the table value. We reject/refuse the hypothesis and conclude to the populations are not homogenous with respect to the type of TV programs preferred, conversely the different age groups vary in choice of TV programs.