1. CHI-SQUARE TEST OF
HOMOGENEITY
Pops P. Macalino
Discussant

2. The test for HOMOGENEITY checked if the
rows come from the same distribution or
appear to come from different distribution
Test of Independence
- two categorical variables on a single population
Test of Homogeneity
- single categorical variable in two or more
population

3. Test of Independence Test of Homogeneity
Males and Females
Master’s graduates and Non-MA’s
Tarlaqueῆo, Novo Ecijano,
Bulakenyo,
Procter and Gamble, Unilever,
Johnson & Johnson
TSU, and CLSU
Republican and Democrat

4. Example:
Suppose that we were to poll registered
voters in reference to charter change. In the
plebiscite, 100 voters from rural, 200 from
the city were taken by random sampling.
The research question is to determine
whether the proportion of voters from each
subgroup is the same.

5. Type of
Residence
Opinion on
Favor
Charter Change
Oppose
Total
Rural 80 20 100
City 112 88 200
Total 192 108 300

6. Ho = There is no difference on the proportion of those who are in
favor of Charter Change in the two groups
Ha = There is a difference on the proportion of those who are in
favor of Charter Change in the two groups

7. Degrees of Freedom = (c – 1) (r – 1)
= (2 – 1) (2 – 1)
= 1
Level of Significance (α) = 0.05

8. Type of
Residence
Opinion on
Favor
Charter Change
Oppose
Total
Rural 80 20 100
City 112 88 200
Total 192 108 300

9. Contingency Table
O E O-E (O-E) ² (O-E)²/E
80.00 64.00 16.00 256.00 4.00
112.00 128.00 -16.00 256.00 2.00
20.00 36.00 -16.00 256.00 7.11
88.00 72.00 16.00 256.00 3.56
∑ = 16.67

10. Decision:
Since the computed χ² (16.67) is more than the
critical value (3.841), the null hypothesis is
rejected.
Conclusion:
The proportion of those who are in favor for
charter change is different (not the same) from
the two groups.

11. Type of
Residence
Opinion on
Favor
Charter Change
Oppose
Total
Rural 80 (64) 20 (36) 100
City 112 (128) 88 (72) 200
Total 192 108 300

12. Sample Problem:
Suppose you are interested in knowing whether the
distribution of income classes (low, middle, high) are the same
for 200 males and 250 females, at 0.05 level of significance.
LOW
INCOME
MIDDLE
INCOME
HIGH
INCOME
TOTAL
MALE 101 78 21 200
FEMALE 142 73 35 250
TOTAL 243 151 56 450

13. Ho = There is no difference in the proportion of the distribution of income for
males and females.
Ha = There is no difference in the proportion of the distribution of income for
males and females.

14. Decision: Accept Null Hypothesis since the computed χ² (5.09) is less
than the critical value of 5.991
O E O-E (O-E) ² (O-E)²/E
101.00 108.00 -7.00 49.00 0.45
142.00 135.00 7.00 49.00 0.36
78.00 67.11 10.89 118.59 1.77
73.00 83.89 -10.89 118.59 1.41
21.00 24.89 -3.89 15.13 0.61
35.00 31.11 3.89 15.13 0.49
∑ = 5.09
Conclusion: There is no difference on the proportion of the
distribution income levels of males and females

15. VARIABLE - is any characteristics, number, or quantity
that can be measured or counted.
Types of Variables
NUMERIC CATEGORICAL
- have values that describe
a measurable quantity.
- have values that describe a
“quality or characteristic” of a data
unit.
Continuous (measurement)
Discrete (countable) ordinal (ranking)
nominal (measures of identity)