Chi-Square test of Homogeneity by Pops P. Macalino (TSU-MAEd)
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Transcript of Chi-Square test of Homogeneity by Pops P. Macalino (TSU-MAEd)
CHI-SQUARE TEST OF HOMOGENEITY
Pops P. MacalinoDiscussant
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
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
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.
Type of Residence
Opinion on
Favor
Charter Change
OpposeTotal
Rural 80 20 100
City 112 88 200
Total 192 108 300
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
Degrees of Freedom = (c – 1) (r – 1) = (2 – 1) (2 – 1) = 1
Level of Significance (α) = 0.05
Critical Value: (Refer to Appendix E) 3.841 , reject Ho
3.841 , accept Ho
Type of Residence
Opinion on
Favor
Charter Change
OpposeTotal
Rural 80 20 100
City 112 88 200
Total 192 108 300
Contingency TableO 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
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.
Type of Residence
Opinion on
Favor
Charter Change
OpposeTotal
Rural 80 (64) 20 (36) 100
City 112 (128) 88 (72) 200
Total 192 108 300
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
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.
df : (r-1)(c-1) = (2-1) (3-1) = 2
α = 0.05
cv = 5.991
χ² Hoχ² Ho
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 1.7773.00 83.89 -10.89 118.59 1.4121.00 24.89 -3.89 15.13 0.6135.00 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
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)