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# Chi-Square test of Homogeneity by Pops P. Macalino (TSU-MAEd)

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### Chi-Square test of Homogeneity by Pops P. Macalino (TSU-MAEd)

1. 1. CHI-SQUARE TEST OF HOMOGENEITY Pops P. Macalino Discussant
2. 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. 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. 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. 5. Type of Residence Opinion on Favor Charter Change Oppose Total Rural 80 20 100 City 112 88 200 Total 192 108 300
6. 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. 7. Degrees of Freedom = (c – 1) (r – 1) = (2 – 1) (2 – 1) = 1 Level of Significance (α) = 0.05
8. 8. Type of Residence Opinion on Favor Charter Change Oppose Total Rural 80 20 100 City 112 88 200 Total 192 108 300
9. 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. 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. 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. 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. 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. 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. 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)

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