Question

Differentiate between Chi-square tests for association and homogeneity of proportions. Also mention the assumptions of these tests.

23 Mar 2023
Answer :
Word Count : 899

Chi-square tests are a family of statistical tests used to determine the association between categorical variables. Two common types of chi-square tests are the Chi-square test for association and the Chi-square test for homogeneity of proportions.

The Chi-square test for association is used to determine if there is a relationship between two categorical variables. The test determines if the distribution of the two variables is independent or not. In other words, it determines if the variables are associated with each other or if they are unrelated.

On the other hand, the Chi-square test for homogeneity of proportions is used to determine if two or more populations have the same proportion of a categorical outcome. This test compares the proportions of different groups and determines if they are equal or not.

Assumptions of the Chi-square test for association:

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A study was conducted on 185 patients aged more than 45 years which are followed until the time of death or up to 10 years, whichever comes first. The patients have different covariates: age, gender (male/female), systolic blood pressure, smoking (yes/no), total serum cholesterol and diabetes (yes/no). The objective of this study is to determine which covariate influences the survival time. An analysis is conducted to investigate differences in all-cause mortality between men and women participating in the study. Suppose we obtain the following results after applying the Cox regression hazard model analyses:

Risk Factor Parameter Estimate SE
Age 0.150 0.010
Gender 0.450 0.150
Systolic Blood Pressure 0.015 0.008
Smoking 0.650 0.170
Total Serum Cholesterol 0.002 0.004
Diabetes -0.350 0.250

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S.
No.		 Serum Cholesterol
(mg/dl)		 Weight (kg) Number of Patients having CHD Total Number of Patients
1 420 60 10 20
2 450 68 15 30
3 400 54 4 15
4 510 74 2 10
5 480 62 1 5

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1 300 150
2 410 270
3 380 210
4 530 310
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13 410 260
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