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Understanding Chi-Squared Tests: Association vs. Homogeneity

Learn about the different types of χ2 tests - Goodness of fit, Homogeneity of proportions, and Association/Independence. Discover how to test relationships between categorical variables and understand the assumptions required for accurate results.

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Understanding Chi-Squared Tests: Association vs. Homogeneity

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  1. Section 13.2 Chi-Squared Test of Independence/Association

  2. The Three Types of χ2 tests • Recall that there are three types of χ2 tests: • Goodness of fit test • Tests whether a sample distribution matches a hypothesized distribution (Does it fit GOOD?) • Homogeneity of proportions • Tests whether p1 = p2 = p3 = … • Association/Independence • Tests whether two categorical variables are related

  3. What are the assumptions? • SRS from the population of interest • None of the expected counts are zero. • Or you can say that all of the expected counts are at least 1. • No more than 20% of the expected counts are less than 5.

  4. χ2 test of Association • When a two-way table compares several populations, we use a χ2 test for homogeneity of proportions. • On the other hand, sometimes we want to classify observations FROM A SINGLE POPULATION by placing them in categories. Then we use a χ2 test of association (also called the χ2 test of independence).

  5. Example My question: “Is there an association between SES level and smoking habits?”

  6. Hypotheses • The χ2 test of association has hypotheses that are written in words: • H0: There is no relationship between smoking and SES level. • Ha: There is some relationship between smoking and SES level.

  7. In other words… • H0: Smoking and SES level are independent. • Ha: Smoking and SES level are not independent. OR • H0: There is no association between smoking and SES level. • Ha: There is some association between smoking and SES level.

  8. Finishing up • The rest of the test is carried out in the same manner as the χ2 test for homogeneity of proportions. • Just make sure your conclusion sentences match the H0 and Ha hypotheses.

  9. So, the difference between the homogeneity of proportions test and the association test is ARE WE COMPARING SEVERAL POPULATIONS or DID THE DATA ARISE BY CLASSIFYING OBSERVATIONS INTO CATEGORIES. χ2 tests Comparison Chart

  10. Homework Chapter 11 # 48, 49, 50, 51, 52

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