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10.1 part2

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This document discusses testing for homogeneity among populations using chi-square tests. It defines homogeneity as populations having the same structure or composition. A test of homogeneity determines if different populations have the same proportions for various categories. It requires using a contingency table and chi-square distribution. An example tests if the same proportion of males and females prefer different pet types using survey data from college students.

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10.1 CHI-SQUARE: TESTS OF INDEPENDENCE AND HOMOGENEITY Part 2: Tests of Homogeneity
Tests of Homogeneity Homogeneous: of the same structure or composed of similar parts When we perform a test of homogeneity, we use a contingency table and the chi-square distribution to determine whether several populations share the same proportions of distinct categories. A test of homogeneity tests the claim that different populations share the same proportions of specified characteristics.
Tests of Independence VS Tests of Homogeneity
How to Test for Homogeneity of Populations Note: when we reject the null hypothesis, we do not know which proportions differ among the populations, we only know that the populations differ in some of the proportions sharing a characteristic.
Example: Test for Homogeneity Tim is doing a research project involving pet preferences among students at his college. He took random samples of 300 female and 250 male students. Each sample member responded to the survey question If you could own only one pet, what kind would you choose? The possible responses were: dog, cat, other pet, no pet. The results of the study follow. Pet Preference Does the same proportion of males as females prefer each type of pet? Use a 1% level of significance. Well answer this question in several steps

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10.1 part2

  • 1. 10.1 CHI-SQUARE: TESTS OF INDEPENDENCE AND HOMOGENEITY Part 2: Tests of Homogeneity
  • 2. Tests of Homogeneity Homogeneous: of the same structure or composed of similar parts When we perform a test of homogeneity, we use a contingency table and the chi-square distribution to determine whether several populations share the same proportions of distinct categories. A test of homogeneity tests the claim that different populations share the same proportions of specified characteristics.
  • 3. Tests of Independence VS Tests of Homogeneity
  • 4. How to Test for Homogeneity of Populations Note: when we reject the null hypothesis, we do not know which proportions differ among the populations, we only know that the populations differ in some of the proportions sharing a characteristic.
  • 5. Example: Test for Homogeneity Tim is doing a research project involving pet preferences among students at his college. He took random samples of 300 female and 250 male students. Each sample member responded to the survey question If you could own only one pet, what kind would you choose? The possible responses were: dog, cat, other pet, no pet. The results of the study follow. Pet Preference Does the same proportion of males as females prefer each type of pet? Use a 1% level of significance. Well answer this question in several steps