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.

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. We’ll
answer this question in several steps