1. Chi-square test or c2 test

2. c2 test for independence
Used with categorical, bivariate data from ONE sample
Used to see if the two categorical variables are associated (dependent) or not associated (independent)

3. Assumptions & formula remain the same!

4. Hypotheses – written in words
H0: two variables are independent
Ha: two variables are dependent
Be sure to write in context!

5. Expected Counts
Assuming H0 is true,

6. Degrees of freedom
Or cover up one row & one column & count the number of cells remaining!

7. A beef distributor wishes to determine whether there is a relationship between geographic region and cut of meat preferred. If there is no relationship, we will say that beef preference is independent of geographic region. Suppose that, in a random sample of 500 customers, 300 are from the North and 200 from the South. Also, 150 prefer cut A, 275 prefer cut B, and 75 prefer cut C.

8. If beef preference is independent of geographic region, how would we expect this table to be filled in?
North
South
Total
Cut A
150
Cut B
275
Cut C 75
300
200
500 90 60
165
110 45 30

9. Now suppose that in the actual sample of 500 consumers the observed numbers were as follows:
  (on your paper)
 Is there sufficient evidence to suggest that geographic regions and beef preference are not independent? (Is there a difference between the expected and observed counts?)

10. c2 test for Independence
H0: geographic region and beef preference are independent
Ha: geographic region and beef preference are dependent
Conditions/Assumptions:
Have a random sample of people
All expected counts are greater than 5.
Calculations:
P-value = df = 2 a = .05
Since p-value < a, I reject H0. There is sufficient evidence to suggest that geographic region and beef preference are dependent.
Expected Counts:
N S A B C

11. c2 test for homogeneity
Used with a single categorical variable from two (or more) independent samples
Used to see if the two populations are the same (homogeneous)

12. Assumptions & formula remain the same!
Expected counts & df are found the same way as test for independence.
Only change is the hypotheses!

13. Hypotheses – written in words
H0: the two (or more) distributions are the same
Ha: the distributions are different
Be sure to write in context!

14. The following data is on drinking behavior for independently chosen random samples of male and female students. Does there appear to be a gender difference with respect to drinking behavior? (Note: low = 1-7 drinks/wk, moderate = 8-24 drinks/wk, high = 25 or more drinks/wk)

15. Run test with calculator
c2 test for Homogeneity
H0: drinking behavior is the same for female & male students Ha: drinking behavior is not the same for female & male students
Conditions/Assumptions:
Have 2 random sample of students
All expected counts are greater than 5.
Calculations:
P-value = .000 df = 3 a = .05
Since p-value < a, I reject H0. There is sufficient evidence to suggest that drinking behavior is not the same for female & male students.
Expected Counts:
M F L M H
Run test with calculator