1.  2 Test of Independence

2. Hypothesis Tests Categorical Data

3.  2 Test of Independence Shows if a relationship exists between 2 categorical variables – One sample is drawn – Does not show nature of relationship – Does not show causality Similar to testing p 1 = p 2 = … = p c Used widely in marketing Uses contingency (XTAB) table

4.  2 Test of Independence Contingency Table Shows # observations from 1 sample jointly in 2 categorical variables Levels of variable 2 Levels of variable 1

5.  2 Test of Independence Hypotheses & Statistic Hypotheses – H 0 : Variables are independent – H 1 : Variables are related (dependent)

6.  2 Test of Independence Hypotheses & Statistic Hypotheses – H 0 : Variables are independent – H 1 : Variables are related (dependent) Test statistic Observed frequency Expected frequency

7.  2 Test of Independence Hypotheses & Statistic Hypotheses – H 0 : Variables are independent – H 1 : Variables are related (dependent) Test statistic Degrees of freedom: (r - 1)(c - 1) Observed frequency Expected frequency Rows Columns

8.  2 Test of Independence Expected Frequencies Statistical independence means joint probability equals product of marginal probabilities – P(A and B) = P(A)·P(B) Compute marginal probabilities Multiply for joint probability Expected frequency is sample size times joint probability

9. Expected Frequencies Calculation 82·112 160 78·48 160 82·48 160 78·112 160 Expected frequency = (row total*column total)/grand total

10. You’re a marketing research analyst. You ask a random sample of 286 consumers if they purchase Diet Pepsi or Diet Coke. At the.05 level, is there evidence of a relationship?  2 Test of Independence Example

11.  2 Test of Independence Solution H 0 : No Relationship H 1 : Relationship  =.05 df = (2 - 1)(2 - 1) = 1 Critical Value(s): Test Statistic: Decision:Conclusion:  =.05

12. Expected Frequencies Solution f e  5 in all cells 132·170 286 154·170 286 132·116 286 132·154 286

13.  2 Test of Independence Test Statistic Solution

14.  2 Test of Independence Solution H 0 : No Relationship H 1 : Relationship  =.05 df = (2 - 1)(2 - 1) = 1 Critical Value(s): Test Statistic: Decision:Conclusion:  =.05

15.  2 Test of Independence Solution H 0 : No Relationship H 1 : Relationship  =.05 df = (2 - 1)(2 - 1) = 1 Critical Value(s): Test Statistic: Decision:Conclusion: Reject at  =.05  =.05

16.  2 Test of Independence Solution H 0 : No Relationship H 1 : Relationship  =.05 df = (2 - 1)(2 - 1) = 1 Critical Value(s): Test Statistic: Decision:Conclusion: Reject at  =.05 There is evidence of a relationship  =.05

17. OK. There is a statistically significant relationship between purchasing Diet Coke & Diet Pepsi. So what do you think the relationship is? Aren’t they competitors?  2 Test of Independence Thinking Challenge AloneGroupClass

18. You Re-Analyze the Data Low Income High Income

19. True Relationships* Apparent relation Underlying causal relation Control or intervening variable (true cause) Diet Coke Diet Pepsi

20. Moral of the Story* Numbers don’t think - People do! © 1984-1994 T/Maker Co.

21. This Class... What was the most important thing you learned in class today? What do you still have questions about? How can today’s class be improved? Please take a moment to answer the following questions in writing: