2. Dr. Michael R. Hyman, NMSU Analysis of Variance (ANOVA) (Click icon for audio)

3. 2

4. 3 Analysis of Variance Sum of Squares

5. 4 Analysis of Variance Sum of Squares Between

6. 5 = individual scores, i.e., the i th observation or test unit in the j th group = grand mean n j = number of all observations or test units in a group

7. 6 Analysis of Variance Sum of Squares Within

8. 7 p i = individual scores, i.e., the i th observation or test unit in the j th group p i = grand mean n = number of all observations or test units in a group c = number of j th groups (or columns)

9. 8 Analysis of Variance Sum of Squares Total

10. 9 Analysis of Variance Sum of Squares p i = individual scores, i.e., the i th observation or test unit in the j th group p i = grand mean n = number of all observations or test units in a group c = number of j th groups (or columns)

11. 10 Analysis of Variance Mean Squares Between

12. 11 Analysis of Variance Mean Square Within

13. 12 Analysis of Variance F-Ratio

14. 13 Analysis of Variance F-Ratio

15. 14 ANOVA Summary Table Source of Variation Between groups Sum of squares –SS between Degrees of freedom –c-1 where c=number of groups Mean squared-MS between –SS between / c-1

16. 15 ANOVA Summary Table Source of Variation Within groups Sum of squares –SS within Degrees of freedom –cn-c where c=number of groups, and n = number of observations in a group Mean squared – MS within –SS within / cn-c

17. 16 ANOVA Summary Table Source of Variation Total Sum of Squares –SStotal Degrees of Freedom –cn-1 where c = number of groups, and n = number of observations in a group

18. 17 Examples

19. 18 Example #1

20. 19

21. 20 Example #2

22. 21 Sales in Units (thousands) Regular Price $.99 130 118 87 84 X 1 =104.75 X=119.58 Reduced Price $.89 145 143 120 131 X 2 =134.75 Cents-Off Coupon Regular Price 153 129 96 99 X 1 =119.25 Test Market A, B, or C Test Market D, E, or F Test Market G, H, or I Test Market J, K, or L Mean Grand Mean Test Market Pricing Experiment Example #3