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

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3 Analysis of Variance Sum of Squares

4 Analysis of Variance Sum of Squares Between

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

6 Analysis of Variance Sum of Squares Within

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)

8 Analysis of Variance Sum of Squares Total

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)

10 Analysis of Variance Mean Squares Between

11 Analysis of Variance Mean Square Within

12 Analysis of Variance F-Ratio

13 Analysis of Variance F-Ratio

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

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

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

17 Examples

18 Example #1

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20 Example #2

21 Sales in Units (thousands) Regular Price $ X 1 = X= Reduced Price $ X 2 = Cents-Off Coupon Regular Price X 1 = 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