1. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Chapter 15 2 k Factorial Experiments and Fractions

2. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.2 The 2 k Factorial: Calculation of Effects and Analysis of Variance

3. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 3 Table 15.1 A 2 2 Factorial Experiment

4. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 4 Figure 15.1 Response suggesting apparent interaction

5. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 5 Table 15.2 2 2 Factorial with No Interaction

6. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 6 Table 15.3 2 2 Factorial with Interaction

7. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 7 Figure 15.2 Interaction plot for data of Table 15.2

8. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 8 Figure 15.3 Interaction plot for data of Table15.3

9. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 9 Table 15.4 Signs for Contrasts in a 2 2 Factorial Experiments

10. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 10 Table 15.5 Signs for Contrasts in a 2 3 Factorial Experiment

11. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 11 Figure 15.4 Geometric view of 2 3

12. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.3 Nonreplicated 2 k Factorial Experiment

13. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 13 Table 15.6 Data for Case Study 15.1

14. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 14 Figure 15.5 Normal quantile-quantile plot of effects for Case Study 15.1

15. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 15 Table 15.7 Illustration of Two- Factor Interaction

16. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 16 Figure 15.6 Interaction plot for Case Study 15.1

17. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 17 Figure 15.7 SAS printout for data of Case Study 15.1

18. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 18 Figure 15.8 ANOVA table for Exercise 15.3

19. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.4 Factorial Experiments in a Regression Setting

20. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 20 Table 15.8 Data for Example 15.2

21. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 21 Figure 15.9 SAS printout for data of Case Study 15.2 continued on next slide

22. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 22 Figure 15.9 SAS printout for data of Case Study 15.2 (cont’d)

23. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.5 The Orthogonal Design

24. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 24 Figure 15.10a Geometric presentation of contrast for the 23 factorial design continued on next slide

25. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 25 Figure 15.10b Geometric presentation of contrast for the 23 factorial design (cont’d) continued on next slide

26. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 26 Figure 15.10c Geometric presentation of contrast for the 23 factorial design (cont’d)

27. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 27 Figure 15.11 A 2 2 design with center runs

28. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 28 Figure 15.12 2 2 factorial with 5 center runs

29. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 29 Figure 15.13 2 2 factorial with runs at (0,0)

30. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 30 Figure 15.14 Graph Exercise 15.17