1. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Chapter 14 Factorial Experiments (Two or More Factors)

2. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 14.1 Introduction

3. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 14.2 Interaction in the Two-Factor Experiment

4. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 4 Figure 14.1 Interaction plot for temperature-drying time data

5. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 14.3 Two-Factor Analysis of Variance

6. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 6 Table 14.1 Two-Factor Experiment with n Replications

7. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 7 Theorem 14.1

8. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 8 Table 14.2 Analysis of Variance for the Two-Factor Experiment with n Replications

9. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 9 Table 14.3 Propellant Burning Rates

10. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 10 Table 14.4 Analysis of Variance for the Data of Table 14.3

11. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 11 Table 14.5 Interpretation of Interaction

12. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 12 Figure 14.2 SAS printout of the analysis of the propellant rate data of Table 14.3

13. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 13 Figure 14.3 Plot of cell means for data of Example 14.1. Numbers represent missile systems

14. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 14 Figure 14.4 Residual plot of data of Example 14.1

15. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 15 Table 14.6 Data for Example 14.3

16. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 16 Figure 14.5 SAS printout for Exercise 14.3

17. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 17 Figure 14.6 SAS output, for Example 14.3. (a) Duncan’s test on gas flow rate; (b) Duncan’s test on power

18. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 14.4 Three-Factor Experiments

19. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 19 Table 14.7 ANOVA for the Three- Factor Experiment with n Replications

20. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 20 Table 14.8 Data for Example 14.4

21. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 21 Table 14.9 ANOVA for a Three-Factor Experiment in a Completely Randomized Design

22. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 22 Table 14.10 Two-Way Table of Means for Example 14.4

23. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 23 Table 14.11 ANOVA with Factor A Noninteracting

24. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 24 Table 14.12 ANOVA for a Two-Factor Experiment in a Randomized Block Design

25. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 25 Table 14.13 Data for Example 14.5

26. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 26 Figure 14.7 ANOVA for Example 14.5, batch interaction pooled with error

27. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 27 Figure 14.8 Interaction plots for Example 14.5

28. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 14.5 Factorial Experiments for Random Effects and Mixed Models

29. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 29 Table 14.14 Expected Mean Squares for a Two-Factor Random Effects Experiment

30. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 30 Table 14.15 Expected Mean Squares for a Three-Factor Random Effects Experiment

31. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 31 Table 14.16 Data for Example 14.6

32. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 32 Table 14.17 Analysis of Variance for Example 14.6

33. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 33 Table 14.18 Expected Mean Squares for a Two-Factor Mixed Model Experiments

34. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14 - 34 Table 14.19 Expected Mean Squares for Mixed Model Factorial Experiments in Three Factors

35. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Potential Misconceptions and Hazards; Relationship to Material in Other Chapters Section 14.16