1. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Chapter 13 One-Factor Experiments: General

2. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 13.1 Analysis-of- Variance Technique

3. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 3 Table 13.1 Absorption of Moisture in Concrete Aggregates

4. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 13.2 The Strategy of Experimental Design

5. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 13.3 One-Way Analysis of Variance: Completely Randomized Design (One-Way ANOVA)

6. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 6 Table 13.2 k Random Samples

7. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 7 Theorem 13.1

8. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 8 Theorem 13.2

9. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 9 Table 13.3 Analysis of Variance for the One-Way ANOVA

10. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 10 Figure 13.1 SAS output for the analysis-of-variance procedure

11. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 11 Figure 13.2 Box-plots for the absorption of moisture in concrete aggregates

12. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 12 Table 13.4 Serum Alkaline Phosphatase Activity Level

13. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 13 Figure 13.3 MINITAB analysis of data in Table 13.4

14. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 13.4 Tests for the Equality of Several Variances

15. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 13.5 Single-Degree-of Freedom Comparisons

16. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 16 Definition 13.1

17. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 17 Definition 13.2

18. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 18 Table 13.5 Analysis of Variance Using Orthogonal Contrasts

19. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 13.6 Multiple Comparisons

20. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 20 Figure 13.4 A set of orthogonal contrasts

21. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 21 Table 13.6 Yield of Reaction

22. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 22 Figure 13.5 SAS printout for Exercise 13.21

23. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 13.7 Comparing a Set of Treatments in Blocks

24. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 13.8 Randomized Complete Block Designs

25. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 25 Table 13.7 k b Array for the RCB Design

26. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 26 Theorem 13.3

27. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 27 Table 13.8 Analysis of Variance for the Randomized Complete Block Design

28. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 28 Table 13.9 Time, in Seconds, to Assemble Product

29. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 29 Table 13.10 Analysis of Variances for the Data of Table 13.9

30. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 30 Figure 13.6 Population means for (a) additive results and (b) interacting effects

31. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 13.9 Graphical Methods and Model Checking

32. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 32 Figure 13.7 Plot of data around the mean for the aggregate data of Table 13.1

33. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 33 Figure 13.8 Plot of residuals for five aggregates, using data in Table 13.1

34. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 34 Figure 13.9 Residual plot for the four machines for the data of Example 13.6

35. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 35 Figure 13.10 Residual plot for the six operators for the data of Example 13.6

36. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 36 Figure 13.11 Residuals plotted against fitted values for the data of Example 13.6

37. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 13.10 Data Transformations in Analysis of Variance

38. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 13.11 Random Effects Models

39. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 39 Theorem 13.4

40. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 40 Table 13.11 Expected Mean Squares for the One-Factor Experiment

41. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 41 Table 13.12 Data for Example 13.7

42. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 42 Table 13.13 Analysis of Variance for Example 13.7

43. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 43 Table 13.14 Expected Mean Squares for the Randomized Complete Block Design

44. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 13.12 Case Study

45. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 45 Figure 13.12 Interaction plot for data of Case Study 13.1

46. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 46 Figure 13.13 Plot of residuals against method for data of Case Study 13.1

47. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 47 Figure 13.14 Normal probability plot of residuals for data the of Case Study 13.1

48. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 48 Figure 13.15 SAS printout for data of Case Study 13.1 continued on next slide

49. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 49 Figure 13.15 SAS printout for data of Case Study 13.1 (cont’d)

50. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 50 Figure 13.16 SAS printout for Review Exercise 13.49

51. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13 - 51 Figure 13.17 SAS printout for Review Exercise 13.50

52. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Potential Misconceptions and Hazards; Relationship to Material in Other Chapters Section 13.13