1. Copyright © 2012 Pearson Education, Inc. All rights reserved. Chapter 12 The Analysis of Variance for Designed Experiments

2. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 12.1 Introduction

3. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 12.2 The Logic Behind an Analysis of Variance

4. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 4 Figure 12.1 Plots of data for two samples

5. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 5 Figure 12.2 Plots of data for two cases

6. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 12.3 One-Factor Completely Randomized Designs

7. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 7 Figure 12.3 MINITAB Random assignments of workers to training programs

8. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 8 Figure 12.4 Layout for a completely randomized design

9. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 9

10. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 10

11. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 11 Figure 12.5 SAS regression printout for the completely randomized design in Example 12.4

12. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 12 Figure 12.6 Rejection region for Example 12.4; numerator df = 2, denominator df =18,  =.05

13. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 13 Figure 12.7 Partitioning of SS(Total) for a completely randomized design

14. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 14 Figure 12.8 MINITAB ANOVA printout for the completely randomized design, Example 12.5

15. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 15

16. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 16

17. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 17

18. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 18

19. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 12.4 Randomized Block Designs

20. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 20 Figure 12.9 General form of a randomized block design (treatment is denoted by T p )

21. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 21 continued on next slide

22. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 22 continued from previous slide

23. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 23

24. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 24 Figure 12.10 SAS regression printout for randomized block design complete model, Example 12.7

25. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 25 Figure 12.11 SAS regression printout for randomized block design reduced model for testing treatments

26. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 26 Figure 12.12 SAS regression printout for randomized block design reduced model for testing blocks

27. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 27 Figure 12.13 Partitioning of the total sum of squares for the randomized block design

28. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 28 continued on next slide

29. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 29 continued from previous slide

30. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 30 Figure 12.14 SPSS ANOVA printout for randomized block design

31. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 31

32. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 32

33. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 33

34. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 12.5 Two-Factor Factorial Experiments

35. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 35 continued on next slide

36. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 36 continued from previous slide

37. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 37 Figure 12.15 Hypothetical plot of the means for the six machine-material combinations

38. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 38 Figure 12.16 Testing guidelines for a two-factor factorial experiment

39. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 39

40. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 40 Figure 12.17a SAS regression printout for complete factorial model

41. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 41 Figure 12.17b SAS regression printout for reduced (main effects) factorial model

42. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 42 Figure 12.18 Partitioning of the total sum of squares for a complete two-factor factorial experiment

43. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 43

44. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 44 continued on next slide

45. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 45 continued from previous slide

46. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 46

47. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 47 Figure 12.19a SAS ANOVA printout for complete factorial design

48. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 48 Figure 12.19b MINITAB plot of profit means illustrating interaction

49. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 49

50. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 50

51. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 51 Figure 12.20 SAS regression printout for complete factorial model with quantitative main effects

52. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 52 Figure 12.21 SAS regression printout for reduced (second-order) factorial model

53. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 53 Figure 12.22 SAS printout of confidence intervals for reduced (second-order) factorial model

54. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 12.6 More Complex Factorial Designs (Optional)

55. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 55

56. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 56

57. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 57 Figure 12.23 SAS ANOVA printout for factorial

58. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 58

59. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 59

60. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 60 Figure 12.24 SPSS ANOVA printout for Example 12.19

61. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 12.7 Follow-Up Analysis: Tukey’s Multiple Comparisons of Means

62. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 62

63. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 63 Figure 12.25a SAS printout of Tukey’s multiple comparisons of means, Example 12.20

64. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 64 Figure 12.25b MINITAB printout of Tukey’s multiple comparisons of means, Example 12.20

65. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 65 Figure 12.25c SPSS printout of Tukey’s multiple comparisons of means, Example 12.20

66. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 66

67. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 67 Figure 12.26 SAS ANOVA printout for Example 12.21

68. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 68

69. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 12.8 Other Multiple Comparisons Methods (Optional)

70. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 70

71. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 71

72. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 72 Figure 12.27 SAS printout of Scheffe’s multiple comparisons of GPA means, Example 12.22

73. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 73

74. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 74

75. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 75 Figure 12.28 SAS printout of Bonferroni’s multiple comparisons of GPA means, Example 12.23

76. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 12.9 Checking ANOVA Assumptions

77. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 77

78. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 78

79. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 79 Figure 12.29 MINITAB histogram for all the GPAs in the completely randomized design

80. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 80 Figure 12.30 MINITAB normal probability plot and normality test for all the GPAs in the completely randomized design

81. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 81 Figure 12.31 MINITAB dot plots for the GPAs in the completely randomized design, by treatment group

82. Copyright © 2012 Pearson Education, Inc. All rights reserved. 11- 82 Figure 12.32 MINITAB printout of tests for homogeneity of GPA variances for the completely randomized design