Chapter 15 2 k Factorial Experiments and Fractions

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

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

Section 15. 2 The 2 k Factorial: Calculation of Effects and Analysis of Variance

Section 15. 2 The 2 k Factorial: Calculation of Effects and Analysis of Variance Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 15. 1 A 22 Factorial Experiment Copyright © 2010 Pearson Addison-Wesley. All rights

Table 15. 1 A 22 Factorial Experiment Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 3

Figure 15. 1 Response suggesting apparent interaction Copyright © 2010 Pearson Addison-Wesley. All rights

Figure 15. 1 Response suggesting apparent interaction Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 4

Table 15. 2 22 Factorial with No Interaction Copyright © 2010 Pearson Addison-Wesley. All

Table 15. 2 22 Factorial with No Interaction Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 5

Table 15. 3 22 Factorial with Interaction Copyright © 2010 Pearson Addison-Wesley. All rights

Table 15. 3 22 Factorial with Interaction Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 6

Figure 15. 2 Interaction plot for data of Table 15. 2 Copyright © 2010

Figure 15. 2 Interaction plot for data of Table 15. 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 7

Figure 15. 3 Interaction plot for data of Table 15. 3 Copyright © 2010

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

Table 15. 4 Signs for Contrasts in a 22 Factorial Experiments Copyright © 2010

Table 15. 4 Signs for Contrasts in a 22 Factorial Experiments Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 9

Table 15. 5 Signs for Contrasts in a 23 Factorial Experiment Copyright © 2010

Table 15. 5 Signs for Contrasts in a 23 Factorial Experiment Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 10

Figure 15. 4 Geometric view of 23 Copyright © 2010 Pearson Addison-Wesley. All rights

Figure 15. 4 Geometric view of 23 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 11

Section 15. 3 Nonreplicated 2 k Factorial Experiment Copyright © 2010 Pearson Addison-Wesley. All

Section 15. 3 Nonreplicated 2 k Factorial Experiment Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 15. 6 Data for Case Study 15. 1 Copyright © 2010 Pearson Addison-Wesley.

Table 15. 6 Data for Case Study 15. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 13

Figure 15. 5 Normal quantile-quantile plot of effects for Case Study 15. 1 Copyright

Figure 15. 5 Normal quantile-quantile plot of effects for Case Study 15. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 14

Table 15. 7 Illustration of Two. Factor Interaction Copyright © 2010 Pearson Addison-Wesley. All

Table 15. 7 Illustration of Two. Factor Interaction Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 15

Figure 15. 6 Interaction plot for Case Study 15. 1 Copyright © 2010 Pearson

Figure 15. 6 Interaction plot for Case Study 15. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 16

Figure 15. 7 SAS printout for data of Case Study 15. 1 Copyright ©

Figure 15. 7 SAS printout for data of Case Study 15. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 17

Figure 15. 8 ANOVA table for Exercise 15. 3 Copyright © 2010 Pearson Addison-Wesley.

Figure 15. 8 ANOVA table for Exercise 15. 3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 18

Section 15. 4 Factorial Experiments in a Regression Setting Copyright © 2010 Pearson Addison-Wesley.

Section 15. 4 Factorial Experiments in a Regression Setting Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 15. 8 Data for Example 15. 2 Copyright © 2010 Pearson Addison-Wesley. All

Table 15. 8 Data for Example 15. 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 20

Figure 15. 9 SAS printout for data of Case Study 15. 2 Copyright ©

Figure 15. 9 SAS printout for data of Case Study 15. 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. continued on next slide 15 - 21

Figure 15. 9 SAS printout for data of Case Study 15. 2 (cont’d) Copyright

Figure 15. 9 SAS printout for data of Case Study 15. 2 (cont’d) Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 22

Section 15. 5 The Orthogonal Design Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 15. 5 The Orthogonal Design Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 15. 10 a Geometric presentation of contrast for the 23 factorial design Copyright

Figure 15. 10 a Geometric presentation of contrast for the 23 factorial design Copyright © 2010 Pearson Addison-Wesley. All rights reserved. continued on next slide 15 - 24

Figure 15. 10 b Geometric presentation of contrast for the 23 factorial design (cont’d)

Figure 15. 10 b Geometric presentation of contrast for the 23 factorial design (cont’d) Copyright © 2010 Pearson Addison-Wesley. All rights reserved. continued on next slide 15 - 25

Figure 15. 10 c Geometric presentation of contrast for the 23 factorial design (cont’d)

Figure 15. 10 c Geometric presentation of contrast for the 23 factorial design (cont’d) Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 26

Figure 15. 11 A 22 design with center runs Copyright © 2010 Pearson Addison-Wesley.

Figure 15. 11 A 22 design with center runs Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 27

Figure 15. 12 22 factorial with 5 center runs Copyright © 2010 Pearson Addison-Wesley.

Figure 15. 12 22 factorial with 5 center runs Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 28

Figure 15. 13 22 factorial with runs at (0, 0) Copyright © 2010 Pearson

Figure 15. 13 22 factorial with runs at (0, 0) Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 29

Figure 15. 14 Graph Exercise 15. 17 Copyright © 2010 Pearson Addison-Wesley. All rights

Figure 15. 14 Graph Exercise 15. 17 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 30