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

Copyright © 2012 Pearson Education, Inc. All rights reserved.

Chapter 12

The Analysis of Variance for Designed Experiments


Section 12.1

Introduction


Section 12.2

The Logic Behind an Analysis of Variance

Copyright © 2012 Pearson Education, Inc. All rights reserved.11- 4

Figure 12.1 Plots of data for two samples


Figure 12.2 Plots of data for two cases


Section 12.3

One-Factor Completely Randomized Designs


Figure 12.3 MINITAB Random assignments of workers to training programs


Figure 12.4 Layout for a completely randomized design




Figure 12.5 SAS regression printout for the completely randomized design in Example 12.4


Figure 12.6 Rejection region for Example 12.4; numerator df = 2, denominator df =18, = .05


Figure 12.7 Partitioning of SS(Total) for a completely randomized design


Figure 12.8 MINITAB ANOVA printout for the completely randomized design, Example 12.5






Section 12.4

Randomized Block Designs


Figure 12.9 General form of a randomized block design (treatment is denoted by Tp)


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Figure 12.10 SAS regression printout for randomized block design complete model, Example 12.7


Figure 12.11 SAS regression printout for randomized block design reduced model for testing treatments


Figure 12.12 SAS regression printout for randomized block design reduced model for testing blocks


Figure 12.13 Partitioning of the total sum of squares for the randomized block design


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Figure 12.14 SPSS ANOVA printout for randomized block design





Section 12.5

Two-Factor Factorial Experiments


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Figure 12.15 Hypothetical plot of the means for the six machine-material combinations


Figure 12.16 Testing guidelines for a two-factor factorial experiment



Figure 12.17a SAS regression printout for complete factorial model


Figure 12.17b SAS regression printout for reduced (main effects) factorial model


Figure 12.18 Partitioning of the total sum of squares for a complete two-factor factorial experiment



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Figure 12.19a SAS ANOVA printout for complete factorial design


Figure 12.19b MINITAB plot of profit means illustrating interaction




Figure 12.20 SAS regression printout for complete factorial model with quantitative main effects


Figure 12.21 SAS regression printout for reduced (second-order) factorial model


Figure 12.22 SAS printout of confidence intervals for reduced (second-order) factorial model


Section 12.6

More Complex Factorial Designs (Optional)




Figure 12.23 SAS ANOVA printout for factorial 2 2 3




Figure 12.24 SPSS ANOVA printout for Example 12.19


Section 12.7

Follow-Up Analysis: Tukey’s Multiple Comparisons of Means



Figure 12.25a SAS printout of Tukey’s multiple comparisons of means, Example 12.20


Figure 12.25b MINITAB printout of Tukey’s multiple comparisons of means, Example 12.20


Figure 12.25c SPSS printout of Tukey’s multiple comparisons of means, Example 12.20



Figure 12.26 SAS ANOVA printout for Example 12.21



Section 12.8

Other Multiple Comparisons Methods (Optional)




Figure 12.27 SAS printout of Scheffe’s multiple comparisons of GPA means, Example 12.22

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Figure 12.28 SAS printout of Bonferroni’s multiple comparisons of GPA means, Example 12.23


Section 12.9

Checking ANOVA Assumptions




Figure 12.29 MINITAB histogram for all the GPAs in the completely randomized design


Figure 12.30 MINITAB normal probability plot and normality test for all the GPAs in the completely randomized design


Figure 12.31 MINITAB dot plots for the GPAs in the completely randomized design, by treatment group


Figure 12.32 MINITAB printout of tests for homogeneity of GPA variances for the completely randomized design

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