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Chapter 12
The Analysis of Variance for Designed Experiments
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Section 12.1
Introduction
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Section 12.2
The Logic Behind an Analysis of Variance
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Figure 12.1 Plots of data for two samples
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Figure 12.2 Plots of data for two cases
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Section 12.3
One-Factor Completely Randomized Designs
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Figure 12.3 MINITAB Random assignments of workers to training programs
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Figure 12.4 Layout for a completely randomized design
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Figure 12.5 SAS regression printout for the completely randomized design in Example 12.4
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Figure 12.6 Rejection region for Example 12.4; numerator df = 2, denominator df =18, = .05
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Figure 12.7 Partitioning of SS(Total) for a completely randomized design
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Figure 12.8 MINITAB ANOVA printout for the completely randomized design, Example 12.5
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Section 12.4
Randomized Block Designs
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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
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Figure 12.11 SAS regression printout for randomized block design reduced model for testing treatments
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Figure 12.12 SAS regression printout for randomized block design reduced model for testing blocks
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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
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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
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Figure 12.16 Testing guidelines for a two-factor factorial experiment
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Figure 12.17a SAS regression printout for complete factorial model
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Figure 12.17b SAS regression printout for reduced (main effects) factorial model
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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
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Figure 12.19b MINITAB plot of profit means illustrating interaction
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Figure 12.20 SAS regression printout for complete factorial model with quantitative main effects
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Figure 12.21 SAS regression printout for reduced (second-order) factorial model
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Figure 12.22 SAS printout of confidence intervals for reduced (second-order) factorial model
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Section 12.6
More Complex Factorial Designs (Optional)
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Figure 12.23 SAS ANOVA printout for factorial 2 2 3
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Figure 12.24 SPSS ANOVA printout for Example 12.19
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Section 12.7
Follow-Up Analysis: Tukey’s Multiple Comparisons of Means
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Figure 12.25a SAS printout of Tukey’s multiple comparisons of means, Example 12.20
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Figure 12.25b MINITAB printout of Tukey’s multiple comparisons of means, Example 12.20
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Figure 12.25c SPSS printout of Tukey’s multiple comparisons of means, Example 12.20
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Figure 12.26 SAS ANOVA printout for Example 12.21
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Section 12.8
Other Multiple Comparisons Methods (Optional)
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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
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Section 12.9
Checking ANOVA Assumptions
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Figure 12.29 MINITAB histogram for all the GPAs in the completely randomized design
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Figure 12.30 MINITAB normal probability plot and normality test for all the GPAs in the completely randomized design
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Figure 12.31 MINITAB dot plots for the GPAs in the completely randomized design, by treatment group
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Figure 12.32 MINITAB printout of tests for homogeneity of GPA variances for the completely randomized design