**comment chapter 7 (comparative designs)
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Outline
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Introduction
      Comparative Designs
      Construction vs. Analysis
      Applications
 
Construction
      Bad Designs / Good Designs
      Randomization
      Blocking
      Design Types
 
Analysis
      Block Plots
      ANOVA
      Complete Analysis
 
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Comparative Designs
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Focus:
 
Goal:
 
 
 
Reference: Box, Hunter & Hunter:
      Chapter 4 (pages 93-106)
      Chapter 6 (pages 165-207)
      Chapter 7 (pages 208-244)
      Chapter 8 (pages 245-287)
 
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Applications
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Garden Tomato Fertilizer Comparison
BHH, pages 94-97
 
Boys Shoe Wear
BHH, pages 97-101 (Chapter 4)
 
Farm Egg Diet Comparison
BHH, page 159
 
Auto MPG Gas Additive Comparison
 
Auto Emissions Gas Additive Comparison
BHH, pages 245-250 (Chapter 8)
 
Film Developer Comparison
Barker, page 99, 275
 
Gas/Gasahol Comnparison
Barker, pages 100-101, 273
 
Comparing 3 Copying Machines
 
Comparison of 2 Suppliers
 
Effect of Diet on Blood Coagulation
BHH, pages 165-207 (Chapter 6)
 
Steel Mill Heat Treatments
 
Comparing Penicillin Formulae
BHH, pages 209-232 (Chapter 7)
 
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Ethidium Usage/Non-Usage in DNA Electrophoresis
 
Training Set Comparison in OCR
 
Re-bar Comparison in Earthquake-resistent Columns
 
Algorithmic Comparison in Voice Recognition Systems
 
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Construction vs. Analysis
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**movewrite 1600 2400 Analysis
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Part 1:  Construction
 
 
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Bad Designs / Good Designs
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Experiment #1:
 
Response Variable Y:
Focus (Primary Factor):
Nuisance Factors:
 
Sample Size n:
 
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Experiment #2:
 
Response Variable Y:
Focus (Primary Factor):
Nuisance Factors:
 
Sample Size n:
 
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Experiment #3:
 
Response Variable Y:
Focus (Primary Factor):
Nuisance Factors:
 
Sample Size n:
 
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Experiment #4:
 
Response Variable Y:
Focus (Primary Factor):
Nuisance Factors:
 
Sample Size n:
 
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Experiment #5:
 
Response Variable Y:
Focus (Primary Factor):
Nuisance Factors:
 
Sample Size n:
 
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Experiment #6:
 
Response Variable Y:
Focus (Primary Factor):
Nuisance Factors:
 
Sample Size n:
 
 
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Experiment #7:  Tomato Plant  (BHH, page 94ff)
 
Response Variable Y:
Focus (Primary Factor):
Nuisance Factors:
 
Sample Size n:
 
 
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Experiment #8:  Boys Shoes (BHH, page 97ff)
 
Response Variable Y:
Focus (Primary Factor):
Nuisance Factors:
 
Sample Size n:
 
 
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Experiment #9:  Blood Coagulation, page 165ff)
 
Response Variable Y:
Focus (Primary Factor):
Nuisance Factors:
 
Sample Size n:
 
 
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Experiment #10:  Penicillin Yield (BHH, page 209ff)
 
Response Variable Y:
Focus (Primary Factor):
Nuisance Factors:
 
Sample Size n:
 
 
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Experiment #11:  Auto Emissions (BHH, pages 245ff)
 
Response Variable Y:
Focus (Primary Factor):
Nuisance Factors:
 
Sample Size n:
 
 
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Experiment #2:
 
Response Variable Y:
Focus (Primary Factor):
Nuisance Factors:
 
Sample Size n:
 
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Construction Summary
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Goal:
   Unambiguous, Crisp Conclusions
   about Primary Factor
 
Strategy:
   1) Avoid ...
   2) Increase Sensitivity
 
Tools:
   1)
   2)
 
Types:
   1)
   2)
   3)
 
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Representation of
Comparative Designs
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Part 2:  Analysis
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1. Block Plot Analysis
 
2. Analysis of Variance
 
3. Complete Analysis
 
 
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Examples
 
1. Blood Coag. Time   BHH, Ch. 6 (165ff)    Diet
2. Boys Shoe Wear     BHH, Ch. 4 (97ff)      Material, Boy
3. Penicillin Yield        BHH, Ch. 7 (208ff)    Formula, Batch
4. Lightbulb Defects   Sheesley                   Weld, Plant, Speed, Shift
5. Auto Emissions       BHH, Ch. 8 (245 ff)   Additive, Car, Drive
6. Funnel Time                                               Ball, Funnel, Ramp
 
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Block Plot
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The Block Plot is a graphical technique
for testing factor significance.
 
 
 
Reference: JJF
 
 
 
Vertical Axis:
 
Horizontal Axis:
 
Plot Character:
 
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Analysis of Variance
(ANOVA)
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The Analysis of Variance is a quantitative
technique for testing factor significance.
 
 
Reference: Fisher
 
 
Box, Hunter, & Hunter ANOVA:
   General: pp. 170-173, 187-190, 241-244
   Blood Coagulation Time: pp. 170-182
   Penicillin Yield: pp. 210-215
   Auto Emissions: pp. 248-249
 
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ANOVA
Identities
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ANOVA
Tables, Decision Rules, & Assumptions
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ANOVA
Advantages/Disadvantages
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Complete Analysis
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... a combination of graphical and quantitative
techniques for:
 
   1) testing factor significance
   2) selecting models
   3) estimating model parameters
   4) validating models
 
 
 
Analysis Cycle:
 
 
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Analysis of
Comparative Designs
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1 Primary Factor
0, 1, 2, 3, ... Nuisance Factors
Analysis: Graphical & Quantitative
 
**setx 0800
Data from DEX Plan
 
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Plot Data:
      1) Factor Plots
      2) Run Sequence Plot
      3) Block Plot
 
Define Model:
 
Estimate Parameters:
      1)
      2)
      3)
      4)
 
Plot Estimated Parameters:
 
Generate Predicted Values & Residuals:
      1) Predicted Values:
      2) Residuals:
 
Analyze Residuals:
      1) Computer Residuals S.D.
      2) Factor Plot of Residuals
      3) Run Sequence Plot of Residuals
      4) Normal Probability Plot of Residuals
 
Test Statistical Significance of Factors:
      H  :
      H  :
      H  :
      Decision Rile: If calculated test statistic > 95% point
                              of reference distribution, then conclude:
                                    factor is significant
 
Summarize Conclusions:
 
      Factor    Significant?    Est. Effects    Range of Est. Eff.
        X            yes/no
        X            yes/no
        X            yes/no
 
        S    of additive mode =
 
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Analysis of Comparative Designs (Funnel Experiment)
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-1. DEX
 
0. Data
 
1. Plot Data:
 
2. Define Model:
 
3. Estimate Parameters:
 
4. Plot Estimated Parameters:
 
5. Compute Predicted Values & Residuals:
 
6. Analyze Residuals:
 
7. Test Significance of Factors:
 
8. Summarize Conclusions:
 
 
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Source        df          SS        MS     F-value
--------------------------------------------------
Total(adj.)   19        112.01
Material       1          0.84     0.84      11.21
Boy            9        110.49    12.28     163.81
Residual       9          0.67     0.075
 
 
s    =   0.075   = .274
