Design and Analysis of Experiments, 9th Edition

CHAPTER 3Experiments with a Single Factor: The Analysis of Variance

CHAPTER OUTLINE

1. 3.1 AN EXAMPLE
2. 3.2 THE ANALYSIS OF VARIANCE
3. 3.3 ANALYSIS OF THE FIXED EFFECTS MODEL
   1. 3.3.1 Decomposition of the Total Sum of Squares
   2. 3.3.2 Statistical Analysis
   3. 3.3.3 Estimation of the Model Parameters
   4. 3.3.4 Unbalanced Data
4. 3.4 MODEL ADEQUACY CHECKING
   1. 3.4.1 The Normality Assumption
   2. 3.4.2 Plot of Residuals in Time Sequence
   3. 3.4.3 Plot of Residuals Versus Fitted Values
   4. 3.4.4 Plots of Residuals Versus Other Variables
5. 3.5 PRACTICAL INTERPRETATION OF RESULTS
   1. 3.5.1 A Regression Model
   2. 3.5.2 Comparisons Among Treatment Means
   3. 3.5.3 Graphical Comparisons of Means
   4. 3.5.4 Contrasts
   5. 3.5.5 Orthogonal Contrasts
   6. 3.5.6 Scheffé’s Method for Comparing All Contrasts
   7. 3.5.7 Comparing Pairs of Treatment Means
   8. 3.5.8 Comparing Treatment Means with a Control
6. 3.6 SAMPLE COMPUTER OUTPUT
7. 3.7 DETERMINING SAMPLE SIZE
   1. 3.7.1 Operating Characteristic and Power Curves
   2. 3.7.2 Confidence Interval Estimation Method
8. 3.8 OTHER EXAMPLES OF SINGLE-FACTOR EXPERIMENTS
   1. 3.8.1 Chocolate and Cardiovascular Health
   2. 3.8.2 A Real Economy Application of a Designed Experiment
   3. 3.8.3 Discovering Dispersion Effects
9. 3.9 THE RANDOM EFFECTS MODEL
   1. 3.9.1 A Single Random Factor
   2. 3.9.2 Analysis of Variance for the Random Model
   3. 3.9.3 Estimating the Model Parameters
10. 3.10 THE REGRESSION APPROACH TO THE ANALYSIS OF VARIANCE
    1. 3.10.1 Least Squares Estimation of the Model Parameters
    2. 3.10.2 The General Regression Significance Test
11. 3.11 NONPARAMETRIC METHODS ...