Preface
Contents
About the Authors
Abbreviations and Notations
1 Linear Estimation
1.1 GaussβMarkov Model
1.2 Estimability
1.3 Least Squares Estimate
1.4 Best Linear Unbiased Estimates
1.5 Linear Estimation with Correlated Observations
1.6 Comments
1.7 Exercises
2 Linear Hypotheses and their Tests
2.1 Linear Hypotheses
2.2 Likelihood Ratio Test of a Linear Hypothesis
2.3 GaussβMarkov Models and Linear Hypotheses
2.4 Confidence Intervals and Confidence Ellipsoids
2.5 Comments
2.6 Exercises
2.7 R-Codes on Linear Estimation and, Linear Hypotheses and their Tests
3 Block Designs
3.1 General Block Design
3.1.1 Rank of the Block Design Model
3.1.2 Estimability
3.1.3 Least Squares Estimates
3.1.4 Best Estimates of elpf's
3.1.5 Tests of Hypotheses
3.1.6 Anova Tables for a Block Design
3.1.7 Anova Table for RBD
3.1.8 Some Criteria for Classification of Block Designs
3.2 Balanced Incomplete Block Design
3.2.1 Estimability
3.2.2 Least Squares Estimates
3.2.3 Best Estimates
3.2.4 Tests of Hypotheses
3.2.5 Recovery of Inter-Block Information
3.3 Partially Balanced Incomplete Block Design
3.3.1 Estimability, Least Squares Estimates
3.3.2 Blue's and their Variances
3.3.3 Tests of Hypotheses
3.3.4 Efficiency Factor of a Block Design
3.4 Exercises
3.5 R-Codes on Block Designs
4 Row-Column Designs
4.1 General Row-Column Design
4.1.1 Rank of the Row-Column Design Model
4.1.2 Estimability
4.1.3 Least Squares Estimates
4.1.4 Blue's and their Variances
4.1.5 Tests of Hypotheses
4.1.6 Anova Table for Testing HΞ± in a Row-Column Design
4.2 Latin Square Design
4.2.1 Anova Table for LSD
4.3 Youden Square Design
4.3.1 Anova Table for Testing HΞ± in YSD
4.4 Exercises
4.5 R-Codes on Row-Column Designs
5 Factorial Experiments
5.1 2M-Factorial Experiment
5.1.1 Factorial Effects
5.1.2 Properties of Vectors Associated with Factorial Effects
5.1.3 Best Estimates of Factorial Effects
5.1.4 Testing the Significance of Factorial Effects
5.1.5 Total of the Sums of Squares Associated with Testing the Significance of Factorial Effects
5.1.6 Anova Table for Testing the Significance of Factorial Effects
5.1.7 Yates' Algorithm to Obtain the Factorial Effect Totals
5.2 Completely Confounded 2M-Factorial Experiment
5.2.1 Rank of C
5.2.2 The Model
5.2.3 Least Squares Estimates
5.2.4 Best Estimates of Estimable Factorial Effects
5.2.5 Testing the Significance of Unconfounded Factorial Effects
5.2.6 Total of Sums of Squares Associated with Testing the Significance of Unconfounded Factorial Effects
5.2.7 Anova Table for Testing the Significance of Unconfounded Factorial Effects
5.3 Partially Confounded 2M-Factorial Experiment
5.3.1 Rank of C
5.3.2 Best Estimates of Factorial Effects
5.3.3 Testing the Significance of Factorial Effects
5.3.4 Total of Sums of Squares Associated with Testing the Significance of Factorial Effects
5.3.5 Anova Table for Testing the Significance of Factorial Effects
5.3.6 A g-Inverse of C
5.4 3M-Factorial Experiment
5.4.1 Factorial Effects
5.4.2 Linear/Quadratic Components of Factorial Effects
5.4.3 Best Estimates of the Components
5.4.4 Testing the Significance of the Components
5.4.5 Total of Sums of Squares Associated with Testing the Significance of the Components
5.4.6 Anova Table for Testing the Significance of the Components
5.4.7 Divisors
5.4.8 Extended Yates' Algorithm to Obtain the Component Totals
5.5 Completely Confounded 3M-Factorial Experiment
5.5.1 Best Estimates
5.5.2 Testing of Hypotheses
5.5.3 Anova Table for Testing the Significance of Unconfounded Factorial Effects
5.6 Exercises
5.7 R-Codes on Factorial Experiments
6 Analysis of Covariance
6.1 General Setup
6.1.1 Least Squares Estimates
6.1.2 Testing the Relevance of the Ancova Model
6.2 Illustrations
6.2.1 Ancova Table for Testing HΞ± in CRD
6.2.2 Ancova Table for Testing HΞ± and HΞ² in RBD
6.3 Exercises
6.4 R-Codes on Analysis of Covariance
7 Missing Plot Technique
7.1 Substitution for Missing Observations
7.2 Implications of Substitution
7.2.1 Missing Plot Technique in RBD with One Missing Observation
7.2.2 Anova Table for Testing HΞ± and HΞ² in RBD with One Missing Observation
7.2.3 Efficiency Factor of RBD with Single Observation Missing
7.2.4 Missing Plot Technique in LSD with One Observation Missing
7.2.5 Anova Table for Testing HΞ±, HΞ², and HΞ³ in LSD with One Missing Observation
7.3 Exercises
7.4 R-Codes on Missing Plot Technique
8 Split-Plot and Split-Block Designs
8.1 Split-Plot Design
8.1.1 The Model
8.1.2 Rank, Estimability, and Least Squares Estimates
8.1.3 Testing of Hypotheses
8.1.4 Anova Table for a Split-Plot Design
8.2 Split-Block Design
8.2.1 The Model
8.2.2 Rank, Estimability, Least Squares Estimates
8.2.3 Testing of Hypotheses
8.2.4 Anova Table for a Split-Block Design
8.3 Exercises
8.4 R-Codes on Split-Plot and Split-Block Designs
Appendix Bibliography
Index