# Variations on Split Plot and Split Block Experiment Designs

# Variations on Split Plot and Split Block Experiment Designs

ISBN: 978-0-470-10858-1

Jul 2006

352 pages

## Description

A complete and up-to-date discussion of optimal split plot and split block designsVariations on Split Plot and Split Block Experiment Designs provides a comprehensive treatment of the design and analysis of two types of trials that are extremely popular in practice and play an integral part in the screening of applied experimental designs--split plot and split block experiments. Illustrated with numerous examples, this book presents a theoretical background and provides two and three error terms, a thorough review of the recent work in the area of split plot and split blocked experiments, and a number of significant results.

Written by renowned specialists in the field, this book features:

* Discussions of non-standard designs in addition to coverage of split block and split plot designs

* Two chapters on combining split plot and split block designs and missing observations, which are unique to this book and to the field of study

* SAS? commands spread throughout the book, which allow readers to bypass tedious computation and reveal startling observations

* Detailed formulae and thorough remarks at the end of each chapter

* Extensive data sets, which are posted on the book's FTP site

The design and analysis approach advocated in Variations on Split Plot and Split Block Experiment Designs is essential in creating tailor-made experiments for applied statisticians from industry, medicine, agriculture, chemistry, and other fields of study.

Preface xiii

**Chapter 1. The standard split plot experiment design 1**

1.1. Introduction 1

1.2. Statistical design 3

1.3. Examples of split-plot-designed experiments 6

1.4. Analysis of variance 9

1.5. F-tests 12

1.6. Standard errors for means and differences between means 14

1.7. Numerical examples 16

1.8. Multiple comparisons of means 23

1.9. One replicate of a split plot experiment design and missing observations 26

1.10. Nature of experimental variation 28

1.11. Repeated measures experiments 29

1.12. Precision of contrasts 29

1.13. Problems 31

1.14. References 32

Appendix 1.1. Example 1.1 code 34

Appendix 1.2. Example 1.2 code 36

**Chapter 2. Standard split block experiment design 39**

2.1. Introduction 39

2.2. Examples 41

2.3. Analysis of variance 43

2.4. F-tests 44

2.5. Standard errors for contrasts of effects 45

2.6. Numerical examples 46

2.7. Multiple comparisons 52

2.8. One replicate of a split block design 53

2.9. Precision 53

2.10. Comments 54

2.11. Problems 55

2.12. References 55

Appendix 2.1. Example 2.1 code 56

Appendix 2.2. Example 2.2 code 56

Appendix 2.3. Problems 2.1 and 2.2 data 60

**Chapter 3. Variations of the split plot experiment design 61**

3.1. Introduction 61

3.2. Split split plot experiment design 62

3.3. Split split split plot experiment design 67

3.4. Whole plots not in a factorial arrangement 73

3.5. Split plot treatments in an incomplete block experiment design within each whole plot 74

3.6. Split plot treatments in a row-column arrangement within each whole plot treatment and in different

whole plot treatments 75

3.7. Whole plots in a systematic arrangement 76

3.8. Split plots in a systematic arrangement 77

3.9. Characters or responses as split plot treatments 77

3.10. Observational or experimental error? 79

3.11. Time as a discrete factor rather than as a continuous factor 80

3.12. Inappropriate model? 86

3.13. Complete confounding of some effects and split plot experiment designs 90

3.14. Comments 91

3.15. Problems 91

3.16. References 93

Appendix 3.1. Table 3.1 code and data 94

**Chapter 4. Variations of the split block experiment design 97**

4.1. Introduction 97

4.2. One set of treatments in a randomized complete block and the other in a Latin square experiment design 98

4.3. Both sets of treatments in split block arrangements 100

4.4. Split block split block or strip strip block experiment design 100

4.5. One set of treatments in an incomplete block design and the second set in a randomized complete block design 106

4.6. An experiment design split blocked across the entire experiment 107

4.7. Confounding in a factorial treatment design and in a split block experiment design 108

4.8. Split block experiment design with a control 111

4.9. Comments 114

4.10. Problems 114

4.11. References 115

Appendix 4.1. Example 4.1 code 115

**Chapter 5. Combinations of SPEDs and SBEDs 120**

5.1. Introduction 120

5.2. Factors A and B in a split block experiment design and factor C in a split plot arrangement to factors A and B 120

5.3. Factor A treatments are the whole plot treatments and factors B and C treatments are in a split block arrangement within each whole plot 125

5.4. Factors A and B in a standard split plot experiment design and factor C in a split block arrangement over both

factors A and B 127

5.5. A complexly designed experiment 130

5.6. Some rules to follow for finding an analysis for complexly designed experiments 135

5.7. Comments 138

5.8. Problems 139

5.9. References 139

Appendix 5.1. Example 5.1 code 139

Appendix 5.2. Example 5.2 data set, code, and output 144

**Chapter 6. World records for the largest analysis of variance table (259 lines) and for the most error terms (62) in one analysis of variance 147**

6.1. Introduction 147

6.2. Description of the experiment 148

6.3. Preliminary analyses for the experiment 152

6.4. A combined analysis of variance partitioning of the degrees of freedom 157

6.5. Some comments 163

6.6. Problems 163

6.7. References 163

Appendix 6.1. Figure 6.1 to Figure 6.6 164

**Chapter 7. Augmented split plot experiment design 169**

7.1. Introduction 169

7.2. Augmented genotypes as the whole plots 170

7.3. Augmented genotypes as the split plots 174

7.4. Augmented split split plot experiment design 176

7.5. Discussion 180

7.6. Problems 180

7.7. References 181

Appendix 7.1. SAS code for ASPED, genotypes as whole plots, Example 7.1 182

Appendix 7.2. SAS code for ASPEDT, genotypes as split plots, Example 7.2 185

Appendix 7.3. SAS code for ASSPED, Example 7.3 186

**Chapter 8. Augmented split block experiment design 188**

8.1. Introduction 188

8.2. Augmented split block experiment designs 188

8.3. Augmented split blocks for intercropping experiments 193

8.4. Numerical example 8.1 194

8.5. Comments 197

8.6. Problems 197

8.7. References 198

Appendix 8.1. Codes for numerical Example 8.1 198

**Chapter 9. Missing observations in split plot and split block experiment designs 202**

9.1. Introduction 202

9.2. Missing observations in a split plot experiment design 203

9.3. Missing observations in a split block experiment design 204

9.4. Comments 204

9.5 Problems 204

9.6. References 206

Appendix 9.1. SAS code for numerical example in Section 9.2 206

Appendix 9.2. SAS code for numerical example in Section 9.3 209

**Chapter 10. Combining split plot or split block designed experiments over sites 213**

10.1. Introduction 213

10.2. Combining split plot designed experiments over sites 213

10.3. Combining split block designed experiments over sites 217

10.4. Discussion 219

10.5. Problems 219

10.6. References 219

Appendix 10.1. Example 10.1 219

Appendix 10.2. Example 10.2 229

**Chapter 11. Covariance analyses for split plot and split block experiment designs 239**

11.1. Introduction 239

11.2. Covariance analysis for a standard split plot design 240

11.3. Covariance analysis for a split block experiment design 250

11.4. Covariance analysis for a split split plot experiment design 255

11.5. Covariance analysis for variations of designs 259

11.6. Discussion 260

11.7. Problems 260

11.8. References 262

Appendix 11.1. SAS code for Example 11.1 263

Appendix 11.2. SAS code for Example 11.2 264

Appendix 11.3. SAS code for Example 11.3 265

Index

*""Variations on Split Plot and Split Block Experiment Designs*reminds me of the classics of design literature, because it contains a plethora of examples of different situations. This structure lets the reader either find exactly what is needed, or something close to it, to build a suitable design. The examples are geared toward the agricultural statistician... As an industrial statistician, I am gratified to see the publication of this book."" (

*Technometrics*, May 2010)