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Variations on Split Plot and Split Block Experiment Designs

ISBN: 978-0-470-08149-5
288 pages
January 2007
Variations on Split Plot and Split Block Experiment Designs (047008149X) cover image
A complete and up-to-date discussion of optimal split plot and split block designs

Variations 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.
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Preface.

Chapter 1. The standard split plot experiment design.

1.1. Introduction.

1.2. Statistical design.

1.3. Examples of split-plot-designed experiments.

1.4. Analysis of variance.

1.5. F-tests.

1.6. Standard errors for means and differences between means.

1.7. Numerical examples.

1.8. Multiple comparisons of means.

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

1.10. Nature of experimental variation.

1.11. Repeated measures experiments.

1.12. Precision of contrasts.

1.13. Problems.

1.14. References.

Appendix 1.1. Example 1.1 code.

Appendix 1.2. Example 1.2 code.

Chapter 2. Standard split block experiment design.

2.1. Introduction.

2.2. Examples.

2.3. Analysis of variance.

2.4. F-tests.

2.5. Standard errors for contrasts of effects.

2.6. Numerical examples.

2.7. Multiple comparisons.

2.8. One replicate of a split block design.

2.9. Precision.

2.10. Comments.

2.11. Problems.

2.12. References.

Appendix 2.1. Example 2.1 code.

Appendix 2.2. Example 2.2 code.

Appendix 2.3. Problems 2.1 and 2.2 data.

Chapter 3. Variations of the split plot experiment design.

3.1. Introduction.

3.2. Split split plot experiment design.

3.3. Split split split plot experiment design.

3.4. Whole plots not in a factorial arrangement.

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

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

3.7. Whole plots in a systematic arrangement.

3.8. Split plots in a systematic arrangement.

3.9. Characters or responses as split plot treatments.

3.10. Observational or experimental error?

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

3.12. Inappropriate model?

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

3.14. Comments.

3.15. Problems.

3.16. References.

Appendix 3.1. Table 3.1 code and data.

Chapter 4. Variations of the split block experiment design.

4.1. Introduction.

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

4.3. Both sets of treatments in split block arrangements.

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

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

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

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

4.8. Split block experiment design with a control.

4.9. Comments.

4.10. Problems.

4.11. References.

Appendix 4.1. Example 4.1 code.

Chapter 5. Combinations of SPEDs and SBEDs.

5.1. Introduction.

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.

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.

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.

5.5. A complexly designed experiment.

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

5.7. Comments.

5.8. Problems.

5.9. References.

Appendix 5.1. Example 5.1 code.

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

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.

6.1. Introduction.

6.2. Description of the experiment.

6.3. Preliminary analyses for the experiment.

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

6.5. Some comments.

6.6. Problems.

6.7. References.

Appendix 6.1. Figure 6.1 to Figure 6.6.

Chapter 7. Augmented split plot experiment design.

7.1. Introduction.

7.2. Augmented genotypes as the whole plots.

7.3. Augmented genotypes as the split plots.

7.4. Augmented split split plot experiment design.

7.5. Discussion.

7.6. Problems.

7.7. References.

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

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

Appendix 7.3. SAS code for ASSPED, Example 7.3.

Chapter 8. Augmented split block experiment design.

8.1. Introduction.

8.2. Augmented split block experiment designs.

8.3. Augmented split blocks for intercropping experiments.

8.4. Numerical example 8.1.

8.5. Comments.

8.6. Problems.

8.7. References.

Appendix 8.1. Codes for numerical Example 8.1.

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

9.1. Introduction.

9.2. Missing observations in a split plot experiment design.

9.3. Missing observations in a split block experiment design.

9.4. Comments.

9.5 Problems.

9.6. References.

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

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

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

10.1. Introduction.

10.2. Combining split plot designed experiments over sites.

10.3. Combining split block designed experiments over sites.

10.4. Discussion.

10.5. Problems.

10.6. References.

Appendix 10.1. Example 10.1.

Appendix 10.2. Example 10.2.

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

11.1. Introduction.

11.2. Covariance analysis for a standard split plot design.

11.3. Covariance analysis for a split block experiment design.

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

11.5. Covariance analysis for variations of designs.

11.6. Discussion.

11.7. Problems.

11.8. References.

Appendix 11.1. SAS code for Example 11.1.

Appendix 11.2. SAS code for Example 11.2.

Appendix 11.3. SAS code for Example 11.3.

Index.

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WALTER T. FEDERER, PHD, is Liberty Hyde Bailey Professor of Biological Statistics, Emeritus, at Cornell University. He has held numerous posts as editor, secretary, and president of various journals and societies, and he is also a Fellow or member of more than a dozen local, regional, national, and international associations. Dr. Federer received the Honor Alumnus Achievement Award and Honored Alumnus Award from Colorado State University and the Distinguished Service in Agriculture Award from Kansas State University.

FREEDOM KING, PHD, is Teaching Support Specialist in the Department of Biological Statistics and Computational Biology at Cornell University. His areas of interest include generalized linear mixed models, experimental designs, categoricaldata analysis, and statistical computing with an emphasis on work sales through SAS® programming techniques.

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"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)

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