Variations on Split Plot and Split Block Experiment Designs

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.

"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)

• Preface xiiiChapter 1. The standard split plot experiment design 11.1. Introduction 11.2. Statistical design 31.3. Examples of split-plot-designed experiments 61.4. Analysis of variance 91.5. F-tests 121.6. Standard errors for means and differences between means 141.7. Numerical examples 161.8. Multiple comparisons of means 231.9. One replicate of a split plot experiment design and missing observations 261.10. Nature of experimental variation 281.11. Repeated measures experiments 291.12. Precision of contrasts 291.13. Problems 311.14. References 32Appendix 1.1. Example 1.1 code 34Appendix 1.2. Example 1.2 code 36Chapter 2. Standard split block experiment design 392.1. Introduction 392.2. Examples 412.3. Analysis of variance 432.4. F-tests 442.5. Standard errors for contrasts of effects 452.6. Numerical examples 462.7. Multiple comparisons 522.8. One replicate of a split block design 532.9. Precision 532.10. Comments 542.11. Problems 552.12. References 55Appendix 2.1. Example 2.1 code 56Appendix 2.2. Example 2.2 code 56Appendix 2.3. Problems 2.1 and 2.2 data 60Chapter 3. Variations of the split plot experiment design 613.1. Introduction 613.2. Split split plot experiment design 623.3. Split split split plot experiment design 673.4. Whole plots not in a factorial arrangement 733.5. Split plot treatments in an incomplete block experiment design within each whole plot 743.6. Split plot treatments in a row-column arrangement within each whole plot treatment and in differentwhole plot treatments 753.7. Whole plots in a systematic arrangement 763.8. Split plots in a systematic arrangement 773.9. Characters or responses as split plot treatments 773.10. Observational or experimental error? 793.11. Time as a discrete factor rather than as a continuous factor 803.12. Inappropriate model? 863.13. Complete confounding of some effects and split plot experiment designs 903.14. Comments 913.15. Problems 913.16. References 93Appendix 3.1. Table 3.1 code and data 94Chapter 4. Variations of the split block experiment design 974.1. Introduction 974.2. One set of treatments in a randomized complete block and the other in a Latin square experiment design 984.3. Both sets of treatments in split block arrangements 1004.4. Split block split block or strip strip block experiment design 1004.5. One set of treatments in an incomplete block design and the second set in a randomized complete block design 1064.6. An experiment design split blocked across the entire experiment 1074.7. Confounding in a factorial treatment design and in a split block experiment design 1084.8. Split block experiment design with a control 1114.9. Comments 1144.10. Problems 1144.11. References 115Appendix 4.1. Example 4.1 code 115Chapter 5. Combinations of SPEDs and SBEDs 1205.1. Introduction 1205.2. Factors A and B in a split block experiment design and factor C in a split plot arrangement to factors A and B 1205.3. Factor A treatments are the whole plot treatments and factors B and C treatments are in a split block arrangement within each whole plot 1255.4. Factors A and B in a standard split plot experiment design and factor C in a split block arrangement over bothfactors A and B 1275.5. A complexly designed experiment 1305.6. Some rules to follow for finding an analysis for complexly designed experiments 1355.7. Comments 1385.8. Problems 1395.9. References 139Appendix 5.1. Example 5.1 code 139Appendix 5.2. Example 5.2 data set, code, and output 144Chapter 6. World records for the largest analysis of variance table (259 lines) and for the most error terms (62) in one analysis of variance 1476.1. Introduction 1476.2. Description of the experiment 1486.3. Preliminary analyses for the experiment 1526.4. A combined analysis of variance partitioning of the degrees of freedom 1576.5. Some comments 1636.6. Problems 1636.7. References 163Appendix 6.1. Figure 6.1 to Figure 6.6 164Chapter 7. Augmented split plot experiment design 1697.1. Introduction 1697.2. Augmented genotypes as the whole plots 1707.3. Augmented genotypes as the split plots 1747.4. Augmented split split plot experiment design 1767.5. Discussion 1807.6. Problems 1807.7. References 181Appendix 7.1. SAS code for ASPED, genotypes as whole plots, Example 7.1 182Appendix 7.2. SAS code for ASPEDT, genotypes as split plots, Example 7.2 185Appendix 7.3. SAS code for ASSPED, Example 7.3 186Chapter 8. Augmented split block experiment design 1888.1. Introduction 1888.2. Augmented split block experiment designs 1888.3. Augmented split blocks for intercropping experiments 1938.4. Numerical example 8.1 1948.5. Comments 1978.6. Problems 1978.7. References 198Appendix 8.1. Codes for numerical Example 8.1 198Chapter 9. Missing observations in split plot and split block experiment designs 2029.1. Introduction 2029.2. Missing observations in a split plot experiment design 2039.3. Missing observations in a split block experiment design 2049.4. Comments 2049.5 Problems 2049.6. References 206Appendix 9.1. SAS code for numerical example in Section 9.2 206Appendix 9.2. SAS code for numerical example in Section 9.3 209Chapter 10. Combining split plot or split block designed experiments over sites 21310.1. Introduction 21310.2. Combining split plot designed experiments over sites 21310.3. Combining split block designed experiments over sites 21710.4. Discussion 21910.5. Problems 21910.6. References 219Appendix 10.1. Example 10.1 219Appendix 10.2. Example 10.2 229Chapter 11. Covariance analyses for split plot and split block experiment designs 23911.1. Introduction 23911.2. Covariance analysis for a standard split plot design 24011.3. Covariance analysis for a split block experiment design 25011.4. Covariance analysis for a split split plot experiment design 25511.5. Covariance analysis for variations of designs 25911.6. Discussion 26011.7. Problems 26011.8. References 262Appendix 11.1. SAS code for Example 11.1 263Appendix 11.2. SAS code for Example 11.2 264Appendix 11.3. SAS code for Example 11.3 265Index