Variations on Split Plot and Split Block Experiment Designs

Variations on Split Plot and Split Block Experiment Designs......Page 4
Contents......Page 10
Preface......Page 16
1.1. Introduction......Page 18
1.2. Statistical design......Page 20
1.3. Examples of split-plot-designed experiments......Page 23
1.4. Analysis of variance......Page 26
1.5. F-tests......Page 29
1.6. Standard errors for means and differences between means......Page 31
1.7. Numerical examples......Page 33
1.8. Multiple comparisons of means......Page 40
1.9. One replicate of a split plot experiment design and missing observations......Page 43
1.10. Nature of experimental variation......Page 45
1.12. Precision of contrasts......Page 46
1.13. Problems......Page 48
1.14. References......Page 49
Appendix 1.1. Example 1.1 code......Page 51
Appendix 1.2. Example 1.2 code......Page 53
2.1. Introduction......Page 56
2.2. Examples......Page 58
2.3. Analysis of variance......Page 60
2.4. F-tests......Page 61
2.5. Standard errors for contrasts of effects......Page 62
2.6. Numerical examples......Page 63
2.7. Multiple comparisons......Page 69
2.9. Precision......Page 70
2.10. Comments......Page 71
2.12. References......Page 72
Appendix 2.2. Example 2.2 code......Page 73
Appendix 2.3. Problems 2.1 and 2.2 data......Page 77
3.1. Introduction......Page 78
3.2. Split split plot experiment design......Page 79
3.3. Split split split plot experiment design......Page 84
3.4. Whole plots not in a factorial arrangement......Page 90
3.5. Split plot treatments in an incomplete block experiment design within each whole plot......Page 91
3.6. Split plot treatments in a row-column arrangement within each whole plot treatment and in different whole plot treatments......Page 92
3.7. Whole plots in a systematic arrangement......Page 93
3.9. Characters or responses as split plot treatments......Page 94
3.10. Observational or experimental error?......Page 96
3.11. Time as a discrete factor rather than as a continuous factor......Page 97
3.12. Inappropriate model?......Page 103
3.13. Complete confounding of some effects and split plot experiment designs......Page 107
3.15. Problems......Page 108
3.16. References......Page 110
Appendix 3.1. Table 3.1 code and data......Page 111
4.1. Introduction......Page 114
4.2. One set of treatments in a randomized complete block and the other in a Latin square experiment design......Page 115
4.4. Split block split block or strip strip block experiment design......Page 117
4.5. One set of treatments in an incomplete block design and the second set in a randomized complete block design......Page 123
4.6. An experiment design split blocked across the entire experiment......Page 124
4.7. Confounding in a factorial treatment design and in a split block experiment design......Page 125
4.8. Split block experiment design with a control......Page 128
4.10. Problems......Page 131
Appendix 4.1. Example 4.1 code......Page 132
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......Page 137
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......Page 142
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......Page 144
5.5. A complexly designed experiment......Page 147
5.6. Some rules to follow for finding an analysis for complexly designed experiments......Page 152
5.7. Comments......Page 155
Appendix 5.1. Example 5.1 code......Page 156
Appendix 5.2. Example 5.2 data set, code, and output......Page 161
6.1. Introduction......Page 164
6.2. Description of the experiment......Page 165
6.3. Preliminary analyses for the experiment......Page 169
6.4. A combined analysis of variance partitioning of the degrees of freedom......Page 174
6.7. References......Page 180
Appendix 6.1. Figure 6.1 to Figure 6.6......Page 181
7.1. Introduction......Page 186
7.2. Augmented genotypes as the whole plots......Page 187
7.3. Augmented genotypes as the split plots......Page 191
7.4. Augmented split split plot experiment design......Page 193
7.6. Problems......Page 197
7.7. References......Page 198
Appendix 7.1. SAS code for ASPED, genotypes as whole plots, Example 7.1......Page 199
Appendix 7.2. SAS code for ASPEDT, genotypes as split plots, Example 7.2......Page 202
Appendix 7.3. SAS code for ASSPED, Example 7.3......Page 203
8.2. Augmented split block experiment designs......Page 205
8.3. Augmented split blocks for intercropping experiments......Page 210
8.4. Numerical example 8.1......Page 211
8.6. Problems......Page 214
Appendix 8.1. Codes for numerical Example 8.1......Page 215
9.1. Introduction......Page 219
9.2. Missing observations in a split plot experiment design......Page 220
9.5 Problems......Page 221
Appendix 9.1. SAS code for numerical example in Section 9.2......Page 223
Appendix 9.2. SAS code for numerical example in Section 9.3......Page 226
10.2. Combining split plot designed experiments over sites......Page 230
10.3. Combining split block designed experiments over sites......Page 234
Appendix 10.1. Example 10.1......Page 236
Appendix 10.2. Example 10.2......Page 246
11.1. Introduction......Page 256
11.2. Covariance analysis for a standard split plot design......Page 257
11.3. Covariance analysis for a split block experiment design......Page 267
11.4. Covariance analysis for a split split plot experiment design......Page 272
11.5. Covariance analysis for variations of designs......Page 276
11.7. Problems......Page 277
11.8. References......Page 279
Appendix 11.1. SAS code for Example 11.1......Page 280
Appendix 11.2. SAS code for Example 11.2......Page 281
Appendix 11.3. SAS code for Example 11.3......Page 282
Index......Page 284