Theory of block designs:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1986
|
| Series: | A Halsted Press book
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 298 S. |
| ISBN: | 0470207531 |
Staff View
MARC
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| 245 | 1 | 0 | |a Theory of block designs |c Aloke Dey |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1986 | |
| 300 | |a VIII, 298 S. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1815801070263205888 |
|---|---|
| adam_text |
Contents
Preface Hi
Introduction 1
Chapter 1. Some Mathematical and Statistical Results 4
1.1. Introduction 4
1.2. Groups, Fields and Some Results on Number
Theory 4
1.3. Vector Spaces 13
1.4. Matrices and Determinants 16
1.5. Finite Geometries 25
1.6. Statistical Distributions 28
1.6.1. Univariate Distributions
1.6.2. Multivariate Normal Distribution
1.6.3. Distribution of Quadratic Forms
1.7. Linear Estimation 32
Problems 35
References and Selected Bibliography 39
Chapter 2. General Properties of Block Designs 41
2.1. Introduction 41
2.2. Intra block Analysis of Block Designs 42
2.3. Balancing in Block Designs 52
2.4. Some Results on Block Structure of
Incomplete Block Designs 60
2.5. Recovery of Inter Block Information 62
2.6. Optimality of Block Designs 71
Problems 75
References and Selected Bibliography 77
Chapter 3. Balanced Incomplete Block Designs—Properties
and Analysis 81
3.1. Introduction^/
vi Contents
3.2. Balanced Incomplete Block Designs—General
Considerations 82
3.3. Tactical Configurations and Doubly Balanced
Designs 91
3.4. Analysis of BIB Designs 93
Problems 101
References and Selected Bibliography 102
Chapter 4. Construction and Existence of Balanced
Incomplete Block Designs 104
4.1. Introduction 104
4.2. Finite Geometries for the Construction of
BIB Designs 104
4.3. Method of Symmetrically Repeated
Differences 110
4.3.1. The Fundamental Theorems on Method of
Differences
4.3.2. BIB Designs with k = 3, A = 1
4.3.3. BIB Designs with k = 3, X = 2
4.3.4. BIB Designs with k = 4, 5 and X = 1
4.3.5. Some Symmetric BIB Designs
4.3.6. Some Further Designs Based on Method
of Differences
4.4. Further Methods of Construction of BIB
Designs 139
4.4.1. BIB Designs Through the Methods of
Block section and Intersection
4.4.2. Family (A) BIB Designs
4.4.3. Miscellaneous Methods of Constructing
BIB Designs
4.5. Non existence of BIB Designs 144
Problems 150
References and Selected Bibliography 152
Chapter 5. Partially Balanced Incomplete Block Designs 156
5.1. Introduction 156
5.2. Association Schemes and PBIB Designs
General Considerations 156
5.3. Two class Association Schemes 162
5.4. Group divisible Designs 166
5.5. Triangular Designs 180
5.6. Latin square Type Designs 186
5.7. Two associate Cyclic Designs 190
Contents vii
5.8. PBIB Designs Based on Partial Geometries 195
5.9. Two associate PBIB Designs with Small
Number of Replicates 196
5.9.1. Designs with Two Replicates
5.9.2. Designs with Three Replicates
5.10. Some Higher Class Association Schemes 201
5.10.1. The M dimensional Triangular Scheme
5.10.2. Nested or Hierarchical Group Divisible
Scheme
5.10.3. Factorial Association Scheme (Fp)
5.10.4. Hypercubic Association Scheme
5.10.5. Group divisible Family of Association
Schemes
5.10.6. The NCm Association Scheme
5.10.7. Product Association Schemes
5.10.8. The Generalised Right Angular Scheme
5.10.9. The Generalised Group divisible Family of
Association Schemes
5.11. Strongly Regular Graphs and Association
Schemes 210
5.12. Lattice Designs 213
5.12.1. Square Lattice Designs
5.12.2. Cubic Lattice Designs
5.12.3. Rectangular Lattice Designs
5.12.4. Circular Lattice Designs
5.13. Reduction of Associate Classes in Certain
Association Schemes and PBIB Designs 216
5.14. Linked Block Designs 220
5.15. Non existence of PBIB Designs 222
5.16. Analysis of PBIB Designs 225
Problems 235
References and Selected Bibliography 237
Chapter 6. Additional Topics in Block Designs 243
6.1. Introduction 243
6.2. Cyclic Designs 243
6.2.1. Introduction to Cyclic Designs
6.2.2. Analysis of Cyclic Designs
6.3. C Designs 249
6.4. Block Designs with Nested Nuisance
Factors 255
6.4.1. Introduction
viii Contents
6.4.2. Nested Balanced Incomplete Block
Designs
6.4.3. Block Designs with Nested Rows and
Columns
6.5. Block Designs with Factorial Structure 263
6.5.1. Introduction
6.5.2. Block Designs with Orthogonal Factorial
Structure
6.5.3. Balanced Factorial Designs
6.6. Block Designs for Biological Assays 272
6.6.1. Introduction to Bio Assays
6.6.2. Block Designs for PL Assays
6.6.3. Block Designs for Slope Ratio
Assays
6.7. Robustness of Block Designs 250
6.7.1. Introduction
6.7.2. Robustness Against the Presence of
Outliers
6.7.3. Robustness Against Non availability of
Data
6.7.4. Trend free Block Designs
Problems 290
References and Selected Bibliography 292
Index 297 |
| any_adam_object | 1 |
| author | Dey, Aloke |
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| ctrlnum | (OCoLC)13794979 (DE-599)BVBBV003506910 |
| dewey-full | 519.5 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV003506910 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-15T15:00:44Z |
| institution | BVB |
| isbn | 0470207531 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002223925 |
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| physical | VIII, 298 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Wiley |
| record_format | marc |
| series2 | A Halsted Press book |
| spelling | Dey, Aloke Verfasser (DE-588)171635981 aut Theory of block designs Aloke Dey New York [u.a.] Wiley 1986 VIII, 298 S. txt rdacontent n rdamedia nc rdacarrier A Halsted Press book Plan bloc Plan d'expérience Block designs Experimental design Blockplan (DE-588)4146038-8 gnd rswk-swf Blockplan (DE-588)4146038-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002223925&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dey, Aloke Theory of block designs Plan bloc Plan d'expérience Block designs Experimental design Blockplan (DE-588)4146038-8 gnd |
| subject_GND | (DE-588)4146038-8 |
| title | Theory of block designs |
| title_auth | Theory of block designs |
| title_exact_search | Theory of block designs |
| title_full | Theory of block designs Aloke Dey |
| title_fullStr | Theory of block designs Aloke Dey |
| title_full_unstemmed | Theory of block designs Aloke Dey |
| title_short | Theory of block designs |
| title_sort | theory of block designs |
| topic | Plan bloc Plan d'expérience Block designs Experimental design Blockplan (DE-588)4146038-8 gnd |
| topic_facet | Plan bloc Plan d'expérience Block designs Experimental design Blockplan |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002223925&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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