Statistical theory of the analysis of experimental designs:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Dekker
1974
|
| Ausgabe: | 1. print. |
| Schriftenreihe: | Statistics
8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 465 S. |
| ISBN: | 0824761162 |
Internformat
MARC
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| 100 | 1 | |a Ogawa, Junjiro |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Statistical theory of the analysis of experimental designs |c J Ogawa |
| 250 | |a 1. print. | ||
| 264 | 1 | |a New York |b Dekker |c 1974 | |
| 300 | |a 465 S. | ||
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| 650 | 4 | |a Plan d'expérience | |
| 650 | 4 | |a Analysis of variance | |
| 650 | 4 | |a Experimental design | |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
PREFACE v
CHAPTER 1: ANALYSIS OF VARIANCE 1
1.1. The Partition of a Sum of Squares Corrected by
the Mean 1
1.2. Normal Theory of Distribution Problems 20
1.3. Testing the Hypothesis on Regression Coefficients 37
1.4. General Linear Hypotheses 43
1.5. Analysis of Variance in an m Way Classification
Design 53
1.6. Analysis of Variance in a Two Way Classification
in Matrix Language 75
References 82
CHAPTER 2: DESIGN OF EXPERIMENTS 83
2.1. General Remarks 83
2.2. Randomization 84
2.3. Randomized Block Design 85
2.4. Latin Square Design, Greco Latin Square Design 106
2.5. Randomization in Latin Square Design 113
2.6. Appendix: Calculation of the Variance of tt_ T t^
with Respect to Its Permutation Distribution
Due to Randomization 131
References 160
CHAPTER 3: FACTORIAL DESIGN 161
3.1. Need for the Factorial Principle 161
3.2. 2n Factorial Designs 163
3.3. 3n Factorial Designs 172
3.4. Fractional Replication of a Factorial Design 177
3.5. Confounding 192
References 201
CHAPTER 4: THEORY OF BLOCK DESIGNS — INTRABLOCK ANALYSIS 202
4.1. Linear Estimation 202
4.2. General Block Designs 208
4.3. Partition of Degrees of Freedom and Sum of Squares 217
4.4. Balanced Incomplete Block Design 223
4.5. Randomization of a Balanced Incomplete Block
Design 236
iii
iv CONTENTS
4.6. The Lattice Design 245
4.7. Partially Balanced Incomplete Block Design 250
4.8. Partially Balanced Incomplete Block Design
with Two Associate Classes 258
4.9. Analysis of Variance of Partially Balanced
Incomplete Block Design 266
4.10.Association Algebra and Relationship Algebra of a
Partially Balanced Incomplete Block Design 278
4.11.Partially Balanced Incomplete Block Design for the
Factorial Combination of Two Factors 292
References 302
CHAPTER 5: THEORY OF BLOCK DESIGNS — INTERBLOCK ANALYSIS 303
5.1. Preliminaries 303
5.2. Interblock Analysis 310
5.3. Application to Special Designs 324
5.4. Analysis of Variance 332
CHAPTER 6: RANDOMIZATION OF PARTIALLY BALANCED INCOMPLETE
BLOCK DESIGNS
6.1. The Null Distribution of the F Statistic for
Testing a Partial Null Hypothesis in a PBIB design
with m Associate Classes under the Neyman Model
before the Randomization m 338
6.2. Calculation of the Exact Moments of 6 and 6 with
Respect to the Permutation Distribution Due to
Randomization 347
6.3. Heuristic Derivation of the Asymptotic Null
Distribution of the F Statistic after
Randomization 359
6.4. Asymptotic Equivalence of Probability
Distributions 366
6.5. Rigorous Derivation of the Asymptotic Null
Distribution of the F Statistic after
Randomization 380
6.6. The Asymptotic Non Null Distribution of the
F Statistic for Testing a Partial Null Hypothesis
in a Randomized PBIB design with m Associate
Classes under the Neyman Model 403
6.7. Appendix 435
Reference 446
BIBLIOGRAPHY 447
INDEX 463
|
| adam_txt |
CONTENTS
PREFACE v
CHAPTER 1: ANALYSIS OF VARIANCE 1
1.1. The Partition of a Sum of Squares Corrected by
the Mean 1
1.2. Normal Theory of Distribution Problems 20
1.3. Testing the Hypothesis on Regression Coefficients 37
1.4. General Linear Hypotheses 43
1.5. Analysis of Variance in an m Way Classification
Design 53
1.6. Analysis of Variance in a Two Way Classification
in Matrix Language 75
References 82
CHAPTER 2: DESIGN OF EXPERIMENTS 83
2.1. General Remarks 83
2.2. Randomization 84
2.3. Randomized Block Design 85
2.4. Latin Square Design, Greco Latin Square Design 106
2.5. Randomization in Latin Square Design 113
2.6. Appendix: Calculation of the Variance of tt_'T t^
with Respect to Its Permutation Distribution
Due to Randomization 131
References 160
CHAPTER 3: FACTORIAL DESIGN 161
3.1. Need for the Factorial Principle 161
3.2. 2n Factorial Designs 163
3.3. 3n Factorial Designs 172
3.4. Fractional Replication of a Factorial Design 177
3.5. Confounding 192
References 201
CHAPTER 4: THEORY OF BLOCK DESIGNS — INTRABLOCK ANALYSIS 202
4.1. Linear Estimation 202
4.2. General Block Designs 208
4.3. Partition of Degrees of Freedom and Sum of Squares 217
4.4. Balanced Incomplete Block Design 223
4.5. Randomization of a Balanced Incomplete Block
Design 236
iii
iv CONTENTS
4.6. The Lattice Design 245
4.7. Partially Balanced Incomplete Block Design 250
4.8. Partially Balanced Incomplete Block Design
with Two Associate Classes 258
4.9. Analysis of Variance of Partially Balanced
Incomplete Block Design 266
4.10.Association Algebra and Relationship Algebra of a
Partially Balanced Incomplete Block Design 278
4.11.Partially Balanced Incomplete Block Design for the
Factorial Combination of Two Factors 292
References 302
CHAPTER 5: THEORY OF BLOCK DESIGNS — INTERBLOCK ANALYSIS 303
5.1. Preliminaries 303
5.2. Interblock Analysis 310
5.3. Application to Special Designs 324
5.4. Analysis of Variance 332
CHAPTER 6: RANDOMIZATION OF PARTIALLY BALANCED INCOMPLETE
BLOCK DESIGNS
6.1. The Null Distribution of the F Statistic for
Testing a Partial Null Hypothesis in a PBIB design
with m Associate Classes under the Neyman Model
before the Randomization m 338
6.2. Calculation of the Exact Moments of 6 and 6 with
Respect to the Permutation Distribution Due to
Randomization 347
6.3. Heuristic Derivation of the Asymptotic Null
Distribution of the F Statistic after
Randomization 359
6.4. Asymptotic Equivalence of Probability
Distributions 366
6.5. Rigorous Derivation of the Asymptotic Null
Distribution of the F Statistic after
Randomization 380
6.6. The Asymptotic Non Null Distribution of the
F Statistic for Testing a Partial Null Hypothesis
in a Randomized PBIB design with m Associate
Classes under the Neyman Model 403
6.7. Appendix 435
Reference 446
BIBLIOGRAPHY 447
INDEX 463 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:18:34Z |
| indexdate | 2024-07-09T20:51:31Z |
| institution | BVB |
| isbn | 0824761162 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015371603 |
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| physical | 465 S. |
| publishDate | 1974 |
| publishDateSearch | 1974 |
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| publisher | Dekker |
| record_format | marc |
| series | Statistics |
| series2 | Statistics |
| spelling | Ogawa, Junjiro Verfasser aut Statistical theory of the analysis of experimental designs J Ogawa 1. print. New York Dekker 1974 465 S. txt rdacontent n rdamedia nc rdacarrier Statistics 8 Analyse de variance Plan d'expérience Analysis of variance Experimental design Statistische Analyse (DE-588)4116599-8 gnd rswk-swf Versuch (DE-588)4188049-3 gnd rswk-swf Statistische Analyse (DE-588)4116599-8 s DE-604 Versuch (DE-588)4188049-3 s Statistics 8 (DE-604)BV000003265 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015371603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ogawa, Junjiro Statistical theory of the analysis of experimental designs Statistics Analyse de variance Plan d'expérience Analysis of variance Experimental design Statistische Analyse (DE-588)4116599-8 gnd Versuch (DE-588)4188049-3 gnd |
| subject_GND | (DE-588)4116599-8 (DE-588)4188049-3 |
| title | Statistical theory of the analysis of experimental designs |
| title_auth | Statistical theory of the analysis of experimental designs |
| title_exact_search | Statistical theory of the analysis of experimental designs |
| title_exact_search_txtP | Statistical theory of the analysis of experimental designs |
| title_full | Statistical theory of the analysis of experimental designs J Ogawa |
| title_fullStr | Statistical theory of the analysis of experimental designs J Ogawa |
| title_full_unstemmed | Statistical theory of the analysis of experimental designs J Ogawa |
| title_short | Statistical theory of the analysis of experimental designs |
| title_sort | statistical theory of the analysis of experimental designs |
| topic | Analyse de variance Plan d'expérience Analysis of variance Experimental design Statistische Analyse (DE-588)4116599-8 gnd Versuch (DE-588)4188049-3 gnd |
| topic_facet | Analyse de variance Plan d'expérience Analysis of variance Experimental design Statistische Analyse Versuch |
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