The design and analysis of experiments and surveys:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
München [u.a.]
Oldenbourg
2007
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | IX, 261 S. graph. Darst. |
| ISBN: | 9783486582994 3486582992 |
Staff View
MARC
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| 245 | 1 | 0 | |a The design and analysis of experiments and surveys |c by Dieter Rasch, L. Rob Verdooren and Jim Gowers |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a München [u.a.] |b Oldenbourg |c 2007 | |
| 300 | |a IX, 261 S. |c graph. Darst. | ||
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| 700 | 1 | |a Gowers, Jim I. |e Verfasser |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text |
Contents
Preface 1
1 Introduction 2
2 Planning Experiments and Surveys and the Description of Simple 7
Designs
2.1 Basic Ideas 7
2.2 Introduction to the Principles of Planning Experiments 9
2.3 Multiple Measurements, the Principle of Replication 12
2.4 Using Strata or Blocks to Eliminate the Effects of Noise Factors 13
2.4.1 Basic Principles 13
2.4.2 Principles of Blocking and Stratification 15
2.5 Randomisation 18
2.5.1 Randomisation in Surveys Random Sampling 19
2.5.2 Randomisation in Experimental Designs Random Allocation 23
2.6 Block Designs 24
2.6.1 Basic Concepts 24
2.6.2 Completely Balanced Incomplete Block Designs 27
2.7 Factorial Designs 29
3 Design and Analysis of Completely Randomised Designs 31
3.1 Point Estimation of Parameters 3 3
3.1.1 Point Estimation of the Parameters of a Normal Distribution 37
3.1.2 Point Estimation of the Parameter p of a Binomial Distribution 39
3.1.3 Point Estimation in Surveys 40
3.2 Interval Estimation 45
3.2.1 Confidence Intervals for the Parameters of a Distribution 45
3.2.1.1 Confidence Intervals for the Expectation of the Normal Distribution 46
3.2.1.2 Confidence Intervals for the Expectation of the Normal Distribution in 52
the Presence of a Noise Factor
3.2.1.3 Confidence Intervals for the Mean and Total from a Survey 54
3.2.1.4 Confidence Intervals for the Variance of the Normal Distribution 55
3.2.1.5 Confidence Intervals for Probabilities 57
3.2.2 Confidence Intervals for the Difference between the Means of Two 60
Normal Distributions
3.2.2.1 The Difference between the Means of Normal Distributions Paired 61
Observations
3.2.2.2 The Difference between the Means of Normal Distributions Two 63
Independent Samples
3.3 Selection Procedures 66
3.4 Hypothesis Testing 71
3.4.1 Testing Hypotheses about the Mean of a Normal Distribution 75
3.4.2 Testing Hypotheses Concerning the Difference between the Means of 79
Two Normal Distributions
3.4.2.1 Paired Observations 79
3.4.2.2 Independent Samples 80
3.4.3 Comparison of the Variances of Two Normal Distributions 87
3.4.4 Comparison between two Proportions using Independent Samples 90
3.4.5 Equivalence Tests 97
VII
4 Analysis of Variance 99
4.1 One way Analysis of Variance 99
4.1.1 One way Analysis of Variance Model I 100
4.1.2 One way Analysis of Variance Model II 106
4.2 Two way Analysis of Variance 108
4.2.1 Two way Analysis of Variance Cross classification 108
4.2.1.1 Two way Analysis of Variance Cross classification Model I 110
4.2.1.2 Two way Analysis of Variance Cross classification Model II 114
4.2.1.3 Two way Analysis of Variance Cross classification Mixed Model 118
4.2.1.4 Two way Analysis of Variance Cross classification Block Designs 122
4.2.2 Two way Analysis of Variance Nested Classification 126
4.2.2.1 Two way Analysis of Variance Nested Classification Model I 128
4.2.2.2 Two way Analysis of Variance Nested Classification Model II 131
4.2.2.3 Two way Analysis of Variance Nested Classification Mixed Model, 134
A Fixed and B Random
4.2.2.4 Two way Analysis of Variance Nested Classification Mixed Model, 135
B Fixed and A Random
4.2.3 Notes on the Procedure for Higher Classifications 136
4.3 Multiple Comparisons of Means 137
4.3.1 Pairwise Comparisons between the Means of ^Populations 139
4.3.1.1 The Multiple/ Test 139
4.3.1.2 The Tukey Test 143
4.3.2 Multiple Comparisons with a Standard Population 144
4.3.2.1 The Multiple/ Test 144
4.3.2.2 The Dunnett Test 145
4.3.3 Overview of Minimal Sample Sizes 147
5 Regression Analysis 149
5.1 Scatter plots 150
5.2 Model I and Model II in Regression Analysis 152
5.3 Parameter Estimation by the Method of Least Squares 155
5.4 Simple Linear Regression 160
5.4.1 Confidence Intervals 160
5.4.2 Optimal Designs in Model I 166
5.4.3 Hypothesis Testing 169
5.4.4 Special Problems in Model II 173
5.5 Multiple Linear Regression 176
5.5.1 Parameter Estimation 17 7
5.5.2 Confidence Intervals and Tests 182
5.5.3 Special Problems in Model II 183
5.5.4 Optimal Designs in Model I 186
5.6 Simple Polynomial Regression 186
5.7 Multiple Quadratic Regression 189
5.8 Intrinsically Non linear Regression 197
6 Theoretical Assumptions and their Practical importance the 203
Robustness of Procedures
VIII
Appendix A Symbols 206
Appendix B Fundamentals in Statistics Overview 209
B.I Descriptive Statistics 209
B.I.I Population 209
B. 1.2 Population Mean and Variance 209
B. 1.3 Graphical Description 211
B.1.4 A Rule of Thumb 213
B.2 Frequencies and Probabilities 213
B.2.1 Introduction 213
B.2.2 Combining Frequencies and Probabilities 214
B.2.2.1 Properties of Relative Frequencies 214
B.2.2.2 Probabilities 217
B.2.3 Probability Distributions 218
B.2.3.1 Definitions 218
B.2.3.2 Quantiles 224
B.2.4 Expectation 227
B.2.5 Variance 229
B.2.6 Covariance 231
B.3 Sampling Distributions 233
B.3.1 Sample Mean x 233
B.3.2 Sample Variance / 236
Appendix C Matrices 238
Tables 243
Table Al /" Quantiles of the / Distribution with f Degrees of Freedom (for 243
/= °o, /' Quantiles of the Standard Normal Distribution)
Table A2 /" QuantilesyC/f^ofthe^ Distribution 244
Table A3 95% Quantiles of the /' Distribution 246
Table A4 95% Quantiles of the Studentised Range Distribution 248
Table A5 95% Quantiles for the Two sided Dunnett Test in an Optimal Design 250
Table A6 95% Quantiles for the Two sided Dunnett Test in a Balanced Design 252
References 254
Subject Index 257
IX |
| adam_txt |
Contents
Preface 1
1 Introduction 2
2 Planning Experiments and Surveys and the Description of Simple 7
Designs
2.1 Basic Ideas 7
2.2 Introduction to the Principles of Planning Experiments 9
2.3 Multiple Measurements, the Principle of Replication 12
2.4 Using Strata or Blocks to Eliminate the Effects of Noise Factors 13
2.4.1 Basic Principles 13
2.4.2 Principles of Blocking and Stratification 15
2.5 Randomisation 18
2.5.1 Randomisation in Surveys Random Sampling 19
2.5.2 Randomisation in Experimental Designs Random Allocation 23
2.6 Block Designs 24
2.6.1 Basic Concepts 24
2.6.2 Completely Balanced Incomplete Block Designs 27
2.7 Factorial Designs 29
3 Design and Analysis of Completely Randomised Designs 31
3.1 Point Estimation of Parameters 3 3
3.1.1 Point Estimation of the Parameters of a Normal Distribution 37
3.1.2 Point Estimation of the Parameter p of a Binomial Distribution 39
3.1.3 Point Estimation in Surveys 40
3.2 Interval Estimation 45
3.2.1 Confidence Intervals for the Parameters of a Distribution 45
3.2.1.1 Confidence Intervals for the Expectation of the Normal Distribution 46
3.2.1.2 Confidence Intervals for the Expectation of the Normal Distribution in 52
the Presence of a Noise Factor
3.2.1.3 Confidence Intervals for the Mean and Total from a Survey 54
3.2.1.4 Confidence Intervals for the Variance of the Normal Distribution 55
3.2.1.5 Confidence Intervals for Probabilities 57
3.2.2 Confidence Intervals for the Difference between the Means of Two 60
Normal Distributions
3.2.2.1 The Difference between the Means of Normal Distributions Paired 61
Observations
3.2.2.2 The Difference between the Means of Normal Distributions Two 63
Independent Samples
3.3 Selection Procedures 66
3.4 Hypothesis Testing 71
3.4.1 Testing Hypotheses about the Mean of a Normal Distribution 75
3.4.2 Testing Hypotheses Concerning the Difference between the Means of 79
Two Normal Distributions
3.4.2.1 Paired Observations 79
3.4.2.2 Independent Samples 80
3.4.3 Comparison of the Variances of Two Normal Distributions 87
3.4.4 Comparison between two Proportions using Independent Samples 90
3.4.5 Equivalence Tests 97
VII
4 Analysis of Variance 99
4.1 One way Analysis of Variance 99
4.1.1 One way Analysis of Variance Model I 100
4.1.2 One way Analysis of Variance Model II 106
4.2 Two way Analysis of Variance 108
4.2.1 Two way Analysis of Variance Cross classification 108
4.2.1.1 Two way Analysis of Variance Cross classification Model I 110
4.2.1.2 Two way Analysis of Variance Cross classification Model II 114
4.2.1.3 Two way Analysis of Variance Cross classification Mixed Model 118
4.2.1.4 Two way Analysis of Variance Cross classification Block Designs 122
4.2.2 Two way Analysis of Variance Nested Classification 126
4.2.2.1 Two way Analysis of Variance Nested Classification Model I 128
4.2.2.2 Two way Analysis of Variance Nested Classification Model II 131
4.2.2.3 Two way Analysis of Variance Nested Classification Mixed Model, 134
A Fixed and B Random
4.2.2.4 Two way Analysis of Variance Nested Classification Mixed Model, 135
B Fixed and A Random
4.2.3 Notes on the Procedure for Higher Classifications 136
4.3 Multiple Comparisons of Means 137
4.3.1 Pairwise Comparisons between the Means of ^Populations 139
4.3.1.1 The Multiple/ Test 139
4.3.1.2 The Tukey Test 143
4.3.2 Multiple Comparisons with a Standard Population 144
4.3.2.1 The Multiple/ Test 144
4.3.2.2 The Dunnett Test 145
4.3.3 Overview of Minimal Sample Sizes 147
5 Regression Analysis 149
5.1 Scatter plots 150
5.2 Model I and Model II in Regression Analysis 152
5.3 Parameter Estimation by the Method of Least Squares 155
5.4 Simple Linear Regression 160
5.4.1 Confidence Intervals 160
5.4.2 Optimal Designs in Model I 166
5.4.3 Hypothesis Testing 169
5.4.4 Special Problems in Model II 173
5.5 Multiple Linear Regression 176
5.5.1 Parameter Estimation 17 7
5.5.2 Confidence Intervals and Tests 182
5.5.3 Special Problems in Model II 183
5.5.4 Optimal Designs in Model I 186
5.6 Simple Polynomial Regression 186
5.7 Multiple Quadratic Regression 189
5.8 Intrinsically Non linear Regression 197
6 Theoretical Assumptions and their Practical importance the 203
Robustness of Procedures
VIII
Appendix A Symbols 206
Appendix B Fundamentals in Statistics Overview 209
B.I Descriptive Statistics 209
B.I.I Population 209
B. 1.2 Population Mean and Variance 209
B. 1.3 Graphical Description 211
B.1.4 A Rule of Thumb 213
B.2 Frequencies and Probabilities 213
B.2.1 Introduction 213
B.2.2 Combining Frequencies and Probabilities 214
B.2.2.1 Properties of Relative Frequencies 214
B.2.2.2 Probabilities 217
B.2.3 Probability Distributions 218
B.2.3.1 Definitions 218
B.2.3.2 Quantiles 224
B.2.4 Expectation 227
B.2.5 Variance 229
B.2.6 Covariance 231
B.3 Sampling Distributions 233
B.3.1 Sample Mean x 233
B.3.2 Sample Variance / 236
Appendix C Matrices 238
Tables 243
Table Al /" Quantiles of the / Distribution with f Degrees of Freedom (for 243
/= °o, /' Quantiles of the Standard Normal Distribution)
Table A2 /" QuantilesyC/f^ofthe^ Distribution 244
Table A3 95% Quantiles of the /' Distribution 246
Table A4 95% Quantiles of the Studentised Range Distribution 248
Table A5 95% Quantiles for the Two sided Dunnett Test in an Optimal Design 250
Table A6 95% Quantiles for the Two sided Dunnett Test in a Balanced Design 252
References 254
Subject Index 257
IX |
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| index_date | 2024-07-02T17:27:46Z |
| indexdate | 2024-07-20T09:16:35Z |
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| isbn | 9783486582994 3486582992 |
| language | English |
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| spelling | Rasch, Dieter 1935- Verfasser (DE-588)133266745 aut The design and analysis of experiments and surveys by Dieter Rasch, L. Rob Verdooren and Jim Gowers 2. ed. München [u.a.] Oldenbourg 2007 IX, 261 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Versuchsplanung (DE-588)4078859-3 gnd rswk-swf Versuchsplanung (DE-588)4078859-3 s DE-604 Verdooren, Leon R. 1936- Verfasser (DE-588)17330365X aut Gowers, Jim I. Verfasser aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2946205&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015635265&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | The design and analysis of experiments and surveys |
| title_auth | The design and analysis of experiments and surveys |
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| title_full | The design and analysis of experiments and surveys by Dieter Rasch, L. Rob Verdooren and Jim Gowers |
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| title_full_unstemmed | The design and analysis of experiments and surveys by Dieter Rasch, L. Rob Verdooren and Jim Gowers |
| title_short | The design and analysis of experiments and surveys |
| title_sort | the design and analysis of experiments and surveys |
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