Optimal experimental design with R:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
2011
|
| Series: | Statistical theory and methods
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 325 S. |
| ISBN: | 9781439816974 |
Staff View
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Record in the Search Index
| _version_ | 1804143845129060352 |
|---|---|
| adam_text | Contents
List of Figures
xi
List of Tables
xiii
Preface
xvii
Acknowledgments
xix
1
Introduction
1
1.1
Experimentation and empirical research
........... 1
1.2
Designing experiments
...................... 4
1.3
Some basic definitions
...................... 6
1.4
Block designs
.......................... 8
1.5
About the R-programs
..................... 11
1 Determining the Minimal Size of an Experiment for
Given Precision
13
2
Sample Size Determination in Completely Randomised
Designs
17
2.1
Introduction
........................... 17
2.1.1
Sample size to be determined
.............. 17
2.1.2
What to do when the size of an experiment is given in
advance
.......................... 19
2.2
Confidence estimation
..................... 20
2.2.1
Confidence intervals for expectations
......... 20
2.2.1.1
One-sample case,
σ2
known
.......... 20
2.2.1.2
One-sample case,
σ2
unknown
........ 22
2.2.1.3
Confidence intervals for the expectation of the
normal distribution in the presence of a noise
factor
...................... 25
2.2.1.4
One-sample case,
σ2
unknown, paired
observations
.................. 27
VI
2.2.1.5
Two-sample case,
σ2
unknown, independent
samples
—
equal variances
........... 28
2.2.1.6
Two-sample case,
σ2
unknown, independent
samples
—
unequal variances
......... 29
2.2.2
Confidence intervals for probabilities
......... 30
2.2.3
Confidence interval for the variance of the normal
distribution
........................ 32
2.3
Selection procedures
...................... 33
2.4
Testing hypotheses
........................ 35
2.4.1
Testing hypotheses about means of normal distributions
36
2.4.1.1
One-sample problem, univariate
....... 36
2.4.1.2
One-sample problem, bivariate
........ 38
2.4.1.3
Two-sample problem, equal variances
.... 41
2.4.1.4
Two-sample problem, unequal variances
... 43
2.4.1.5
Comparing more than two means, equal
variances
.................... 44
2.4.2
Testing hypotheses about probabilities
......... 47
2.4.2.1
One-sample problem
.............. 47
2.4.2.2
Two-sample problem
............. 48
2.4.3
Comparing two variances
................ 50
2.5
Summary of sample size formulae
............... 51
3
Size of Experiments in Analysis of Variance Models
55
3.1
Introduction
........................... 55
3.2
One-way layout
......................... 59
3.3
Two-way layout
......................... 65
3.3.1
Two-way analysis of variance
—
cross-classification.
. . 66
3.3.1.1
Two-way analysis of variance
—
cross-classification
—
Model I
......... 68
3.3.1.2
Two-way analysis of variance
—
cross-classification
—
mixed model
...... 72
3.3.2
Nested-classification Ay
В
.............. 74
3.3.2.1
Two-way analysis of variance
—
nested
classification
—
Model I
............ 74
3.3.2.2
Two-way analysis of variance
—
nested
classification
—
mixed model, A fixed and
В
random
..................... 76
Vil
3.3.2.3
Two-way analysis of variance
—
nested
classification
—
mixed model,
В
fixed and A
random
..................... 78
3.4
Three-way layout
........................ 79
3.4.1
Three-way analysis of variance
—
cross-classification
Αχ Β χ
С .......................
80
3.4.1.1
Three-way analysis of variance
—
classification
Ax
B x C—
Model I
............ 81
3.4.1.2
Three-way analysis of variance
—
cross classifi¬
cation Ax
B x C
—
Model III
........ 85
3.4.1.3
Three-way analysis of variance
—
cross classifi¬
cation AxB
χ
C—Model IV
........ 86
3.4.2
Three-way analysis of variance
—
nested classification
Ay
В У С.......................
90
3.4.2.1
Three-way analysis of variance
—
nested
classification
—
Model I
............ 91
3.4.2.2
Three-way analysis of variance
—
nested
classification
—
Model III
........... 93
3.4.2.3
Three-way analysis of variance
—
nested
classification
—
Model IV
........... 95
3.4.2.4
Three-way analysis of variance
—
nested
classification
—
Model V
............ 98
3.4.2.5
Three-way analysis of variance
—
nested
classification
—
Model VI
........... 99
3.4.2.6
Three-way analysis of variance
—
nested
classification
—
Model
VII
........... 100
3.4.2.7
Three-way analysis of
varianœ
—
nested
classification—Model
VIII .......... 101
3.4.3
Three-way analysis of variance
—
mixed classification
(A X
В) У С......................
102
3.4.3.1
Three-way analysis of variance
—
mixed classi¬
fication (AxB)
У С—
Model I
....... 104
3.4.3.2
Three-way analysis of variance
—
mixed classi¬
fication (Ax
В) У С—
Model III
..... 106
3.4.3.3
Three-way analysis of
varianœ
—
mixed classi¬
fication (Ax
В) У С—
Model IV
...... 107
3.4.3.4
Three-way analysis of variance
—
mixed classi¬
fication (Ax
В) У С—
Model V
...... 108
3.4.3.5
Three-way analysis of variance
—
mixed classi¬
fication (Ax
В) У С—
Model VI
..... 110
Vlil
3.4.4
Three-way
analysis
of variance
—
mixed classification
(А У В)
X
С
......................
Ш
3.4.4.1
Three-way analysis of variance
—
mixed classi¬
fication (A
У
B) X C—Model I
...... 112
3.4.4.2
Three-way analysis of variance
—
mixed classi¬
fication
(А У В)
X
С—
Model
III
..... 116
3.4.4.3
Three-way
analysis
of variance
—
mixed classi¬
fication
(АУ
B) X C—Model IV
...... 118
3.4.4.4
Three-way analysis of variance
—
mixed classi¬
fication
(А У В)
X
С—
Model
V
...... 119
3.4.4.5
Three-way
analysis
of variance
—
mixed classi¬
fication
(А У В)
X C—
Model
VI
...... 121
3.4.4.6
Three-way analysis of variance
—
mixed classi¬
fication (Ay B) X C—Model
VII
..... 123
3.4.4.7
Three-way analysis of variance
—
mixed classi¬
fication
(АУ
B) X C—Model
VIII..... 124
4
Sample Size Determination in Model II of Regression
Analysis
127
4.1
Introduction
........................... 127
4.2
Confidence intervals
....................... 128
4.2.1
Confidence intervals for the slope
............ 129
4.2.2
A confidence interval for the correlation coefficient
. . 130
4.2.3
Confidence intervals for partial correlation coefficients
131
4.2.4
A confidence interval for E(y x)
=
β0 + βιχ......
131
4.3
Hypothesis testing
........................ 133
4.3.1
Comparing the correlation coefficient with a constant
133
4.3.2
Comparing two correlation coefficients
........ 134
4.3.3
Comparing the slope with a constant
.......... 135
4.3.4
Test of parallelism of two regression lines
....... 135
4.4
Selection procedures
....................... 136
5
Sequential Designs
139
5.1
Introduction
........................... 139
5.2
Wald s sequential likelihood ratio test (SLRT) for
one-parametric exponential families
.............. 142
5.3
Test about means for unknown variances
........... 149
5.3.1
The sequential i-test
.................. 149
їх
5.3.2 Approximation
of the likelihood function for the
construction of an approximate i-test
......... 151
5.3.3
Approximate tests for binary data
........... 154
5.3.4
Approximate tests for the two-sample problem
.... 156
5.4
Triangular designs
....................... 159
5.4.1
Basic principles
...................... 159
5.4.2
Testing hypotheses about means of normal distributions
160
5.4.2.1
One-sample problem
.............. 160
5.4.2.2
Two-sample problem
............. 161
5.4.3
Testing hypotheses about probabilities
......... 163
5.4.3.1
One-sample problem
.............. 163
5.4.3.2
Two-sample problem
............. 165
5.5
A sequential selection procedure
................ 166
II Construction of Optimal Designs
171
6
Constructing Balanced Incomplete Block Designs
175
6.1
Introduction
........................... 175
6.2
Basic definitions
......................... 177
6.3
Construction of BIBD
...................... 185
6.3.1
Specific methods
..................... 185
6.3.2
General method
..................... 209
7
Constructing Fractional Factorial Designs
211
7.1
Introduction and basic notations
................ 211
7.2
Factorial designs
—
basic definitions
.............. 214
7.3
Fractional factorial designs with two levels of each factor
(2p-i:-designs)
.......................... 221
7.4
Fractional factorial designs with three levels of each factor
(3p-m-designs)
......................... 228
8
Exact Optimal Designs and Sample Sizes in Model I
of Regression Analysis
235
8.1
Introduction
........................... 235
8.1.1
The multiple linear regression Model I
........ 236
8.1.2
Simple polynomial regression
.............. 238
8.1.3
Intrinsically non-linear regression
........... 239
8.2
Exact
Ф
-optimal
designs
.................... 245
χ
8.2.1 Simple linear
regression
................. 246
8.2.2
Polynomial regression
.................. 248
8.2.3
Intrinsically non-linear regression
........... 249
8.2.4
Replication-free designs
................. 255
8.3
Determining the size of an experiment
............ 255
8.3.1
Simple linear regression
................. 255
III Special Designs
259
9
Second Order Designs
263
9.1
Central composite designs
................... 264
9.2
Doehlert designs
........................ 268
9.3
D-optimum and G-optimum second order designs
...... 270
9.4
Comparing the determinant criterion for some examples
. . 271
9.4.1
Two factors
........................ 271
9.4.2
Three factors
....................... 274
10
Mixture Designs
279
10.1
Introduction
........................... 279
10.2
The simplex lattice designs
................... 283
10.3
Simplex centroid designs
.................... 284
10.4
Extreme
vertice
designs
.................... 284
10.5
Augmented designs
....................... 285
10.6
Constructing optimal mixture designs with
R
........ 285
10.7
An example
........................... 286
A Theoretical Background
289
A.I Non-central distributions
.................... 289
A.2 Groups, fields and finite geometries
.............. 290
A.3 Difference sets
.......................... 295
A.4
Hadamard
matrices
....................... 300
A.
5
Existence and non-existence of non-trivial BIBD
...... 303
A.
6
Conference matrices
...................... 305
References
307
Index
319
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| spelling | Optimal experimental design with R Dieter Rasch ... Boca Raton, Fla. [u.a.] CRC Press 2011 XIX, 325 S. txt rdacontent n rdamedia nc rdacarrier Statistical theory and methods Versuchsplanung (DE-588)4078859-3 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf R Programm (DE-588)4705956-4 s Versuchsplanung (DE-588)4078859-3 s b DE-604 Rasch, Dieter 1935- Sonstige (DE-588)133266745 oth Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021150586&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Optimal experimental design with R Versuchsplanung (DE-588)4078859-3 gnd R Programm (DE-588)4705956-4 gnd |
| subject_GND | (DE-588)4078859-3 (DE-588)4705956-4 |
| title | Optimal experimental design with R |
| title_auth | Optimal experimental design with R |
| title_exact_search | Optimal experimental design with R |
| title_full | Optimal experimental design with R Dieter Rasch ... |
| title_fullStr | Optimal experimental design with R Dieter Rasch ... |
| title_full_unstemmed | Optimal experimental design with R Dieter Rasch ... |
| title_short | Optimal experimental design with R |
| title_sort | optimal experimental design with r |
| topic | Versuchsplanung (DE-588)4078859-3 gnd R Programm (DE-588)4705956-4 gnd |
| topic_facet | Versuchsplanung R Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021150586&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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