Multiple comparisons: theory and methods
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Chapman & Hall/CRC
1999
|
| Ausgabe: | 1. ed., 1. CRC Press repr. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 277 S. graf. Darst. |
| ISBN: | 0412982811 |
Internformat
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| 100 | 1 | |a Hsu, Jason C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Multiple comparisons |b theory and methods |c Jason C. Hsu |
| 250 | |a 1. ed., 1. CRC Press repr. | ||
| 264 | 1 | |a London [u.a.] |b Chapman & Hall/CRC |c 1999 | |
| 300 | |a XIV, 277 S. |b graf. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
| _version_ | 1804140815558115328 |
|---|---|
| adam_text | Contents
Preface
χι
1
Introduction
to simultaneous statistical inference
1
1.1
The one-way model
1
1.1.1
Example: treatment
χ
age combination
2
1.2
Modeling
4
1.3
Simultaneous confidence intervals
7
1.3.1
The Studentized maximum modulus method
7
1.3.2
Example: treatment
χ
age combination (continued)
9
1.3.3
A product inequality method
10
1.3.4
Example: treatment
χ
age combination (continued)
12
1.3.5
The Bonferroni inequality method
13
1.3.6
Example: treatment
χ
age combination (continued)
13
1.3.7
Scheffé s
method
14
1.3.8
Example: treatment
χ
age combination (continued)
16
1.4
Simultaneous testing
16
1.4.1
The Shaffer-Holm stepwise testing method
18
1.5
Unequal variances
20
1.6
Nonparametric methods
21
1.7
Deduced inference versus direct inference
21
1.8
Exercises
22
2
Classification of multiple comparison methods
24
2.1
Types of multiple comparisons inference
24
2.1.1
Direct inference versus deduced inference
26
2.2
Strength of multiple comparisons inference
27
2.2.1
Confidence intervals methods
28
2.2.2
Confident directions methods
28
2.2.3
Confident inequalities methods
29
2.2.4
Tests of homogeneity
29
2.2.5
Individual comparison methods
30
2.3
Inferential tasks of multiple comparison methods
33
2.3.1
Example: effect of smoking on pulmonary health
33
2.3.2
Example: Bovine growth hormone
toxicity
studies
34
Contents
2.4
Choosing a multiple comparison method
36
2.5
Exercises
39
Multiple comparisons with a control
43
3.1
One-sided multiple comparisons with a control
43
3.1.1
Balanced one-way model
43
3.1.1.1
Dunnett s method
44
3.1.1.2
The stepdown method of Naik, Marcus,
Peritz and Gabriel
45
3.1.1.3
Dunnett and Tamhane s stepup method
50
3.1.2
Example: smoking and pulmonary health (continued)
52
3.1.3
Unbalanced one-way model
54
3.1.3.1
Dunnett s method
55
3.1.3.2
The Miller-Winer method
56
3.1.3.3
Methods based on probabilistic inequalities
57
3.1.4
Example: smoking and pulmonary health (continued)
59
3.2
Two-sided multiple comparisons with a control
60
3.2.1
Balanced one-way model
60
3.2.1.1
Dunnett s method
60
3.2.2
Example: bovine growth hormone safety (continued)
61
3.2.3
Unbalanced one-way model
63
3.2.3.1
Dunnett s method
63
3.2.3.2
The Miller-Winer method
64
3.2.3.3
Methods based on probabilistic inequalities
65
3.2.4
Example: human food safety of
recombinant
insulin-
like growth factor-I (rIGF-I)
66
3.3
Nonparametric methods
67
3.3.1
Pairwise ranking methods
69
3.3.2
Joint ranking methods
73
3.4
Other approaches to stepwise testing
75
3.5
Appendix: detailed proofs
76
3.5.1
Proof of the validity of the stepdown method
76
3.5.2
Proof of the validity of the stepup method
78
3.6
Exercises
79
Multiple comparisons with the best
81
4.1
Constrained multiple comparison with the best
82
4.1.1
Balanced one-way model
83
4.1.2
Example: insect traps
86
4.1.3
Comparison with the sample best
87
4.1.4
Unbalanced one-way model
89
4.1.5
Example: SAT scores
94
4.1.6
Connection with bioequivalence
95
4.1.7
Connection with ranking and selection
100
Contents
4.2
Unconstrained
multiple
comparisons with the best
103
4.2.1
Balanced One-way Model
103
4.2.1.1
Deduction from all-pairwise comparisons
103
4.2.1.2
The Edwards-Hsu method
105
4.2.2
Example: insect traps (continued)
107
4.2.3
Comparison with the sample best
108
4.2.4
Unbalanced one-way model
109
4.2.4.1
Deduction from all-pairwise comparisons
110
4.2.4.2
The Edwards-Hsu method 111
4.2.5
Example: SAT scores (continued)
113
4.3
Nonparametric methods
115
4.4
Exercises
116
All-pairwise comparisons
119
5.1
Balanced one-way model
119
5.1.1
Tukey s method
119
5.1.2
Bofinger s confident directions method
121
5.1.3
Hayter s one-sided comparisons
123
5.1.4
Multiple range tests
125
5.1.4.1
Newman-Keuls multiple range test
127
5.1.4.2
The Methods of Ryan, Einot and Gabriel,
and
Welsch 128
5.1.4.3
Duncan s multiple range test
129
5.1.5
Scheffé s
method
130
5.1.6
A general stepdown testing scheme, with application
to multiple F-tests
132
5.1.7
The closed testing method, with applications to
closed multiple range tests
137
5.1.8
Fisher s least significant difference methods
139
5.1.9
Example: insect traps
140
5.2
Unbalanced one-way model
144
5.2.1
The Tukey-Kramer method
145
5.2.1.1
Graphical representation of the Tukey-
Kramer method
146
5.2.2
Hayter s method
153
5.2.3
Scheffé s
method
154
5.2.4
Stepdown tests
157
5.2.5
The Miller-Winer method
158
5.2.6
Fisher s least significant difference methods
158
5.2.7
Methods based on probabilistic inequalities
159
5.2.8
Example: SAT scores
160
5.3
Nonparametric methods
165
5.3.1
Pairwise ranking methods
165
5.3.2
Joint ranking methods
168
viii Contents
5.4
Exercises
170
6
Abuses and misconceptions in multiple
comparisons
175
6.1
Not adjusting for multiplicity
175
6.2
Inflation of strength of inference
175
6.3
Conditional inference
177
6.4
Post hoc comparisons
179
6.5
Recommendations
180
7
Multiple comparisons in the general linear model
181
7.1
Models with one-way structure
185
7.1.1
Variance-balanced designs
187
7.1.2
Orthogonal designs
188
7.1.2.1
Two-way model with proportional cell fre¬
quencies
188
7.1.2.2
One-way ANCOVA model with different
slopes
191
7.1.2.3
Example: Pooling batches in drug stability
studies
192
7.2
Multiple comparisons with a control
195
7.2.1
Deterministic approximation methods
197
7.2.1.1
Methods based on probabilistic inequalities
197
7.2.1.2
The factor analytic method
200
7.2.1.3
The linear programming method
204
7.2.2
Stochastic approximation methods
209
7.2.2.1
The method of Edwards and Berry
209
7.2.2.2
A variance reduction method
210
7.2.2.3
Example: blood pressure in dogs
210
7.3
Multiple comparisons with the best
213
7.4
AU-pairwise comparisons
215
7.4.1
Methods based on probabilistic inequalities
216
7.4.2
Stochastic approximation methods
218
7.5
Scheffé s
method for all contrasts
218
7.6
Nonparametric methods
220
7.6.1
Pairwise ranking methods based on signed ranks
220
7.6.2
Joint ranking methods based on Friedman rank sums
222
7.7
Two-way mixed models
223
7.8
One-way repeated measurement models
225
7.9
Exercises
226
A Some useful probabilistic inequalities
227
A.I An inequality for conditionally independent random vari¬
ables
227
A.2 The Bonferroni inequality
228
Contents
¡χ
Α.
3
Slepian s
inequality
228
A.4
Šidák s
inequality
229
Α.
5
The Hunter-Worsley Inequality
229
В
Some useful geometric lemmas
231
B.I Projecting spheres
231
B.2 Projecting rectangles
233
B.3 Deriving confidence sets by pivoting tests
233
С
Sample size computations
236
C.I Sample size computation for Tukey s MCA method
237
C.2 Sample size computation for MCB
238
C.3 Sample size computation for Dunnett s
MCC
method
240
C.4 An Example
240
D
Accessing computer codes
243
D.I Online access to codes
243
D.2 Critical value computations
243
D.3 Sample size computations
244
Б
Tables of critical values
245
Bibliography
258
Author index
271
Subject index
274
|
| any_adam_object | 1 |
| author | Hsu, Jason C. |
| author_facet | Hsu, Jason C. |
| author_role | aut |
| author_sort | Hsu, Jason C. |
| author_variant | j c h jc jch |
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| bvnumber | BV035845356 |
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| ctrlnum | (OCoLC)248099485 (DE-599)GBV317788388 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. ed., 1. CRC Press repr. |
| format | Book |
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| id | DE-604.BV035845356 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:05:58Z |
| institution | BVB |
| isbn | 0412982811 |
| language | English |
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| physical | XIV, 277 S. graf. Darst. |
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| publishDateSort | 1999 |
| publisher | Chapman & Hall/CRC |
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| spelling | Hsu, Jason C. Verfasser aut Multiple comparisons theory and methods Jason C. Hsu 1. ed., 1. CRC Press repr. London [u.a.] Chapman & Hall/CRC 1999 XIV, 277 S. graf. Darst. txt rdacontent n rdamedia nc rdacarrier Multipler Mittelwertvergleich (DE-588)4123804-7 gnd rswk-swf Multipler Mittelwertvergleich (DE-588)4123804-7 s DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018703559&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hsu, Jason C. Multiple comparisons theory and methods Multipler Mittelwertvergleich (DE-588)4123804-7 gnd |
| subject_GND | (DE-588)4123804-7 |
| title | Multiple comparisons theory and methods |
| title_auth | Multiple comparisons theory and methods |
| title_exact_search | Multiple comparisons theory and methods |
| title_full | Multiple comparisons theory and methods Jason C. Hsu |
| title_fullStr | Multiple comparisons theory and methods Jason C. Hsu |
| title_full_unstemmed | Multiple comparisons theory and methods Jason C. Hsu |
| title_short | Multiple comparisons |
| title_sort | multiple comparisons theory and methods |
| title_sub | theory and methods |
| topic | Multipler Mittelwertvergleich (DE-588)4123804-7 gnd |
| topic_facet | Multipler Mittelwertvergleich |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018703559&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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