Permutation, parametric and bootstrap tests of hypotheses:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2005
|
| Edition: | 3. ed. |
| Series: | Springer series in statistics
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013094909&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Bis 2. Aufl. u.d.T.: Good, Phillip I.: Permutation tests Includes bibliographical references (p. [279]-302) and indexes |
| Physical Description: | XIX, 315 S. graph. Darst. 25 cm |
| ISBN: | 038720279X 9781441919076 |
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MARC
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| 100 | 1 | |a Good, Phillip I. |d 1937- |e Verfasser |0 (DE-588)130601152 |4 aut | |
| 245 | 1 | 0 | |a Permutation, parametric and bootstrap tests of hypotheses |c Phillip Good |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York, NY |b Springer |c 2005 | |
| 300 | |a XIX, 315 S. |b graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in statistics | |
| 500 | |a Bis 2. Aufl. u.d.T.: Good, Phillip I.: Permutation tests | ||
| 500 | |a Includes bibliographical references (p. [279]-302) and indexes | ||
| 650 | 7 | |a Analyse multivariée - Statistique |2 ram | |
| 650 | 7 | |a Bootstrap (statistique) |2 ram | |
| 650 | 7 | |a Hypothesetoetsing |2 gtt | |
| 650 | 7 | |a Permutaties |2 gtt | |
| 650 | 4 | |a Rééchantillonnage (Statistique) | |
| 650 | 7 | |a Statistique mathématique - Théorie asymptotique |2 ram | |
| 650 | 4 | |a Tests d'hypothèses (Statistique) | |
| 650 | 4 | |a Statistical hypothesis testing | |
| 650 | 4 | |a Resampling (Statistics) | |
| 650 | 0 | 7 | |a Bootstrap-Hypothese |0 (DE-588)4146294-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Statistischer Test |0 (DE-588)4077852-6 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1819345840833036288 |
|---|---|
| adam_text | Contents
Preface to the Third Edition......................................... v
Preface to the Second Edition ....................................... vii
Preface to the First Edition......................................... ix
1 A Wide Range of Applications..................................... 1
1.1 Basic Concepts.............................................. 1
1.1.1 Stochastic Phenomena............................... 1
1.1.2 Distribution Functions............................. 3
1.1.3 Hypotheses......................................... 3
1.2 Applications................................................ 5
1.3 Testing a Hypothesis........................................ 7
1.3.1 Five Steps to a Test............................... 8
1.3.2 Analyze the Experiment ............................ 8
1.3.3 Choose a Test Statistic ........................... 8
1.3.4 Compute the Test Statistic......................... 9
1.3.5 Determine the Frequency Distribution of
the Test Statistic................................. 9
1.3.6 Make a Decision................................... 10
1.3.7 Variations on a Theme............................. 10
1.4 A Brief History of Statistics in Decision-Making........... 10
1.5 Exercises.................................................. 12
2 Optimal Procedures............................................... 13
2.1 Defining Optimal........................................... 13
2.1.1 Trustworthy....................................... 13
2.1.2 Two Types of Error................................ 14
2.1.3 Losses and Risk................................... 10
2.1.4 Significance Level and Power ..................... 17
Contents
XII
2.1.4.1 Power and thè Magnitudi· of thè Ettect . . . 18
. . 18
2.1.4.2 1 ower alici оаицлі ..................
2.1.5 2.1.4.3 Power and tlie Ашчпаїїла............ . . 21
Lxact, unoiaseci, vanist i val ivi............. *22
2.1.0
0 17 . . 23
n 0 2.1.7 IVIOSI oc,! iligC ilL lEM-n ..................... . . 23
2.2 Basic . . 23
2.2.1 ІПООреіШеИГ. C/l/hi l veli-11x1 ir*....................
2.2.2 м rr/mKI/i i ìlwiTVot ІПМ S . ........... . . 21
0 4 oi JGiXCn ai igearne wust 1 Viti .................. . . 25
2.o uecibj
9 4 1 . . 2(i
z.o. 1
9 4 9 . . 27
z.o.z
O Q O Олплго lif/n/1 Tini lUinìW ............... . . 28
2.4 ¿à.Kj.yJ VJtlH.l CUim-Vl .......................... . . 29
3 Testing Hypotheses
33
3.1
3.2
3.3
Testing a Simple Hypothesis...............................*·*
One-Sample Tests for a Location Parameter...................M
3.2.1 A Permutation Test............................... 34
3.2.2 A Parametric Test ............................... 30
3.2.3 Properties of the Parametric Test................ 37
3.2.4 Student’s t...................................... 38
3.2.5 Properties of the Permutation Test............... 39
3.2.6 Exact Significance Levels: A Digression.......... 39
Confidence Intervals...................................... 40
3.3.1
Confidence Intervals Based on Permutation
Tests........................................... 41
3.3.2 Confidence Intervals Based on Parametric
Tests........................................... 42
3.3.3 Confidence Intervals Based on the Bootstrap .... 43
3.3.4 Parametric Bootstrap............................ 45
3.3.5 Better Confidence Intervals..................... 46
3.4 Comparison Among the Test Procedures................... 46
3.5 One-Sample Tests for a Scale Parameter................. 48
3.5.1 Semiparametric Tests............................ 48
3.5.2 Parametric Tests: Sufficiency................... 48
3.5.3 Unbiased Tests ................................. 50
3.5.4 Comparison Among the Test Procedures............ 50
3.6 Comparing the Location Parameters of Two
Populations............................................ 51
3.6.1
3.6.2
3.6.3
3.6.4
A UMPU Parametric Test: Student’s t............ 51
A UMPU Semiparametric Procedure ............... 51
An Example..................................... 54
Comparison of the Tests: The Behrens-Fisher
Problem........................................ 54
Contents
XIII
3.7 Comparing the Dispersions of Two Populations.............. 57
3.7.1 The Parametric Approach......................... 57
3.7.2 The Permutation Approach........................ 58
3.7.3 The Bootstrap Approach........................... 61
3.8 Bivariate Correlation..................................... 62
3.9 Which Test?............................................... 63
3.10 Exercises................................................. 63
4 Distributions ................................................... 67
4.1 Properties of Independent Observations.................... 67
4.2 Binomial Distribution..................................... 67
4.3 Poisson: Events Rare in Time and Space.................... 68
4.3.1 Applying the Poisson............................. 69
4.3.2 A Poisson Distribution of Poisson
Distributions.................................... 70
4.3.3 Comparing Two Poissons........................... 70
4.4 Time Between Events....................................... 71
4.5 The Uniform Distribution.................................. 71
4.6 The Exponential Family of Distributions................... 72
4.6.1 Proofs of the Properties......................... 73
4.6.2 Normal Distribution.............................. 74
4.7 Which Distribution?....................................... 75
4.8 Exercises................................................. 75
5 Multiple Tests................................................... 79
5.1 Controlling the Overall Error Rate ....................... 79
5.1.1 Standardized Statistics.......................... 80
5.1.2 Paired Sample Tests.............................. 81
5.2 Combination of Independent Tests.......................... 81
5.2.1 Omnibus Statistics............................... 82
5.2.2 Binomial Random Variables........................ 82
5.2.3 Bayes’ Factor.................................... 83
5.3 Exercises................................................. 84
6 Experimental Designs ........................................... 85
6.1 Invariance................................................ 85
6.1.1 Some Examples................................... 86
6.2 ¿֊Sample Comparisons—Least-Squares Loss Function......... 87
6.2.1 Linear Hypotheses ............................... 87
6.2.2 Large and Small Sample Properties of the F-ratio
Test............................................ 89
6.2.3 Discrete Data and Time-to-Event Data............. 90
6.3 ¿-Sample Comparisons—Other Loss Functions................ 91
6.3.1 F-ratio................................... 6 * * 9^
6.3.2 Pitman Correlation.............................. 92
XIV
Contents
6.4
6.5
6.6
6.7
6.8
6.9
6.3.3 Effect of Ties..............................
6.3.4 Cochran-Armitage Test.......................
6.3.5 Linear Estimation...........................
6.3.6 A Unifying Theory...........................
Four Ways to Control Variation.......................
6.4.1 Control the Environment.....................
6.4.2 Block the Experiment .......................
6.4.2.1 Using Ranks.........................
6.4.2.2 Matched Pairs.......................
6.4.3 Measure Factors That Cannot Bo C ontrollod
6.4.3.1 Eliminate the Functional Relationship
6.4.3.2 Selecting Variables.................
6.4.3.3 Restricted Randomization............
6.4.4 Randomize...................................
Latin Square.........................................
Very Large Samples...................................
Sequential Analysis..................................
6.7.1 A Vaccine Trial.............................
6.7.2 Determining the Boundary Values.............
6.7.3 Power of a Sequential Analysis..............
6.7.4 Expected Sample Size .......................
6.7.5 Curtailed Inspection........................
6.7.6 Restricted Sequential Sampling Schemes......
Sequentially Adaptive Treatment Allocation...........
6.8.1 Group Sequential Trials.....................
6.8.2 Determining the Sampling Ratio..............
6.8.3 Exact Random Allocation Tests...............
Exercises...........................................
95
96
96
97
97
98
98
99
100
101
101
102
102
103
104
106
107
107
110
110
111
112
112
113
113
113
114
115
7 Multifactor Designs.............................................119
7.1 Multifactor Models........................................119
7.2 Analysis of Variance......................................120
7.3 Permutation Methods: Main Effects .......................124
7.3.1 An Example.......................................125
7.4 Permutation Methods: Interactions........................126
7.5 Synchronized Rearrangements...............................127
7.5.1 Exchangeable and Weakly Exchangeable
Variables.......................................12g
7.5.2 Two Factors........................................
7.5.3 Three or More Factors...........................132
7.5.4 Similarities.......................................
7.5.5 Test for Interaction...............................
7.6 Unbalanced Designs....................................... 137
7.6.1 Missing Combinations............................138
7.6.2 The Boot-Perm Test.............. 1 qo
Contents
XV
7.7 Which Test Should You Use?...............................140
7.8 Exercises................................................140
8 Categorical Data ..............................................143
8.1 Fisher’s Exact Test......................................143
8.1.1 Hypergeometric Distribution.....................145
8.1.2 One-Tailed and Two-Tailed Tests ................145
8.1.3 The Two-Tailed Test.............................146
8.1.4 Determining the p~Value.........................146
8.1.5 What is the Alternative?........................148
8.1.6 Increasing the Power ...........................148
8.1.7 Ongoing Controversy.............................149
8.2 Odds Ratio...............................................150
8.2.1 Stratified 2 x 2’s..............................151
8.3 Exact Significance Levels................................152
8.4 Unordered r x c Contingency Tables.......................154
8.4.1 Agreement Between Observers.....................156
8.4.2 What Should We Randomize? ......................157
8.4.3 Underlying Assumptions..........................158
8.4.4 Symmetric Contingency Tables ...................158
8.5 Ordered Contingency Tables...............................160
8.5.1 Ordered 2xc Tables..............................160
8.5.1.1 Alternative Hypotheses..................161
8.5.1.2 Back-up Statistics......................162
8.5.1.3 Directed Chi-Square.....................162
8.5.2 More Than Two Rows and Two Columns..............163
8.5.2.1 Singly Ordered Tables...................163
8.5.2.2 Doubly Ordered Tables...................163
8.6 Covariates...............................................164
8.6.1 Bross’ Method...................................104
8.6.2 Blocking........................................165
8.7 Exercises................................................166
9 Multivariate Analysis..........................................169
9.1 Nonparametric Combination of Univariate Tests............169
9.2 Parametric Approach......................................171
9.2.1 Canonical Form..................................171
9.2.2 Hotelling’s T2 .................................172
9.2.3 Multivariate Analysis of Variance
(MANOVA)........................................173
9.3 Permutation Methods......................................173
9.3.1 Which Test-Parametric or Permutation?...........175
9.3.2 Interpreting the Results........................176
XVI
Contents
9.4 Alternative Statistics....
9.4.1 Maximum-* ......
9.4.2 Block Effects
9.4.3 Runs Test.......
9.4.4 Which Statistic? .
9.5 Repeated Measures.........
9.5.1 An Example......
9.5.2 Matched Pairs . . .
9.5.3 Response Profiles
9.5.4 Missing Data
9.5.5 Bioequivalence . . .
9.6 Exercises.................
177
177
177
178
ISO
181
181
182
183
183
184
185
10 Clustering in Time and Space .....................................
10.1 The Generalized Quadratic Form............................ls )
10.1.1 Mantel’s .......................................*‘s·*
10.1.2 An Example.......................................
10.2 Applications..............................................
10.2.1 The MRPP Statistic...............................P)(l
10.2.2 The BW Statistic of Cliff and Ord [1973]..........191
10.2.3 Equivalances .....................................19?
10.2.4 Extensions........................................PI?
10.2.5 Another Dimension.................................19?
10.3 Alternate Approaches.......................................193
10.3.1 Quadrant Density..................................193
10.3.2 Nearest-Neighbor Analysis ........................193
10.3.3 Comparing Two Spatial Distributions...............193
10.4 Exercises.................................................194
11 Coping with Disaster...............................................195
11.1 Missing Data...............................................195
11.2 Covariates After the Fact..................................197
11.2.1 Observational Studies............................197
11.3 Outliers...................................................198
11.3.1 Original Data.....................................199
11.3.2 Ranks.............................................199
11.3.3 Scores..............................................
11.3.4 Robust Transformations............................201
11.3.5 Use an L Test ...................................201
11.3.6 Censoring...........................................
11.3.7 Discarding....................................... շօշ
11.4 Censored Data............................................. շօշ
11.4.1 GAMP Tests............ . . * * * * ՜ ’ ’ “ * ‘ 20շ
11.4.2 Fishery and Animal Counts ....................... 904
Contents
XVII
11.5 Censored Match Pairs.....................................204
11.5.1 GAMP Test for Matched Pairs.....................205
11.5.2 Ranks...........................................206
11.5.3 One-Sample: Bootstrap Estimates.................206
11.6 Adaptive Tests...........................................207
11.7 Exercises................................................208
12 Solving the Unsolved and the Insolvable........................209
12.1 Key Criteria.............................................209
12.1.1 Sufficient Statistics......................... 209
12.1.2 Three Stratagems................................210
12.1.3 Restrict the Alternatives.......................210
12.1.4 Consider the Loss Function......................212
12.1.5 Impartiality....................................213
12.2 The Permutation Distribution.............................213
12.2.1 Ensuring Exchangeability........................213
12.2.1.1 Test for Parallelism...................214
12.2.1.2 Linear Transforms That Preserve
Exchangeability.................................215
12.3 New Statistics ..........................................216
12.3.1 Nonresponders...................................216
12.3.1.1 Extension to K-samples.................217
12.3.2 Animal Movement.................................217
12.3.3 The Building Blocks of Life.....................217
12.3.4 Structured Exploratory Data Analysis............218
12.3.5 Comparing Multiple Methods of Assessment........219
12.4 Model Validation.........................................221
12.4.1 Regression Models...............................221
12.4.1.1 Via the Bootstrap......................221
12.4.1.2 Via Permutation Tests..................221
12.4.2 Models With a Metric............................222
12.5 Bootstrap Confidence Intervals...........................223
12.5.1 Hall֊Wilson Criteria............................224
12.5.2 Bias-Corrected Percentile ......................225
12.6 Exercises................................................225
13 Publishing Your Results........................................229
13.1 Design Methodology.......................................229
13.1.1 Randomization in Assignment ....................229
13.1.2 Choosing the Experimental Unit..................230
13.1.3 Determining Sample Size.........................231
13.1.4 Power Comparisons ..............................231
13.2 Preparing Manuscripts for Publication....................231
13.2.1 Reportable Elements ............................232
13.2.2 Details of the Analysis.........................232
xviii
Contents
14
Increasing Computational Efficiency.................
14.1 Seven Techniques..............................
14.2 Monte Carlo...................................
14.2.1 Stopping Rules ......................
14.2.2 Variance of the Result...............
14.2.3 Cutting the Computation Time.........
14.3 Rapid Enumeration and Selection Algorithms . . .
14.3.1 Matched Pairs........................
14.4 Recursive Relationships.......................
14.5 Focus on the Tails............................
14.5.1 Contingency Tables...................
14.5.1.1 Network Representation.....
14.5.1.2 The Network Algorithm......
14.5.2 Play the Winner Allocation ..........
14.5.3 Directed Vertex Peeling..............
14.6 Gibbs Sampling................................
14.6.1 Metropolis-Hastings Sampling Methods
14.7 Characteristic Functions......................
14.8 Asymptotic Approximations.....................
14.8.1 A Central Limit Theorem..............
14.8.2 Edgeworth Expansions.................
14.8.3 Generalized Correlation..............
14.9 Confidence Intervals..........................
14.10 Sample Size and Power.........................
14.10.1 Simulations..........................
14.10.2 Network Algorithms...................
14.11 Some Conclusions..............................
14.12 Software .....................................
14.12.1 Do-It-Yourself.......................
14.12.2 Complete Packages....................
14.12.2.1 Freeware...................
14.12.2.2 Shareware..................
14.12.2.3 $$$$.......................
14.13 Exercises.....................
233
233
233
234
235
235
236
236
236
237
239
239
241
242
242
243
244
245
246
, 246
. 246
. 247
. 247
. 248
. 248
. 249
. 250
. 251
. 251
. 252
. 252
. 252
. 252
. 253
Appendix: Theory of Testing Hypotheses........................255
A.l Probability........................................... 255
A.2 The Fundamental Lemma..................................257
A.3 Two-Sided Tests ...................................... 253
A.3.1 One-Parameter Exponential Families.............259
A.4 Tests for Multiparameter Families......................262
A.4.1 Basu’s Theorem..................................
A.4.2 Conditional Probability and Expectation........263
A.4.3 Multiparameter Exponential Families............263
Contents xix
A.5 Exchangeable Observations...............................268
A.5.1 Order Statistics...............................269
A.5.2 Transformably Exchangeable ....................270
A.5.3 Exchangeability-Preserving Transforms..........271
A.6 Confidence Intervals....................................272
A.7 Asymptotic Behavior.....................................273
A.7.1 A Theorem on Linear Forms......................273
A.7.2 Monte Carlo....................................274
A.7.3 Asymptotic Efficiency .........................274
A.7.4 Exchangeability................................275
A.7.5 Improved Bootstrap Confidence Intervals........276
A.8 Exercises...............................................276
Bibliography..................................................279
Author Index..................................................303
Subject Index ................................................309
|
| any_adam_object | 1 |
| author | Good, Phillip I. 1937- |
| author_GND | (DE-588)130601152 |
| author_facet | Good, Phillip I. 1937- |
| author_role | aut |
| author_sort | Good, Phillip I. 1937- |
| author_variant | p i g pi pig |
| building | Verbundindex |
| bvnumber | BV019768724 |
| callnumber-first | Q - Science |
| callnumber-label | QA277 |
| callnumber-raw | QA277.G643 2005 QA277 |
| callnumber-search | QA277.G643 2005 QA277 |
| callnumber-sort | QA 3277 G643 42005 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 850 SK 830 SK 840 |
| ctrlnum | (OCoLC)55473971 (DE-599)BVBBV019768724 |
| dewey-full | 519.5/6 519.5/622 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/6 519.5/6 22 |
| dewey-search | 519.5/6 519.5/6 22 |
| dewey-sort | 3519.5 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV019768724 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:05:27Z |
| institution | BVB |
| isbn | 038720279X 9781441919076 |
| language | English |
| lccn | 2004050436 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013094909 |
| oclc_num | 55473971 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-521 DE-11 DE-188 DE-578 DE-703 DE-473 DE-BY-UBG |
| owner_facet | DE-19 DE-BY-UBM DE-521 DE-11 DE-188 DE-578 DE-703 DE-473 DE-BY-UBG |
| physical | XIX, 315 S. graph. Darst. 25 cm |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spellingShingle | Good, Phillip I. 1937- Permutation, parametric and bootstrap tests of hypotheses Analyse multivariée - Statistique ram Bootstrap (statistique) ram Hypothesetoetsing gtt Permutaties gtt Rééchantillonnage (Statistique) Statistique mathématique - Théorie asymptotique ram Tests d'hypothèses (Statistique) Statistical hypothesis testing Resampling (Statistics) Bootstrap-Hypothese (DE-588)4146294-4 gnd Statistischer Test (DE-588)4077852-6 gnd Randomisierter Test (DE-588)4294178-7 gnd Resampling (DE-588)4288033-6 gnd |
| subject_GND | (DE-588)4146294-4 (DE-588)4077852-6 (DE-588)4294178-7 (DE-588)4288033-6 |
| title | Permutation, parametric and bootstrap tests of hypotheses |
| title_auth | Permutation, parametric and bootstrap tests of hypotheses |
| title_exact_search | Permutation, parametric and bootstrap tests of hypotheses |
| title_full | Permutation, parametric and bootstrap tests of hypotheses Phillip Good |
| title_fullStr | Permutation, parametric and bootstrap tests of hypotheses Phillip Good |
| title_full_unstemmed | Permutation, parametric and bootstrap tests of hypotheses Phillip Good |
| title_short | Permutation, parametric and bootstrap tests of hypotheses |
| title_sort | permutation parametric and bootstrap tests of hypotheses |
| topic | Analyse multivariée - Statistique ram Bootstrap (statistique) ram Hypothesetoetsing gtt Permutaties gtt Rééchantillonnage (Statistique) Statistique mathématique - Théorie asymptotique ram Tests d'hypothèses (Statistique) Statistical hypothesis testing Resampling (Statistics) Bootstrap-Hypothese (DE-588)4146294-4 gnd Statistischer Test (DE-588)4077852-6 gnd Randomisierter Test (DE-588)4294178-7 gnd Resampling (DE-588)4288033-6 gnd |
| topic_facet | Analyse multivariée - Statistique Bootstrap (statistique) Hypothesetoetsing Permutaties Rééchantillonnage (Statistique) Statistique mathématique - Théorie asymptotique Tests d'hypothèses (Statistique) Statistical hypothesis testing Resampling (Statistics) Bootstrap-Hypothese Statistischer Test Randomisierter Test Resampling |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013094909&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT goodphillipi permutationparametricandbootstraptestsofhypotheses |