Randomization tests:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2007
|
| Edition: | 4. ed. |
| Series: | Statistics
[191] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | 345 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 1584885890 9781584885894 |
Staff View
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Record in the Search Index
| _version_ | 1804152794195689472 |
|---|---|
| adam_text | Table of Contents
1 Statistical Tests that Do Not Require Random Sampling..........1
1.1 Randomization Tests............................................2
1.2 Numerical Examples.............................................2
1.3 Randomization Tests and Nonrandom Samples......................6
1.4 The Prevalence of Nonrandom Samples in Experiments.............6
1.5 The Irrelevance of Random Samples for
the Typical Experiment........................................7
1.6 Generalizing from Nonrandom Samples............................8
1.7 Intelligibility................................................8
1.8 Respect for the Validity of Randomization Tests................9
1.9 Versatility...................................................12
1.10 Practicality..................................................13
1.11 Precursors of Randomization Tests.............................13
1.12 Other Applications of Permutation Tests.......................17
1.13 Questions and Exercises.......................................18
Notes..............................................................19
References.....................................................19 2 3
2 Randomized Experiments........................................21
2.1 Unique Benefits of Experiments................................21
2.2 Experimentation without Manipulation of Treatments............22
2.3 Matching: A Precursor of Randomization........................23
2.4 Randomization of Experimental Units...........................23
2.5 Experimental Units.......................................... 24
2.6 Groups as Experimental Units..................................25
2.7 Control over Confounding Variables............................25
2.8 Between-Subject and Within-Subject Randomization..............27
2.9 Conventional Randomization Procedures.........................28
2.10 Randomization Procedures for Randomization Tests..............29
2.11 Further Reading...............................................31
2.12 Questions and Exercises.......................................31
3 Calculating P-Values..........................................33
3.1 Introduction..................................................33
3.2 Systematic Reference Sets.....................................33
3.3 Criteria of Validity for Randomization Tests...............
3.4 Randomization Test Null Hypotheses.....···■■.
3.5 Permuting Data for Experiments with Equal Sample i i/es....^
3.6 Monte Carlo Randomization Tests............................^
3.7 Equivalent Test Statistics................................. ,
3.8 Randomization Test Computer Programs.......................
3.9 Writing Programs for Randomization Tests................... 0
3.10 How to Test Systematic Data Permutation Programs...........
3.11 How to Test Random Data Permutation Programs...............*
3.12 Nonexperimental Applications of the Programs...............~
3.13 Questions and Exercises....................................^
References......................................................
4 Between-Subjects Designs
4.1 Introduction.................................................
4.2 One-Way ANOVA with Systematic Reference Sets.................57
4.3 A Simpler Test Statistic Equivalent to F......................61
4.4 One-Way ANOVA with Equal Sample Sizes.........................63
4.5 One-Way ANOVA with Random Reference Sets......................66
4.6 Analysis of Covariance........................................67
4.7 One-Tailed t Tests and Predicted Direction of Difference......68
4.8 Simpler Equivalent Test Statistics to t.......................69
4.9 Tests of One-Tailed Null Hypotheses for t Tests...............70
4.10 Unequal-N One-Tailed Null Hypotheses..........................72
4.11 Fast Alternatives to Systematic Data Permutation
for Independent t Tests......................................74
4.12 Independent t Test with Random Reference Sets.................74
4.13 Independent t Test and Planned Comparisons....................77
4.14 Independent t Test and Multiple Comparisons...................77
4.15 Loss of Experimental Subjects.................................79
4.16 Ranked Data...................................................81
4.17 Dichotomous Data..............................................82
4.18 Outliers.......................................................
4.19 Questions and Exercises.......................................86
References................ 07
5 Factorial Designs............................................. 39
5.1 Advantages of Randomization Tests for Factorial Designs 90
5.2 Factorial Designs for Completely Randomized Experiments........90
5.3 Proportional Cell Frequencies................................. 92
5.4 Program for Tests of Main Effects......ZZZZZZZZZ. . Z ........93
5.5 Completely Randomized Two-Factor Experiments...................95
5.6 Completely Randomized Three-Factor Experiments...................99
5.7 Interactions in Completely Randomized Experiments..............100
5.8 Randomization Test Null Hypotheses and Test Statistics.........103
5.9 Designs with Factor-Specific Dependent Variables...............105
5.10 Dichotomous and Ranked Data.....................................106
5.11 Fractional Factorial and Response Surface Designs...............106
5.12 Questions and Exercises.........................................107
References............................................................108
6 Repeated-Measures and Randomized Block Designs.............109
6.1 Carry-Over Effects in Repeated-Measures Designs............109
6.2 The Power of Repeated-Measures Tests.......................110
6.3 Systematic Listing of Data Permutations....................112
6.4 A Nonredundant Listing Procedure...........................114
6.5 IT2 as an Equivalent Test Statistic to F...................115
6.6 Repeated-Measures ANOVA with Systematic
Data Permutation...........................................116
6.7 Repeated-Measures ANOVA with Random Data Permutation.......118
6.8 Correlated t test with Systematic Data Permutation.........119
6.9 Fast Alternatives to Systematic Data Permutation
for Correlated t Tests.....................................120
6.10 Correlated t Test with Random Data Permutation.............120
6.11 Correlated t Test and Planned Comparisons..................121
6.12 Correlated t Test and Multiple Comparisons.................121
6.13 Rank Tests.................................................122
6.14 Dichotomous Data...........................................123
6.15 Counterbalanced Designs....................................123
6.16 Outliers...................................................126
6.17 Factorial Experiments with Repeated Measures...............127
6.18 Interactions in Repeated-Measures Experiments..............128
6.19 Randomized Block Designs...................................130
6.20 Randomized Complete Blocks.................................130
6.21 Incomplete Blocks..........................................131
6.22 Treatments-by-Subjects Designs.............................132
6.23 Disproportional Cell Frequencies...........................135
6.24 Test Statistic for Disproportional Cell Frequencies........137
6.25 Data Adjustment for Disproportional Cell Frequency Designs.138
6.26 Restricted-Alternatives Random Assignment..................140
6.27 Combining P-Values.........................................143
6.28 Additive Method of Combining P-Values......................146
6.29 Combining One-Tailed and Two-Tailed P-Values...............147
6.30 Questions and Exercises....................................148
References......................................................149
7
151
Multivariate Designs....................................
7 1 Importance of Parametric Assumptions Underlying MANOVA
7.2 Randomization Tests for Conventional MANOVA..............
7.3 Custom-Made Multivariate Randomization Tests.............
7.4 Effect of Units of Measurement...........................
7 5 Multivariate Tests Based on Composite ; Scores............
7.6 Combining t or F Values over Dependent Variables.........
7.7 A Geometrical Model......................................
7.8 Tests of Differences in Composition......................
7.9 Evaluation of Three MANOVA Tests.........................
7.10 Multivariate Factorial Designs...........................
7.11 Combining Univariate and Multivariate P-Values...........
7.12 Questions and Exercises..................................
References....................................................
151
152
153
154
155
159
160
162
166
167
169
169
170
8 Correlation.........................................
8.1 Determining P-Values by Data Permutation.........
8.2 Computer Program for Systematic Data Permutation
8.3 Correlation with Random Data Permutation.........................178
8.4 Multivariate Correlation.........................................179
8.5 Point-Biserial Correlation.......................................180
8.6 Correlation between Dichotomous Variables........................182
8.7 Spearman s Rank Correlation Procedure............................182
8.8 Kendall s Rank Correlation Procedure.............................183
8.9 Questions and Exercises..........................................184
References.............................................................185
9 Trend Tests...................................................187
9.1 Goodness-of-Fit Trend Test...................................187
9.2 Power of the Goodness-of-Fit Trend Test.......................189
9.3 Test Statistic for the Goodness-of-Fit Trend Test............190
9.4 Computation of Trend Means..................................191
9.5 Computer Program for Goodness-of-Fit Trend Test...............194
9.6 Modification of the Goodness-of-Fit Trend Test Statistic......194
9.7 Correlation Trend Test.........................................
9.8 Correlation Trend Test for Factorial Designs.........*.....***.*..*... 197
9.9 Disproportional Cell Frequencies......................... 198
9.10 Data Adjustment for Disproportional Cell Frequency Designs....200
9.11 Combining of P-Values for Trend Tests
for Factorial Experiments...
9.12 Repeated-Measures Trend Tests
203
204
9.13 Differences in Trends.....................................205
9.14 Correlation Trend Test and Simple Correlation.............206
9.15 Ordered Levels of Treatments..............................207
9.16 Ranked and Dichotomous Data...............................208
9.17 Questions and Exercises...................................209
References......................................................210
10 Matching and Proximity Experiments........................213
10.1 Randomization Tests for Matching..........................213
10.2 Randomization Tests of Proximity..........................217
10.3 Matching and Proximity Tests Based on Random
Selection of Treatment Levels.............................218
10.4 Questions and Exercises...................................222
References.................................................... 223
11 N-of-1 Designs............................................225
11.1 The Importance of N-of-1 Designs..........................225
11.2 Fisher s Lady-Tasting-Tea Experiment......................227
11.3 The Concept of Choosing as a Random Process...............228
11.4 Limitations of the Random Sampling Model for
N-of-1 Experiments........................................230
11.5 Random Assignment Model...................................231
11.6 Carry-Over Effects........................................232
11.7 The N-of-1 Randomization Test: An Early Model.............233
11.8 Factorial Experiments.....................................235
11.9 Randomized Blocks.........................................236
11.10 Correlation...............................................238
11.11 Operant Research and Treatment Blocks.....................238
11.12 ABAB Design...............................................239
11.13 Random Assignment of Treatment Blocks to Treatments.......240
11.14 Randomization Tests for Treatment Intervention............241
11.15 Effects of Trends.........................................243
11.16 Randomization Tests for Intervention and Withdrawal.......245
11.17 Multiple Schedule Experiments.............................246
11.18 Power of N-of-1 Randomization Tests.......................249
11.19 Replicated N-of-1 Experiments.............................249
11.20 N-of-1 Clinical Trial Facilities..........................250
11.21 Single-Cell and Other Single-Unit Neuroscience Experiments.251
11.22 Books on N-of-1 Design and Analysis.......................254
11.23 Software for N-of-1 Randomization Tests...................254
11.24 Questions and Exercises...................................255
References......................................................256
12 Tests of Quantitative Laws
261
12.1 Generic and Specific Null Hypotheses
12.2 The Referent of a Law or Model.....
12.3 Test of Incremental Effects........
12.4 Weber s Law........................
12.5 Other Psychophysical Laws..........
12.6 Foraging Behavior of Hawks.........
12.7 Complications......................
12.8 Questions and Exercises............
References...............................
262
263
263
265
264
271
.272
,273
.274
13 Tests of Direction and Magnitude of Effect
275
13.1 Tests of One-Tailed Null Hypotheses for Correlated / Tests
13.2 Other Tests of One-Tailed Null Hypotheses Using TA
or ( A—B) as Test Statistics..............................
13.3 Tests of One-Tailed Null Hypotheses about Differences
in Variability............................................
13.4 Tests of One-Tailed Null Hypotheses for Correlation.......
13.5 Testing Null Hypotheses about Magnitude of Effect.........
13.6 Testing Null Hypotheses about Specific Additive Effects....
13.7 Questions and Exercises...................................
References.......................................................
275
277
279
279
282
.283
.285
.286
14 Fundamentals of Validity..................................287
14.1 Randomization Tests as Distribution-Free Tests............288
14.2 Differences between Randomization Test Theory
and Permutation Test Theory...............................288
14.3 Parametric Tests as Approximations to Randomization Tests.289
14.4 Randomization Test Theory.................................291
14.5 Systematically Closed Reference Sets......................292
14.6 Permutation Groups........................................292
14.7 Data-Permuting and Randomization-Referral Procedures......293
14.8 Invariance of Measurements under the Null Hypothesis......297
14.9 General and Restricted Null Hypotheses....................297
14.10 Reference Sets for General Null Hypotheses................298
14.11 Reference Subsets for General Null Hypotheses.............299
14.12 Reference Subsets for Restricted Null Hypotheses..........301
14.13 Reference Subsets for Planned and Multiple Comparisons....302
14.14 Reference Subsets for Factorial Designs...................303
14.15 Open Reference Sets: Treatment Intervention and Withdrawal....305
14.16 Closed Reference Sets: Dropouts..............................306
14.17 Open Reference Sets: Permuting Residuals...................307
14.18 Sampling a List of Randomizations..........................307
14.19 Random Data Permutation: Hypothesis
Testing vs. Estimation.....................................308
14.20 Stochastic Closure When Assignments Are Equally Probable...310
14.21 Systematic Expansion of a Random Reference Set.............311
14.22 Random Ordering of Measurements within Treatments..........312
14.23 Fixed, Mixed, and Random Models............................314
14.24 Deriving One-Tailed P-Values from Two-Tailed P-Values
with Unequal N.............................................316
14.25 Test Statistics and Adaptive Tests.........................317
14.26 Stochastic Closure When Assignments Are Not
Equally Probable...........................................319
14.27 Questions and Exercises....................................324
References.......................................................325
15 General Guidelines and Software Availability................327
15.1
15.2
15.3
15.4
Randomization: Multistage Model..............................
Permuting Data: Data-Exchanging Model........................
Maximizing Power.............................................
15.3.1 Homogeneity of Subjects..............................
15.3.2 Statistical Control over Between-Subject Variability.
15.3.3 Number of Subjects...................................
15.3.4 Unequal Sample Sizes.................................
15.3.5 Restricted-Alternatives Random Assignment............
15.3.6 Equal Sample Sizes...................................
15.3.7 Counterbalancing.....................................
15.3.8 Treatments-by-Subjects Designs.......................
15.3.9 Precision of Measurements............................
15.3.10 Precision of Test Statistics.........................
15.3.11 Composite Measurements...............................
15.3.12 Combining Test Statistics over Dependent Variables...
15.3.13 Directional Test Statistics..........................
15.3.14 Control over Systematic Trends.......................
15.3.15 Random Sampling of Levels of Treatments..............
15.3.16 Combining of P-values................................
Randomization Test Computer Programs on the CD...............
15.4.1 Modifying Programs...................................
15.4.2 Equivalent Test Statistics...........................
15.4.3 Random Data Permutation..............................
15.4.4 Systematic Listing Procedure.........................
15.4.5 Elimination of Redundant Data Permutations...........
15.4.6 Output...............................................
15.4.7 Testing Programs.....................................
327
328
329
329
329
329
330
330
330
330
331
331
331
331
331
331
332
332
332
332
333
333
333
334
334
334
334
15.5 Other Computer Programs......................................335
15.5.1 Other Free Computer Programs.......................335
15.5.1.1 BLOSSOM....................................335
15.5.1.2 NPC-Test...................................335
15.5.1.3 NPSTAT and NPFACT..........................335
15.5.1.4 RESAMPLING.................................335
15.5.2 Commercial Computer Programs........................336
15.5.2.1 RESAMPLING STATS...........................336
15.5.2.2 RT.........................................336
15.5.2.3 SAS........................................336
15.5.2.4 SC.........................................337
15.5.2.5 SPSS.......................................337
15.5.2.6 StatXact and LogXact.......................337
15.5.2.7 Testimate..................................337
References.........................................................337
Index................................................................
|
| any_adam_object | 1 |
| author | Edgington, Eugene S. 1924- Onghena, Patrick 1965- |
| author_GND | (DE-588)14251070X (DE-588)1064185797 |
| author_facet | Edgington, Eugene S. 1924- Onghena, Patrick 1965- |
| author_role | aut aut |
| author_sort | Edgington, Eugene S. 1924- |
| author_variant | e s e es ese p o po |
| building | Verbundindex |
| bvnumber | BV042249013 |
| classification_rvk | SK 830 |
| ctrlnum | (OCoLC)635027831 (DE-599)BVBBV042249013 |
| dewey-full | 519.56 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.56 |
| dewey-search | 519.56 |
| dewey-sort | 3519.56 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV042249013 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:16:22Z |
| institution | BVB |
| isbn | 1584885890 9781584885894 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027687033 |
| oclc_num | 635027831 |
| open_access_boolean | |
| owner | DE-83 DE-473 DE-BY-UBG DE-703 |
| owner_facet | DE-83 DE-473 DE-BY-UBG DE-703 |
| physical | 345 S. graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Statistics |
| series2 | Statistics |
| spelling | Edgington, Eugene S. 1924- Verfasser (DE-588)14251070X aut Randomization tests Eugene S. Edgington ; Patrick Onghena 4. ed. Boca Raton [u.a.] Chapman & Hall/CRC 2007 345 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Statistics [191] Literaturangaben Testtheorie (DE-588)4131939-4 gnd rswk-swf Randomisierter Test (DE-588)4294178-7 gnd rswk-swf Statistische Hypothese (DE-588)4182959-1 gnd rswk-swf Statistischer Test (DE-588)4077852-6 gnd rswk-swf Randomisierter Test (DE-588)4294178-7 s DE-604 Testtheorie (DE-588)4131939-4 s 1\p DE-604 Statistischer Test (DE-588)4077852-6 s 2\p DE-604 Statistische Hypothese (DE-588)4182959-1 s 3\p DE-604 Onghena, Patrick 1965- Verfasser (DE-588)1064185797 aut Statistics [191] (DE-604)BV000003265 191 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027687033&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Edgington, Eugene S. 1924- Onghena, Patrick 1965- Randomization tests Statistics Testtheorie (DE-588)4131939-4 gnd Randomisierter Test (DE-588)4294178-7 gnd Statistische Hypothese (DE-588)4182959-1 gnd Statistischer Test (DE-588)4077852-6 gnd |
| subject_GND | (DE-588)4131939-4 (DE-588)4294178-7 (DE-588)4182959-1 (DE-588)4077852-6 |
| title | Randomization tests |
| title_auth | Randomization tests |
| title_exact_search | Randomization tests |
| title_full | Randomization tests Eugene S. Edgington ; Patrick Onghena |
| title_fullStr | Randomization tests Eugene S. Edgington ; Patrick Onghena |
| title_full_unstemmed | Randomization tests Eugene S. Edgington ; Patrick Onghena |
| title_short | Randomization tests |
| title_sort | randomization tests |
| topic | Testtheorie (DE-588)4131939-4 gnd Randomisierter Test (DE-588)4294178-7 gnd Statistische Hypothese (DE-588)4182959-1 gnd Statistischer Test (DE-588)4077852-6 gnd |
| topic_facet | Testtheorie Randomisierter Test Statistische Hypothese Statistischer Test |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027687033&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003265 |
| work_keys_str_mv | AT edgingtoneugenes randomizationtests AT onghenapatrick randomizationtests |