The foundations of statistics: a simulation-based approach
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Heidelberg [u.a.]
Springer
2011
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 175 - 176 |
| Physical Description: | XV, 178 S. graph. Darst. 24 cm |
| ISBN: | 9783642163128 |
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Record in the Search Index
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| adam_text |
IMAGE 1
CONTENTS
1 GETTING STARTED 1
1.1 INSTALLATION: R, WT^I, AND EMACS 1
1.2 HOW TO READ THIS BOOK 2
1.3 SOME SIMPLE COMMANDS IN R 2
1.4 GRAPHICAL SUMMARIES 6
2 RANDOMNESS AND PROBABILITY 9
2.1 ELEMENTARY PROBABILITY THEORY 9
2.1.1 THE SUM AND PRODUCT RULES 9
2.1.2 STONES AND RAIN: A VARIANT ON THE COIN-TOSS PROBLEM. 11 2.2 THE
BINOMIAL DISTRIBUTION 19
2.3 BALLS IN A BOX 22
2.4 STANDARD DEVIATION AND SAMPLE SIZE 33
2.4.1 ANOTHER INSIGHT: MEAN MINIMIZES VARIANCE 36 2.5 THE BINOMIAL
VERSUS THE NORMAL DISTRIBUTION 39
PROBLEMS 41
3 THE SAMPLING DISTRIBUTION OF THE SAMPLE MEAN 43
3.1 THE CENTRAL LIMIT THEOREM 47
3.2 A AND OEI 49
3.3 THE 95% CONFIDENCE INTERVAL FOR THE SAMPLE MEAN 50 3.4 REALISTIC
STATISTICAL INFERENCE 52
3.5 S IS AN UNBIASED ESTIMATOR OF A 52
3.6 THE T-DISTRIBUTION 55
3.7 THE ONE-SAMPLE T-TEST 56
3.8 SOME OBSERVATIONS ON CONFIDENCE INTERVALS 57
3.9 SAMPLE SD, DEGREES OF FREEDOM, UNBIASED ESTIMATORS 61 3.10 SUMMARY
OF THE SAMPLING PROCESS 63
3.11 SIGNIFICANCE TESTS 64
3.12 THE NULL HYPOTHESIS 65
3.13 Z-SCORES 66
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1006508058
DIGITALISIERT DURCH
IMAGE 2
XIV CONTENTS
3.14 P-VALUES 67
3.15 HYPOTHESIS TESTING: A MORE REALISTIC SCENARIO 71
3.16 COMPARING TWO SAMPLES 75
3.16.1 FIO IN TWO-SAMPLE PROBLEMS 76
PROBLEMS 79
4 POWER 81
4.1 HYPOTHESIS TESTING REVISITED 81
4.2 TYPE I AND TYPE II ERRORS 82
4.3 EQUIVALENCE TESTING 91
4.3.1 EQUIVALENCE TESTING EXAMPLE 91
4.3.2 TOST APPROACH TO THE STEGNER ET AL. EXAMPLE 92
4.3.3 EQUIVALENCE TESTING EXAMPLE: CIS APPROACH 94 4.4 OBSERVED POWER
AND NULL RESULTS 94
PROBLEMS 96
5 ANALYSIS OF VARIANCE (ANOVA) 97
5.1 COMPARING THREE POPULATIONS 97
5.2 ANOVA 99
5.2.1 STATISTICAL MODELS 100
5.2.2 VARIANCE OF SAMPLE MEANS AS A POSSIBLE STATISTIC 103 5.2.3
ANALYZING THE VARIANCE 105
5.3 HYPOTHESIS TESTING I LL
5.3.1 MS-WITHIN, MS-BETWEEN AS STATISTICS 112
5.3.2 THE F-DISTRIBUTION 113
5.3.3 ANOVA IN R 118
5.3.4 MS-WITHIN, THREE NON-IDENTICAL POPULATIONS 118 5.3.5 THE
F-DISTRIBUTION WITH UNEQUAL VARIANCES 120
5.4 ANOVA AS A LINEAR MODEL 121
PROBLEMS 125
6 BIVARIATE STATISTICS AND LINEAR MODELS 127
6.1 VARIANCE AND HYPOTHESIS TESTING FOR REGRESSION 137
6.1.1 SUM OF SQUARES AND CORRELATION 142
PROBLEMS 142
7 AN INTRODUCTION TO LINEAR MIXED MODELS 145
7.1 INTRODUCTION 145
7.2 SIMPLE LINEAR MODEL 146
7.3 THE LEVELS OF THE COMPLEX LINEAR MODEL 155
7.4 FURTHER READING 159
IMAGE 3
CONTENTS XV
A RANDOM VARIABLES 161
A.I THE PROBABILITY DISTRIBUTION IN STATISTICAL INFERENCE 162 A.2
EXPECTATION 162
A.3 PROPERTIES OF EXPECTATION 164
A.4 VARIANCE 165
A.5 IMPORTANT PROPERTIES OF VARIANCE 165
A.6 MEAN AND SD OF THE BINOMIAL DISTRIBUTION 166
A.7 SAMPLE VERSUS POPULATION MEANS AND VARIANCES 167 A.8 SUMMING UP 168
PROBLEMS 169
B BASIC R COMMANDS AND DATA STRUCTURES 171
REFERENCES 175
INDEX 177 |
| any_adam_object | 1 |
| author | Vasishth, Shravan Broe, Michael |
| author_facet | Vasishth, Shravan Broe, Michael |
| author_role | aut aut |
| author_sort | Vasishth, Shravan |
| author_variant | s v sv m b mb |
| building | Verbundindex |
| bvnumber | BV037203299 |
| classification_rvk | SK 830 |
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| dewey-full | 001.422 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 001 - Knowledge |
| dewey-raw | 001.422 |
| dewey-search | 001.422 |
| dewey-sort | 11.422 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Allgemeines Mathematik |
| format | Book |
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| indexdate | 2024-07-20T10:57:34Z |
| institution | BVB |
| isbn | 9783642163128 |
| language | English |
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| physical | XV, 178 S. graph. Darst. 24 cm |
| publishDate | 2011 |
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| publisher | Springer |
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| spelling | Vasishth, Shravan Verfasser aut The foundations of statistics a simulation-based approach Shravan Vasishth ; Michael Broe Heidelberg [u.a.] Springer 2011 XV, 178 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 175 - 176 Computersimulation (DE-588)4148259-1 gnd rswk-swf Statistischer Test (DE-588)4077852-6 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s Statistischer Test (DE-588)4077852-6 s Computersimulation (DE-588)4148259-1 s DE-604 Broe, Michael Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-16313-5 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3532047&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021117491&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vasishth, Shravan Broe, Michael The foundations of statistics a simulation-based approach Computersimulation (DE-588)4148259-1 gnd Statistischer Test (DE-588)4077852-6 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4148259-1 (DE-588)4077852-6 (DE-588)4056995-0 |
| title | The foundations of statistics a simulation-based approach |
| title_auth | The foundations of statistics a simulation-based approach |
| title_exact_search | The foundations of statistics a simulation-based approach |
| title_full | The foundations of statistics a simulation-based approach Shravan Vasishth ; Michael Broe |
| title_fullStr | The foundations of statistics a simulation-based approach Shravan Vasishth ; Michael Broe |
| title_full_unstemmed | The foundations of statistics a simulation-based approach Shravan Vasishth ; Michael Broe |
| title_short | The foundations of statistics |
| title_sort | the foundations of statistics a simulation based approach |
| title_sub | a simulation-based approach |
| topic | Computersimulation (DE-588)4148259-1 gnd Statistischer Test (DE-588)4077852-6 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Computersimulation Statistischer Test Statistik |
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