An introduction to statistical inference and its applications with R:
"Emphasizing concepts rather than recipes, An Introduction to Statistical Inference and Its Applications with R provides a clear exposition of the methods of statistical inference for students who are comfortable with mathematical notation. Numerous examples, case studies, and exercises are inc...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2009
|
| Series: | Texts in statistical science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "Emphasizing concepts rather than recipes, An Introduction to Statistical Inference and Its Applications with R provides a clear exposition of the methods of statistical inference for students who are comfortable with mathematical notation. Numerous examples, case studies, and exercises are included. R is used to simplify computation, create figures, and draw pseudorandom samples - not to perform entire analyses. After discussing the importance of chance in experimentation, the text develops basic tools of probability. The plug-in principle then provides a transition from populations to samples, motivating a variety of summary statistics and diagnostic techniques. The heart of the text is a careful exposition of point estimation, hypothesis testing, and confidence intervals. The author then explains procedures for 1- and 2-sample location problems, analysis of variance, goodness-of-fit, and correlation and regression. He concludes by discussing the role of simulation in modern statistical inference."--Publisher's description. |
| Physical Description: | XXVII, 467 S. |
| ISBN: | 9781584889472 |
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MARC
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Record in the Search Index
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Contents
List of Figures
xv
List of Tables
xix
Preface
xxiii
1
Experiments
1
1.1
Examples
. 1
1.1.1
Spinning a Penny
. 2
1.1.2
The Speed of Light
. 3
1.1.3
Termite Foraging Behavior
. 5
1.2
Randomization
. 7
1.3
The Importance of Probability
. 12
1.4
Games of Chance
. 14
1.5
Exercises
. 19
2
Mathematical Preliminaries
23
2.1
Sets
. 23
2.2
Counting
. 27
2.3
Functions
. 34
2.4
Limits
. 35
2.5
Exercises
. 36
3
Probability
43
3.1
Interpretations of Probability
. 43
3.2
Axioms of Probability
. 44
3.3
Finite Sample Spaces
. 52
3.4
Conditional Probability
. 58
3.5
Random Variables
. 69
ix
x
CONTENTS
3.6
Case Study:
Padrolling
in Milton Murayama's All I asking
for is my body
. 77
3.7
Exercises
. 82
4
Discrete Random Variables
89
4.1
Basic Concepts
. 89
4.2
Examples
. 90
4.3
Expectation
. 94
4.4
Binomial Distributions
. 105
4.5
Exercises
. 110
5
Continuous Random Variables
117
5.1
A Motivating Example
. 117
5.2
Basic Concepts
. 120
5.3
Elementary Examples
. 124
5.4
Normal Distributions
. 128
5.5
Normal Sampling Distributions
. 132
5.6
Exercises
. 136
6
Quantifying Population Attributes
141
6.1
Symmetry
. 141
6.2
Quantités
. 143
6.2.1
The Median of a Population
. 146
6.2.2
The Interquartile Range of a Population
. 147
6.3
The Method of Least Squares
. 148
6.3.1
The Mean of a Population
. 148
6.3.2
The Standard Deviation of a Population
. 149
6.4
Exercises
. 150
7
Data
153
7.1
The Plug-In Principle
. 154
7.2
Plug-In Estimates of Mean and Variance
. 156
7.3
Plug-In Estimates of Quantiles
. 158
7.3.1
Box Plots
. 160
7.3.2
Normal Probability Plots
. 163
7.4
Kernel Density Estimates
. 164
7.5
Case Study: Forearm Lengths
. 167
7.6
Transformations
. 173
7.7
Exercises
. 175
CONTENTS xi
8
Lots of Data
181
8.1
Averaging Decreases Variation
.183
8.2
The Weak Law of Large Numbers
.185
8.3
The Central Limit Theorem
.187
8.4
Exercises
.194
9
Inference
197
9.1
A Motivating Example
. 198
9.2
Point Estimation
. 200
9.2.1
Estimating a Population Mean
. 200
9.2.2
Estimating a Population Variance
. 201
9.3
Heuristics of Hypothesis Testing
. 202
9.4
Testing Hypotheses about a Population Mean
. 212
9.4.1
One-Sided Hypotheses
. 216
9.4.2
Formulating Suitable Hypotheses
. 217
9.4.3
Statistical Significance and Material Significance
. . . 221
9.5
Set Estimation
. 222
9.5.1
Sample Size
. 225
9.5.2
One-Sided Confidence Intervals
. 226
9.6
Exercises
. 227
10
1-Sample Location Problems
233
10.1
The Normal 1-Sample Location Problem
.236
10.1.1
Point Estimation
.236
10.1.2
Hypothesis Testing
.237
10.1.3
Set Estimation
.241
10.2
The General 1-Sample Location Problem
.243
10.2.1
Hypothesis Testing
.243
10.2.2
Point Estimation
.246
10.2.3
Set Estimation
.247
10.3
The Symmetric 1-Sample Location Problem
.248
10.3.1
Hypothesis Testing
.249
10.3.2
Point Estimation
.254
10.3.3
Set Estimation
.256
10.4
Case Study: Deficit Unawareness
.257
10.5
Exercises
.262
11
2-Sample Location Problems
269
11.1
The Normal 2-Sample Location Problem
.271
11.1.1
Known Variances
.274
xii CONTENTS
11.1.2
Unknown Common Variance
.275
11.1.3
Unknown Variances
.278
11.2
The Case of a General Shift Family
.282
11.2.1
Hypothesis Testing
.283
11.2.2
Point Estimation
.287
11.2.3
Set Estimation
.289
11.3
Case Study: Etruscan versus Italian Head Breadth
.290
11.4
Exercises
.294
12
The Analysis of Variance
305
12.1
The Fundamental Null Hypothesis
.306
12.2
Testing the Fundamental Null Hypothesis
.307
12.2.1
Known Population Variance
.308
12.2.2
Unknown Population Variance
.309
12.3
Planned Comparisons
.313
12.3.1
Orthogonal Contrasts
.318
12.3.2
Bonferroni
i-Tests
.321
12.4
Post Hoc Comparisons
.323
12.4.1
Bonferroni
i-Tests
.323
12.4.2
Scheffé F-Tests
.324
12.5
Case Study: Treatments of Anorexia
.325
12.6
Exercises
.328
13
Goodness-of-Fit
337
13.1
Partitions
.337
13.2
Test Statistics
.338
13.3
Testing Independence
.341
13.4
Exercises
.344
14
Association
349
14.1
Divariate
Distributions
. 350
14.2
Normal Random Variables
. 351
14.2.1
Divariate
Normal Samples
. 353
14.2.2
Inferences about Correlation
. 357
14.3
Monotonie
Association
. 362
14.4
Explaining Association
. 368
14.5
Case Study: Anorexia Treatments Revisited
. 369
14.6
Exercises
. 372
CONTENTS xiii
15 Simple Linear Regression 379
15.1 The Regression Line.380
15.2
The Method of Least
Squares.385
15.3
Computation
.393
15.4
The Simple Linear Regression Model
.395
15.5
Assessing Linearity
.400
15.6
Case Study: Are Thick Books More Valuable?
.406
15.7
Exercises
.408
16
Simulation-Based Inference
417
16.1
Termite Foraging Revisited
.418
16.2
The Bootstrap
.423
16.3
Case Study: Adventure Racing
.427
16.4
Exercises
.431
R
A Statistical Programming Language
435
R.I Introduction
.435
R.I.I What Is R?
.435
R.1.2 Why Use R?
.435
R.1.3 Installing
R
.436
R.1.4 Learning about
R
.437
R.2 Using
R
.437
R.2.1 Vectors
.438
R.2.2
R
Is a Calculator!
.440
R.2.3 Some Statistics Functions
.440
R.2.4 Matrices
.440
R.2.
5
Creating New Functions
.443
R.3 Functions That Accompany This Book
.445
R.3.1 Inferences about a Center of Symmetry
.446
R.3.
2
Inferences about a Shift Parameter
.449
R.3.3 Inferences about
Monotonie
Association
.452
R.3.
4
Exploring Bivariate Normal Data
.455
R.3.
5
Simulating Random Termite Foraging
.459
Index
463 |
| any_adam_object | 1 |
| author | Trosset, Michael W. |
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| indexdate | 2024-12-06T15:16:47Z |
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| isbn | 9781584889472 |
| language | English |
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| spelling | Trosset, Michael W. Verfasser aut An introduction to statistical inference and its applications with R Michael W. Trosset Boca Raton [u.a.] CRC Press 2009 XXVII, 467 S. txt rdacontent n rdamedia nc rdacarrier Texts in statistical science "Emphasizing concepts rather than recipes, An Introduction to Statistical Inference and Its Applications with R provides a clear exposition of the methods of statistical inference for students who are comfortable with mathematical notation. Numerous examples, case studies, and exercises are included. R is used to simplify computation, create figures, and draw pseudorandom samples - not to perform entire analyses. After discussing the importance of chance in experimentation, the text develops basic tools of probability. The plug-in principle then provides a transition from populations to samples, motivating a variety of summary statistics and diagnostic techniques. The heart of the text is a careful exposition of point estimation, hypothesis testing, and confidence intervals. The author then explains procedures for 1- and 2-sample location problems, analysis of variance, goodness-of-fit, and correlation and regression. He concludes by discussing the role of simulation in modern statistical inference."--Publisher's description. Afleiding (logica) gtt R (computerprogramma) gtt Statistische methoden gtt Mathematical statistics Probabilities R (Computer program language) R Programm (DE-588)4705956-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s R Programm (DE-588)4705956-4 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=017736465&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Trosset, Michael W. An introduction to statistical inference and its applications with R Afleiding (logica) gtt R (computerprogramma) gtt Statistische methoden gtt Mathematical statistics Probabilities R (Computer program language) R Programm (DE-588)4705956-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4056995-0 |
| title | An introduction to statistical inference and its applications with R |
| title_auth | An introduction to statistical inference and its applications with R |
| title_exact_search | An introduction to statistical inference and its applications with R |
| title_full | An introduction to statistical inference and its applications with R Michael W. Trosset |
| title_fullStr | An introduction to statistical inference and its applications with R Michael W. Trosset |
| title_full_unstemmed | An introduction to statistical inference and its applications with R Michael W. Trosset |
| title_short | An introduction to statistical inference and its applications with R |
| title_sort | an introduction to statistical inference and its applications with r |
| topic | Afleiding (logica) gtt R (computerprogramma) gtt Statistische methoden gtt Mathematical statistics Probabilities R (Computer program language) R Programm (DE-588)4705956-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Afleiding (logica) R (computerprogramma) Statistische methoden Mathematical statistics Probabilities R (Computer program language) R Programm Statistik |
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