Introduction to statistics and data analysis: with exercises, solutions and applications in R
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[Cham]
Springer
[2016]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiii, 456 Seiten Diagramme |
| ISBN: | 9783319461601 |
Internformat
MARC
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| 020 | |a 9783319461601 |c hbk. |9 978-3-319-46160-1 | ||
| 035 | |a (OCoLC)991543841 | ||
| 035 | |a (DE-599)BVBBV044038938 | ||
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| 100 | 1 | |a Heumann, Christian |d 1962- |e Verfasser |0 (DE-588)115847227 |4 aut | |
| 245 | 1 | 0 | |a Introduction to statistics and data analysis |b with exercises, solutions and applications in R |c Christian Heumann, Michael Schomaker, Shalabh |
| 264 | 1 | |a [Cham] |b Springer |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a xiii, 456 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Statistics | |
| 650 | 4 | |a Econometrics | |
| 650 | 4 | |a Macroeconomics | |
| 650 | 4 | |a Statistical Theory and Methods | |
| 650 | 4 | |a Statistics for Business/Economics/Mathematical Finance/Insurance | |
| 650 | 4 | |a Macroeconomics/Monetary Economics//Financial Economics | |
| 650 | 4 | |a Statistik | |
| 650 | 0 | 7 | |a Statistik |0 (DE-588)4056995-0 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Schomaker, Michael |e Verfasser |0 (DE-588)141687967 |4 aut | |
| 700 | 0 | |a Shalabh |e Verfasser |0 (DE-588)171638417 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-319-46162-5 |w (DE-604)BV044023487 |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-029446020 | ||
Datensatz im Suchindex
| _version_ | 1804177048101453824 |
|---|---|
| adam_text | Contents
Part I Descriptive Statistics
1 Introduction and Framework...................................
1.1 Population, Sample, and Observations................
1.2 Variables.........................................
1.2.1 Qualitative and Quantitative Variables.......
1.2.2 Discrete and Continuous Variables............
1.2.3 Scales.......................................
1.2.4 Grouped Data ................................
1.3 Data Collection......................................
1.4 Creating a Data Set..............................
1.4.1 Statistical Software.........................
1.5 Key Points and Further Issues .......................
1.6 Exercises............................................
2 Frequency Measures and Graphical Representation of Data
2.1 Absolute and Relative Frequencies....................
2.2 Empirical Cumulative Distribution Function...........
2.2.1 ECDF for Ordinal Variables...................
2.2.2 ECDF for Continuous Variables................
2.3 Graphical Representation of a Variable...............
2.3.1 Bar Chart....................................
2.3.2 Pie Chart....................................
2.3.3 Histogram....................................
2.4 Kernel Density Plots.................................
2.5 Key Points and Further Issues....................
2.6 Exercises............................................
3 Measures of Central Tendency and Dispersion..................
3.1 Measures of Central Tendency.........................
3.1.1 Arithmetic Mean..............................
3.1.2 Median and Quantiles.........................
3.1.3 Quantile-Quantile Plots (QQ-Plots)...........
3.1.4 Mode.........................................
3
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27
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32
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vii
viii Contents
3.1.5 Geometric Mean......................................... 46
3.1.6 Harmonic Mean.......................................... 48
3.2 Measures of Dispersion......................................... 48
3.2.1 Range and Interquartile Range.......................... 49
3.2.2 Absolute Deviation, Variance, and Standard
Deviation............................................ 50
3.2.3 Coefficient of Variation............................... 55
3.3 Box Plots..................................................... 56
3.4 Measures of Concentration...................................... 57
3.4.1 Lorenz Curve........................................ 58
3.4.2 Gini Coefficient. ..................................... 60
3.5 Key Points and Further Issues ................................. 63
3.6 Exercises...................................................... 63
4 Association of Two Variables. ...................................... 67
4.1 Summarizing the Distribution of Two Discrete Variables...... 68
4.1.1 Contingency Tables for Discrete Data................... 68
4.1.2 Joint, Marginal, and Conditional Frequency
Distributions ......................................... 70
4.1.3 Graphical Representation of Two Nominal or
Ordinal Variables..................................... 72
4.2 Measures of Association for Two Discrete Variables............. 74
4.2.1 Pearson’s x2 Statistic. ............................... 76
4.2.2 Cramer’s V Statistic................................ 77
4.2.3 Contingency Coefficient C.............................. 77
4.2.4 Relative Risks and Odds Ratios........................ 78
4.3 Association Between Ordinal and Continuous Variables........ 79
4.3.1 Graphical Representation of Two Continuous
Variables............................................. 79
4.3.2 Correlation Coefficient. . .......................... 82
4.3.3 Spearman’s Rank Correlation Coefficient................ 84
4.3.4 Measures Using Discordant and Concordant Pairs. ... 86
4.4 Visualization of Variables from Different Scales............... 88
4.5 Key Points and Further Issues.............................. 89
4.6 Exercises.................................................. 90
Part II Probability Calculus
5 Combinatorics....................................................... 97
5.1 Introduction.................................................. 97
5.2 Permutations.................................................. 101
5.2.1 Permutations without Replacement...................... 101
5.2.2 Permutations with Replacement......................... 101
5.3 Combinations................................................. 102
Contents ix
5.3.1 Combinations without Replacement
and without Consideration of the Order.............. 102
5.3.2 Combinations without Replacement
and with Consideration of the Order .............. 103
5.3.3 Combinations with Replacement
and without Consideration of the Order............ 103
5.3.4 Combinations with Replacement
and with Consideration of the Order................. 104
5.4 Key Points and Further Issues................................ 105
5.5 Exercises.................................................... 105
6 Elements of Probability Theory.................................... 109
6.1 Basic Concepts and Set Theory................................ 109
6.2 Relative Frequency and Laplace Probability................... 113
6.3 The Axiomatic Definition of Probability...................... 115
6.3.1 Corollaries Following from Kolomogorov’s
Axioms.............................................. 116
6.3.2 Calculation Rules for Probabilities.................. 117
6.4 Conditional Probability...................................... 117
6.4.1 Bayes’ Theorem..................................... 120
6.5 Independence................................................. 121
6.6 Key Points and Further Issues................................ 123
6.7 Exercises.................................................. 123
7 Random Variables.................................................. 127
7.1 Random Variables............................................. 127
7.2 Cumulative Distribution Function (CDF)....................... 129
7.2.1 CDF of Continuous Random Variables................... 129
7.2.2 CDF of Discrete Random Variables..................... 131
7.3 Expectation and Variance of a Random Variable................ 134
7.3.1 Expectation.......................................... 134
7.3.2 Variance............................................. 135
7.3.3 Quantiles of a Distribution.......................... 137
7.3.4 Standardization...................................... 138
7.4 Tschebyschev’s Inequality.................................... 139
7.5 Bivariate Random Variables................................... 140
7.6 Calculation Rules for Expectation and Variance............... 144
7.6.1 Expectation and Variance of the Arithmetic Mean ... 145
7.7 Covariance and Correlation................................... 146
7.7.1 Covariance........................................... 147
7.7.2 Correlation Coefficient.............................. 148
7.8 Key Points and Further Issues................................ 149
7.9 Exercises.................................................... 149
X
Contents
8 Probability Distributions. ............................................. 153
8.1 Standard Discrete Distributions. . . .......................... 154
8.1.1 Discrete Uniform Distribution.......................... 154
8.1.2 Degenerate Distribution................................ 156
8.1.3 Bernoulli Distribution................................. 156
8.1.4 Binomial Distribution................................ 157
8.1.5 Poisson Distribution................................... 160
8.1.6 Multinomial Distribution............................... 161
8.1.7 Geometric Distribution................................. 163
8.1.8 Hypergeometrie Distribution............................ 163
8.2 Standard Continuous Distributions . ......................... 165
8.2.1 Continuous Uniform Distribution........................ 165
8.2.2 Normal Distribution. .................................. 166
8.2.3 Exponential Distribution............................. 170
8.3 Sampling Distributions............ .......................... 171
8.3.1 x2-Distribution........................................ 171
8.3.2 i-Distribution..........................*............ 172
8.3.3 F-Distribution......... . ........................... 173
8.4 Key Points and Further Issues................................ 174
8.5 Exercises.................................................... 175
Part III Inductive Statistics
9 Inference............................. . . ........................... 181
9.1 Introduction................................................. 181
9.2 Properties of Point Estimators................................ 183
9.2.1 Unbiasedness and Efficiency ........................... 183
9.2.2 Consistency of Estimators............................ 189
9.2.3 Sufficiency of Estimators. ............................ 190
9.3 Point Estimation ........ ................................... 192
9.3.1 Maximum Likelihood Estimation......................... 192
9.3.2 Method of Moments . ................................... 195
9.4 Interval Estimation......................................... 195
9.4.1 Introduction. . ..................................... 195
9.4.2 Confidence Interval for the Mean of a Normal
Distribution........................................ 197
9.4.3 Confidence Interval for a Binomial Probability....... 199
9.4.4 Confidence Interval for the Odds Ratio ............ 201
9.5 Sample Size Determinations.................................... . 203
9.6 Key Points and Further Issues................................. 205
9.7 Exercises...................................................... 205
10 Hypothesis Testing.................................................. 209
10.1 Introduction.................................................. 209
10.2 Basic Definitions. . .......................................... 210
Contents
XI
10.2.1 One- and Two-Sample Problems....................... 210
10.2.2 Hypotheses......................................... 210
10.2.3 One- and Two-Sided Tests........................... 211
10.2.4 Type I and Type II Error........................... 213
10.2.5 How to Conduct a Statistical Test.................. 214
10.2.6 Test Decisions Using the /7-Value.................. 215
10.2.7 Test Decisions Using Confidence Intervals.......... 216
10.3 Parametric Tests for Location Parameters................... 216
10.3.1 Test for the Mean When the Variance
is Known (One-Sample Gauss Test)................. 216
10.3.2 Test for the Mean When the Variance
is Unknown (One-Sample f-Test)................... 219
10.3.3 Comparing the Means of Two Independent
Samples............................................ 221
10.3.4 Test for Comparing the Means
of Two Dependent Samples (Paired t-Test)......... 225
10.4 Parametric Tests for Probabilities......................... 227
10.4.1 One-Sample Binomial Test for the Probability p... 227
10.4.2 Two-Sample Binomial Test........................... 230
10.5 Tests for Scale Parameters................................. 232
10.6 Wilcoxon—Mann—Whitney (WMW) U-Test......................... 232
10.7 x2-Goodness-of-Fit Test.................................... 235
10.8 x2-Independence Test and Other x2-Tests.................... 238
10.9 Key Points and Further Issues.............................. 242
10.10 Exercises................................................ 242
11 Linear Regression................................................. 249
11.1 The Linear Model........................................... 250
11.2 Method of Least Squares.................................... 252
11.2.1 Properties of the Linear Regression Line........... 255
11.3 Goodness of Fit............................................ 256
11.4 Linear Regression with a Binary Covariate.................. 259
11.5 Linear Regression with a Transformed Covariate............. 261
11.6 Linear Regression with Multiple Covariates................. 262
11.6.1 Matrix Notation.................................... 263
11.6.2 Categorical Covariates............................. 265
11.6.3 Transformations.................................... 267
11.7 The Inductive View of Linear Regression.................... 269
11.7.1 Properties of Least Squares and Maximum
Likelihood Estimators.............................. 273
11.7.2 The ANOVA Table.................................... 274
11.7.3 Interactions....................................... 276
11.8 Comparing Different Models................................. 280
11.9 Checking Model Assumptions................................. 285
Contents
xii
11.10 Association Versus Causation............................... 288
11.11 Key Points and Further Issues.......................... 289
11.12 Exercises. . . .......................................... 290
Appendix A: Introduction to R.......................................... 297
Appendix B: Solutions to Exercises................................... 321
Appendix C: Technical Appendix ........................................ 423
Appendix D: Visual Summaries. ......................................... 443
References............................................................. 449
Index............................................................ 451
|
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| spelling | Heumann, Christian 1962- Verfasser (DE-588)115847227 aut Introduction to statistics and data analysis with exercises, solutions and applications in R Christian Heumann, Michael Schomaker, Shalabh [Cham] Springer [2016] © 2016 xiii, 456 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Statistics Econometrics Macroeconomics Statistical Theory and Methods Statistics for Business/Economics/Mathematical Finance/Insurance Macroeconomics/Monetary Economics//Financial Economics Statistik Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s DE-604 Schomaker, Michael Verfasser (DE-588)141687967 aut Shalabh Verfasser (DE-588)171638417 aut Erscheint auch als Online-Ausgabe 978-3-319-46162-5 (DE-604)BV044023487 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029446020&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Heumann, Christian 1962- Schomaker, Michael Shalabh Introduction to statistics and data analysis with exercises, solutions and applications in R Statistics Econometrics Macroeconomics Statistical Theory and Methods Statistics for Business/Economics/Mathematical Finance/Insurance Macroeconomics/Monetary Economics//Financial Economics Statistik Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4151278-9 |
| title | Introduction to statistics and data analysis with exercises, solutions and applications in R |
| title_auth | Introduction to statistics and data analysis with exercises, solutions and applications in R |
| title_exact_search | Introduction to statistics and data analysis with exercises, solutions and applications in R |
| title_full | Introduction to statistics and data analysis with exercises, solutions and applications in R Christian Heumann, Michael Schomaker, Shalabh |
| title_fullStr | Introduction to statistics and data analysis with exercises, solutions and applications in R Christian Heumann, Michael Schomaker, Shalabh |
| title_full_unstemmed | Introduction to statistics and data analysis with exercises, solutions and applications in R Christian Heumann, Michael Schomaker, Shalabh |
| title_short | Introduction to statistics and data analysis |
| title_sort | introduction to statistics and data analysis with exercises solutions and applications in r |
| title_sub | with exercises, solutions and applications in R |
| topic | Statistics Econometrics Macroeconomics Statistical Theory and Methods Statistics for Business/Economics/Mathematical Finance/Insurance Macroeconomics/Monetary Economics//Financial Economics Statistik Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistics Econometrics Macroeconomics Statistical Theory and Methods Statistics for Business/Economics/Mathematical Finance/Insurance Macroeconomics/Monetary Economics//Financial Economics Statistik Einführung |
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