Introduction to Statistics and Data Analysis: With Exercises, Solutions and Applications in R

✍ Scribed by Heumann, Christian;Schomaker, Michael;Shalabh

• Publisher: Springer International Publishing AG
• Year: 2017
• Tongue: English
• Leaves: 457
• Category: Library

✦ Synopsis

This introductory statistics textbook conveys the essential concepts and tools needed to develop and nurture statistical thinking. It presents descriptive, inductive and explorative statistical methods and guides the reader through the process of quantitative data analysis. In the experimental sciences and interdisciplinary research, data analysis has become an integral part of any scientific study. Issues such as judging the credibility of data, analyzing the data, evaluating the reliability of the obtained results and finally drawing the correct and appropriate conclusions from the results are vital.

The text is primarily intended for undergraduate students in disciplines like business administration, the social sciences, medicine, politics, macroeconomics, etc. It features a wealth of examples, exercises and solutions with computer code in the statistical programming language R as well as supplementary material that will enable the reader to quickly adapt all methods to their own applications.

✦ Table of Contents

Preface......Page 5
Contents......Page 7
About the Authors......Page 13
Part I Descriptive Statistics......Page 14
1.1 Population, Sample, and Observations......Page 15
1.2 Variables......Page 16
1.2.1 Qualitative and Quantitative Variables......Page 17
1.2.3 Scales......Page 18
1.2.4 Grouped Data......Page 19
1.3 Data Collection......Page 20
1.4 Creating a Data Set......Page 21
1.4.1 Statistical Software......Page 24
1.5 Key Points and Further Issues......Page 25
1.6 Exercises......Page 26
2.1 Absolute and Relative Frequencies......Page 28
2.2 Empirical Cumulative Distribution Function......Page 30
2.2.1 ECDF for Ordinal Variables......Page 31
2.2.2 ECDF for Continuous Variables......Page 33
2.3.1 Bar Chart......Page 35
2.3.2 Pie Chart......Page 37
2.3.3 Histogram......Page 38
2.4 Kernel Density Plots......Page 40
2.5 Key Points and Further Issues......Page 42
2.6 Exercises......Page 43
3 Measures of Central Tendency and Dispersion......Page 47
3.1.1 Arithmetic Mean......Page 48
3.1.2 Median and Quantiles......Page 50
3.1.3 Quantile--Quantile Plots (QQ-Plots)......Page 54
3.1.4 Mode......Page 55
3.1.5 Geometric Mean......Page 56
3.2 Measures of Dispersion......Page 58
3.2.1 Range and Interquartile Range......Page 59
3.2.2 Absolute Deviation, Variance, and Standard Deviation......Page 60
3.2.3 Coefficient of Variation......Page 65
3.3 Box Plots......Page 66
3.4 Measures of Concentration......Page 67
3.4.1 Lorenz Curve......Page 68
3.4.2 Gini Coefficient......Page 70
3.5 Key Points and Further Issues......Page 72
3.6 Exercises......Page 73
4 Association of Two Variables......Page 77
4.1.1 Contingency Tables for Discrete Data......Page 78
4.1.2 Joint, Marginal, and Conditional Frequency Distributions......Page 80
4.1.3 Graphical Representation of Two Nominal or Ordinal Variables......Page 82
4.2 Measures of Association for Two Discrete Variables......Page 84
4.2.1 Pearson's χ2 Statistic......Page 86
4.2.3 Contingency Coefficient C......Page 87
4.2.4 Relative Risks and Odds Ratios......Page 88
4.3.1 Graphical Representation of Two Continuous Variables......Page 89
4.3.2 Correlation Coefficient......Page 92
4.3.3 Spearman's Rank Correlation Coefficient......Page 94
4.3.4 Measures Using Discordant and Concordant Pairs......Page 96
4.4 Visualization of Variables from Different Scales......Page 98
4.5 Key Points and Further Issues......Page 99
4.6 Exercises......Page 100
Part II Probability Calculus......Page 105
5.1 Introduction......Page 106
5.2 Permutations......Page 109
5.2.2 Permutations with Replacement......Page 110
5.3.1 Combinations without Replacement and without Consideration of the Order......Page 111
5.3.3 Combinations with Replacement and without Consideration of the Order......Page 112
5.3.4 Combinations with Replacement and with Consideration of the Order......Page 113
5.5 Exercises......Page 114
6.1 Basic Concepts and Set Theory......Page 117
6.2 Relative Frequency and Laplace Probability......Page 121
6.3 The Axiomatic Definition of Probability......Page 123
6.3.1 Corollaries Following from Kolomogorov's Axioms......Page 124
6.4 Conditional Probability......Page 125
6.4.1 Bayes' Theorem......Page 128
6.5 Independence......Page 129
6.7 Exercises......Page 131
7.1 Random Variables......Page 134
7.2.1 CDF of Continuous Random Variables......Page 136
7.2.2 CDF of Discrete Random Variables......Page 138
7.3.1 Expectation......Page 141
7.3.2 Variance......Page 142
7.3.3 Quantiles of a Distribution......Page 144
7.3.4 Standardization......Page 145
7.4 Tschebyschev's Inequality......Page 146
7.5 Bivariate Random Variables......Page 147
7.6 Calculation Rules for Expectation and Variance......Page 151
7.6.1 Expectation and Variance of the Arithmetic Mean......Page 152
7.7 Covariance and Correlation......Page 153
7.7.1 Covariance......Page 154
7.7.2 Correlation Coefficient......Page 155
7.9 Exercises......Page 156
8 Probability Distributions......Page 160
8.1.1 Discrete Uniform Distribution......Page 161
8.1.3 Bernoulli Distribution......Page 163
8.1.4 Binomial Distribution......Page 164
8.1.5 Poisson Distribution......Page 167
8.1.6 Multinomial Distribution......Page 168
8.1.8 Hypergeometric Distribution......Page 170
8.2.1 Continuous Uniform Distribution......Page 172
8.2.2 Normal Distribution......Page 173
8.2.3 Exponential Distribution......Page 177
8.3.1 χ2-Distribution......Page 178
8.3.2 t-Distribution......Page 179
8.3.3 F-Distribution......Page 180
8.4 Key Points and Further Issues......Page 181
8.5 Exercises......Page 182
Part III Inductive Statistics......Page 186
9.1 Introduction......Page 187
9.2 Properties of Point Estimators......Page 188
9.2.1 Unbiasedness and Efficiency......Page 189
9.2.2 Consistency of Estimators......Page 195
9.2.3 Sufficiency of Estimators......Page 196
9.3.1 Maximum Likelihood Estimation......Page 198
9.4.1 Introduction......Page 201
9.4.2 Confidence Interval for the Mean of a Normal Distribution......Page 203
9.4.3 Confidence Interval for a Binomial Probability......Page 205
9.4.4 Confidence Interval for the Odds Ratio......Page 207
9.5 Sample Size Determinations......Page 209
9.7 Exercises......Page 211
10.1 Introduction......Page 215
10.2.2 Hypotheses......Page 216
10.2.3 One- and Two-Sided Tests......Page 217
10.2.4 Type I and Type II Error......Page 219
10.2.5 How to Conduct a Statistical Test......Page 220
10.2.6 Test Decisions Using the p-Value......Page 221
10.3.1 Test for the Mean When the Variance is Known (One-Sample Gauss Test)......Page 222
10.3.2 Test for the Mean When the Variance is Unknown (One-Sample t-Test)......Page 225
10.3.3 Comparing the Means of Two Independent Samples......Page 227
10.3.4 Test for Comparing the Means of Two Dependent Samples (Paired t-Test)......Page 231
10.4.1 One-Sample Binomial Test for the Probability p......Page 233
10.4.2 Two-Sample Binomial Test......Page 236
10.6 Wilcoxon--Mann--Whitney (WMW) U-Test......Page 238
10.7 χ2-Goodness-of-Fit Test......Page 241
10.8 χ2-Independence Test and Other χ2-Tests......Page 244
10.9 Key Points and Further Issues......Page 247
10.10 Exercises......Page 248
11 Linear Regression......Page 254
11.1 The Linear Model......Page 255
11.2 Method of Least Squares......Page 257
11.2.1 Properties of the Linear Regression Line......Page 260
11.3 Goodness of Fit......Page 261
11.4 Linear Regression with a Binary Covariate......Page 264
11.5 Linear Regression with a Transformed Covariate......Page 266
11.6 Linear Regression with Multiple Covariates......Page 267
11.6.1 Matrix Notation......Page 268
11.6.2 Categorical Covariates......Page 270
11.6.3 Transformations......Page 272
11.7 The Inductive View of Linear Regression......Page 274
11.7.1 Properties of Least Squares and Maximum Likelihood Estimators......Page 278
11.7.2 The ANOVA Table......Page 279
11.7.3 Interactions......Page 281
11.8 Comparing Different Models......Page 285
11.9 Checking Model Assumptions......Page 290
11.10 Association Versus Causation......Page 293
11.11 Key Points and Further Issues......Page 294
11.12 Exercises......Page 295
Background......Page 301
Installation and Basic Functionalities......Page 302
Statistical Functions......Page 313
Data Sets......Page 321
B Appendix:Solutions to Exercises......Page 324
More details on Chap. 3......Page 425
More details on Chap. 8......Page 426
More details on Chap. 10......Page 429
More details on Chap. 11......Page 436
Distribution Tables......Page 437
Summary of Tests for Nominal Variables......Page 445
References......Page 451
Index......Page 452