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

Preface to the Second Edition
Preface to the First Edition
Contents
About the Authors
Part IDescriptive 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
		1.3.1 Survey
		1.3.2 Experiment
		1.3.3 Observational Data
		1.3.4 Primary and Secondary Data
	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
		2.1.1 Discrete Data
		2.1.2 Grouped Metric Data
	2.2 Empirical Cumulative Distribution Function
		2.2.1 ECDF for Ordinal Variables
		2.2.2 ECDF for Metric 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
		3.1.5 Geometric Mean
		3.1.6 Harmonic Mean
	3.2 Measures of Dispersion
		3.2.1 Range and Interquartile Range
		3.2.2 Absolute Deviation, Variance and Standard Deviation
		3.2.3 Coefficient of Variation
	3.3 Box Plots
	3.4 Measures of Concentration
		3.4.1 Lorenz Curve
		3.4.2 Gini Coefficient
	3.5 Key Points and Further Issues
	3.6 Exercises
4 Association of Two Variables
	4.1 Summarizing the Distribution of Two Discrete Variables
		4.1.1 Contingency Tables for Discrete Data
		4.1.2 Joint, Marginal, and Conditional Frequency Distributions
		4.1.3 Graphical Representation of Two Nominal or Ordinal Variables
	4.2 Measures of Association for Two Discrete Variables
		4.2.1 Pearson\'s χ2 Statistic
		4.2.2 Cramer\'s V Statistic
		4.2.3 Contingency Coefficient C
		4.2.4 Relative Risks and Odds Ratios
	4.3 Association Between Ordinal and Metrical Variables
		4.3.1 Graphical Representation of Two Metrical Variables
		4.3.2 Correlation Coefficient
		4.3.3 Spearman\'s Rank Correlation Coefficient
		4.3.4 Measures Using Discordant and Concordant Pairs
	4.4 Visualization of Variables from Different Scales
	4.5 Key Points and Further Issues
	4.6 Exercises
Part IIProbability Calculus
5 Combinatorics
	5.1 Introduction
	5.2 Permutations
		5.2.1 Permutations Without Replacement
		5.2.2 Permutations with Replacement
	5.3 Combinations
		5.3.1 Combinations Without Replacement and Without Consideration of the Order
		5.3.2 Combinations Without Replacement and with Consideration of the Order
		5.3.3 Combinations with Replacement and Without Consideration of the Order
		5.3.4 Combinations with Replacement and with Consideration of the Order
	5.4 Key Points and Further Issues
	5.5 Exercises
6 Elements of Probability Theory
	6.1 Basic Concepts and Set Theory
	6.2 Relative Frequency and Laplace Probability
	6.3 The Axiomatic Definition of Probability
		6.3.1 Corollaries Following from Kolomogorov\'s Axioms
		6.3.2 Calculation Rules for Probabilities
	6.4 Conditional Probability
		6.4.1 Bayes\' Theorem
	6.5 Independence
	6.6 Key Points and Further Issues
	6.7 Exercises
7 Random Variables
	7.1 Random Variables
	7.2 Cumulative Distribution Function (CDF)
		7.2.1 CDF of Continuous Random Variables
		7.2.2 CDF of Discrete Random Variables
	7.3 Expectation and Variance of a Random Variable
		7.3.1 Expectation
		7.3.2 Variance
		7.3.3 Quantiles of a Distribution
		7.3.4 Standardization
	7.4 Tschebyschev\'s Inequality
	7.5 Bivariate Random Variables
	7.6 Calculation Rules for Expectation and Variance
		7.6.1 Expectation and Variance of the Arithmetic Mean
	7.7 Covariance and Correlation
		7.7.1 Covariance
		7.7.2 Correlation Coefficient
	7.8 Key Points and Further Issues
	7.9 Exercises
8 Probability Distributions
	8.1 Standard Discrete Distributions
		8.1.1 Discrete Uniform Distribution
		8.1.2 Degenerate Distribution
		8.1.3 Bernoulli Distribution
		8.1.4 Binomial Distribution
		8.1.5 The Poisson Distribution
		8.1.6 The Multinomial Distribution
		8.1.7 The Geometric Distribution
		8.1.8 Hypergeometric Distribution
	8.2 Standard Continuous Distributions
		8.2.1 Continuous Uniform Distribution
		8.2.2 The Normal Distribution
		8.2.3 The Exponential Distribution
	8.3 Sampling Distributions
		8.3.1 The χ2-Distribution
		8.3.2 The t-Distribution
		8.3.3 The F-Distribution
	8.4 Key Points and Further Issues
	8.5 Exercises
Part IIIInductive Statistics
9 Inference
	9.1 Introduction
	9.2 Properties of Point Estimators
		9.2.1 Unbiasedness and Efficiency
		9.2.2 Consistency of Estimators
		9.2.3 Sufficiency of Estimators
	9.3 Point Estimation
		9.3.1 Maximum Likelihood Estimation
		9.3.2 Method of Moments
	9.4 Interval Estimation
		9.4.1 Introduction
		9.4.2 Confidence Interval for the Mean of a Normal Distribution
		9.4.3 Confidence Interval for a Binomial Probability
		9.4.4 Confidence Interval for the Odds Ratio
	9.5 Sample Size Determinations
		9.5.1 Sample Size Calculation for µ
		9.5.2 Sample Size Calculation for p
	9.6 Key Points and Further Issues
	9.7 Exercises
10 Hypothesis Testing
	10.1 Introduction
	10.2 Basic Definitions
		10.2.1 One- and Two- Sample Problems
		10.2.2 Hypotheses
		10.2.3 One- and Two-Sided Tests
		10.2.4 Type I and Type II Error
		10.2.5 How to Conduct a Statistical Test
		10.2.6 Test Decisions Using the p-Value
		10.2.7 Test Decisions Using Confidence Intervals
	10.3 Parametric Tests for Location Parameters
		10.3.1 Test for the Mean When the Variance is Known (One-Sample Gauss-Test)
		10.3.2 Test for the Mean When the Variance is Unknown (One-Sample t-Test)
		10.3.3 Comparing the Means of Two Independent Samples
		10.3.4 Test for Comparing the Means of Two Dependent Samples (Paired t-Test)
	10.4 Parametric Tests for Probabilities
		10.4.1 One-Sample Binomial Test for the Probability p
		10.4.2 Two-Sample Binomial Test
	10.5 Tests for Scale Parameters
	10.6 Wilcoxon–Mann–Whitney (WMW) U-Test
	10.7 χ2-Goodness of Fit Test
	10.8 χ2-Independence Test and Other χ2-Tests
	10.9 Beyond Dichotomies
		10.9.1 Compatibility
		10.9.2 The S-Value
		10.9.3 Graphs of p- and S-Values
		10.9.4 Unconditional Interpretations
	10.10 Key Points and Further Issues
	10.11 Exercises
11 Linear Regression
	11.1 The Linear Model
	11.2 Method of Least Squares
		11.2.1 Properties of the Linear Regression Line
	11.3 Goodness of Fit
	11.4 Linear Regression with a Binary Covariate
	11.5 Linear Regression with a Transformed Covariate
	11.6 Linear Regression with Multiple Covariates
		11.6.1 Matrix Notation
		11.6.2 Categorical Covariates
		11.6.3 Transformations
	11.7 The Inductive View of Linear Regression
		11.7.1 Properties of Least Squares and Maximum Likelihood Estimators
		11.7.2 The ANOVA Table
		11.7.3 Interactions
	11.8 Comparing Different Models
	11.9 Checking Model Assumptions
	11.10 Association Versus Causation
	11.11 Key Points and Further Issues
	11.12 Exercises
12 Logistic Regression
	12.1 Parameter Interpretation
	12.2 Estimation of Parameters and Predictions
	12.3 Logistic Regression in R
	12.4 Model Selection and Goodness-of-Fit
	12.5 Key Points and Further Issues
	12.6 Exercises
Part IVAdditional Topics
13 Simple Random Sampling and Bootstrapping
	13.1 Introduction
	13.2 Methodology of Simple Random Sampling
		13.2.1 Procedure of Selection of a Random Sample
		13.2.2 Probabilities of Selection
	13.3 Estimation of the Population Mean and Population Variance
		13.3.1 Estimation of the Population Total
		13.3.2 Confidence Interval for the Population Mean
	13.4 Sampling for Proportions
		13.4.1 Estimation of the Total Count
		13.4.2 Confidence Interval Estimation of P
	13.5 Bootstrap Methodology
	13.6 Nonparametric Bootstrap Methodology
		13.6.1 The Empirical Distribution Function
		13.6.2 The Plug-in Principle
		13.6.3 Steps in Applying the Bootstrap
		13.6.4 Bootstrap Estimator and Bootstrap Variance
		13.6.5 Bootstrap Estimate of the Bias and Standard Error
		13.6.6 Bootstrap Confidence Intervals
	13.7 Key Points and Further Issues
	13.8 Exercises
14 Causality
	14.1 Potential Outcomes
	14.2 Causal Questions
	14.3 The Causal Model: Directed Acyclic Graphs
		14.3.1 Confounders and Confounding
		14.3.2 Colliders
		14.3.3 Mediators
	14.4 Identification
		14.4.1 Randomization
	14.5 The Statistical Model: Estimation
		14.5.1 The g-formula
		14.5.2 Regression
	14.6 Roadmap
	14.7 Key Points and Further Issues
	14.8 Exercises
A Introduction to R
	A.1  Background
	A.2  Installation and Basic Functionalities
	A.3  Statistical Functions
	A.4  Data Sets
		A.4.1 Pizza Delivery Data
		A.4.2  Decathlon Data
		A.4.3  Theatre Data
		A.4.4  Cattaneo Data
B Solutions to Exercises
C Technical Appendix
	C.1  More Details on Chap.3摥映數爠eflinkchapter333
	C.2  More Details on Chap.7摥映數爠eflinkchapter777
	C.3  More Details on Chap.8摥映數爠eflinkchapter888
	C.4  More Details on Chap.9摥映數爠eflinkchapter999
	C.5  More Details on Chap.10摥映數爠eflinkchapter101010
	C.6  More Details on Chap.11摥映數爠eflinkchapter111111
	C.7  More Details on Chap.12摥映數爠eflinkchapter121212
	C.8  More Details on Chap.13摥映數爠eflinkchapter131313
	C.9  Distribution Tables
D Visual Summaries
	D.1  Descriptive Data Analysis
	D.2  Summary of Tests for Metric and Ordinal Variables
	D.3  Summary of Tests for Nominal Variables
References
Index