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

✍ Scribed by Christian Heumann, Michael Schomaker, Shalabh

• Publisher: Springer
• Year: 2017
• Tongue: English
• Leaves: 457
• Edition: 1st ed. 2016
• 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
Contents
About the Authors
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
3.1.5 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 Continuous Variables
4.3.1 Graphical Representation of Two Continuous 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 II Probability 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 Poisson Distribution
8.1.6 Multinomial Distribution
8.1.7 Geometric Distribution
8.1.8 Hypergeometric Distribution
8.2 Standard Continuous Distributions
8.2.1 Continuous Uniform Distribution
8.2.2 Normal Distribution
8.2.3 Exponential Distribution
8.3 Sampling Distributions
8.3.1 χ2-Distribution
8.3.2 t-Distribution
8.3.3 F-Distribution
8.4 Key Points and Further Issues
8.5 Exercises
Part III Inductive 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
9.6 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 Key Points and Further Issues
10.10 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
A Appendix:Introduction to R
Background
Installation and Basic Functionalities
Statistical Functions
Data Sets
B Solutions to Exercises
C Technical Appendix
More details on Chap. 3
More details on Chap. 7
More details on Chap. 8
More details on Chap. 9
More details on Chap. 10
More details on Chap. 11
Distribution Tables
D Visual Summaries
Descriptive Data Analysis
Summary of Tests for Continuous and Ordinal Variables
Summary of Tests for Nominal Variables
References
Index