Contents Part I Descriptive Statistics 1 Introduction and Framework Population, Sample, and Observations Variables Quali

Transcription

1 Part I Descriptive Statistics 1 Introduction and Framework Population, Sample, and Observations Variables Qualitative and Quantitative Variables Discrete and Continuous Variables Scales Grouped Data Data Collection Creating a Data Set Statistical Software Key Points and Further Issues Exercises Frequency Measures and Graphical Representation of Data Absolute and Relative Frequencies Empirical Cumulative Distribution Function ECDF for Ordinal Variables ECDF for Continuous Variables Graphical Representation of a Variable Bar Chart Pie Chart Histogram Kernel Density Plots Key Points and Further Issues Exercises Measures of Central Tendency and Dispersion Measures of Central Tendency Arithmetic Mean Median and Quantiles Quantile Quantile Plots (QQ-Plots) Mode vii

2 viii Geometric Mean Harmonic Mean Measures of Dispersion Range and Interquartile Range Absolute Deviation, Variance, and Standard Deviation Coefficient of Variation Box Plots Measures of Concentration Lorenz Curve Gini Coefficient Key Points and Further Issues Exercises Association of Two Variables Summarizing the Distribution of Two Discrete Variables Contingency Tables for Discrete Data Joint, Marginal, and Conditional Frequency Distributions Graphical Representation of Two Nominal or Ordinal Variables Measures of Association for Two Discrete Variables Pearson s χ 2 Statistic Cramer s V Statistic Contingency Coefficient C Relative Risks and Odds Ratios Association Between Ordinal and Continuous Variables Graphical Representation of Two Continuous Variables Correlation Coefficient Spearman s Rank Correlation Coefficient Measures Using Discordant and Concordant Pairs Visualization of Variables from Different Scales Key Points and Further Issues Exercises Part II Probability Calculus 5 Combinatorics Introduction Permutations Permutations without Replacement Permutations with Replacement Combinations

3 ix Combinations without Replacement and without Consideration of the Order Combinations without Replacement and with Consideration of the Order Combinations with Replacement and without Consideration of the Order Combinations with Replacement and with Consideration of the Order Key Points and Further Issues Exercises Elements of Probability Theory Basic Concepts and Set Theory Relative Frequency and Laplace Probability The Axiomatic Definition of Probability Corollaries Following from Kolomogorov s Axioms Calculation Rules for Probabilities Conditional Probability Bayes Theorem Independence Key Points and Further Issues Exercises Random Variables Random Variables Cumulative Distribution Function (CDF) CDF of Continuous Random Variables CDF of Discrete Random Variables Expectation and Variance of a Random Variable Expectation Variance Quantiles of a Distribution Standardization Tschebyschev s Inequality Bivariate Random Variables Calculation Rules for Expectation and Variance Expectation and Variance of the Arithmetic Mean Covariance and Correlation Covariance Correlation Coefficient Key Points and Further Issues Exercises

4 x 8 Probability Distributions Standard Discrete Distributions Discrete Uniform Distribution Degenerate Distribution Bernoulli Distribution Binomial Distribution Poisson Distribution Multinomial Distribution Geometric Distribution Hypergeometric Distribution Standard Continuous Distributions Continuous Uniform Distribution Normal Distribution Exponential Distribution Sampling Distributions χ 2 -Distribution t-distribution F-Distribution Key Points and Further Issues Exercises Part III Inductive Statistics 9 Inference Introduction Properties of Point Estimators Unbiasedness and Efficiency Consistency of Estimators Sufficiency of Estimators Point Estimation Maximum Likelihood Estimation Method of Moments Interval Estimation Introduction Confidence Interval for the Mean of a Normal Distribution Confidence Interval for a Binomial Probability Confidence Interval for the Odds Ratio Sample Size Determinations Key Points and Further Issues Exercises Hypothesis Testing Introduction Basic Definitions

5 xi One- and Two-Sample Problems Hypotheses One- and Two-Sided Tests Type I and Type II Error How to Conduct a Statistical Test Test Decisions Using the p-value Test Decisions Using Confidence Intervals Parametric Tests for Location Parameters Test for the Mean When the Variance is Known (One-Sample Gauss Test) Test for the Mean When the Variance is Unknown (One-Sample t-test) Comparing the Means of Two Independent Samples Test for Comparing the Means of Two Dependent Samples (Paired t-test) Parametric Tests for Probabilities One-Sample Binomial Test for the Probability p Two-Sample Binomial Test Tests for Scale Parameters Wilcoxon Mann Whitney (WMW) U-Test χ 2 -Goodness-of-Fit Test χ 2 -Independence Test and Other χ 2 -Tests Key Points and Further Issues Exercises Linear Regression The Linear Model Method of Least Squares Properties of the Linear Regression Line Goodness of Fit Linear Regression with a Binary Covariate Linear Regression with a Transformed Covariate Linear Regression with Multiple Covariates Matrix Notation Categorical Covariates Transformations The Inductive View of Linear Regression Properties of Least Squares and Maximum Likelihood Estimators The ANOVA Table Interactions Comparing Different Models Checking Model Assumptions

6 xii Association Versus Causation Key Points and Further Issues Exercises Appendix A: Introduction to R Appendix B: Solutions to Exercises Appendix C: Technical Appendix Appendix D: Visual Summaries References Index

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