Probability, Statistics, and Data: A Fresh Approach Using R

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
	Software Installation
1. Data in R
	1.1. Arithmetic and variable assignment
	1.2. Help
	1.3. Vectors
	1.4. Indexing vectors
	1.5. Data types
	1.6. Data frames
	1.7. Reading data from files
	1.8. Packages
	1.9. Errors and warnings
	1.10. Useful idioms
	Vignette: Data science communities
	Vignette: An R Markdown primer
	Exercises
2. Probability
	2.1. Probability basics
	2.2. Simulations
	2.3. Conditional probability and independence
	2.4. Counting arguments
	Vignette: Negative surveys
	Exercises
3. Discrete Random Variables
	3.1. Probability mass functions
	3.2. Expected value
	3.3. Binomial and geometric random variables
	3.4. Functions of a random variable
	3.5. Variance, standard deviation, and independence
	3.6. Poisson, negative binomial, and hypergeometric
	Vignette: Loops in R
	Exercises
4. Continuous Random Variables
	4.1. Probability density functions
	4.2. Expected value
	4.3. Variance and standard deviation
	4.4. Normal random variables
	4.5. Uniform and exponential random variables
	4.6. Summary
	Exercises
5. Simulation of Random Variables
	5.1. Estimating probabilities
	5.2. Estimating discrete distributions
	5.3. Estimating continuous distributions
	5.4. Central Limit Theorem
	5.5. Sampling distributions
	5.6. Point estimators
	Vignette: Stein’s paradox
	Exercises
6. Data Manipulation
	6.1. Data frames and tibbles
	6.2. dplyr verbs
	6.3. dplyr pipelines
	6.4. The power of dplyr
	6.5. Working with character strings
	6.6. Structure of data
	6.7. The apply family
	Vignette: dplyr murder mystery
	Vignette: Data and gender
	Exercises
7. Data Visualization with ggplot
	7.1. ggplot fundamentals
	7.2. Visualizing a single variable
	7.3. Visualizing two or more variables
	7.4. Customizing
	Vignette: Choropleth maps
	Vignette: COVID-19
	Exercises
8. Inference on the Mean
	8.1. Sampling distribution of the sample mean
	8.2. Confidence intervals for the mean
	8.3. Hypothesis tests of the mean
	8.4. One-sided confidence intervals and hypothesis tests
	8.5. Assessing robustness via simulation
	8.6. Two sample hypothesis tests
	8.7. Type II errors and power
	8.8. Resampling
	Exercises
9. Rank Based Tests
	9.1. One sample Wilcoxon signed rank test
	9.2. Two sample Wilcoxon tests
	9.3. Power and sample size
	9.4. Effect size and consistency
	9.5. Summary
	Vignette: ROC curves and the Wilcoxon rank sum statistic
	Exercises
10. Tabular Data
	10.1. Tables and plots
	10.2. Inference on a proportion
	10.3. X2 tests
	10.4. X2 goodness of fit
	10.5. X2 tests on cross tables
	10.6. Exact and Monte Carlo methods
	Vignette: Tables
	Exercises
11. Simple Linear Regression
	11.1. Least squares regression line
	11.2. Correlation
	11.3. Geometry of regression
	11.4. Residual analysis
	11.5. Inference
	11.6. Simulations for simple linear regression
	11.7. Cross validation
	11.8. Bias-variance tradeoff
	Vignette: Simple logistic regression
	Exercises
12. Analysis of Variance and Comparison of Multiple Groups
	12.1. ANOVA
	12.2. The ANOVA test
	12.3. Unequal variance
	12.4. Pairwise
	Vignette: Reproducibility
	Exercises
13. Multiple Regression
	13.1. Two explanatory variables
	13.2. Categorical variables
	13.3. Variable selection
	Vignette: External data formats
	Exercises
Image Credits
Index
Index of Data Sets and Packages