PROBABILITY AND STATISTICS WITH R, 2ND EDITION

What Is R?
Introduction to R
Downloading and Installing R
Vectors
Mode and Class of an Object
Getting Help
External Editors
RStudio
Packages
R Data Structures
Reading and Saving Data in R
Working with Data
Using Logical Operators with Data Frames
Tables
Summarizing Functions
Probability Functions
Flow Control
Creating Functions
Simple Imputation
Using plot()
Coordinate Systems and Traditional Graphic’s States

Exploring Data
What Is Statistics?
Data
Displaying Qualitative Data
Displaying Quantitative Data
Summary Measures of Location
Summary Measures of Spread
Bivariate Data
Complex Plot Arrangements
Multivariate Data

General Probability and Random Variables
Introduction
Counting Techniques
Axiomatic Probability
Random Variables
Moment Generating Functions

Univariate Probability Distributions
Introduction
Discrete Univariate Distributions
Continuous Univariate Distributions

Multivariate Probability Distributions
Joint Distribution of Two Random Variables
Independent Random Variables
Several Random Variables
Conditional Distributions
Expected Values, Covariance, and Correlation
Multinomial Distribution
Bivariate Normal Distribution

Sampling and Sampling Distributions
Sampling
Parameters
Estimators
Sampling Distribution of the Sample Mean
Sampling Distribution for a Statistic from an Infinite Population
Sampling Distributions Associated with the Normal Distribution

Point Estimation
Introduction
Properties of Point Estimators
Point Estimation Techniques

Confidence Intervals
Introduction
Confidence Intervals for Population Means
Confidence Intervals for Population Variances
Confidence Intervals Based on Large Samples

Hypothesis Testing
Introduction
Type I and Type II Errors
Power Function
Uniformly Most Powerful Test
?-Value or Critical Level
Tests of Significance
Hypothesis Tests for Population Means
Hypothesis Tests for Population Variances
Hypothesis Tests for Population Proportions

Nonparametric Methods
Introduction
Sign Test
Wilcoxon Signed-Rank Test
The Wilcoxon Rank-Sum or the Mann-Whitney U-Test
The Kruskal-Wallis Test
Friedman Test for Randomized Block Designs
Goodness-of-Fit Tests
Categorical Data Analysis
Nonparametric Bootstrapping
Permutation Tests

Experimental Design
Introduction
Fixed Effects Model
Analysis of Variance (ANOVA) for the One-Way Fixed Effects Model
Power and the Non-Central F Distribution
Checking Assumptions
Fixing Problems
Multiple Comparisons of Means
Other Comparisons among the Means
Summary of Comparisons of Means
Random Effects Model (Variance Components Model)
Randomized Complete Block Design
Two-Factor Factorial Design

Regression
Introduction
Simple Linear Regression
Multiple Linear Regression
Ordinary Least Squares
Properties of the Fitted Regression Line
Using Matrix Notation with Ordinary Least Squares
The Method of Maximum Likelihood
The Sampling Distribution of ß
ANOVA Approach to Regression
General Linear Hypothesis
Model Building
Model Validation
Interpreting a Logarithmically Transformed Model
Qualitative Predictors
Estimation of the Mean Response for New Values Xh
Prediction and Sampling Distribution of New Observations Yh(new)
Simultaneous Confidence Intervals

Appendix A: R Commands
Appendix B: Quadratic Forms and Random Vectors and Matrices

Bibliography

Index

Cohesively Incorporates Statistical Theory with R Implementation
Since the publication of the popular first edition of this comprehensive textbook, the contributed R packages on CRAN have increased from around 1,000 to over 6,000. Designed for an intermediate undergraduate course, Probability and Statistics with R, Second Edition explores how some of these new packages make analysis easier and more intuitive as well as create more visually pleasing graphs.
New to the Second Edition
• Improvements to existing examples, problems, concepts, data, and functions
• New examples and exercises that use the most modern functions
• Coverage probability of a confidence interval and model validation
• Highlighted R code for calculations and graph creation

Gets Students Up to Date on Practical Statistical Topics
Keeping pace with today’s statistical landscape, this textbook expands your students’ knowledge of the practice of statistics. It effectively links statistical concepts with R procedures, empowering students to solve a vast array of real statistical problems with R.
Web Resources
A supplementary website offers solutions to odd exercises and templates for homework assignments while the data sets and R functions are available on CRAN.