Probability and Statistics with R

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
ρ-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 β
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 X_h
Prediction and Sampling Distribution of New Observations Y_h(new)
Simultaneous Confidence Intervals

Problems appear at the end of each chapter.

Biography

María Dolores Ugarte is a professor of statistics in the Department of Statistics and Operations Research at the Public University of Navarre (UPNA). She is an associate editor of Statistical Modelling, TEST, and Computational Statistics and Data Analysis and an editorial board member of Spatial and Spatio-temporal Epidemiology. She received a rating of "Excellent Teacher" from UPNA in 2008 and the INNOLEC Lectureship Award from Masaryk University in 2007. She earned a PhD in statistics from UPNA and completed her postdoctoral training in the Department of Mathematics and Statistics at Simon Fraser University.

Ana F. Militino is a professor of statistics at the Public University of Navarre. She is co-editor in chief of TEST, official journal of the Spanish Society of Statistics and Operations Research. She received the John Griffiths teaching award in 2011 and was a visiting researcher at Oxford University and Simon Fraser University. She earned a PhD in statistics from the University of Extremadura.

Alan T. Arnholt is a professor in the Department of Mathematical Sciences at Appalachian State University, where he has taught undergraduate and graduate statistics since 1993. He earned a PhD in applied statistics from the University of Northern Colorado.

Praise for the First Edition:
"This book covers a wide range of topics in both theoretical and applied statistics … Detailed executable codes and codes to generate the figures in each chapter are available online … nicely blend[s] mathematical statistics, statistical inference, statistical methods, and computational statistics using S language ... . Students or self-learners can learn some basic techniques for using R in statistical analysis on their way to learning about various topics in probability and statistics. This book also could serve as a wonderful stand-alone textbook in probability and statistics if the computational statistics portions are skipped."
—Technometrics, May 2009

"The book is comprehensive and well written. The notation is clear and the mathematical derivations behind nontrivial equations and computational implementations are carefully explained. Rather than presenting a collection of R scripts together with a summary of relevant theoretical results, this book offers a well-balanced mix of theory, examples and R code."
—The American Statistician, February 2009

"… an impressive book …　this is a good reference book with comprehensive coverage of the details of statistical analysis and application that the social researcher may need in their work. I would recommend it as a useful addition to the bookshelf."
—Significance, December 2008