Probability and Statistics with R
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Book Description
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.
Table of Contents
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
ρValue 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 SignedRank Test
The Wilcoxon RankSum or the MannWhitney UTest
The KruskalWallis Test
Friedman Test for Randomized Block Designs
GoodnessofFit Tests
Categorical Data Analysis
Nonparametric Bootstrapping
Permutation Tests
Experimental Design
Introduction
Fixed Effects Model
Analysis of Variance (ANOVA) for the OneWay Fixed Effects Model
Power and the NonCentral 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
TwoFactor 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
Appendix A: R Commands
Appendix B: Quadratic Forms and Random Vectors and Matrices
Bibliography
Index
Problems appear at the end of each chapter.
Author(s)
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 Spatiotemporal 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 coeditor 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.
Reviews
Praise for the First Edition:
"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 wellbalanced mix of theory, examples and R code."
"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 selflearners 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 standalone textbook in probability and statistics if the computational statistics portions are skipped."
—Technometrics, May 2009
—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
Support Material
Ancillaries

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