Probability and Statistics with R
Purchasing Options
Features
- Provides real-world examples of how R can be used to solve problems in probability and statistics
- Contains an overview on how to use R so that novices understand how to solve the problems
- Explains the mathematics behind computational implementations
- Covers both traditional methods and nonparametric techniques, including goodness-of-fit tests, categorical data analysis, nonparametric bootstrapping, and permutation tests
- Uses regression analysis procedures to solve three interesting case studies based on real data
- Presents thoroughly worked-out derivations, detailed graphs, and abundant problems
- Offers data sets, functions, and other ancillary material on a supporting website
- Includes a solutions manual upon qualifying course adoptions
Summary
Designed for an intermediate undergraduate course, Probability and Statistics with R shows students how to solve various statistical problems using both parametric and nonparametric techniques via the open source software R. It provides numerous real-world examples, carefully explained proofs, end-of-chapter problems, and illuminating graphs to facilitate hands-on learning.
Integrating theory with practice, the text briefly introduces the syntax, structures, and functions of the S language, before covering important graphically and numerically descriptive methods. The next several chapters elucidate probability and random variables topics, including univariate and multivariate distributions. After exploring sampling distributions, the authors discuss point estimation, confidence intervals, hypothesis testing, and a wide range of nonparametric methods. With a focus on experimental design, the book also presents fixed- and random-effects models as well as randomized block and two-factor factorial designs. The final chapter describes simple and multiple regression analyses.
Demonstrating that R can be used as a powerful teaching aid, this comprehensive text presents extensive treatments of data analysis using parametric and nonparametric techniques. It effectively links statistical concepts with R procedures, enabling the application of the language to the vast world of statistics.
Table of Contents
A Brief Introduction to S
The Basics of S
Using S
Data Sets
Data Manipulation
Probability Functions
Creating Functions
Programming Statements
Graphs
Exploring Data
What Is Statistics?
Data
Displaying Qualitative Data
Displaying Quantitative Data
Summary Measures of Location
Summary Measures of Spread
Bivariate Data
Multivariate Data (Lattice and Trellis Graphs)
General Probability and Random Variables
Introduction
Counting Rules
Probability
Random Variables
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 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
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 Selection and 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: S Commands
Appendix B: Quadratic Forms and Random Vectors and Matrices
Quadratic Forms
Random Vectors and Matrices
Variance of Random Vectors
References
Index
Problems appear at the end of each chapter.
Editorial Reviews
… This book covers a wide range of topics in both theoretical and applied statistics … the authors list both R and S–PLUS commands and clearly note when a command is applicable only in either S–PLUS or R. Therefore, S–PLUS users also should find this book useful. Detailed executable codes and codes to generate the figures in each chapter are available online at http://www1.appstate.edu/~arnholta/PASWR/front.htm … 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, Vol. 51, No. 2
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.
—Raquel Prado, University of California, Santa Cruz, The American Statistician, February 2009
… an impressive book … Overall, 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.
—Eirini Koutoumanou, University College London, Significance, December 2008
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