Psychology Press

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• Price: $94.95 $85.46
• Hardback: 728 pages
• Also available in e-Book and e-Book
• Published: April 2008
• ISBN: 978-1-58488-891-8
• Publisher: Chapman and Hall/CRC
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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 X_h

Prediction and Sampling Distribution of New Observations Y_h(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.

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