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 ß 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.