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: Foundations and Applications of Statistics: An Introduction Using R, Second Edition
: Randall Pruim
: American Mathematical Society
ISBN: 1470428482
: 2018
: 842
: pdf (true)
: 16.0 MB

Foundations and Applications of Statistics simultaneously emphasizes both the foundational and the computational aspects of modern statistics. Engaging and accessible, this book is useful to undergraduate students with a wide range of backgrounds and career goals. The exposition immediately begins with statistics, presenting concepts and results from probability along the way. Hypothesis testing is introduced very early, and the motivation for several probability distributions comes from p-value computations. Pruim develops the students' practical statistical reasoning through explicit examples and through numerical and graphical summaries of data that allow intuitive inferences before introducing the formal machinery. The topics have been selected to reflect the current practice in statistics, where computation is an indispensible tool.

The inclusion of R code has been improved through the use of knitr, which did not exist at the time I began the first edition but has now replaced my inferior, homespun solution. I encourage my students to take advantage of knitr as well, typically through R Markdown within RStudio.

The R code has been changed throughout to reflect my increased sensitivity to coding style and the availability of new R packages, including mosaic, which has subsumed a large fraction of what was in fastR; the packages of Hadley Wickhams tidyverse, which provide a suite of tools for working with data; and ggformula, a new package that provides a formula interface to ggplot2 and is used for nearly all of the plots in the book.

In this vein, the statistical computing environment $\mathsf{R}$ is used throughout the text and is integral to the exposition. Attention is paid to developing students' mathematical and computational skills as well as their statistical reasoning. Linear models, such as regression and ANOVA, are treated with explicit reference to the underlying linear algebra, which is motivated geometrically. Foundations and Applications of Statistics discusses both the mathematical theory underlying statistics and practical applications that make it a powerful tool across disciplines. The book contains ample material for a two-semester course in undergraduate probability and statistics. A one-semester course based on the book will cover hypothesis testing and confidence intervals for the most common situations. In the second edition, the $\mathsf{R}$ code has been updated throughout to take advantage of new $\mathsf{R}$ packages and to illustrate better coding style. New sections have been added covering bootstrap methods, multinomial and multivariate normal distributions, the delta method, numerical methods for Bayesian inference, and nonlinear least squares. Also, the use of matrix algebra has been expanded, but remains optional, providing instructors with more options regarding the amount of linear algebra required.

Foundations and Applications of Statistics: An Introduction Using R, Second Edition


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