Preface

This book is a first course in probability and statistics, using R. The book assumes a mathematical background of Calculus II, though much of the book can be read with a much lower level of mathematics. The book incorporates R throughout all chapters via simulations, data wrangling and/or data visualization. Tidyverse and base R tools are interspersed, depending on which is better for a particular job. For most visualizations, ggplot is used, and for most data wrangling, dplyr is used. An emphasis is placed on understanding results (and robustness to departures from assumptions) via simulation.

Data in this book is either provided in its data directory or through freely available R packages. You will need to install these packages to access the data. Our philosophy in this book is to not shy away from messy data sets. The book contains extensive sections and many exercises that require data cleaning and manipulation. This is an essential part of the course.

We are assuming a knowledge of calculus through the Fundamental Theorem of Calculus, some knowledge of infinite series, and integration including integrating over regions in the plane. However, many parts of the book do not require calculus, and since the book emphasizes simulations, most parts of the book can be understood without using calculus. Proofs of many results are provided, and justifications via simulations for many more, but this text is not intended to support a proof based course. Readers are encouraged to follow the proofs, but often one wants to understand a proof only after first understanding the result and why it is important.

This is book is written in rmarkdown using the bookdown package. If, or rather when, you find typos, mistakes or ideas for improvement, please contact the authors. The original idea for a course of this type is due to Michael Lamar. The authors wish to thank Matt Schuelke for helpful discussions regarding aspects of this book.

This book is copyright 2020, Darrin Speegle and Bryan Clair. Do not transmit or reuse without express permission.

0.1 Further reading

No book like this would be complete without a list of books that would be useful for the student who wishes to learn more. Here is a list of other resources that that the authors have enjoyed learning from.

  1. ggplot2, by Hadley Wickham, gives a nice overview of the capabilities of the ggplot2 package. Students interested in data visualization would find this book interesting.
  2. Advanced R, by Hadley Wickham, provides much more information on R than what we cover in this book. Computer Science students might enjoy reading this book.
  3. The Statistical Sleuth, by Ramsey and Schafer, will help the student think more like a statistician when dealing with data sets.
  4. Modern Applied Statistics with S, by Venables and Ripley, is a more advanced book.
  5. Introductory Statistics with R, by Peter Dalgaard, is a concise introduction to using R for many types of statistical procedures.
  6. Mathematical Statistics with Applications, by Wackerly, Mendenhall and Schaeffer, is a more mathematical (but still only requiring multivariate calculus and perhaps basic linear algebra) look at the topics of this book. Students interested in the theory and proofs behind the material in this book would enjoy reading it.
  7. Datacamp is an on-line, interactive tutorial based method of learning data science in general, and R in particular.
  8. The package data.table. If we were going to inculde a package that isn’t part of the tidyverse, this would be it. It is widely used for data manipulation, and can be significantly faster than other R tools for many classes of problems. If you find that your code is running too slowly, it may be time to learn data.table.

0.2 Installing R and RStudio

R is a programming language, distributed as its own software program.

To install R:

Mac users

  1. Visit the CRAN archive, at https://cran.r-project.org
  2. Find the link that looks like “R-x.x.x.pkg” under the Latest release heading.
  3. Download the “R-x.x.x.pkg” file, double-click it to open, and follow the installation instructions.

Windows users

  1. Visit the CRAN archive, at https://cran.r-project.org
  2. Click on the “Download R for Windows” link at the top of the page.
  3. Click on the “base” link.
  4. Click the large “Download R x.x.x for Windows” link and save the executable file somewhere on your computer.
  5. Run the .exe file and follow the installation instructions.

RStudio is a graphical interface to R. R can work without RStudio, but RStudio requires R to work. Though you may choose to use R in its native form, the improvements that come with RStudio are absolutely worth the effort to install it. In fact, once you have RStudio installed, there is little need to ever run the R program itself.

To install RStudio:

  1. Go to www.rstudio.com and click on the “Download RStudio” button.
  2. Click on “Download RStudio Desktop.”
  3. Click on the version recommended for your system and install it.

Finally, you might choose to install the tidyverse at this time, by finding the Console in RStudio and typing:

More details on package installation are in Section 1.7.