The Foundations of Statistics: A Simulation-based Approach

Read it online.
ERRATA . Several errors have been identified by users of this book. This document serves as a summary of the main typos and other types of mistakes in the book. In addition, see the corrected pages, which are downloadable from the link immediately below this line.
Corrected pages. Christian Robert identified several important errors (as opposed to typos) in the book. Corrected versions of these pages are downloadable by clicking the above link. I have highlighted the changes so that they are easy to find. Please inform me of any further errors. These and other problems in the book will be corrected in the second printing of the book.



Shravan Vasishth and Michael Broe. The Foundations of Statistics: A Simulation-based Approach. Springer, 2010. ISBN: 978-3-642-16312-8. [ bib ]

who is this book aimed at?

Here is a simple test to decide whether this book is aimed at your current ability level:

Define y as: y=x/(1-x). Can you define x in terms of y?

If you cannot answer the above question without effort (or cannot answer it at all), this book is probably at the right level for you. If you can answer this question easily, the book may still be for you; just take a look and decide for yourself. If it proves too informal for your taste, I give some recommendations for more technically demanding alternatives below.

alternative books
If this book is below your level, and/or if you want a more mathematical introduction, you might find these books useful:
  • Introduction to probability and statistics using R
  • Introduction to statistical thought


    • how to get the book
    There are several ways:
  • You can read it online.
  • The book is available as an e-book as well as a low-priced hard copy (i.e., a physical) book in soft cover under Springer's new MyCopy Print-On-Demand program. Here are details in English on how to get a MyCopy.
  • You can also buy the book from Amazon.com, Amazon.de, or Springer.com.

    • blog accompanying the book
    Here is a blog for the book; it should be used for submitting comments, suggestions for improvements, and anything else related to the textbook.

    downloadable errata, code, datasets
  • ERRATA
  • Corrected Pages
  • VasishthBroebook.R
  • beauty.txt
  • mathachieve.txt
  • mathachschool.txt
  • vb library (coming soon); for now, you can simply download this R file containing all the R functions, then save the file in the directory where you plan to run the code. Then, start up R, and type: 
    source("vb.R")
    This will load all the functions needed for the book.

    • To run the simulations in the book, you just need to download the code and data provided above.

    how to set up a pleasant working environment
    Note: To start using this book, you only need to download the data and vb.R files above, the Vasishthbroebook.R code, and the Errata plus Corrected Pages. No knowledge of LaTeX, emacs, etc., is required. The advice below is for people who want to go beyond the beginner level and use a more refined typesetting environment than the usual commercial options.
  • Install Emacs, LaTeX on your system
  • Install Emacs Speaks Statistics
  • Install the following tools: Noweb (literate programming tool), Rubber.
  • Write LaTeX and R code in an .Rnw file, then do Sweave.sh file.Rnw after installing this bash shell script written by ggorjan (if you don't want to use rubber, then look at his web page version for a texi2dvi version).
  • Use (x)emacs with AucTeX and preview-latex.
  • LaTeX and PDF-based presentations tools.
  • When in doubt about almost any question about R, you can get help. But be careful! Some people can bite your head off if you don't RTFM first.
  • How to install packages: See section 6.3 of the R manual.

    additional material
    1. An R mailing list for language: here.
    2. I also maintain a listing of articles that use lme4 or predecessors: see here. Email me if you want your articles included (I need it in bibtex-format, and the subject of the email should be lme4bib).
    3. Everyone should read Stuff Worth Knowing by Paul Johnson.
    4. Here's a brief tutorial I wrote on the matrix formulation of linear models.
    5. Here is some additional material on ANOVA and linear models; it should be read after finishing the book, as optional reading.
    6. Here is some additional material degrees of freedom.



    Comments, criticism, and requests for specific topics are most welcome (email: vasishth squiggle rz dot uni-potsdam dot de).