Think Stats: Probability and Statistics for Programmers is a textbook for a new
kind of introductory prob-stat class. It emphasizes the use of statistics to
explore large datasets. It takes a computational approach, which has several
advantages:
• Students write programs as a way of developing and testing their un-
derstanding. For example, they write functions to compute a least
squares fit, residuals, and the coefficient of determination. Writing
and testing this code requires them to understand the concepts and
implicitly corrects misunderstandings.
• Students run experiments to test statistical behavior. For example,
they explore the Central Limit Theorem (CLT) by generating samples
from several distributions. When they see that the sum of values from
a Pareto distribution doesn’t converge to normal, they remember the
assumptions the CLT is based on.
• Some ideas that are hard to grasp mathematically are easy to under-
stand by simulation. For example, we approximate p-values by run-
ning Monte Carlo simulations, which reinforces the meaning of the
p-value.
• Using discrete distributions and computation makes it possible to
present topics like Bayesian estimation that are not usually covered
in an introductory class. For example, one exercise asks students to
compute the posterior distribution for the “German tank problem,”
which is difficult analytically but surprisingly easy computationally.
• Because students work in a general-purpose programming language
(Python), they are able to import data from almost any source. They
are not limited to data that has been cleaned and formatted for a par-
ticular statistics tool.
vi
Chapter 0. Preface
The book lends itself to a project-based approach. In my class, students
work on a semester-long project that requires them to pose a statistical ques-
tion, find a dataset that can address it, and apply each of the techniques they
learn to their own data.
To demonstrate the kind of analysis I want students to do, the book presents
a case study that runs through all of the chapters. It uses data from two
sources:
• The National Survey of Family Growth (NSFG), conducted by the
U.S. Centers for Disease Control and Prevention (CDC) to gather
“information on family life, marriage and divorce, pregnancy, infer-
tility, use of contraception, and men’s and women’s health.” (See
❤tt♣✿✴✴❝❞❝✳❣♦✈✴♥❝❤s✴♥s❢❣✳❤t♠.)
• The Behavioral Risk Factor Surveillance System (BRFSS), conducted
by the National Center for Chronic Disease Prevention and Health
Promotion to “track health conditions and risk behaviors in the United
States.” (See ❤tt♣✿✴✴❝❞❝✳❣♦✈✴❇❘❋❙❙✴.)
Other examples use data from the IRS, the U.S. Census, and the Boston
Marathon.
How I wrote this book
When people write a new textbook, they usually start by reading a stack of
old textbooks. As a result, most books contain the same material in pretty
much the same order. Often there are phrases, and errors, that propagate
from one book to the next; Stephen Jay Gould pointed out an example in his
essay, “The Case of the Creeping Fox Terrier1.”
I did not do that. In fact, I used almost no printed material while I was
writing this book, for several reasons:
• My goal was to explore a new approach to this material, so I didn’t
want much exposure to existing approaches.
• Since I am making this book available under a free license, I wanted to
make sure that no part of it was encumbered by copyright restrictions.
1A breed of dog that is about half the size of a Hyracotherium (see ❤tt♣✿✴✴✇✐❦✐♣❡❞✐❛✳
♦r❣✴✇✐❦✐✴❍②r❛❝♦t❤❡r✐✉♠).
vii
• Many readers of my books don’t have access to libraries of printed ma-
terial, so I tried to make references to resources that are freely available
on the Internet.
• Proponents of old media think that the exclusive use of electronic re-
sources is lazy and unreliable. They might be right about the first part,
but I think they are wrong about the second, so I wanted to test my
theory.
The resource I used more than any other is Wikipedia, the bugbear of li-
brarians everywhere. In general, the articles I read on statistical topics were
very good (although I made a few small changes along the way). I include
references to Wikipedia pages throughout the book and I encourage you to
follow those links; in many cases, the Wikipedia page picks up where my
description leaves off. The vocabulary and notation in this book are gener-
ally consistent with Wikipedia, unless I had a good reason to deviate.
Other resources I found useful were Wolfram MathWorld and (of course)
Google. I also used two books, David MacKay’s Information Theory, In-
ference, and Learning Algorithms, which is the book that got me hooked on
Bayesian statistics, and Press et al.’s Numerical Recipes in C. But both books
are available online, so I don’t feel too bad.
Allen B. Downey
Needham MA
Allen B. Downey is a Professor of Computer Science at the Franklin W. Olin
College of Engineering.
Contributor List
If you have a suggestion or correction,
please send email to
❞♦✇♥❡②❅❛❧❧❡♥❞♦✇♥❡②✳❝♦♠.
If I make a change based on your feed-
back, I will add you to the contributor list (unless you ask to be omitted).
If you include at least part of the sentence the error appears in, that makes it
easy for me to search. Page and section numbers are fine, too, but not quite
as easy to work with. Thanks!
• Lisa Downey and June Downey read an early draft and made many correc-
tions and suggestions.
viii
Chapter 0. Preface
• Steven Zhang found several errors.
• Andy Pethan and Molly Farison helped debug some of the solutions, and
Molly spotted several typos.
• Andrew Heine found an error in my error function.
• Dr. Nikolas Akerblom knows how big a Hyracotherium is.
• Alex Morrow clarified one of the code examples.
• Jonathan Street caught an error in the nick of time.
• Gábor Lipták found a typo in the book and the relay race solution.
• Many thanks to Kevin Smith and Tim Arnold for their work on plasTeX,
which I used to convert this book to DocBook.
• George Caplan sent several suggestions for improving clarity.
• Julian Ceipek found an error and a number of typos.
• Stijn Debrouwere, Leo Marihart III, Jonathan Hammler, and Kent Johnson
found errors in the first print edition.
• Dan Kearney found a typo.
• Jeff Pickhardt found a broken link and a typo.
• Jörg Beyer found typos in the book and made many corrections in the doc-
strings of the accompanying code.
• Tommie Gannert sent a patch file with a number of corrections.
Contents