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Why I wrote this book
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
understanding. 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
understand by simulation. For example, we approximate p-values by
running Monte Carlo simulations, which reinforces the meaning of the
- 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
- 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 particular statistics tool.
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
question, 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,
infertility, use of contraception, and men’s and women’s health.”
- 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 http://cdc.gov/BRFSS/.)
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.
- Many readers of my books don’t have access to libraries of
printed material, 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 resources 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 librarians 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 generally 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, Inference, 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
Allen B. Downey is a Professor of Computer Science at
the Franklin W. Olin College of Engineering.
If you have a suggestion or correction, please send email to
email@example.com. If I make a change based on your
feedback, 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.
- Lisa Downey and June Downey read an early draft and made many
corrections and suggestions.
- 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 docstrings of the accompanying code.
- Tommie Gannert sent a patch file with a number of corrections.
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