Allen B. Downey - Think Stats

• 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 doesnt 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 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 particular statistics tool.

• 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 mens and womens health. (See http://cdc.gov/nchs/nsfg.htm.)

• 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/.)

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 Terrier.[]I did not do that. In fact, I used almost no printed material while I was writing this book, for several reasons:

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 MacKays 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 dont feel too bad.