Statistics learning recommendations

Generalities

Statistics is a fundamental tool in the social sciences, medical sciences, actuarial science and finance. Aside from being useful professionally, some of the basic concepts of statistics are also crucial to quantitative literacy.

Students should be warned that statistics expositions sometimes conceptually misguided. Arguably the focus on frequentist statistics rather than Bayesian statistics is an example of this. However, it's important to learn the standard perspectives in order to understand and communicate with people who use them.

Statistical intuition isn't the same as technical knowledge of things like how to perform factor analysis. One can have the technical knowledge without the intuition or the intuition without the technical knowledge. If you're planning on going into a line of work where statistics is used, you need to acquire the technical knowledge, but for general quantitative literacy, reading the material on "statistical intuition with real world examples" may suffice.

AP Statistics is generally regarded as unsubstantive and inadequate – students who want to build quantitative literacy should supplement the material with other materials such as those listed below.

Recommendations

Statistical intuition with real world examples

• Naked Statistics: Stripping the Dread from the Data by Charles Wheelan

• The Signal and the Noise by Nate Silver

Frequentist approach textbook

Statistics in Plain English by Timothy C. Urdan is a lucid book that's only 200 pages long. It's somewhat terse and may not give enough examples. No exercises.

Statistics for Dummies, and Statistics II for Dummies offer a more leisurely exposition. Statistics Workbook for Dummies offers exercises.

Bayesian statistics

Chapter 8 of The Signal and the Noise by Nate Silver gives some history of Bayesian statistics and an exposition of the basics of the subject. (Silver's book is well-worth skimming in entirety for developing statistical intuition.)

Some blog posts

• A History of Bayes' Theorem by Luke Muehlhauser
• An Intuitive Explanation of Bayes' Theorem by Eliezer Yudkowsky.
• Bayes' Theorem Illustrated (My Way) by Komponisto.

Programming and Bayesian statistics

Good if you want to actually do statistical analysis. Good for becoming more familiar with programming.

• Discovering Statistics Using R by Andy Field, Jeremy Miles and Zoe Field.
• Think Bayes: Bayesian Statistics Made Simple by Allen Downey teaches statistics through Python programming.
• Doing Bayesian Data Analysis: A Tutorial with R and BUGS by John Kruschke.

Data analysis

We don't have subject matter knowledge, but these books are very highly reviewed on Amazon.

• Doing Data Science: Straight Talk from the Frontline by Cathy O'Neil and Rachel Schutt.
• Data Science for Business: What you need to know about data mining and data-analytic thinking by Foster Provost and Tom Fawcett.
• Data Smart: Using Data Science to Transform Information into Insight by John Foreman

Online classes

• Statistics.com offers over 110 online courses on various topics in statistics. The courses are expensive: $500 for a 4-week long course. We don't have any inside knowledge of the quality of the courses.
• Coursera offers ~45 courses on a variety of subjects in statistics. Their offerings include Statistics One, an introductory course.