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. The focus on frequentist statistics rather than Bayesian statistics is arguably 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 our recommendations for statistical intuition .

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

These are non-technical books that illustrate the concepts of statistics with real world examples. Because they illustrate the ideas in context, helpful for building statistical intuition.

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

• The Signal and the Noise by Nate Silver. This book is organized around the theme of predicting the future.

• The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century by David Salsburg. This provides an early history of statistics.

Frequentist approach textbook

The most commonly taught approach to statistics is the frequentist approach.

• Statistics in Plain English by Timothy C. Urdan is a lucid book that covers a lot of material in only 200 pages. It's somewhat terse and some readers may find it to be short on examples.
• Statistics for Dummies, and Statistics II for Dummies offer a more leisurely exposition. Statistics Workbook for Dummies offers exercises.

Bayesian statistics

Bayesian statistics is thought by many people to be a superior alternative to frequentist statistics.

Chapter 8 of The Signal and the Noise by Nate Silver gives the history of Bayesian statistics and an exposition of the basics of the subject.

Some blog posts that overlap with the content of Silver's book but that the reader may find helpful for slightly different perspectives are:

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

For a full technical introduction to Bayesian statistics, Introduction to Bayesian Statistics by William Bolstad may be helpful, but the book is very expensive.

Programming statistics

If you enjoy programming, are looking to learn programming, or will be implementing statistical algorithms in your work, these books may be good choices:

• 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.

Online classes

If you find it easier to learn from lectures than from a textbook, we encourage you to check out free online courses. You can try out different lecturers until you find one who you find especially easy to learn from.

• Coursera offers ~45 statistics courses. Their offerings include Statistics One, an introductory course.
• edX offers ~20 statistics courses, including Introduction to Statistics: Descriptive Statistics, Introduction to Statistics: Inference and Introduction to Statistics: Probability, which are associated with UC Berkeley.
• Udacity offers Intro to Statistics and Statistics.
• MIT OCW offers an math courses that include "Introduction to Probability and Statistics" and "Statistics for Applications."
• Carnegie Mellon University's Open Learning Initiative offers a course on probability and statistics.

Statistics.com offers over 110 statistics courses. The courses are expensive: $500 for a 4-week long course. We don't have any inside knowledge of the quality of the courses.