Simple Ain't Easy: Real-World Problems with Basic Summary Statistics

In applied statistical work, the use of even the most basic summary statistics, like means, medians and modes, can be seriously problematic. When forced to choose a single summary statistic, many considerations come into practice.

This repo attempts to describe some of the non-obvious properties possessed by standard statistical methods so that users can make informed choices about methods.

Reading

If you just want to read the book, download it here.

Note that the formatting of the book is quite simple. This is intentional: it's easier to iterate on changes if you don't have to worry about typesetting until the copy is finalized.

Contributing

The reason I chose to announce a book of examples isn't just pedagogical: by writing fully independent examples, it's possible to write a book as a community working in parallel. If 30 people each contributed 10 examples over the next month, we'd have a full-length book containing 300 examples in our hands. In practice, things are complicated by the need to make sure that examples aren't redundant or low quality, but it's still possible to make this book a large-scale community project.

As such, I hope you'll consider contributing. To contribute, just submit a new example. If your example only requires text, you only need to write a short LaTeX-flavored Markdown document. If you need images, please include R code that generates your images.

If you contribute, make sure you're happy with the following terms:

• All code will be released under the MIT license
• All text will be released under the CC-BY 4.0
• The finished book will be published with all proceeds going to a to-be-determined charity

Layout

The main text for the book lives in the text directory. Each example is categorized in terms of the statistic being considered: there are directories for median, mean, etc.

If an example uses supporting images, those images are generated by R scripts stored in the scripts directory. The generated images go into the images directory.

The full book is specified in terms of the ordered examples that should be merged together into a full-length book. This merging is done, for the moment, in Perl using the merge_text.pl script.

Dependencies

Build dependencies:

• R: Used to generate images
• Perl: Used to build up one book-length document from individual examples
• Pandoc: Used to translate LaTeX-flavored Markdown to pure LaTeX
• LaTeX: Used to build a PDF from LaTeX

Building

Everything is controlled using a Makefile, whose main target is called book. You can create a PDF of the book as follows:

make book