book review Statistics

Thoughts on ‘Naked Statistics’ (by Charles Wheelan)

Let’s begin this post with a comment by Chris Schuck on my recent video about The Data Detective by Tim Harford. Chris wrote:

Some of the books in this genre look really great, but I was also thinking about how these statistical/quant critical thinking analyses are often at their most effective when placed in the context of a specific debate or social problem, often by attentive journalists. Zeynep Tufekci’s writing on the pandemic these past two years is a great example of how to teach these critical thinking skills on the fly by carefully unpacking misunderstandings or misrepresentations as they come up in the media. But she brings an additional sociological lens (why did some interpretations gain traction but not others; why so much institutional inertia adapting to new evidence).

Chris’s comments are always insightful and point out important layers in the discussion I’d otherwise miss. The comment is a response to a specific version of the general question, “Why read?” in relation to a particular genre (statistical reasoning + critical thinking + … ). There wouldn’t be a point in reading a text, if we knew it won’t have an effect. “Why read X?” is equivalent to “What desirable effect will reading X have on the reader?”

To paraphrase Chris, popular books on statistics would be ineffective without an engagement with a particular problem, question, or debate. It is hard to imagine how one would benefit from a “general overview” of statistics and statistical reasoning without connecting the topic to something they care about. Sometimes tying the work to real-life problems is taken care of by the author, but other times, e.g., in the case of textbooks, the reader has to do most of the work of connecting the material to their interests and projects.

I’d like to think that my interest in theory, communication, and forms of writing can serve as a basis for engaging with these texts. That is the basis from which a critic works. But is that enough? Should the critic lose touch with other concerns and problems? Chris’s comment, therefore, is an invitation to ask once again Why? Why else? What else can I do with this? The comment itself indicates an interest in critique and reflection. The perspective from which Chris’s comment is written is, I believe, the very same perspective from which we think about our engagement (or lack of engagement) and interest (or disinterest) in relation to a particular book.

Let us now turn to Charles Wheelan’s book, Naked Statistics: Stripping the Dread from the Data, and ask: “What desirable effect could this book have on the reader? Who is the ideal reader of this book?” I think there are several reasons why someone might want to read this book. The book is intended to be an easy and accessible introduction to statistical concepts and basic methods. If, for whatever reason, you hate statistics, Wheelan’s book attempts to offer a fresh entry point into the field, helping you associate statistics with things you might love or at least find easier to think about (i.e., sports, jokes, or plain language).

If you’re taking a course in statistics, you could use this book as a supplement to your textbook/lectures. The aim should not be to read switch your textbook with a more engaging book, but to learn from the more engaging book how to engage with your textbook. If you regularly run into statistical concepts referenced in news articles, this book might help organize some of those concepts.

A few things are explained especially well in the book. A chapter is devoted to the Central Limit Theorem. Wheelan’s explanation is simple and interesting, especially considering his hatred of calculus, because I think a full understanding of the theorem requires an understanding of calculus, in addition to probability. We are imagining that we are taking samples from a population and measuring sample means. We imagine the sample sizes increase, approaching infinity. Consequently, according to the theorem, the shape of the distribution of sample means approaching a normal distribution. The normal distribution, in this context, is understood as a theoretical tool, and for that reason we wouldn’t expect it to be perfectly reliable in practice. Wheelan’s treatment of the Central Limit Theorem is simple, but it was more accurate than the treatment I recently saw given by a “data science expert.”

His discussion of precision vs. accuracy is helpful (he uses “precision” to refer to a superficial feature, namely being fine-grained, which could mistaken with accuracy), as is his explanation of the binomial distribution, using as example the 1981 blind beer-tasting competition organized by Joseph Schlitz Brewery, his explanation(s) of the Monty Hall problem, and his explanation of the 2008 financial crisis, which is combined with an introduction of Value at Risk (VaR) models.

Here is a passages:

The VaR was like a faulty speedometer, which is arguably worse than no speedometer at all. If you place too much faith in the broken speedometer, you will be oblivious to other signs that your speed is unsafe. In contrast, if there is no speedometer at all, you have no choice but to look around for clues as to how fast you are really going. (p. 97)

Statistics cannot be any smarter than the people who use them. And in some cases, they can make smart people do dumb things. (p. 95)

Connecting statistics to real-life domains doesn’t just make the topic relatable. It is an effective way of communicating the imperfections statistical concepts in relation to real-life problems. Understanding that imperfection–the fact that statistical concepts involve trade-offs–might be missed in purely technical introduction to statistics.

In one of the final chapters, Wheelan includes memorable examples of “natural experiments,” situations where a randomized controlled experiment isn’t possible, and researchers find clever ways of testing the relationship among variables. We read about the economist, Adriana Lleras-Muney, who asked whether more education is associated with longer life expectancy. She relied on differences in length of mandatory schooling (six vs. seven years) across different states in the US and found a positive correlation. Similarly, we read about researchers who asked whether the mere presence of police officers in an area has an effect on frequency of crime. They relied on terrorism alerts, which increased the number of officers in areas of Washington DC on certain occasions. Frequency of (unrelated) crimes was found to be negatively correlated with the presence of police officers. Dale and Kruger tested the relationship between college type (ivy league vs. non-Ivy league) and future income, by focusing on students who were admitted to both types of college and selected one over the other. They didn’t find college type to be predictive of income later in life.

Finally, throughout the book, Wheelan emphasizes the difference between statistical and social significance, which is an important part of separating statistical practices from the social context of those practices and demystifies the field of statistics, while at the same time showing its possible relevance and usefulness. Even though this book is unlikely to become a frequently revisited treasure in your personal library, it might become an enjoyable read you’ll later give to friends or students.

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