Tag Archives: books on statistics

Seven Pillars of Statistical Wisdom

I don’t review a lot of business books on my blog…mostly because I don’t like a lot of business books. A ridiculous percentage of business books seem to me either to be one-trick ponies (a good idea that could be expressed fully in a magazine article expanded to book length) or thinly veiled self-help books (self help books with ties as described in this spot-on Slate article). I HATE self-help books. Grit, Courage, Indecisiveness. It’s all the same to me.

On the other hand, The Seven Pillars of Statistical Wisdom isn’t really a business book. It’s a short (200 small pages), crisp, philosophical exploration of what makes statistics interesting. Written by a Univ. of Chicago Professor and published by Harvard University Press, it’s the best quasi-business book I’ve read in a long time.

I say quasi-business book because I’m not really sure who the intended audience is. It’s not super technical (thank god you can read it and know very little math), but it sometimes veers into explanations that assume a fairly deep understanding of statistics. Deeper, at least, than I have though I am most certainly not a formally trained statistician.

What Seven Pillars does extraordinarily well is examine a small core set of statistical ideas, explicate their history, and show why they are important, fundamental, and, in some cases, still controversial. In doing this, Seven Pillars provides a profound introduction into how to think statistically – not do statistics. Instead of focusing on how specific methods work, on definitions of statistical methods, or on specific issues in modern statistics (like big data), Seven Pillars tries to define what makes statistics an important way to think.

To give you a sense of this, here are the seven pillars:

Aggregation: Probably the core concept at the heart of all statistical thinking is the idea that you can sometimes GAIN insight while losing data. Stigler delves into basic concepts like the mean, shows how they evolved over the centuries (and it did take centuries) and explains why this fundamental insight is so important. It’s a brilliant discussion.

Information: If we gain information by losing data, how do we know how much information we’ve gained? Or how much data we need? With this pillar, Stigler lays out why more is sometimes less and how the value of observations usually declines sharply. Another terrific discussion around a fundamental insight that comes from statistics but is constantly under siege from folk common-sense.

Likelihood: In this section, Stigler tackles how the concepts around confidence levels and estimation of likelihood evolved over time. This section contains an amusing and historically interesting discussion on arguments for and against the likelihood of miracles!

Intercomparison: Stigler’s fourth pillar is the idea that we can use interior measurements of the data (there’s an excellent discussion of the historical derivation of Standard Deviation for example) to understand it. This section includes a superb discussion of the pitfalls of purely internal comparison and the tendency of humans to find patterns and of data to exhibit patterns that are not meaningful.

Regression: The idea of regression to the mean is fundamental to statistical thinking. It’s an amazingly powerful but consistently non-intuitive concept. Stigler uses a genetics example (and a really cool Quincunx visualization) to help explain the concept. This is one of the best discussions in a very fine book. On the other hand, the last part of this section which covers multivariate and Bayesian developments is less wonderful. If you don’t already understand these concepts, I’m not sure Stigler’s discussion is going to help.

Design: The next pillar is all about experimental design – surely a concept that is fundamental not just to statistics but to our everyday practical application of it. I found the discussion of randomization in this section particularly interesting and potentially noteworthy and thought-provoking.

Residual: Pillar seven is, appropriately enough, about what’s left over. Stigler is concerned here to show how examining the unexplained part of the analysis leads to a great deal of productive thinking in science and elsewhere. The idea of nested models is introduced and this section somehow transitions into a discussion of data visualization with illustrations from Florence Nightingale (apparently a mean hand with a chart). I’m not sure this transition made perfect sense in the context of the chapter, but the discussion is fascinating, enjoyable and pointed enough to generate some real insight.

Stigler concludes with some thoughts around whether and where an eighth pillar might arise. There’s some interesting stuff here that’s highly appropriate to anyone in digital trying to extend analytics into high-dimensional, machine-learning spaces. The discussion is (too) brief but I think intentionally so.

 

Seven Pillars isn’t quite a great book, and I mean that as high-praise. I don’t read many books that I could plausibly describe as almost great. The quality of the explanations is extremely high. But it does a better job explicating the intellectual basis behind simpler statistical concepts than more complicated ones and there are places where I think it’s insufficiently forceful in illuminating the underlying ways of thinking not just the statistical methods. Perhaps that’s inevitable, but greatness isn’t easy!

I do think the book occasionally suffers from a certain ambiguity around its audience. Is it intended as a means to get deep practitioners thinking about more fundamental concepts? I don’t think so – too many of the explanations are historical and basic.

Is it intended for a lay audience? Please.

I think it fits two audiences very well, but perhaps neither perfectly.

First, there are folks like me who use statistics and statistical thinking on an everyday basis but are not formally trained. I’m assuming that’s also a pretty broad swath of my readers. I know I found it both useful and enlightening, with only a few spots where the discussion became obscure and overtly professional.

The second audience is students and potential students of statistics who need something that pulls them away from the trenches (here’s how you do a regression) and gets them to think about what their discipline actually does. For that audience, I think the book is consistently brilliant.

If there’s a better short introduction into the intellectual basis and foundation of statistical thinking, I don’t know it. And for those who confuse statistical thinking with the ability to calculate a standard deviation or run a regression, Seven Pillars is a heady antidote