Books : reviews

Stephen M. Stigler.
The Seven Pillars of Statistical Wisdom.
Harvard University Press. 2016

rating : 3.5 : worth reading
review : 3 February 2018

What gives statistics its unity as a science? Stephen Stigler sets forth the seven foundational ideas of statistics—a scientific discipline related to but distinct from mathematics and computer science.

Even the most basic idea—aggregation, exemplified by averaging—is counterintuitive. It allows one to gain information by discarding information, namely, the individuality of the observations. Stigler’s second pillar, information measurement, challenges the importance of “big data” by noting that observations are not all equally important: the amount of information in a data set is often proportional to only the square root of the number of observations, not the absolute number. The third idea is likelihood, the calibration of inferences with the use of probability. Intercomparison is the principle that statistical comparisons do not need to be made with respect to an external standard. The fifth pillar is regression, both a paradox (tall parents on average produce shorter children; tall children on average have shorter parents) and the basis of inference, including Bayesian inference and causal reasoning. The sixth concept captures the importance of experimental design—for example, by recognizing the gains to be had from a combinatorial approach with rigorous randomization. The seventh idea is the residual: the notion that a complicated phenomenon can be simplified by subtracting the effect of known causes, leaving a residual phenomenon that can be explained more easily.

The Seven Pillars of Statistical Wisdom presents an original, unified account of statistical science that will fascinate the interested layperson and engage the professional statistician.

The Seven Pillars of Statistical Wisdom provides an historical account of how the identified pillars were invented and developed. It is fascinating, but I feel the focus on the history detracts somewhat from the actual technicalities. Indeed, in several cases the author seems to assume prior knowledge of the very statistical concepts being introduced.

The book is richly illustrated with figures and tables from the original publications, some dating back hundreds of years. It is good to see this original material, but it would be nice also to see a modern rendering of the key figures, as the originals can sometimes be over-embellished and obscure.

This is worth reading for the historical insights. I learned lots of delicious little snippets, such as the fact that for many years after its publication, no one used Student’s t-test, not even Student (William Sealy Gosset) himself! However, I didn’t learn as much statistics as I had hoped.