The Seven Pillars of Statistical Reasoning

Originally published in The Reasoner Volume 10, Number 8– August 2016
stiglerStatistician Stephen Stigler put forward in the 1980’s the amusing Law of Eponymy which bears his name(!). According to Stigler’s Law, the vast majority (some say all) of scientific discoveries are not named after those who actually made the discovery. Wikipedia lists a rather impressive number of instances of Stigler’s Law, featuring the Higgs Boson, Halley’s comet, Euler’s formula, the Cantor-Bernstein-Schroeder theorem, and of course Newton’s first two laws of mechanics. Of particular interest is the case of Gauss, who according to this list, has his name mistakenly attached to three items.

Rather coherently his recent book, S. Stigler (2016: The Seven Pillars of Statistical Wisdom, Harvard University Press), presents the fascinating edifice of statistics by giving more emphasis to the key ideas on which its foundations rest, rather than to the figures who came up with them. The seven pillars are: Aggregation, or how to discard information to make things clearer; Information measurement, or why not all pieces of information are equally important; Likelihood, or how probability plays a fundamental role in the calibration of statistical inference; Intercomparison, or why the internal variation in data sets is fundamental in statistical comparisons; Regression, explaining why tall parents tend to have, on average, children who are shorter than themselves; Design, or why asking well-posed questions is fundamental in statistics; and Residual, or how to simplify the analysis of complicated phenomena by abstracting from the effects of known causes. To each of the seven pillars, Stigler devotes a chapter which outlines the history of the idea, and illustrates its relevance with many examples, ranging from astronomy to biology to medicine – as the saying goes statisticians do really get to play in everyone’s backyard. In the concluding chapter Stigler identifies “the site” for the eight pillar, which is nonetheless still waiting for someone to be wrongly credited with its introduction.

Interestingly, logicians also have some merit in the construction of the seven pillars of statistical wisdoms. In the chapter devoted to Design, for instance, Stigler points out that C.S. Peirce explicitly theorised on the key concept of randomisation in his criticism to the then emerging theory of just noticeable differences in psychophysiology. In the 1885 essay On Small Differences in Sensation, published in Memoirs of the National Academy of Sciences, 3, 73-83, C. Peirce and J. Jastrow, argued experimentally against the existence of a discrete threshold past which a detectable stimulus ceases to be so. The crux of their argument, as reported by Stigler, consists in the extremely careful experimental design, of which Peirce and Jastrow give ample documentation, aimed at ensuring the most rigorous randomisation in their lifted weights experiment. Stigler suggests that Peirce was aware of the methodological importance of randomisation well beyond the specific case of this experiment. To this effect it is recalled that Peirce had defined “induction” as “reasoning from a sample taken at random to the whole lot sampled”.