## Description

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