The Seven Pillars of Statistical Wisdom
Stephen M. Stigler
Harvard University Press
<p>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.</p><p>Even the most basic idea―<i>aggregation</i>, exemplified by averaging―is counterintuitive. It allows one to gain information by discarding information, namely, the individuality of the observations. Stigler’s second pillar, <i>information measurement, </i>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 <i>likelihood</i>, the calibration of inferences with the use of probability. <i>Intercomparison</i> is the principle that statistical comparisons do not need to be made with respect to an external standard. The fifth pillar is <i>regression</i>, 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 <i>experimental design</i>―for example, by recognizing the gains to be had from a combinatorial approach with rigorous randomization. The seventh idea is the <i>residual</i>: 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.</p><p><i>The Seven Pillars of Statistical Wisdom</i> presents an original, unified account of statistical science that will fascinate the interested layperson and engage the professional statistician.</p>