The Seven Pillars of Statistical Wisdom by Stephen M. Stigler (PDF)

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.

User’s Reviews

Editorial Reviews: Review “The hardest kind of scientific thinking concerns what’s in a field’s basement―and Stigler has brought a bright flashlight to his subterranean investigations of the ever-more-influential field of statistics.”―Bradley Efron, Stanford University“Distilled from centuries of statistical research and garnished with wit, this masterfully prepared seven-course food for thought is a real treat for anyone who wants to reason with data, big or small.”―Xiao-Li Meng, Harvard University“Statistics has a core set of ideas that touch every aspect of our lives. Stigler has tapped into these and brought them to life.”―Persi Diaconis, Stanford University“This lively account of a radically counter-intuitive past at least encourages us to question big data’s reputation. Never entrust measurement to a monarch―or judgment to a computer.”―Jonathon Keats, New Scientist“Wonderful…Each of the seven pillars that Stigler, in his wisdom, has hewn from the past two centuries of statistical thought provides surprising insights.”―Howard Wainer, Science“Learning to reason statistically helps to make one a clearer and more logical thinker about important issues in the world. Part of the achievement of this book is that it makes some of this available to the general reader without the necessity of having to delve into more technical aspects of the subject.”―Michael J. Evans, Mathematical Reviews (starred review) About the Author Stephen M. Stigler is Ernest DeWitt Burton Distinguished Service Professor Emeritus in the Department of Statistics at the University of Chicago.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This a great interesting book, that helped me understanding concepts that I always used and taken them for given, but always puzzled me. The author guides the reader to the development of these concepts through an historical perspective, merging philosophical with science. Some parts of the book are very clear and well written, but I found other parts more nebulous and not as well written, requiring deeper familiarity of the concept itself to be understood. Nevertheless, I really enjoyed reading this unique book.

⭐As someone working in the field of data analytics, I found the Seven Pillars of Statistical Wisdom to be an exceptional guide to the history of the basic concepts of statistics. A few caveats, however. The book assumes a basic knowledge of these concepts, so non-scientists may be better off choosing a different book if they simply want a introduction to statistics. Second, the balance between the history of these ideas and explanation of them sometimes leans in the historical direction (in my personal opinion too much) so only scientists who like learning about the history of the analytic tools they use will find the book engaging. All that said, Professor Stigler is not only a accomplished statistician but a good writer who can make a discussion of routine statistical concepts interesting to someone whose work involves these every day. Highly recommended but to a select circle of readers.

⭐I thought that this book was directed to someone who had a somewhat broader and deeper grasp of statistics than I have. My background in statistics is fair, but certainly not at a PhD level. I found the categorization into seven “pillars of wisdom” to be a useful perspective. I also thought that the historical incidents discussed in the book were very interesting, and in some cases eye-opening for me. I especially appreciated the discussion of twentieth century statistics, but this does not proceed very far into that fruitful century. The book has very much fired my love of the field, and induced me to read some of the old books that are mentioned in the book. I can strongly recommend this book if you have a background in statistics to draw on.

⭐This book would be more accurately titled “The obscure history of 7 simple statistics principles”. The ideas are pretty simple – like the mean (average) – which are laboriously researched as to who was the first person to use this idea. There is an emphasis on obscure historical facts, and less emphasis on mathematical thinking or ideas, or the value of the idea. There is a little bit of mathematical reasoning but not as much as I would have liked. Also lacking is any connection between these old ideas and modern uses of these ideas.Also, one nitpicking thing – but he attributes the method of Least Squares to Legendre and totally ignores the more widely held view that Gauss developed the idea earlier but did not publish the method until after Legendre to explain his accurate prediction of a comet’s position.

⭐If you’re interested in the history and philosophy behind statistics, not just the equations, this book is recommended. Sometimes things like this can help you see and internalize the ‘big picture’ in the way random collections of blog posts or papers can’t.

⭐Fascinating read if you are into statistics. As other reviewers have noted, much of this book won’t make sense to someone with no background in statistics. However for those who do have such a background, it is fascinating. I learned a lot about some ideas I am familiar with but hadn’t thought of in this way or hadn’t placed into their historical context. I bought the book for my graduate statistics professor — my hunch is he will get even more out of it than I did.

⭐Statistical wisdom, hum? First, Stigler assumes we did our homework being familiar with basic statistics. Second, seems that “wisdom” means mastering fundamental concepts together with awareness of their interrelations. Then he goes about telling the history of such concepts always sharing original plots and tables to make us wiser about where + why the ideas germinated. The whole thing is full of references to the clever people who developed these ideas, here called seven pillars of statistics.

⭐Interesting historical reading giving some explanation of how statistics today was derived. However, a bit dry at some places and, if the reader doesn’t put some thought into the explanations of origins, seemingly pointless to the non-statistically oriented. In other words, not a needed reference but (after working with statistics for a while) some explanation of how and why statistics got its recognition of being important.

⭐Every student of an abstract subject like maths, physics or even philosophy is familiar with this: you are introduced to a foundational concept yet it seems pretty counterintuitive, and you can think of a number of reasons why the said concept ought to be considered problematic. Yet somehow, the textbooks are less than sympathetic.My advice is to check the history of the under-motivated concept. The original formulations were often so much more compelling, especially when you realise precisely what problem their authors were trying to solve. Your own misgivings may well be represented in critiques by the innovator’s contemporaries.It was the very success of later generations which led to the wholesale reconceptualisation of their subject’s foundations.And so it is with statistics, a subject where deep ideas are often obscured by a focus on technique, and where it sometimes seems that little distinguishes a correct line of argument from an equally plausible, but fallacious, alternative.Professor Stephen Stigler, in this determinedly historical book, starts with a concept as apparently trivial as the mean, or average, of a sequence of observations. Even this is counterintuitive as it requires discarding information, the individuality of the observations. By what right are ‘bad’ measurements to be treated in the same way as ones we think, or know, to be of higher quality? It took quite a few years for the idea to catch on.Stigler’s second pillar, information measurement, looks at the processing of large data sets. Opinion polls have made us somewhat aware that the accuracy of the proposed mean is proportional to the square root of the number of observations, not the absolute number.Sampling was applied to the Royal Mint in Isaac Newton’s time, to ensure that the coins they produced used the right amount of gold. In the absence of a correct theory of standard deviation, the tolerance boundaries were set way too wide. Stigler dryly notes that Newton was warden, then master of the Royal Mint from 1696 to 1727 and that on his death in that year left a sizeable fortune. “But evidently his wealth can be attributed to investments, and there is no reason to cast suspicion that he had seen the flaw in the Mint’s procedures and exploited it for personal gain.”Later chapters deal with hypothesis testing (pillar 3); statistical processing within the dataset itself, without reference to population norms – as in Student’s t-test (pillar 4); regression to the mean – a concept which proved very hard to pin down (pillar 5); experimental design, particularly when varying multiple qualities at the same time (pillar 6); and finally pillar 7, the notion that a complicated phenomenon may be simplified by subtracting the effect of known causes, leaving a residual phenomenon to which attention may now be focused.If you are both interested and well-versed in statistics, you will find this book illuminating and witty. The converse also applies.

⭐Aside from academic statisticians who have run out of reading material I can’t see who this book is aimed at. The writing style is overly academic and the author makes the mistake of assuming that the reader is familiar with statistical language, concepts and the associated mathematical notation. If you’re not familiar with these then avoid this book and look for something by David Spiegelhalter or David Salsburg. If you are a statistician then you will be familiar with the concepts in this book already. Despite the title of the book there is little insight or wisdom to surprise the typical researcher. The bulk of the text actually focuses on the history of statistics, but in such a disjointed and dry fashion that the story is never entertaining. All I have learnt after reading this is (a) it was a complete waste of time and money, and (b) it should never, ever, be given as a gift.

⭐Thought it would be more insightful. Fairly ordinary book

⭐In interesting read and a useful insight into the historical and structural core of statistics. Many people will have studied stats to pass exams and will understand the concepts from this perspective. This book goes beyond this level to provide a deeper understanding of where and when the ideas emerged. Not a ‘necessary’ read but one that cements stats in your memory in a way that no other book that I’ve read has.

⭐Statistic history, not really about statistic methods per say.

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