# What is the single most influential book every statistician should read?

If you could go back in time and tell yourself to read a specific book at the beginning of your career as a statistician, which book would it be?

• There are really three separate questions here! 1) What is the single most influential book in statistics; 2) What book should every statistician read; 3) What book have you read that you most wish you'd read much earlier. (2) and (3) probably have considerable overlap; (1) may be quite distinct. – onestop Feb 20 '11 at 8:50
• This question is another way of looking at this question. I hope that it will provide a good complement, once it gets some good answers. – naught101 Feb 29 '12 at 13:50

Here are two to put on the list:

• Both are worth a periodic re-reading, maybe once a decade, just to refresh the ideas. Concerning Tukey: it's great to sit down just with pencil and paper once in a while and do a deep analysis of an interesting dataset. – whuber Sep 9 '10 at 22:55
• For graphics for a statistician, I prefer William Cleveland's books to Tufte's. – Peter Flom Oct 2 '12 at 22:46
• I have a feeling these books were meant to analyze non-linear data when non-linear methods weren't as available? – Robert Kubrick Jan 25 '17 at 13:57

The Elements of Statistical Learning from Hastie, Tibshirani and Friedman http://www-stat.stanford.edu/~tibs/ElemStatLearn/ should be in any statistician's library !

• I disagree - that one is closely related to machine learning, not statistics per se! – aL3xa Sep 20 '11 at 18:06
• @aL3xa: it is certainly focussed on machine learning...which is why I think statisticians should be exposed to it early on. – Cliff AB Feb 8 '19 at 3:58
• Apparently I'm in the minority in thinking this book is overrated. It seems to be written for a graduate-level student, but one who doesn't care about the details of how anything works. – The Laconic Mar 23 '19 at 16:14

I am no statistician, and I haven't read that much on the topic, but perhaps

Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century

should be mentioned? It is no textbook, but still worth reading.

• I second this. Also, there is quite a lot of suggestions for further reading which I think are useful in the book. – Chris Beeley Mar 17 '11 at 8:55
• I think this book speaks to those who knew nothing at the beginning but the obtuseness of the language and the cultural baggage associated with the field. This book gave the mind wings - it says that statistics is about finding useful truth in a sea of noise and misunderstanding. – EngrStudent Oct 22 '14 at 12:53
• Many people have reported this as entertaining, but it's full of extraordinary errors. If you can find it, my review in Biometrics 57: 1273-1274 (2001) gives a far from complete list. (Salsburg gets various Bernoullis mixed up, which is easier to do.) – Nick Cox Jan 16 '16 at 16:07
• Back when this was a \$3.95 and then a \$4.95 paperback, I bought copies by the dozen and gave them away to friends, clients, and anyone else who might be interested. – whuber Sep 9 '10 at 22:54
• It's deservedly remembered. But the non-statistical content dates it unfortunately, not least an extraordinarily large fraction of cartoons featuring people (and even babies) smoking. 60+ years on, that's not amusing any more. (Some reprints e.g. one in the UK updated the cartoons.) – Nick Cox Jan 16 '16 at 16:02
• This book is tough. It is about the foundations of probability, and even in that part of Statistics, I don't think it is a reference text. I do believe there can be 14 people on planet Earth who read and understood its full message, but I would probably classify this as a must read for probabilists, for the sake of the thousands of others that are deep in stuff like GLMs, GAMs, Bayesian models and other things. – means-to-meaning Nov 6 '13 at 0:57
• It is also a bit sad that some of the later chapters are missing and/or under developed - for example there is no chapter on regression, but a draft unpublished manuscript was available with some fascinating insights into "measurement error" regressions. Some very cool stuff on time series though. – probabilityislogic Apr 9 '14 at 7:53

Not a book, but I recently discovered an article by Jacob Cohen in American Psychologist entitled "Things I have learned (so far)." It's available as a pdf here.

• Thats a wonderful article, written in Cohen's lucid and conversational style. – richiemorrisroe Feb 20 '11 at 15:30

Long ago, Jack Kiefer's little monograph "Introduction to Statistical Inference" peeled away the mystery of a great deal of classical statistics and helped me get started with the rest of the literature. I still refer to it and warmly recommend it to strong students in second-year stats courses.

• Great recommendation, thank you -- I got a copy recently based on this and it really is quite good. – ars Oct 1 '10 at 19:14
• I'm glad to hear someone else appreciates this book! – whuber Oct 1 '10 at 20:14

I wouldn't argue that either of these should be considered "the most influential book... [for] statistician[s]", but for those who are just starting to learn about the topic, two helpful books are:

1. Robert Abelson, Statistics as Principled Argument
2. Paul Murrell, Introduction to Data Technologies
• Abelson would be useful to many who re not just starting out, as well. – Peter Flom Feb 7 '19 at 11:24

William Cleveland's book "The Elements of Graphing Data" or his book "Visualizing Data"

• I'm currently reading through The Elements (Visualizing Data is not in my current schools library). What is the difference between Elements & Visualizing Data? I haven't been able to find detailed enough descriptions to formulate what is exactly the difference between the two. – Andy W Nov 10 '11 at 19:36
• I agree. I think that, for statisticians, Cleveland is better than Tufte. – Peter Flom Jan 22 '12 at 12:41
• +1 to Robert Alberts, & +1 to Peter Flom (Cleveland's books are definitely better for statisticians, although Tufte's are beautiful as well, and I have read all of them). @AndyW, Elements is introductory, e.g., it has guidelines for making an informative graphic. Visualizing demonstrates how to center your data exploration process around graphics; it starts with preliminary visualization of the data, talks about the issues at hand and walks all the way through to assessing the final model (e.g., residual analysis) via graphics. The latter is much more informative than the former. – gung - Reinstate Monica Jan 23 '12 at 4:03
• @AndyW One of them is a bit more technical than the other (I forget which is which though!) – Peter Flom Oct 2 '12 at 22:48
• As @gung says, Visualizing is a more advanced sequel to Elements. There is some overlap but it's helpful rather than irritating. Both strongly recommended. Last revision dates 1993 and 1994, but they are still fresh 20+ years later. Note that non-technical readers would get value from both: I can vouch personally that high school mathematics is sufficient background. – Nick Cox Jan 16 '16 at 15:59

I think every statistician should read Stigler's The History of Statistics: The Measurement of Uncertainty before 1900

It is beautifully written, thorough and it isn't a historian's perspective but a mathematician's, hence it doesn't avoid the technical details.

I say the visual display of quantitative information by Tufte, and Freakonomics for something fun.

Andrew Gelman's interesting book recommendations are here:

http://thebrowser.com/interviews/andrew-gelman-on-statistics

In addition to "The History of Statistics" suggested by Graham, another Stigler book worth reading is

Statistics on the Table: The History of Statistical Concepts and Methods

On the math/foundations side: Harald Cramér's Mathematical Methods of Statistics.

• By the way, this is the earliest place I have found mention of Cramer's phi. Amazing how a lovely little sidenote in that book became a well known method many decades later. – Tal Galili Jan 5 '13 at 22:56

For a clear exposition of what should be in social science journal articles (assistance if you're writing or peer reviewing) I like The Reviewer's Guide to Quantitative Methods in the Social Sciences. In particular I like the table desideratra as a synopsis of the minimum that a paper (article, thesis, dissertation) should contain. The chapters are separated by analysis technique, which is nice. I think the book has wider applications than "just" the social sciences as the techniques covered are used across many fields.

Quite early on, so perhaps not covered by the question, I was introduced to Ott's Introduction to Statistical Methods and Data Analysis. It's quite expensive, but is a wonderful resource at showing the underlying statistical models for various GLM methods. I dream of the day that journals require articles to contain show the formula of the statistical model tested.

For checking test assumptions, looking at the effects of various options within a test, and so forth, this is the one book I wish I had when I was studying. I have the previous edition and it is one of the best general resources I have purchased because of the clear and consistent manner in which information about the tests is laid out. It contains nice examples illustrating the test(s), and does not require the reader to have a particular statistical package in order to follow the expositions.

Fooled By Randomness by Taleb

Taleb is a professor at Columbia and an options trader. He made about \$800 million dollars in 2008 betting against the market. He also wrote Black Swan. He discusses the absurdity of using the normal distribution to model markets, and philosophizes on our ability to use induction.

• A terrible book, written by someone who does not understand statistics... – Xi'an Jan 22 '12 at 9:14
• Xi'an, care to expand, or provide links to some critiques? – naught101 Feb 29 '12 at 13:56
• There are a bunch of comments on The Black Swan (and Taleb more generally) here – Peter Flom Oct 2 '12 at 22:50
1. Michael Oakes' Statistical Inference: A Commentary for the Social and Behavioral Sciences.
2. Elazar Pedhazur's Multiple Regression in Behavioral Research. If you can stand the immense detail and the self-important tone.

In case you're interested, I've reviewed both on Amazon and at http://www.integrativestatistics.com/favorites.htm

I have read the above recommendations and was surprised to find that most of the people who answered the question were people who are not statisticians themselves. With 2 or 3 exceptions ... As an industrial statistician who also happened to work with social scientists and health professionals I would say that if I could take only one book with me to a desert island it would be George E.P Box, Statistics for Experimenters (Wiley). In his inimitable humorous and lucid style he explains the essence and the philosophy of building mathematical models for real data. Rigorous thinking, no mathematical frivolities, no nonsense, teaches us to think statistically, plot and visualize whatever you can. A masterpiece of a competent applied scientist (chemical engineer turned statistician). Always fun to read again.

• Good choice! His coauthor the late William Hunter and J. Stuart Hunter also contributed to the book. – Michael R. Chernick Jan 23 '17 at 23:21
• The first edition is cleaner and fresher than the second. Box was a great statistician but in later life a poor proof-reader. – Nick Cox Jan 24 '17 at 11:26

Lots of good books already suggested. But here is another: Gerd Gigerenzer's "Reckoning With Risk" because understanding how statistics affect decisions is more important than getting all the theory right. In fact number one sin of statisticians is failing to communicate clearly. His book talks about the consequences of poor communication and how to avoid it.

• "understanding how statistics affect decisions is more important than getting all the theory right..." Ain't it the truth? I come from an architecture background, and I can tell you, sometimes theory just gets in the way... – naught101 Feb 29 '12 at 13:54

I am going to go ahead and propose a standard textbook in the field. I am talking about Probability and Statistics by Degroot and Schervish, first published in 1975.

This book has served as a textbook for many students and is considered a classic, rightfully so in my opinion. It covers topics such as combinatorics, distributions, bayesian statistics, likelihood inference and regression analysis. As far as I know no other textbook is so thorough so I believe it is a must-have.

I learned a great deal from the Bible of Bayesian statistics:

Jose Bernardo and Adrian Smith (2000) Bayesian Theory.

The Essential Guide to Effect Sizes: Statistical Power, Meta-Analysis, and the Interpretation of Research Results by Paul D. Ellis

This book if a "must have" for everyone conducting any scientific research, especially one that comes not from pure stats/maths. The book below extends the first one regarding confidence intervals.

Understanding The New Statistics: Effect Sizes, Confidence Intervals, and Meta-Analysis by Geoff Cumming

"Most influential" is a very different notion from "everyone should read". I am not qualified to answer the first - you'd need someone who is an historian of statistics - but for the second, here are some:

1. Statistics as Principled Argument by Robert Abelson should be read by anyone doing or using statistics in the pursuit of science, humanities, etc.

2. William S. Cleveland's two books on graphics: The elements of graphing data and Visualizing Data. For statisticians, I'd put these ahead of even Tufte's work, bot because Tufte isn't worthwhile but because a) Cleveland wrote with statisticians as his intended audience and b) Cleveland based his recommendations on experimental data about how people look at graphs, rather than intuition.

3. Exploratory Data Analysis by John Tukey. It's dated but valuable - you can do a lot with a pencil and paper and a brain (at least, if your brain is as good as Tukey's!)

It would probably be Bayesian Data Analysis by Gelman or Deep Learning with Python. But that's a bit like taking streptomycin to the middle ages. These were not written when I started my career and quite a few things from the books would have been big news back then. Some of the most influential things everyone should know are in no single source though (perhaps they should be, but...).

Kennedy's A Guide to Econometrics contains a wealth of practical advice about a wide range of statistical analysis. It's somehow both incredibly information-dense and easy to read, and I still learn something new every time I pick it up.

Wooldridge's Introductory Econometrics has a good amount of this kind of discussion too, but as an introductory textbook it is more self-contained. I wish I'd had a course based around it.