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What book is the most thorough treatment of fundamental concepts in statistics? I am not asking for a book on details of the methods of calculations and procedures, I am mainly interested in a book that thoroughly explains the foundational concepts ... an intuitive/illustrated/visual approach to the core ideas ... rather than load of mathematics equations etc. Size of the book is no problem ... even a large multi-volume text would do ... heck even a web resource would do.

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up vote 6 down vote accepted

It's hard to know exactly what you're looking for based on your post. Maybe you can edit it to clarify a little. I will say that to really understand statistics well, then you'll need to learn some math.

For fairly broad, low-level, introductory concepts, both

  1. Gonick and Smith, A Cartoon Guide to Statistics, and
  2. D. Huff, How to Lie with Statistics

are light, easy reads that present a lot of the core ideas. Another book directed at a more "popular" audience that I think every person should read is J. A. Paulos' Innumeracy. It is not about probability or statistics, per se, and has more elementary probability than statistics, but it's framed in a way that I think most people can easily relate to.

If you have some calculus background and want to understand (introductory, frequentist) theoretical statistics, find a copy of Mood, Graybill and Boes, Introduction to the Theory of Statistics, 3rd. ed. It's old, but in my opinion, still better than any of the more "modern" treatments. But, it's a book for which you'll have to be comfortable with mathematical notation.

For a "modern" view of applied statistics and the interface between it and machine learning, along with good examples, and good intuition, then Hastie et al., Elements of Statistical Learning, is the most popular choice. Many people also tend to like Harrell's Regression Modeling Strategies, which is a solid book, though I'm apparently not quite as big of a fan as others tend to be. Again, in both cases, you'll need to at least be comfortable with some calculus, linear algebra, and standard math notation.

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(+1) Would you mind expanding on your opinion on the RMS textbook (of course, it's purely off-topic)? –  chl Feb 13 '11 at 22:26
    
@chl, I'll see if I can dig out the notes I jotted down on it and will post a couple (if I can find them). As I was reading the book, I recall coming across several remarks and recommendations that struck me as incorrect or very questionable. This colored my opinion of it. But, as I stated above, my overall impression is generally positive. –  cardinal Feb 13 '11 at 22:36
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If you're interested in the philosophy of Statistics, you can't do much better than Abelson's "Statistics As Principled Argument".

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I think Harvey Motulsky's Intuitive Biostatistics is pretty good for non-mathematical "intuitive" explanations to basic statistical methods most commonly employed in the biological and medical sciences.

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I like Kennedy's Guide to Econometrics, which treats every topic on three levels, the first of which is a non-technical description, in so far as this is possible.

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I like the book too, but the OP didn't really ask about Econometrics. –  Dirk Eddelbuettel Feb 14 '11 at 20:56
    
Just going by the Contents, he will find the linear regression model and violations of its assumptions, bayesian approach, Logit, Probit, Tobit models, time series analysis, forecasting and robust estimation. So, even if the title is econometrics, I suppose it covers a large amount of statistical tools that are usefull outside of econometrics. –  Owe Jessen Feb 14 '11 at 21:23
    
On further reflection, I would not quote the book as the definitve, most thorough source on concepts, as the OP requires. –  Owe Jessen Feb 14 '11 at 23:18
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