After that, my recommendation is to study the distributions suggested - from Bernoulli to Hypergeometric - and any source you "understand" will do.
The important thing is not the source, but to understand how these things work together, how they "articulate" - i.e. why taking a bunch of samples that follow any distribution will get you something that follow a normal law (LLN, CLT, etc) - even if the law they follow has a big hole in the middle, that'll where the mean of the normal law will be. Or under which conditions you can replace a law by another law, etc.
Then it's a good time to learn what moments do - how they shape the graphs you get. After that, you can try intervals - calculate intervals given a population parameters to see how a sample can predictably differ, then from a sample of a given size how you can estimate the population parameters.
I've recently "refreshed" my knowledge of statistics, and used the slides from 15 075 as a base. They get to the point and give a better mathematical understanding - something important to build your knowledge on a solid base after you understand how the things work together and what to go down the rabbit hole.
The course suggests the Tamhane and Dunlop book (which I haven't purchased yet but which is on my buy list) ; some other people recommended it to me for the demonstrations - I did the E(S^2n) E(S^n-1) by hand and I would love to see the proof for the Chi2 stuff, because I usually understand better after I see or do the demonstration.
Regarding Chi2, "Introduction to business statistics" has a great chapter #13, giving practical application, but I strongly suggest you understand the basics first - it's too easy to make mistakes with statistics.
Yes I don't fully trust myself with a tool as powerful as statistics - it takes a professional - but even with my limited understanding, I can see the value it provides, the warnings it gives (ie the article read like some basic logical stuff, but then I realized it wouldn't have been that obvious if I hadn't known basic statistics.)
I usually recommend E.T. Jaynes' "Probability Theory: The Logic of Science", which is one of the most beautiful and comprehensive books on the subject.
To get the "logic of science" part, you also need to have (IMHO) some fairly decent grasp of combinatorics, for which I quite recently stumbled upon one of the best books in this field: "Notes on Introductory to Combinatorics." (I like the links to many of Polya's gems of "How to solve it.")
For many other references, a quick HN search for publicly available references will result in other endorsements, too (a preliminary version of the Jaynes' book used to be available, too)
- Any of Wainer's books (the author of the original pdf)
(Added later): books that explain the history of statistical thought are surprisingly good, because they explain the context and the problems the statistics were originally meant to solve. I really enjoyed "the lady tasting tea" and I think I learned from it.
I'd just say I understand the basic ideas such as DeMoivre or the Central Limit Theorem, and it helps me a lot.
First I'll assume you have a basic understanding of probabilities (odds, dices, cards, etc).
If you don't yet get probabilities, try the CK-12 books probabilities and advanced probabilities book - free on the kindle, and easy to read : http://www.amazon.com/CK-12-Probability-Statistics-Course-eb...
After that, my recommendation is to study the distributions suggested - from Bernoulli to Hypergeometric - and any source you "understand" will do.
The important thing is not the source, but to understand how these things work together, how they "articulate" - i.e. why taking a bunch of samples that follow any distribution will get you something that follow a normal law (LLN, CLT, etc) - even if the law they follow has a big hole in the middle, that'll where the mean of the normal law will be. Or under which conditions you can replace a law by another law, etc.
Then it's a good time to learn what moments do - how they shape the graphs you get. After that, you can try intervals - calculate intervals given a population parameters to see how a sample can predictably differ, then from a sample of a given size how you can estimate the population parameters.
After learning all that, to bind all this knowledge I'd suggest the free courseware on MIT 15_075 (even reading only the slides online on http://ocw.mit.edu/courses/sloan-school-of-management/15-075...)
I've recently "refreshed" my knowledge of statistics, and used the slides from 15 075 as a base. They get to the point and give a better mathematical understanding - something important to build your knowledge on a solid base after you understand how the things work together and what to go down the rabbit hole.
The course suggests the Tamhane and Dunlop book (which I haven't purchased yet but which is on my buy list) ; some other people recommended it to me for the demonstrations - I did the E(S^2n) E(S^n-1) by hand and I would love to see the proof for the Chi2 stuff, because I usually understand better after I see or do the demonstration.
Regarding Chi2, "Introduction to business statistics" has a great chapter #13, giving practical application, but I strongly suggest you understand the basics first - it's too easy to make mistakes with statistics.
Yes I don't fully trust myself with a tool as powerful as statistics - it takes a professional - but even with my limited understanding, I can see the value it provides, the warnings it gives (ie the article read like some basic logical stuff, but then I realized it wouldn't have been that obvious if I hadn't known basic statistics.)