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This question has been asked many times before but I didnt find great references - so here's another try :)

I am looking for basic statistics book that would be of the level of advanced undergrad. Should go into type I, II error, hypothesis testing, p values, t distr, chi sq testing etc. What would be a great book for that ?

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In addition to sharing a nice collection of books in the Quora thread that I've referenced in my comment above, I would like to share my personal selection of the IMHO top core statistics (excluding machine learning, econometrics and other specialized domains) books from my extensive Amazon wishlist's statistical books section (not sure about some of them being considered "best" or "classical", though). I plan to revamp the foundation of my statistical knowledge eventually (I have no formal education in statistics), based on studying these books:

Probability and General Statistics

Regression and Statistical Modeling Strategies

Bayesian Statistics

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I wholeheartedly suggest

"Introduction to Mathematical Statistics" by Hogg, Craig and McKean.

Browse it and you will see it has everything you are looking for and is particularly strong for maximum likelihood theory, sufficiency and hypothesis testing, see chapters 6 to 8.

I have used a number of popular books, such as Casella and Berger, Wasserman, MGB and so on but this is by far my favourite. And although I am a postgrad now, I stil find it immensely useful.

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