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I have a new position in a biology department (after being housed in a maths department) working on cognitive and population modeling. People in my lab are asking for help with applying statistical tests to their data set, but when people say "chi-squared", I say, "wikipedia".

I'd like to pick up a statistics book that is aimed at teaching someone with a fairly solid background in math and probability theory how to apply standard statistical tests to real data sets, and that goes into some of the practical issues with doing so.

Ideally I'd like a book that focuses on frequentist statistics -- my own research deals with Bayesian modeling, and (ironicly) I have a far easier time understanding and working with the more complex Bayesian data analyses that people bring to me than simpler frequentist analyses e.g. ANOVA hybrids

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    $\begingroup$ I would not send someone looking to do chi-squared analyses to wikipedia. It's usually okay for definitions, but it's not much use as a way of finding out what to do. You might do better flagging this and asking to move it to stats.stackexchange.com (if it's not too late to do that). $\endgroup$ – Glen_b Apr 22 '14 at 2:27
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Adding to the other answers, look at: https://mathoverflow.net/questions/31655/statistics-for-mathematicians

And this one: https://stats.stackexchange.com/questions/63760/inference-for-the-skeptical-but-not-math-averse-reader (especially my answer, which I still think is good!)

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I might suggest Parts II and III Wasserman's "All of Statistics." Wasserman's a good mathematician and great statistician, although the book is not aimed at people with an unusually good mathematical background-just at those wanting to use statistics well and quickly. In particular, "well" implies that it's rigorous. The book is essentially frequentist. There's a followup, IIRC, on non-parametric stats.

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  • $\begingroup$ All of statistics is a nice book, but its more for people in machine learning-related areas than anything else. You aren't going to learn anything about ANOVA there, for example. $\endgroup$ – Batman May 13 '14 at 9:26

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