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I would like to learn basic statistical methods for quantitative data analysis in the social sciences. I volunteer for a nonprofit, and I want to take on a quantitative research project analyzing things like demographic and law-enforcement data. The (admittedly rather vague) goal is to learn things from existing raw data that would be useful in informing policy decisions.

I have a Master's in pure math, focus on algebra. I know how to learn independently out of dense textbooks, but I'm quite weak on applied math and statistics.

I think what I want is to give myself the crash course version of an "Intro to Quantitative Research Methods" class taken by sociology PhD students, but leaning more on mathematical sophistication. (I'm not claiming to be any more "sophisticated" than sociology students. I'm guessing that embracing the math side of things helps you learn enough to do basic research, and I want to take advantage of my background.) So I want a book that does not presuppose any knowledge of statistics but also does not shy away from expounding on the theoretical framework when it's helpful.

If it matters, I'll be using R. Yes, I am prepared to invest plenty of time in the learning curve.

Does anyone have suggestions as to resources? Thanks for the help!

P.S. I thought this question might have been asked before, but I couldn't find it. If I've started a duplicate thread then my apologies and I'd be grateful to be directed to the existing question.

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    $\begingroup$ Might I suggest considering learning how to explore data first? If you learn that, you will already have tools that are more useful and more powerful for learning from data than those used by most people in the social sciences. $\endgroup$ – whuber Oct 13 '15 at 22:23
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Basic Search on Google

On google you can search about this with #tags like:

R social science On youtube you will find this free-course for psychologists.

R for Social Science

Besides, the CRAN have a task view about Statistical methods in Social Science in this link where shows many packages for support this field;

CRAN Task View: Statistics for the Social Sciences

Books

You can get this book "Applied R for the quantitative social scientist By Rense Nieuwenhuis" in this link Book

Alternatively, Springer offers a book that covers recent advances for quantitative researchers with practical examples from social sciences, called "Advances in Social Science Research Using R " You can buy the book following this link Book.

Note:I don't know if it will solve your question.

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There has been some similar questions before. This mathoverflow question https://mathoverflow.net/questions/31655/statistics-for-mathematicians has a lot of good advice. Good advice on math SE: https://math.stackexchange.com/questions/735075/statistics-primer-for-the-unwary-mathematician

I especially like my answer to Inference for the skeptical (but not math-averse) reader

From the varied advice on this pages, I will highlight:

Young and Smith, "Essentials of Statistical Inference." A more recent book on: Likelihood, pseudolikelihood, saddlepoint approximations, p∗ formula, modified profile likelihoods and more which should fit you well. Very good.

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