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I was just hired to a new job and some knowledge of statistics is needed. In my mathematics undergraduate studies (which I finished very recently), I studied quite a bit of probability but not at all statistics.

I'm looking to learn about tests and estimators specifically. t tests, z test, p test, kaplan-meier estimator, wilcoxon signed rank test etc

Where do I start? What are the most important and widely used tests and where can I learn more?

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Because study is motivated by your job, I suppose you are mainly interested in procedures rather than theory at the start. Except for Kaplan-Meier, satisfactory introductions to all of the tests you mentioned can be found in almost any calculus-prerequisite statistics book. Everyone has their own favorites, and there is no reason for you take advice from any one of us over another. Kaplan-Meier is usually covered in courses on survival analysis.

The American Statistical Association manages a couple of major meetings each year, the Joint Statistics Meetings in late July or early August; and another about six months later devoted mainly to statistical practice (www.amstat.org). I hope you will be able to attend one of these meetings soon. Goals should to find out about new developments, to network with other statisticians with similar interests, and to visit the vast display of books from various publishers where you can browse what is available. Outside North America there are the International Biometric Society, the Bernoulli Society, and the (British) Royal Statistical Society, among many others. (All have web sites; many have reduced membership rates for people transitioning from university to employment.)

You should try to accumulate a reference library of general statistics books (z tests, t tests, Wilcoxon tests, etc.) books on experimental design (ANOVA), and books on regression analysis. If as i suspect) you are in a health-related industry, you should include books on biostatistics and survival analysis.

For specific topics, you can also get good help on the Internet: from university course notes, software user groups, discussion boards of statistical societies, and often Wikipedia. But choose your sources wisely because there is a lot of incorrect and misleading 'information' on various web sites.

Whatever books you choose, I hope you will start to become familiar with statistical software. As you learn each new statistical procedure, you can see how it is implemented in software for practical use. Traditional software packages are SAS, SPSS, and Minitab (all fairly costly for commercial use), and R and Python (excellent, free, open source software). SAS is widely used in biostatistics; Minitab is widely used in quality management.

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    $\begingroup$ @MatthewAnderson: Thanks for fixing typos. $\endgroup$ – BruceET Mar 12 '17 at 23:12
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Any Inference Book is good for this. I suggest INTRODUCTION TO THE THEORY OF STATISTICS, by M.MOOD, A.GRAYBILL, C.BOES. For good Regression Analysis book, read INTRODUCTION TO LINEAR REGRESSION ANALYSIS by C.MONTGOMERY, A.PECK, G.GEOFFREY VINING. Otherwise if you have any freind who study statistics, class note would be enough.

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I recommend:

Statistical Inference by George Casella and Roger L. Berger

The Elements of Statistical Learning by Trevor Hastie, Robert Tibshirani, and Jerome Friedman

Plus, the quantitative section of CFA level I and level II would be a very good entry-level introduction - it gives you a very intuitive and pragmatic way over topics of statistical tests, linear regression and adjustments, time series analysis etc. The drawback is that it does not go deep and strict

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