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I'm looking for an as complete as possible statistics book with exercises, including the following topics:
Probability Review
Random Variables and Samples
Descriptive Statistics
Estimation (confidence intervals for mean of population, probability, difference of means of population etc)
Hypothesis Tests
Chi Square Test
Linear Regression
Analysis of Variance
Non parametric tests (Kolmogorov-Smirnov, Friedman, Kruskal-Wallis, Sign test etc)
Here are three rather complementary recommendations:
Introductory Mathematical Statistics: Principles and Methods by Erwin Kreyszig
This classic is an elementary introduction which presents in the first part Descriptive statistics, followed by Probability Theory and the main part is Statistical Inference.
E. Kreyszig has the talent to make things easily understandable, he comes straight to the point and puts the focus on the essentials. The book covers what you need and is full of nice examples which help to make the theory behind it clear and comprehensible.
Note: Years ago I became acquainted with one of his books when I was reading Introductory Functional Analysis. This is a great, very simple introduction into the subject without requiring measure theory. Since that time I am a fan of him.
The next two recommendations are example centered.
Schaum's Statistics by Murray R. Spiegel and Larry J. Stephens
No need to explain anything about Schaum's outline. They all contain typically good and sometimes great examples for training.
I'd like to instead cite from chapter XXII from Indiscrete Thoughts by Gian-Carlo Rota:
Anyone who is about to teach the undergraduate mathematics curriculum should come down to earth by looking through The Schaum's Outlines before burdening the class with those well printed, many-colored, highly advertised hardcover volumes that are pathetically passed off as textbooks.
and the third one:
Introductory Statistics with R by Peter Dalgaard
In order to improve understanding and get a better feeling for the material it is extraordinary helpful to play around with many, many examples. So, if a computer is available and you are willing and able to write some code snippets, I strongly recommend to heavily use it for many examples.
Since I'm somewhat experienced in R programming, I recommend the book above. But any other computer language with statistics package and some supporting literature may also do the job.
May I recommend "The Practice of Statistics" by Daren S. Starnes. It is a great comprehensive textbook that I used in my AP Statistics class when I was in high school, and I still use it to this day in my everyday statistics problems.
https://www.amazon.com/Practice-Statistics-Daren-S-Starnes/dp/1464108730
