I think one reason it is so hard to answer this is that R is so powerful and flexible that a real introduction to R programming goes well beyond what is normally needed in an introduction to statistics. The books that teach statistics using MiniTab, JMP or SPSS are doing relatively straightforward things with the software that barely scratch the surface of what R is capable of when it comes to data manipulation, simulations, custom-built functions, etc.
Having said that, I think that Wilcox's Modern Statistics for the Social and Behavioral Sciences: A Practical Introduction (2012) is a brilliant new book. It assumes no statistical knowledge and takes you from scratch right through to a big range of modern robust techniques; and assumes not much more R knowledge than the ability to open it up and load a dataset. It covers many of the classical techniques too including ANOVA (mentioned in the OP).
I would see this book as the equivalent of the books that introduce stats and a stats package like SPSS at the same time. However, it won't teach you to program in R - only how to do modern statistical analysis with it, with an emphasis on robust techniques that address the known problems with classical analysis that are sidelined by most other approaches to teaching statistics.
The three problems with classical methods that this book particularly addresses right from the beginning are sampling from heavy-tailed distributions; skewness; and heteroscedasticity.
Wilcox uses R because "In terms of taking advantage of modern statistical techniques, R clearly dominates. When analyzing data, it is undoubtedly the most important software development during the last quarter of a century. And it is free. Although classic methods have fundamental flaws, it is not suggested that they be completely abandoned... Consequently, illustrations are provided on how to apply standard methods with R. Of particular importance here is that, in addition, illustrations are provided regarding how to apply modern methods using over 900 R functions written for this book."
This book is so excellent that after we bought a copy for work I purchased my own copy at home.
The chapter headings are:
- numerical and graphical summaries of data;
- probability and related concepts;
- sampling distributions and confidence intervals;
- hypothesis testing;
- regression and correlation;
- bootstrap methods;
- comparing two independent groups;
- comparing two dependent groups;
- one-way ANOVA;
- two-way and three-way designs;
- comparing more than two dependent groups;
- multiple comparisons;
- some multivariate methods;
- robust regression and measures of association;
- basic methods for analyzing categorical data;
Further edit - having checked out the David Moore example of what you are looking for, I really think Wilcox's book meets the need.
I personally thought that Modern Applied Statistics with S-Plus ticks all of the boxes you have outlined. Every example has R code, they give good references to other sources, and Venables and Ripley have a wonderfully terse and explanatory writing style which I really appreciated. I tend to re-read the book every so often, and each time I get more from it. Of course, your mileage may vary.
Best Answer
Judging by your question, your program sounds similar to the many accelerated MS degrees with 6-8 week courses on each subject. I would recommend to go for statistics or econometrics texts for executive MBAs to survive. The EMBA level texts are easy to follow and do not expect strong math background. e.g. Wharton's EMBA program has Stat 613 as core course, and it uses Stine and Foster's text.
It's good to set the expectations right though. It's impossible to learn statistics without at least calculus and linear algebra, so if your definition of "easy" is without these two skills, then you're not going to learn anything useful in one month, but it's Ok. It's just the nature of these degrees, you only need to get an exposure to the field, i.e. very similar to EMBA objectives.
For programmers I'd recommend fun books such as R by Example in Springer's Use R! series. I read it while learning R already knowing statistics, but think that it can be used to learn both R and statistics. R is rather interesting language for programmers, it's based loosely on functional programming (FP) paradigm. That's why if your programmer friend is a hardcore programmer, he must know stuff like Haskell or Scala, and will feel comfortable picking a new FP language, especially because FP is fashionable again these days.
Another title in the same series is An Introduction to Applied Multivariate Analysis with R. If your friend is in good school, he will probably have SpringerLink access through his library, i.e. free PDF download of a book.