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.
Best Answer
They're quite different.
(A) is explicitly introductory (but in many ways not elementary). That may seem contradictory: perhaps it's fair to say that (A) assumes intelligent readers willing to think hard, but not previous knowledge of statistics. There are no gimmicks such as colour photographs of happy people, boxes of various kinds with extra materials, or rude stories based on the author's wilder experiences or over-fertile imagination. (I allude without references to some of the more appalling alternatives in the market.) A smart high school student or anyone who remembered most of their high school mathematics would find it rewarding, as well as the more obvious undergraduate market.
(B) is more a second text and would be tough going for anybody who didn't find the content of (A) familiar. I'd say (B) depends on readers having encountered most of the material at least once before, because many of the explanations are cleverly concise but equally rather condensed. I'd say it's really for researchers, minimally final-year undergraduates preparing a dissertation or research paper. It's also more opinionated, which you'll love or loathe according to whether you agree with Freedman, whose high standards often excluded almost anybody else's work.
I re-read (A) with profit and pleasure every few years and have done so since the first edition (with skimming and skipping).
Disclosure: I am not a statistician either; nor I have ever taken courses taught by statisticians.
Gossip: A biography of John Tukey (see here for details and a review) twice includes an undocumented story that David Freedman as a graduate student at Princeton really couldn't get on with Tukey's sometimes elliptical and elusive teaching style. It is tempting to speculate that this may have been an underlying reason why (A) avoids box plots and Tukeyish exploratory methods generally.