Statistics
David Freedman, Robert Pisani, Roger Purves
Fourth edition: 2007, First edition: 1978
As an undergraduate studying philosophy, I was asked to analyze some data for a small study that I was working on with a physician. Needless to say, I found myself somewhat overwhelmed, but was able to get by by mimicking some old Stata code that a biostatistician friend had given me. The analysis turned out to be good enough to help get the study published, and I had suddenly become interested in this curious field of study called statistics.
The first book on statistics that I read was Statistics, by David Freedman and colleagues. What I liked most about it was its focus on explaining the fundamental concepts of statistical analysis (what do p-values actually mean, why is it important to visualize data, what does it mean for a test to be significant, etc) with concise and accurate language, but without too much mathematics. With that conceptual background, I found it much easier to go on to read more advanced literature with more advanced mathematics.
This book covers all topics covered in a first year statistics course, but does not cover time series or aggregation of large data sets. I feel it does a very good job at teaching a non-statistician how to think like a statistician. From there, adding new methods, like time series, should be relatively easy, and the non-statistician should be well on his way to becoming a life-long student of statistics.
BBC's More or Less is often concerned with numeracy and statistical literacy issues. But it's not specifically about statistics. Their About page has some background.
More or Less is devoted to the powerful, sometimes beautiful, often abused but ever ubiquitous world of numbers.
The programme was an idea born of the sense that numbers were the principal language of public argument.
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Best Answer
http://www.r-bloggers.com/ is an aggregated blog from lots of blogs that talk about statistics using R, and the #rstats hashtag on twitter is also helpful. I write quite a bit about statistics and R in genetics research.