You might want to check out the following:

http://www.stochas.org/
http://www1.appstate.edu/~arnholta/PASWR/index.htm
http://turtle.gis.umn.edu/pmwiki/pmwiki.php/StatisticsandDatawithR/HomePage
http://www.janehorgan.com/

I own all of these books and like them.

The book by Dr. Jan Horgan:
"Probability with R: An Introduction with Computer Science
Applications" is nice in that it's quick and right to the point.
Don't let the title fool you, there's plenty of information applicable
to all fields.

The book by Dr. Kenneth Baclawski:
"Introduction to Probability with R" is has more theory than the
previous book and also has lots of worked problems.

The other two books are general prob/stat books, I find they're both
extremely well written with the Arnholt book with a little more
theory.

All of these books start from first principles (no required stat
background, just some math) but I suspect that all of these may be a
good next step to bridge the gaps that you mention.  In addition, I
think that owners of PASWR and SADWR may be able to get a solution
manual from the author (if you're working on your own and not taking a
class).

Cheers,

Dan Viar
Chesapeake, VA


On Fri, Jan 23, 2009 at 11:57 AM, Monte Milanuk <memila...@gmail.com> wrote:
>
> Hello,
>
> I'm looking for a textbook that can explain some of the math behind
> the intro-to-intermediate stuff like ANOVA, multiple regression, non-
> parametric tests, etc.
>
> A little background:  I took an intro stats course last year and
> would like to further my education.  Being as that was the highest
> (and only) stats class the local community college offers, it looks
> like I'm on my own from here.  I've been working through some of the
> online 'stats with R' tutorials as well as Dalgaard's ISWR.  Where
> I'm running into problems is the transition from Bluman's 'A Brief
> Introduction to Elementary Statistics' (covers up through paired t-
> tests, chi-squared/goodness-of-fit, simple linear regression &
> correlation, and just barely mentions ANOVA) with a TI-83+, to even
> books like ISWR... when they start getting into the things like one
> and two-way ANOVA, multiple regression, model selection, survival,
> etc. I start feeling like I have one hand tied behind my back - I
> just don't have enough theoretical exposure to really understand what
> techniques I would use when, relative to my own projects outside the
> book.
>
> Several of the 'intro to stats using R' books and pdf tutorials
> mention that they are not really meant as a standalone statistics
> text book, but in addition to a traditional stats textbook (Verzani
> mentions Kitchen's book specifically).  So I guess what I'm looking
> for is any other recommendations on intro or intermediate textbooks
> that deal primarily with the math/theory behind the processes.  If
> they were oriented towards R that's be great, but otherwise I guess
> I'd be most interested in something relatively platform-agnostic -
> I've seen some books that were slanted heavily towards a particular
> software package (Minitab) that I cannot afford or justify for
> personal use.
>
> TIA,
>
> Monte
>        [[alternative HTML version deleted]]
>
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