I recommend the textbook that saved my brane recently as I've been agonising over the appropriate stats to use on my rather complex and hairy research data: "Discovering Statistics using SPSS" 3rd edition, by Andy Field. (If you buy a new copy, it'll likely have a disc in the back with a year's license for SPSS (and the software, natch), which will help if you want to work through any of the exercises.
This book explains the background, the math and the logic of most of the statistical procedures commonly used in the social sciences, and does so using examples that justify the "and sex and drugs and rock and roll" subtitle (that you won't see on the outer jacket of the book). Andy's a great teacher, and explains this stuff so clearly that even I can understand it, and that's a rare gift. If you want ONE textbook to demystify stats, this is it. It'll answer all of the questions you pose in your post, and more.
Ooh, I think that would be a really good idea. Thank you!
What I really want to do (in the end) is work on a masters' degree in stats in my spare time (something I'd recognize as foolhardy if I didn't have a master's in math already...), but this sounds like the perfect thing to kick me off. Real, useful stuff so I don't get bored-to-death with theory and repetition :-).
Younger Son uses a lot of statistics in his research -- has had graduate-level courses. I can inquire and might* even get an answer, if you don't come up with better sources.
*He's kinda up to his ass in alligators right now, grant applications and such.
If you can inquire, I'd be grateful... that's exactly the kind of thing I'd like to learn about. Someday, I hope to ping actual statisticians at universities (possibly pursuant to attending one), so knowing what people are reading these days (or have recently) would help.
I've sent him an email with your query cut-'n-pasted in. Will pass any reply along when I get it. Or don't, as I warned above.
Just got a reply from Younger Son:
"A lot of introductory statistics textbooks will explain why a formula exists in the first place. Mine was "Stats: Data and models" by De Veaux, Velleman, & Bock, and I used the second edition but they seem to be up to a third now."
He has also offered to send the query on to his old PhD adviser, who was/is a bit of a statistics wonk.
Okay, further advice from "higher up" in the pecking order:
"I have been advised to direct the person to start with Roger E. Kirk.
This is the author of another introductory statistics text, and one
with a lot in it. There are plenty of alternative tests and suchlike
for the different circumstances in which statisticians may find
themselves. I do not have it in front of me in order to check, but
I'm fairly certain that it gives citations to the people who developed
the various tests. (And if it doesn't then there's always the
internet. And, also, if it doesn't then that would be pretty weird
for a scientific text.) This therefore is not a "history of
statistics" book, but if one were to go into it (in more depth than
the quick version a college undergrad gets) one will find a lot.
I still use De Veaux, Velleman, & Bock, but (if I recall correctly)
this is because I don't need all the alternative tests which Kirk
I can check with my cousin the maths professor and see if he can recommend anybody, if you'd like. I don't think sadistics is his usual classroom, but he should at least know some people who are; he was made head of his college at the university because he didn't run fast enough and because he's very good at writing grants.
Hee. Yes, that's the kind of thing I'd really appreciate. I'm hoping to self-study my way to an equivalent of a master's degree in stats, and I might end up back at school, so real-live "people are using this text book" is one of the things that will help me the most.
I have just sent him an email. I hope you don't mind, but I took the liberty of including the text of your post above (properly attributed, of course).
Ben found a source for a college professor who teaches college-level math and science courses online, and was using it to teach himself calculus. I can check to see if it offers statistics.