Some meta-thinking about learning statistics... Something that I found really helpful (recently in fact) was just going through and understanding why the "moment generating function" is called a "moment generating function". That is, why on earth would someone take a random variable, say X, and then take the exponential of it e^Xt and then find the expectation value of such an arbitrary quantity. Next, I spent some time understanding why on earth someone would then take the log of this function, and then derive something called a "cumulant", which for the first three "cumulants" is exactly the same as the first three "moments". But, before all this, I spent time learning the "why" someone would want to know anything other than the mean and variance, and "what" they could possibly learn about a distribution beyond these two...
Somehow, the "why?" makes mathematical statistics all the more appealing. Without it, its pretty dry and unpalatable to me. I find that I learn best when I ask a question first, then proceed to answer it, rather than going through a text from page 1 to page N... the learning process is highly nonlinear, but after sufficient struggle (and associated pain) and continuous exposure, it all just converges into a mass of "aaha!". My method may not be as "efficient" as some others (in fact, its pretty slow), but I find that I gain an intuitive perspective that people who regularly "talk" about statistics don't really have... but then, i've always been one to ask "why?" rather than "how?" first. p ----- Original Message ----- From: "Peter Flom" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Tuesday, May 11, 2004 1:41 PM Subject: Re: [edstat] Getting a deeper look inside statistics and more > I recently asked a similar question (here, I think) and someone > recommended Freund's Mathematical Statistics. I have been looking this > over, and it looks very good, and intermediate between the green books > and Hogg and Craik. > > At least some of the green series is very good, and Hogg and Craik is a > classic, but the former (mostly) aren't that theoretical and the latter > is very hard (at least for me). > > But I'd be interested in a discussion of how and what to learn about > math stat - my background is in psychometrics; I;ve done a fair amount > of data analysis, and have had a couple semesters of calculus (long > ago). I am plowing through Khuri's book on Advanced Calculus with > applications in statistics, which is a stretch for me. > > Peter > > Peter L. Flom, PhD > Assistant Director, Statistics and Data Analysis Core > Center for Drug Use and HIV Research > National Development and Research Institutes > 71 W. 23rd St > www.peterflom.com > New York, NY 10010 > (212) 845-4485 (voice) > (917) 438-0894 (fax) > > > > >>> [EMAIL PROTECTED] 5/11/2004 2:24:49 PM >>> > > Hi Daniel, > > The first thing to do is make sure that your mathematics background is > both sufficient and up-to-date. You will need a working knowledge of > matrix algebra (linear algebra) and some calculus at a minimum for deep > theoreticial understanding. > > The deep understanding comes from theoretical probability and > statistics. In my day "Hogg and Craig" was the basic text of choice for > this. Lots of proofs and basic theory. > > If you don't want to go quite that deep, I think a good place to start > would be the Sage Quantitative Series green books. They are short, > relatively easy to understand, and go a level or two deeper than > Tabachnick and Fidell, but not as deep as Hogg and Craig. I believe the > website is www.sagepub.com. > > The Sage books would be my first choice for self study. > > MG > **************************************************** > Michael Granaas [EMAIL PROTECTED] > Assoc. Prof. Phone: 605 677 5295 > Dept. of Psychology FAX: 605 677 3195 > University of South Dakota > 414 E. Clark St. > Vermillion, SD 57069 > ***************************************************** > > ----- Original Message ----- > From: [EMAIL PROTECTED] (Daniel Menke) > Date: Monday, May 10, 2004 2:22 am > Subject: [edstat] Getting a deeper look inside statistics and more > > > Hello all, > > > > I?m a psychology graduate student. Our stats education was mostly an > > introductory text on basic statistical methods (descriptive stats > and > > inferential stats, like some basic probability, t-test, one-way > ANOVA, > > correlation and regression, some non-parametric tests) and > Tabachnick > > & Fidell?s ?Understanding multivariate statistics? (also an > > introductory SPSS course). We didn?t get a look inside fields like > > computational statistics, data / data base management, neural > networks > > or system theory. > > > > In my opinion, this is not enough. Personally, I want to get a much > > deeper look inside statistics and data analysis, as well as > > mathematical backgrounds (a mathematical ?backbone?) to get a > profound > > knowledge of (and become more competent in) these fields. > > > > My goal would be to cope mostly in fields like market research, > > biometry (e.g. pharmaceutical research or any kind of clinical > > research) or (program) evaluation, but also in fields like complex > > behavior prediction / prognosis (e.g. costumer?s behavior or traffic > > behavior), decision making processes, development of decision > > strategies, development of complex psychological assessment tools > > (based on IRT Models) or even statistical consulting. > > > > Are there any recommendations on books (a books list / curriculum) I > > should / could study (English or German)? It will take ?some? time, > > I?m aware of that, but I really want to try. > > > > > > Thanks and regards, > > Daniel > > . > > . > > ================================================================= > > Instructions for joining and leaving this list, remarks about the > > problem of INAPPROPRIATE MESSAGES, and archives are available at: > > . http://jse.stat.ncsu.edu/ . > > ================================================================= > > > > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= > . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
