Donald Burrill wrote: > On Sat, 24 Nov 2001, L.C. wrote: > > > Thanks for the reply! > > > > As for the iid, it's reasonable to believe the questions could be > > drawn from some population. Why not the answers? > > If the questions are selected in accordance with some table of > specifications, they are not from _a_ population, but from many; > and there is no _a priori_ reason I can think of to suppose that > their item characteristics are iid.
Actually, it's not so much the questions, but the answers that must be iid. Also, suppose we have two subject areas. The specific questions for each are largely arbitrary, but the kind of question, particularly in, say, high school is not. So you get pools of two kinds of questions. I claim the responses to each may indeed be iid. If you take the sums of any proportion of the answers to one kind with those of another, you get iid responses. If you take sums of those, you get ~N. Your remark about the number of questions may be fulfilled by, say, a final or midterm. > > > As for the answers, the usual reason for wanting to evaluate students > is precisely because they are (or one hopes they are!) different in > their levels of skill (or whatever): the task is to assess these skill > levels, and it is nonsense to assume that all the persons are id on the > measure on which one hopes to identify differences. > > > (Hey! I've heard much worse justifications for > > statistical assumptions! :) At any rate, bell curves do > > arise often enough in this context to be written about. > > Of course, "bell curve" does not necessarily imply "normal distribution". > On the contrary. It does, as it is normally used > You can get quite nice bell curves from binomial distributions, e.g. > Also of course, any real data must be discrete, not continuous, so > cannot technically be normally distributed anyway. > (It is possible that the distribution may be more or less well > approximated by a normal distribution with the same mean & variance, > but that's not the same thing.) > > > > As for wanting gaps in the resulting distribution... That > > was my point. When you do have a bell curve, it shouldn't > > be satisfying; it should be disturbing. > > Depends on how "bell-like" the curve is. For almost any interesting > variable that can be measured on humans, one expects rather a lot of > people in the middle, and progressively fewer toward the extremes, of > the distribution; doesn't one? (And if not, why not?) > > > This is the maddening > > aspect of psychometry - they engineer these nice normal > > distributions on which to base their diagnoses. You'd think > > they'd *want* bimodal, discrete, or mixed continuous/discrete > > distributions, but no. They diagnose by Z scores (thereby > > defining their own prevalences :) and assert that they are > > discovering diseases, and not punishing unusual people. > > > > Best Regards, > > -Larry (And they get to testify in court) C. > > Hmm. This thread started out as "evaluating students", in the context of > classes and teacher-made tests, as I recall. Not exactly the same thing > as "diagnosing" (in a quasi-medical sense)" or discovering diseases", I > shouldn't think. > One wonders, then, why you aren't posting these complaints in a > newsgroup of psychometricians, rather than one of statistics teachers? > I didn't post the complaints. I sent them to you. AND, I continue to thank you for the response. I admit the original question was a bit of an idle troll, and I got what I deserved. -Love and Regards > > ------------------------------------------------------------------------ > Donald F. Burrill [EMAIL PROTECTED] > 184 Nashua Road, Bedford, NH 03110 603-471-7128 Donald Burrill wrote: > On Sat, 24 Nov 2001, L.C. wrote: > > > Thanks for the reply! > > > > As for the iid, it's reasonable to believe the questions could be > > drawn from some population. Why not the answers? > > If the questions are selected in accordance with some table of > specifications, they are not from _a_ population, but from many; > and there is no _a priori_ reason I can think of to suppose that > their item characteristics are iid. > > As for the answers, the usual reason for wanting to evaluate students > is precisely because they are (or one hopes they are!) different in > their levels of skill (or whatever): the task is to assess these skill > levels, and it is nonsense to assume that all the persons are id on the > measure on which one hopes to identify differences. > > > (Hey! I've heard much worse justifications for > > statistical assumptions! :) At any rate, bell curves do > > arise often enough in this context to be written about. > > Of course, "bell curve" does not necessarily imply "normal distribution". > You can get quite nice bell curves from binomial distributions, e.g. > Also of course, any real data must be discrete, not continuous, so > cannot technically be normally distributed anyway. > (It is possible that the distribution may be more or less well > approximated by a normal distribution with the same mean & variance, > but that's not the same thing.) > > > As for wanting gaps in the resulting distribution... That > > was my point. When you do have a bell curve, it shouldn't > > be satisfying; it should be disturbing. > > Depends on how "bell-like" the curve is. For almost any interesting > variable that can be measured on humans, one expects rather a lot of > people in the middle, and progressively fewer toward the extremes, of > the distribution; doesn't one? (And if not, why not?) > > > This is the maddening > > aspect of psychometry - they engineer these nice normal > > distributions on which to base their diagnoses. You'd think > > they'd *want* bimodal, discrete, or mixed continuous/discrete > > distributions, but no. They diagnose by Z scores (thereby > > defining their own prevalences :) and assert that they are > > discovering diseases, and not punishing unusual people. > > > > Best Regards, > > -Larry (And they get to testify in court) C. > > Hmm. This thread started out as "evaluating students", in the context of > classes and teacher-made tests, as I recall. Not exactly the same thing > as "diagnosing" (in a quasi-medical sense)" or discovering diseases", I > shouldn't think. > One wonders, then, why you aren't posting these complaints in a > newsgroup of psychometricians, rather than one of statistics teachers? > > ------------------------------------------------------------------------ > Donald F. Burrill [EMAIL PROTECTED] > 184 Nashua Road, Bedford, NH 03110 603-471-7128 > > ================================================================= > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > ================================================================= ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
