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?
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Donald F. Burrill [EMAIL PROTECTED]
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