In article <[EMAIL PROTECTED]>,
Donald Burrill <[EMAIL PROTECTED]> wrote:
>On Sat, 24 Nov 2001, L.C. wrote:
................
>> 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.
Much of the psychological theory here is derived from testing
short-term memorization of nonsense syllables, to try to get
to the model used. There is no reason that this should be
relevant to evaluating how well students understand subjects.
>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?)
There are likely to be SAMPLE gaps.
>> 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.
Anyone who converts data to normality, or even standardizes
variances, is using statistics as pure ritual.
There is often a justification for using procedures based
on the normal distribution; they often work well in general.
Least squares is one of these.
>> 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?
He may have questions about the religious ritual, and want
to get opinions from those who have not been brainwashed
by the priests.
Psychometricians and educationists do act as if those who
are outstanding are in the category of diseased. They
are doing their best to keep them from learning anything
near what they can learn.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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