In article <[EMAIL PROTECTED]>,
L.C. <[EMAIL PROTECTED]> wrote:
>The question got me thinking about this problem as a
>multiple comparison problem. Exam scores are typically
>sums of problem scores. The problem scores may be
>thought of as random variables. By the central limit theorem,
>the distribution of a large number of test scores should look
>like a Normal distribution, and it typically (though not always)
>does. Hence the well known bell curve. (Assume, for the sake
>of argument that it holds here.)
This is so completely erroneous as to demand being put in the
garbage and removed completely. For one thing, few tests have
that many problems, and better tests have fewer and longer
problems, with unequal weights. Even then, the problem scores
are not independent, but at least highly correlated.
>Here's the problem. Is the bell curve the result of a distribution
>of abilities/preparations, or is it a distribution of totally random
>nonsense?
If it is a good test, ability should predominate, and there is
absolutely no reason for ability to even have close to a normal
distribution. If one has two groups with different normal
distributions, combining them will never get normality.
When testing, say, the efficacy of a similar number
>of, say, drugs, we might be disturbed at a normal distribution.
>We would say that drugs A and B were in the top 5%, but
>that proves nothing because that many drugs would have turned
>out that way at random.
There is no reason here for anything like the normal distribution.
OTOH with students, we immediately
>leap to the conclusion that the top testers are suprior to the others.
>Is either perspective justifiable? Why?
With most tests, it is questionable, but that is not because
of the random variation, but because the tests are designed
to test "trivial pursuit", not long-term understanding. A
good test is one who has merely memorized the book would not
achieve a high score, but one who understands the concepts
and has not looked at many of the details would ace.
--
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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