Donald Burrill wrote:
>
> On Fri, 23 Nov 2001, L.C. 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,
>
> Provided, of course, that the test scores in question are iid. Now it is
> possible to imagine that test scores for different persons are measured
> independently (although I am aware of skepticism in the ranks on this
> point!), but that they are identically distributed seems unlikely at
> best.
I'd argue that they probably aren't that independent. If I ask three
questions all involving simple algebra and a student doesn't
understand simple algebra they'll probably get all three wrong. In
my experience most statistics exams are better represented by a
bimodal (possibly a mix of two skewed normals) than a normal
distribution. Essay based exams tend to end up with a more unimodal
distribution (though usually still skewed).
Thom
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