There seems to be some confusion here about where the normal distribution comes
from. The number of people that are providing scores is irrelevant, except for
the fact that with a large number of people, the shape of the underlying
distribution will be more obvious. For example, if a characteristic is normally
distributed in a population, and a measure of that characteristic is made on 3
people, the scores from those 3 people will not appear to be normally
distributed. That does not mean that the characteristic is not normally
distributed.
We often assume that test scores are normally distributed, not because of the
number of people in the class that are providing these scores, but because of the
number of items on the test that contribute to each score. We assume that, with
a large number of items, the central limit theorem will apply. My favorite
version of CLT is, "The distribution of the sum, or a sum-like quantity (e.g.,
mean, proportion) of a large number of independent random variables will be
approximately normal, regardless of the distributions of the individual random
variables."
A test score represents a sum across a large number of items. Of course, it is
unlikely that responses to these items are independent. If each item asked,
"What is your name?", 97% of my students would get a pretty high grade. On the
other hand, if each item was, "What is the base 2 log of 8?", 3% might get a
pretty high grade. We commonly run into less extreme examples, when a test is
too easy or too hard--resulting in skew.
None of this however, has anything to do with the number of students taking the
test. It is a characteristic of the test and whether it has been designed well
to do what it is supposed to do, make discriminations between those who know the
material and those who don't.
I suspect (and this would be an interesting research question), that instructors
are more likely to grade on a well-specified curve early in their careers. With
experience, the curve may become more subjective, or the assessments that are
used become more realistic. For example, I have taught undergraduate statistics
for 14 years and, at first, applied generous curves (probably a good idea at the
time, my expectations may have been too high). In the last few years, I have
felt comfortable grading without a curve, and have had a reasonable grade
distribution. This semester, grades are horrible. Should I go back to a curve
to bring them up? No--I know what can reasonably be expected. Should I look at
whether I am doing something differently this semester? Absolutely.
Paul Brandon wrote:
> At 8:46 AM -0600 12/2/99, Jean Edwards wrote:
> >Hi Tipsters:
> >
> >Statistics (and any math for that matter) is not one of my strong points but
> >doesn't the normal curve phenomenon apply to large numbers of people?
>
> At best, and only if they're randomly sampled.
> I would guess that a class population is both truncated and skewed.
> I'd have trouble justifying its use in classes of less than several hundred.
>
--
*****************************************************************
* Mike Scoles * [EMAIL PROTECTED] *
* Department of Psychology * voice: (501) 450-5418 *
* University of Central Arkansas * fax: (501) 450-5424 *
* Conway, AR 72035-0001 * *
********* http://www.coe.uca.edu/psych/scoles/index.html ********
