In article <[EMAIL PROTECTED]>,
jim clark <[EMAIL PROTECTED]> wrote:
>Hi
>On 25 Nov 2001, Herman Rubin wrote:
>> 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.
>I think that "no reason" is too strong. The typical explanation
>for normally distributed polygenic traits (ability, height, or
>whatever) is that each of a large number of genes contributes
>some small component to the trait. With enough genes, the
>ultimate distribution will be reasonably well approximated by the
>normal (analogous to the normal approximation to the binomial).
There are several objections. It is by no means clear that
there are that many important genes. It is even less clear
that the effects should be additive. Single genes can
have large effects, and also single environmental variables.
I would say that going through the public schools, for those
who have the ability for a decent college education, will be
a big negative.
The normal approximation to the binomial comes from adding
identically distributed random variables. Even then, it
is quite poor in the tails.
>You don't need to accept genetic mechanisms to find some
>reasonable reason to think that test performance and other trait
>measures will be normally distributed, or at least approximately
>so. If we appreciate that performance depends on a host of
>differentiated factors (e.g., having a good night's sleep, having
>just happened to study a particular kind of problem more than
>some other, having distracting thoughts or not, not misreading
>the question, different kinds of ability, and so on ...), then
>again a normal-like distribution will emerge.
These are not small effects, but big ones. Adding big
effects does not produce near normality unless they are
already nearly normal.
>This isn't to deny Herman's basic point that a set of marks can
>contain results from different underlying populations.
There is another point. When I see a transcript, I want to
know what that means in absolute terms, at least for the
important courses.
--
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
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
