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). 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. This isn't to deny Herman's basic point that a set of marks can contain results from different underlying populations. Best wishes Jim ============================================================================ James M. Clark (204) 786-9757 Department of Psychology (204) 774-4134 Fax University of Winnipeg 4L05D Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED] CANADA http://www.uwinnipeg.ca/~clark ============================================================================ ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
