On Sat, 20 Jan 2001, Will Hopkins wrote:
> Yes, I was wrong about the need for normality of the residuals. I somehow
> had the idea that estimates of the precision of estimates come directly
> from normality of the individual errors, but it just ain't so. Estimating
> the confidence limits for the mean of a sample is the way to see how the
> central limit theorem smooths out a nasty distribution of
> residuals. According to Bill Ware and Paul Swank, the distribution of the
> variance of the mean takes a bigger sample to settle down than the
> distribution of the mean, but I can't really see how that matters, unless
> you can make it the basis of the kind of test for non-normality I am
> looking for.
If that's what I said, it's not what I meant... The deominator is not an
estimate of the variation of the mean. Rather, it is pooled estimate of
the population variance, based on the within group variance
estimates... Estimates of variance (s^2) will only be chi-squared
distributed if the populations are normal...
But once again, the F-statistic is robust with regard to this problem as
long as the populations are of similar shape...
BW
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
