Re: [Phys-l] Basic statistics

["Folkerts, Timothy J" <FolkertsT@bartonccc.edu>]

Jack

You & I seem to be talking past each other.  Let's see if I can make my point more clearly and then see if we can reach common ground.  


> When I said "carefully stated" I was trying to exclude puns.  
> Tim  makes a pun on the phrase "applies to."   

While I like puns as much - usually more ;-) - than the next guy, I'm not sure what I said that could be construed as a pun.

Your basic statement of the CLT was
"The texts tell us, as I understand them, that the means of vary 
large samples taken from finite variance distributions are normally 
distributed about a central value.  I do not know whether there is a proof 
that relaxes the limiting conditions."

That sounds like a pretty decent summary.  


> While his statement is correct, it doesn't contradict mine, 
> namely, the chi-square distribution does not become normal 
> in the large N limit.  

and

> In the case of the chi-square distribution it is easy to demonstrate 
> by example with MathCad or a similar program that the large N limit 
> is not Gaussian.

I still disagree.  I ran a simulation using a chi square with 2 degrees of freedom (which looks far from normal).  I added 100 (i.e. a large N) results from this chi square distribution.  I repeated this process 1000 times.  The distribution of these 1000 points looks normally distributed.  It also passes the standard Anderson-Darling test for normality.  (Or more precisely, it doesn't fail the test.)

And actually, I will admit I WAS wrong on one point.  The chi-square distribution does approach a normal distribuion for large degrees offreedom.  It doesn't look very close for small degress of fredom, but it does eventually start to look like the normal distribution.  

So whether N means "degrees of freedom" or N is a large sample as intended for the CLT, either one approaches normality for large N.

 
Tim F