[extropy-chat] the structure of randomness

[gts]

On Sat, 31 Dec 2005 01:58:03 -0500, Russell Wallace  
<russell.wallace at gmail.com> wrote:

> The part I don't understand is: the distribution apparently deviated from
> the bell curve; is it the case that the deviation was no greater than  
> would be expected by chance?

The distributions do not deviate in any significant way from normal, but  
the *fine structures* of multiple histograms seem correlated in time. For  
example a bell-curve with a slightly "m-ish" shape (two subtle peaks) will  
tend to appear again in the next test. That "m-ish" propensity then falls  
off with time.

> If so, suppose the number of samples were increased by some factor and  
> the shape stayed the same (ratherthan converging on the bell curve as  
> the number approached infinity),would it start failing the test for  
> normalcy at some point?

My intuition is no; I think these distributions will always appear normal.  
(I don't know why I think this is so, except that I don't think the  
universe is going to give it up that easy. :)

What is needed here is a test for similarities in the fine structures of  
the histograms. John Walker used the chi-square goodness of fit test.

-gts