Re: Determining if samples are normal

[Mike Miller]

On Mon, 26 Sep 2005, Paul Kienzle wrote:

> On Sep 26, 2005, at 8:11 PM, Mike Miller wrote:
>
> > On Mon, 26 Sep 2005, Paul Kienzle wrote:
> >
> > > Using n=400, 60% of the triangular samples are rejected at a .1 level, 
> > > but of course 10% of the normal samples are as well.
> >
> >
> > So maybe the q-q correlation method is more powerful than 
> > Anderson-Darling in this case.  In the q-q correlation method, with 
> > n=300, we could reject 49% at the .05 level.  Of course 49% is less 
> > than 60%, but that was achieved with a smaller sample size and half the 
> > type-1 error rate.
>
> For n=300, I get 25% correct rejection at the 5% level compared to the 
> triangular distribution, so not so great.


In other words, 25% power to reject normality of the triangular data, but 
the q-q correlation method yielded 49% power for the same triangular 
distribution.  That is impressive.

The tricky thing about the correlational method is that you need to either 
rely on tables for critical values, or generate them by simulation.  So 
the q-q correlation method would be more computationally demanding than 
Anderson-Darling.

This is kinda fun, truly, but I have to say that data are nearly always 
non-normal to some degree and most statistical tests can tolerate some 
degree of deviation from normality.  We also have tests that don't require 
normality and are always valid.  So I have to say that I suspect that 
having a powerful test of normality is often not all that important.  I 
haven't read any of the literature on normality tests in a long time so I 
don't know what people are saying these days.

Mike



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