[R] normality tests [Broadcast]

[Liaw, Andy]

From: gatemaze at gmail.com
> 
> On 25/05/07, Frank E Harrell Jr <f.harrell at vanderbilt.edu> wrote:
> > gatemaze at gmail.com wrote:
> > > Hi all,
> > >
> > > apologies for seeking advice on a general stats question. I ve run
> > > normality tests using 8 different methods:
> > > - Lilliefors
> > > - Shapiro-Wilk
> > > - Robust Jarque Bera
> > > - Jarque Bera
> > > - Anderson-Darling
> > > - Pearson chi-square
> > > - Cramer-von Mises
> > > - Shapiro-Francia
> > >
> > > All show that the null hypothesis that the data come from a normal
> > > distro cannot be rejected. Great. However, I don't think 
> it looks nice
> > > to report the values of 8 different tests on a report. One note is
> > > that my sample size is really tiny (less than 20 
> independent cases).
> > > Without wanting to start a flame war, are there any 
> advices of which
> > > one/ones would be more appropriate and should be reported 
> (along with
> > > a Q-Q plot). Thank you.
> > >
> > > Regards,
> > >
> >
> > Wow - I have so many concerns with that approach that it's 
> hard to know
> > where to begin.  But first of all, why care about 
> normality?  Why not
> > use distribution-free methods?
> >
> > You should examine the power of the tests for n=20.  You'll probably
> > find it's not good enough to reach a reliable conclusion.
> 
> And wouldn't it be even worse if I used non-parametric tests?

I believe what Frank meant was that it's probably better to use a
distribution-free procedure to do the real test of interest (if there is
one) instead of testing for normality, and then use a test that assumes
normality.

I guess the question is, what exactly do you want to do with the outcome
of the normality tests?  If those are going to be used as basis for
deciding which test(s) to do next, then I concur with Frank's
reservation.

Generally speaking, I do not find goodness-of-fit for distributions very
useful, mostly for the reason that failure to reject the null is no
evidence in favor of the null.  It's difficult for me to imagine why
"there's insufficient evidence to show that the data did not come from a
normal distribution" would be interesting.

Andy

 
> >
> > Frank
> >
> >
> > --
> > Frank E Harrell Jr   Professor and Chair           School 
> of Medicine
> >                       Department of Biostatistics   
> Vanderbilt University
> >
> 
> 
> -- 
> yianni
> 
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