[R] normality tests

Frank E Harrell Jr f.harrell at vanderbilt.edu
Fri May 25 18:45:11 CEST 2007

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.


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

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