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# Re: st: re: conflicting tests for normality

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: re: conflicting tests for normality Date Fri, 25 Feb 2011 14:10:10 +0000 (GMT)

```--- On Fri, 25/2/11, Kouji Asakura wrote:
> I need help with a problem I'm having. I'm testing for
> normality of a variable and I made use of the tests in
> Stata;  Shapiro-Wilk, the sktest, and Shapiro-Francia.
> However, I obtained conflicting results.
<snip>
> So you see, the -sktest- says it's not normal, while both
> Shapiro tests say the opposite, at least at a 0.05 alpha.

This is a rather difuse hypothesis: there are many ways in
which a distribution can deviate from a theoretical
distribution. This makes it a hard hypothesis to test, and
often leads to not very powerful tests. So it is no surprise
that different tests give different outcomes.

The first thing I would do is graph the distribution and
see to what extend and, more importantly, in what way the
distribution deviates from normality/Gaussianity. Two
useful graphs for this purpose are -qnorm- and -hangroot-,
whereby the latter is user written and can be downloaded
by typing in Stata -ssc install hangroot-.

Once you have figured out how the distribution deviates
from normality/Gaussianity, you can make an informed
decision on whether you want to do something about it,
and if so, what. This is just another way of saying that
you need to know what the problem is before you can think
about how to fix it.

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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