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Re: st: re: conflicting tests for normality

From   Maarten buis <>
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.  
> 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 L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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