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Re: st: re: conflicting tests for normality


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: re: conflicting tests for normality
Date   Fri, 25 Feb 2011 14:27:58 +0000

In addition, note that there need be no contradiction here. For
example, a distribution might be
approximately symmetric but have fatter tails than the normal, or
asymmetric but happen to have about the same kurtosis as a normal.

Furthermore, it is rare that the marginal normality of a variable is
quite what you should be worried about. Even when normality is an
assumption, it is usually that responses are conditionally normal
given predictors, or equivalently that disturbances are normal, and
that's usually the least important assumption being made, although for
bizarre reasons it's often the assumption that is most scrutinised.

Nick

On Fri, Feb 25, 2011 at 2:10 PM, Maarten buis <maartenbuis@yahoo.co.uk> wrote:
> --- 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.

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