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Re: st: Normal Distribution

From   Maarten Buis <[email protected]>
To   [email protected]
Subject   Re: st: Normal Distribution
Date   Wed, 14 Sep 2011 14:44:50 +0200

On Wed, Sep 14, 2011 at 12:39 PM, Arman Eshaghi wrote:
> I have a question concerning normal distribution and normal plots. I have a
> sample of 250 subjects with some psychological scores that are not normally
> distributed. With scaled score conversion and cumulative distribution
> function I tried to approximate the distribution to normal distribution.
> However, kolmogorov-smirnov test is still significant which refutes the normality.
> Q-Q plots on the other hand show promising results for scaled scores. Does
> my data considered normally distributed in this case? My goal is to use
> these scores in discriminant analysis which presumes the data has a
> multivariate normal distribution.

The Kolmogorov-Smirnov test is particularly sensitive to deviations in
the middle of the distribution, while QQ-plots (-qnorm-) are
particularly sensitive to what happens in the tails. So, it is no
surprise that these two approaches lead to different conclusions.
Apparently there is something interesting going on in the center of
the distribution, which you can better see with a PP-plot (-pnorm-).

Anyhow, what you are looking at is the marginal distribution, and that
does _not_ have to look anything like a normal distribution. So for
your aim these tests and graphs are useless.

Hope this helps,

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