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Re: st: qnorm

From   Maarten Buis <[email protected]>
To   [email protected]
Subject   Re: st: qnorm
Date   Mon, 5 Mar 2012 10:17:02 +0100

On Mon, Mar 5, 2012 at 4:26 AM, amir gahremanpour wrote:
> In one of my lectures about distributions, I was taught that in QQ-plot all points should be within z=+/-2 !, If we have such a definition we should be able
> to calculate p-value for QQ plot, right? visual assessment of qqplot is very subjective !

I would say that that the rule +/- 2 is very subjective. Not only is
your test subjective, it is also wrong. A normal distribution is a
distribution for a variable that can take values from -infinity to
+infinity not -2*standard_deviation to +2*standard_deviation. In fact
we know that if your variable truly follows a normal/Gaussian
distribution than we would expect that about 4.5% of the observations
should fall outside that range.

A statistical test requires a null hypothesis, and the null hypothesis
has to refer to a concrete statistic, so it cannot be "the
distribution is normally distributed". In your case the statistic
would be the range of your variable and the null hypothesis would be
"the range is less than or equal to (-2*standard_deviaiton,
+2*standard_deviation)", which, as I said above, does not make any
sense when you want to test for normality. There are other tests that
make more sense, and these look for example for specific values of the
skewness (0) and the kurtosis (3), but those focus on very particular
aspects of the normal distribution.  In that sense statistical tests
are more subjective than looking at plots; tests look at some aspects
but ignore others, and the choice of which aspect to look at is
typically guided by computational convenience rather than a
substantive argument.

Hope this helps,

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