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Re: st: qnorm


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: qnorm
Date   Mon, 5 Mar 2012 09:03:54 +0000

If by z is meant observed (value - mean) / SD, then |z| <= 2 is
neither necessary nor sufficient for univariate normality. It is often
true that very large |z| is a sign of problems, but all z being in
that range does not guarantee normality.

Even with some other hypothetical criterion that must be true for all
the data, that would lead to a yes-no decision, not a P-value. If
there were some infallible criterion for establishing (non-)normality,
there would clearly be no need for any test or graphical assessment.

Some people have used the correlation between observed and expected
quantiles as shown graphically by -qnorm- and if I recall correctly
the Shapiro-Wilk test has an interpretation in terms of that
correlation.

By "very subjective" I take you to mean that you must use your
statistical or scientific judgement, drawing on experience. You have
to do that any way in deciding what to do. Conclusions are made easier
by comparisons:

1. Simulate several samples from a distribution with the same mean and
standard deviation (or more generally an appropriate mean and standard
deviation) and use the resulting portfolio of plots in assessing what
kind of variability is to be expected. Some people formalise that with
an envelope procedure.

2. Often the decision is quite easy, because e.g. the -qnorm- plot for
log y is much better behaved than that for y, so a transformation is
indicated.

3. Often the decision is quite easy, because e.g. a quantile-quantile
plot for some other distribution is much better behaved than the
-qnorm- plot, so a different distribution is indicated.

All that said, the most common situation is that approximate normality
of errors is a secondary assumption for some model. Multivariate
normality is often checked when it is not really required for any
method.

I don't know a graph associated with the Doornik-Hansen test. I doubt
that such a graph would help in diagnosing what is responsible for
non-normality when it is detected.

A graph "like in R": This may make sense to some R experts, but I have
no idea what you have in mind.

You could just look at all the univariate distributions, subject to
the usual caveats.

Nick

On Mon, Mar 5, 2012 at 3:26 AM, amir gahremanpour <gamirali@hotmail.com> 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 !
>
> Is that possible to create QQ plot in stata for multivariate normality  (like in R), for example using "mvtest normality" (default is dhansen test).
>
>
>> Date: Sun, 4 Mar 2012 08:36:04 +0000
>> Subject: Re: st: qnorm
>> From: njcoxstata@gmail.com
>> To: statalist@hsphsun2.harvard.edu
>>
>> -qnorm- is just a graphical comparison; there is no associated
>> P-value. There are various tests for more formal comparisons. If only
>> allowed -qnorm- or a test, I would always choose -qnorm-.
>>
>> Which multivariate normality test and what kind of graph do you have in mind?
>>
>> Nick
>>
>> On Sun, Mar 4, 2012 at 3:45 AM, amir gahremanpour <gamirali@hotmail.com> wrote:
>>
>> > I appreciate it if someone can teach me how to get p-value for qnorm and how to generate graph for multivariate normality test.

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