Date:         Sat, 8 Jul 2006 23:05:59 -0700
Reply-To:     David L Cassell <davidlcassell@MSN.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         David L Cassell <davidlcassell@MSN.COM>
Subject:      Re: Normality
In-Reply-To:  <200607080727.k682Cwij011070@mailgw.cc.uga.edu>
Content-Type: text/plain; format=flowed

Madan.Kundu@RANBAXY.COM wrote:
>Hi,=0D
>
>=0D
>
>I have following output from SAS on test of normality.=0D
>
>                       Tests for Normality
>
>=0D
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>    Test                  --Statistic---    -----p Value------
>
>=0D
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>    Shapiro-Wilk          W     0.981333    Pr < W      0.0002
>
>    Kolmogorov-Smirnov    D     0.046238    Pr > D      0.0703
>
>    Cramer-von Mises      W-Sq  0.164991    Pr > W-Sq   0.0164
>
>    Anderson-Darling      A-Sq  1.358803    Pr > A-Sq  <0.0050
>
>=0D
>
>What does the above result indicates about normality? Normal or Non
>normal?

Well, what did I say about these tests and their power just the other day?

If you have a large enough data set, things will almost always come out
as significantly different form normality.  That does NOT mean that the
difference is noticeable, or even meaningful.

And if you have not done the parametric analysis and then looked at the
residuals, this is meaningless.  The normality of Y is usually utterly
useless.
Unless your set of X variables together with your Y variable is multivariate
normal, then the normality of Y just does not matter.  (Hint: the data
are never multivariate normal, even when the individual variables look
fairly normal.  It is a really, really strong assumption.)

Just do the cotton-picking analysis and look at a residual plot.  :-)  Do
not
try to automate this.

HTH,
David
--
David L. Cassell
mathematical statistician
Design Pathways
3115 NW Norwood Pl.
Corvallis OR 97330

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