Allow me to offer a few useful references on test for normality:
Lilliefors, H.W.,
"On the Kolmogorov-Smirnov Tests for Normality with Mean and Variance
Unknown"
JASA, 62, 399-402, 1967.
Shapiro, S.S. and Francia, R.S.,
"An Approximate Analysis of Variance Test for Normality"
JASA, 67, 215-216, 1972.
Shapiro, S.S., and Wilk, M.B.,
"An Analysis of Variance Test for Normality"
Biometrika, 52, 591-611, 1965.
Shapiro, S.S., Wilk, M.B., and Chen, H.J.,
"A comparative study of various tests of normality"
JASA, 63, 1343-1372, 1968.
Stephens, M.A.,
"EDF statistics for goodness of fit and some comparisons"
JASA, 69, 730-737, 1974.
Andrews, Gnanadesikan, and Warner, (or perhaps just two of them -
I can't remember) have a book circa 1972 entitled
"Multivariate ..." something or other
in which they address testing multivariate normality by looking at
the normality of the respective marginal distributions.
Takes 3 minutes to find it at your library.
I hope the original poster finds these helpful, as they are the
seminal works on this subject (there are, of course, others, but
this should give you an excellent start).
I trust we can now return to the normal business of the list.
Best wishes,
Eric Gibson, Ph.D.
Novartis Pharmaceuticals
{The opinions expressed herein do not in any way represent Novartis
Pharmaceuticals}
"Gunter, Bert" <bert_gunter@merck.com> on 02/26/99 02:48:00 PM
To: s-news@wubios.wustl.edu, "'David F. Parkhurst'"
<parkhurs@indiana.edu>
cc: Nicholas Barrowman <barrowma@mscs.dal.ca> (bcc: Eric
Gibson/PH/Novartis)
Subject: RE: [S] Tests for multivariate NON-normality?
I hesitate to engage in this discussion, as it is rapidly degenerating into
the usual sort of blather when people get sloppy. So briefly:
1. NO data *are* normal. Normality is a mathematical entity, not a property
of data. One may use a normal distribution as an empirical model that
approximates data. One may also use any of 562 other distributions that may
do equally well. As George Box remarked: "All models are wrong, but some
are
useful."
2. Given enough real data, any test of normality will reject (a
meta-theorem?); this does not necessarily mean that a normal model does not
usefully characterize the data.
3. Given little enough data, any test of normality will fail to reject;
this
does not necessarily mean that a normal model will usefully characterize
the
data.
4. The above 2 points are why power/sample size (or versions thereof like
OC
curves) must be considered in applying N-P theory.
5. If the above 3 points bother you, become a Bayesian.
Bert Gunter
Biometrics Research RY 70-38
Merck & Company
P.O. Box 2000
Rahway, NJ 07065-0900
Phone: (732) 594-7765 Fax: (732) 594-1565
"The business of the statistician is to catalyze the scientific learning
process." -- George E.P. Box
> ----------
> From: David F. Parkhurst[SMTP:parkhurs@indiana.edu]
> Sent: Friday, February 26, 1999 2:08 PM
> To: s-news@wubios.wustl.edu
> Cc: Nicholas Barrowman
> Subject: Re: [S] Tests for multivariate NON-normality?
>
>
> There is more to the issue than just termiology. If your car gets across
> town in the snowstorm, then you know that it *can* travel through snow.
> If
> your car doesn't make it, then you know it *doesn't* do well. This test
> has
> a yes or no answer. My point was that normality tests (no matter how you
> refer to them) tend to be "one-way"---they can make you fairly confident
> of
> non-normality if you get a "significant" result, but (except with very
> large
> sample size), they shouldn't leave you confident that your data *are*
> normal.
>
> Dave Parkhurst
>
> -----Original Message-----
> From: Nicholas Barrowman <barrowma@mscs.dal.ca>
> To: David F. Parkhurst <parkhurs@indiana.edu>
> Date: Friday, February 26, 1999 12:16 PM
> Subject: Re: [S] Tests for multivariate NON-normality?
>
>
> >I think the issue is partly one of terminology.
> >I would talk about a test OF multivariate normality (not "for"),
> >(and similarly a test OF equality of variances).
> >The sense is that you are putting multivariate normality TO THE TEST,
> >just as you might put your car to the test in a snow storm.
> ------------------------
> >Nick Barrowman, Ph.D. Student,
> >Dalhousie University Department of
> >Mathematics, Statistics, & Computing Science
> >barrowma@mscs.dal.ca
> >http://www.mscs.dal.ca/~barrowma
>
>
>
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