[R] shapiro wilk normality test

Robert A LaBudde ral at lcfltd.com
Sat Jul 12 20:56:01 CEST 2008

At 12:48 PM 7/12/2008, Bunny, lautloscrew.com wrote:
>first of all thanks yall. it´s always good to get it from people that
>know for sure.
>my bad, i meant to say it´s compatible with normality. i just wanted
>to know if it wouldnt be better to test for non-normality in order to
>know for "sure".
>and if so, how can i do it?

Doing a significance test may seem complicated, 
but it's an almost trivial concept.

You assume some "null hypothesis" that specifies 
a unique distribution that you can use to 
calculate probabilities from. Then use this 
distribution to calculate the probability of 
finding what you found in your data, or more 
extreme. This is the P-value of the test. It is 
the probability of finding what you found, given 
that the null hypothesis is true. You give up 
("reject") the null hypothesis if this P-value is 
too unbelievably small. The conventional measure 
for ordinary, repeatable experiments is 0.05. 
Sometimes a smaller value like 0.01 is more reasonable.

Doing what has been suggested, i.e., using a null 
hypothesis of "nonnormality", is unworkable. 
There are uncountably infinite ways to specify a 
"nonnormal" distribution. Is it discrete or 
continuous? Is it skewed or symmetric? Does it go 
from zero to infinity, from 0 to 1, from 
-infinity to infinity, or anything else? Does it 
have one mode or many? Is it continuous or differentiable? Etc.

In order to do a statistical test, you must be 
able to calculate the P-value. That usually means 
your null hypothesis must specify a single, unique probability distribution.

So "nonnormal" in testing means "reject normal as 
the distribution". "Nonnormal" is not defined 
other than it's not the normal distribution.

If you wish to test how the distribution is 
nonnormal, within some family of nonnormal 
distributions, you will have to specify such a 
null hypothesis and test for deviation from it.

E.g., testing for coefficient of skewness = 0.

Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

"Vere scire est per causas scire"

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