# Re: [R] shapiro wilk normality test

From: Robert A LaBudde <ral_at_lcfltd.com>
Date: Sat, 12 Jul 2008 14:56:01 -0400

At 12:48 PM 7/12/2008, Bunny, lautloscrew.com wrote:
>first of all thanks yall. itīs always good to get it from people that
>know for sure.
>
>my bad, i meant to say itīs 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/
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