[R] shapiro.test() output

[Matthew.Findley at ch2m.com]

R Users:

My question is probably more about elementary statistics than the
mechanics of using R, but I've been dabbling in R (version 2.2.0) and
used it recently  to test some data . 

I have a relatively small set of observations (n = 12) of arsenic
concentrations in background groundwater and wanted to test my
assumption of normality.  I used the Shapiro-Wilk test (by calling
shapiro.test() in R) and I'm not sure how to interpret the output.
Here's the input/output from the R console:

	>As = c(13, 17, 23, 9.5, 20, 15, 11, 17, 21, 14, 22, 13)
	>shapiro.test(As)

      	  Shapiro-Wilk normality test

	data:  As 
	W = 0.9513, p-value = 0.6555

How do I interpret this?  I understand, from poking around the internet,
that the higher the W statistic the "more normal" the data.

What is the null hypothesis - that the data is normally distributed?  

What does the p-value tell me?  65.55% chance of what - getting
W-statistic greater than or equal to 0.9513 (I picked this up from the
Dalgaard book, Introductory Statistics with R, but its not really
sinking in with respect to how it applies to a Shipiro Wilk test).? 

The method description - retrieved using ?shapiro.test() - is a bit
light on details.

Thanks much.

-------------------------------------
Matthew C. Findley, CPSSc
Environmental Scientist
 
CH2M HILL
mfindley at ch2m.com