[R] Normality test

[rkevinburton at charter.net]

I am having a hard time interpreting the results of the 'shapiro.test' for normality. If I do ?shapiro.test I see two examples using rnorm and runif. When I run the test using rnorm I get a wide variation of results. Most of this may be from variability of rnorm, samll sample size (limited to 5000 for the test), etc but if I repeat the test multiple times I can get:

> shapiro.test(rnorm(4900, mean = 5, sd = 3))

        Shapiro-Wilk normality test

data:  rnorm(4900, mean = 5, sd = 3) 
W = 0.9994, p-value = 0.09123

With a p-value of 0.09 it doesn't give me alot of confidence that either rnorm is producing a normal distirbution of this test is very reliable. Obivously this test has gained wide acceptance so I was wondering if I am expecting too much? Is there a "better" test?

Thanks for sharing your experience and your recomendations.

Kevin