[R] Normality test

[Duncan Murdoch]

On 10/22/2009 9:48 AM, rkevinburton at charter.net wrote:
> 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?


I think you don't understand what p-values mean.  If the null is true, p 
is distributed as U(0,1).

You can see

Murdoch, D.J., Tsai, Y.-L. and Adcock, J. (2008).  P-values are random
variables.  {\em The American Statistician}, 242-245.

for more details (and exceptions to this very general rule).

Duncan Murdoch