[R] Shapiro-Welch W value interpretation

[Omar Baqueiro]

Hello,

I have tested a distribution for normality using the Shapiro-Welch
statistic. The result of this is the following:


        Shapiro-Wilk normality test

data: mydata
W = 0.9989, p-value = 0.8791


I know that the p-value > 0.05 (for my purposes) means that the data
IS normally distributed but what I am not sure is with the W value,
what values tell me that the data is normally distributed.   I know
that my data is normally distributed, but what I want to know if how
to interpret the W value, I have read that "if W is very small then
the distribution is probably not normally distributed", but how
"small"  is "very small", and also, what happens is, say W = 0.000001
but the p-value is > my significance level (0.05)? is the hypothesis
rejected?

thank you!

Omar