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Interpretation of Shapiro-Wilk

3 messages · Clive Jenkins, Kurt Hornik, Peter Dalgaard

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Can anybody tell me the exact meaning of the $statistic and $p.value
calculated by shapiro.test? Unfortunately it is not covered in my few
text books, and I cannot find the explanation in the R documentatiom or
on-line.

If I have a test statistic, T, which is Normally distributed with mean=m
and sd=s under the null hypothesis, then I can convert T to a p-value
(one-sided) using:

p <- pnorm(T, mean=m, sd=s)

If the distribution of T deviates from Normality, how can I modify the
above expression using the results of shapiro.test?

TIA,
Clive Jenkins

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You can use shapiro.test(x) for testing whether x (a numeric vector with
length in [3, 5000]) comes from a normal distribution.  The test is
based on the correlation between the ranks of the sample and those of a
standard normal distribution.  The p value indicates how significant the
deviation from 1 (the correlation under the null of normality) is, i.e.,
how significantly the sample deviates from normality.

I don't see how you could use shapiro.test() in the above situation.

-k
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Kurt Hornik <Kurt.Hornik at ci.tuwien.ac.at> writes:
Um. The *ideal* linear correlation under normality. Even for truly normal
samples, the correlation is of course always < 1.