# [R] shapiro.test

Ernesto Jardim ernesto at ipimar.pt
Mon Feb 10 16:18:02 CET 2003

```Ok, let me put it the other way around.

On another test I have W = 0.9907, p-value = 6.024e-06. The same
question stands, with such huge W should it be expected to be normal ?

EJ

On Mon, 2003-02-10 at 14:47, Richard A. Bilonick wrote:
> Ernesto Jardim wrote:
>
> >Hi
> >
> >The shapiro.test function outputs a value of the W statistic, which
> >should be 1 if the distribution is normal, and a p-value for the test
> >(as the documentation states).
> >
> >I'm a bit confused with some results. I'm getting a W=0.9977 and a
> >p-value=0.1889.
> >
> >I was expecting that a W of 0.9977 would tell me that the distribution
> >is normal so p-value should be small ...
> >
> >What am I missing ?
> >
> >Thanks
> >
> >EJ
> >
> >______________________________________________
> >R-help at stat.math.ethz.ch mailing list
> >http://www.stat.math.ethz.ch/mailman/listinfo/r-help
> >
> >
> >
> >
> You have it backwards. The null hypothesis is that the distribution is
> Normal. You reject this null when the p-value is small. If the
> distribution is Normal, the p-value will tend to be large.
>
>  > shapiro.test(rnorm(100))
>
>         Shapiro-Wilk normality test
>
> data:  rnorm(100)
> W = 0.9877, p-value = 0.4894
>
>
> Rick B.
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> http://www.stat.math.ethz.ch/mailman/listinfo/r-help

```