# Re: st: Shapiro Wilk: data interpretation

 From "Svend Juul" To Subject Re: st: Shapiro Wilk: data interpretation Date Wed, 28 Feb 2007 10:16:00 +0100

```Vanessa Mahlperg wrote:

I've got a question concerning the interpretation of the Shapiro-Wilk
test results.
I don't know the correct meaning of V, z and Prob>z in German. Could
anybody tell me how to identify the normal distribution in the following
case:

swilk c_ws6m c_ws2j c_stelle if zugeh==2
Shapiro-Wilk W test for normal data

Variable  Obs        W      V       z   Prob>z
c_ws6m     87  0.88729  8.290   4.656  0.00000
c_ws2j     87  0.99142  0.631  -1.015  0.84484
c_stelle   87  0.98980  0.750  -0.632  0.73638

------------------------------------------------------------------------
----

W and V are specific to the Shapiro-Wilk test; if you need to know more
(I don't), Google will point to explanations.

z is the z-statistic; you will find it in any statistical textbook and
in the output from numerous commands. Essentially it is an estimate
divided by its standard error.

Prob>z is one of Stata's strange shorthand habits; you will find it in
the output from numerous commands. It does NOT mean that a probability
is larger than z, but (in the line for c_ws6m) that - if the
null-hypothesis of normality is true - the probability of z being 4.656
or more extreme, is < 0.00001.

The above results would lead most of us to reject the null-hypothesis of
normality for c_ws6m, and accept it for c_ws2j and c_stelle. But some of
us prefer to assess normality visually rather than by statistical
testing; -histogram- and -qnorm- are useful commands for that.

Hope this helps
Svend

__________________________________________

Svend Juul
Institut for Folkesundhed, Afdeling for Epidemiologi
(Institute of Public Health, Department of Epidemiology)
Vennelyst Boulevard 6
DK-8000  Aarhus C, Denmark
Phone: +45 8942 6090
Home:  +45 8693 7796
Email: sj@soci.au.dk
__________________________________________

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```