st: Interpreting Shapiro-Wilk-Test (swilk)

[Christian Schroetel <christian.schroetel@googlemail.com>]

Dear statistics and/or Stata experts,

actually, I'm used to find out or clear up things myself using FAQs,
helps or such. But this time, I'm quite confused so I decided to use
the chance to get help via Statalist. It's my first time, though.

For my master thesis, I'm performing several regressions on panel data
with up to 13 independent variables (xtreg). To check for normality of
the residuals, I did the following:

- xtreg sgrowth l.sgrowth l.slnsales slnage scfratio  srdintensity
sleverage spersonalpremium sintangibles sinternationalsales sroa
stobinsq sclr scurrentratio, fe -
- predict r, ue -
- kdensity r, normal -
- iqr r -
- swilk r -

The kdensity graphics for the combined resiudal indicate quite some
normality, iqr doesn't show any severe outliers and only less than
0.5% mild outliers indicating a quite symmetric distribution of the
residuals as well. Also, pnorm and qnorm deliver decent graphics
indicating normality. But now I get the following result with swilk:


    Variable |    Obs       W           V         z       Prob>z
-------------+--------------------------------------------------
           r |   2830    0.99739      4.245     3.723    0.00010

As far as I know, a high value of W should indicate normality, so,
again, that would say I've got normally distributed residuals.
Nevertheless, the p-value indicates rejection of the null hypothesis
of normality.
So, now I wonder whether I'm doing something wrong or whether I should
just not pay too much attention to the p-value. It's just that I'd
like to say in my thesis that the Shapiro-Wilk test indicates
normality, which I probably couldn't the way i is now. Respectively,
what could be the reason for the low p-value combined with a high
value for W?

I'd appreciate any thoughts, comments or help on that issue and thank
you in advance for your efforts.

Best regards

Christian

Btw: I tried all the same with - predict r, e - (as I ddin't exactly
know which way to test for normality of the residuals) and - sfrancia
r - delivering similar results.
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