st: R: Interpreting Shapiro-Wilk-Test (swilk)

["Carlo Lazzaro" <carlo.lazzaro@tiscalinet.it>]

With 2830 observations Christian would be probably better off with a visual
inspection of regression residuals instead of relying on Shapiro-Wilk-Test
(or the like).

Kind regards,
Carlo
-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Christian
Schroetel
Inviato: martedì 10 settembre 2013 12:18
A: statalist@hsphsun2.harvard.edu
Oggetto: st: Interpreting Shapiro-Wilk-Test (swilk)

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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