test for normality

[Michael Stobernack]

Dear all,

I run two tests for normalty of one variable: Kolmogorov-Smirnov and
Shapiro-Wilk and I get two very different p-values: 0,200 and 0,0007.
So the first test leads to a confirmation of normality, but the second
test leads to a rejection of normality.
Which one should I trust?

I would be very glad about any hints.

Best regards,

Michael

[Marta García-Granero]

Hi Michael

MS> I run two tests for normalty of one variable: Kolmogorov-Smirnov and
MS> Shapiro-Wilk and I get two very different p-values: 0,200 and 0,0007.
MS> So the first test leads to a confirmation of normality,

Wrong, it only is unable to point to non-normality (could be true, the
variable is really normal, or it could also be lack of power - type II
error). "Absence of evidence is not evidence of absence" (quoting
Bland&Altman Statitcs Note at British Medical Journal).

MS>  but the second test leads to a rejection of normality.

Shapiro&Wilk published a paper (sorry, I can't recall right now)
proving that their normality test was superior to K-S (Lilliefors). If
you don't want to take that for granted:

Check:
- skewness (is it bigger than 1 and than twice its SE?)
- kurtosis (it is bigger than twice its standard error?)
- outliers (mainly extreme outliers, use the box-plot)

Is the general picture consistent with normality or not?

MS> Which one should I trust?

Neither, use your common sense after close examination of your data.


--
Regards,
Dr. Marta García-Granero,PhD           mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)

[Swank, Paul R]

 Listen to Marta and understand that these tests are significance tests
just like any other and can have type one or type two errors. A lot
depends on the sample size. A large sample size makes for a sensisitve
test of assumptions just like it makes for a sensitive test of your
hypothesis. So, if you have a large sample size, you may find trivial
departures from normality are statitically significant. However, this is
when violations of assumptions have least effect, when the sample size
is large. When you really need to know if you have normality (when
sample size is small) you have the least sensitivity to discover it. It
is far better to look at your data, get really involved in your data, so
as to understand what is going on and what impact it can have on what
you are trying to do. There is no substitute for a thorough knowledge of
your data.


Paul R. Swank, Ph.D.
Professor, Developmental Pediatrics
Director of Research, Children's Learning Institute
Medical School
University of Texas Health Science Center at Houston

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Michael Stobernack
Sent: Wednesday, September 06, 2006 11:36 AM
To: [hidden email]
Subject: test for normality

Dear all,

I run two tests for normalty of one variable: Kolmogorov-Smirnov and
Shapiro-Wilk and I get two very different p-values: 0,200 and 0,0007.
So the first test leads to a confirmation of normality, but the second
test leads to a rejection of normality.
Which one should I trust?

I would be very glad about any hints.

Best regards,

Michael