As always, failure to reject the null hypothesis does not mean that the distribution id normally distributed. It means that the evidence is insufficient to reject the null. The distribution might be non-normal and you are unable to reject the null due to, as Marta says, a lack of power. Tests of assumptions are only useful when properly powered. Too small an n and you rarely find signficant results even when they are justified, and too large an n means finding significance even when the discrepencies are small.
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:
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Sent: Monday, October 02, 2006 5:03 AM
To:
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Subject: Re: Shapiro-Wilks test
Hi Tolis
A statistic, like the sample mean, when divided by the sample standard error, can follow a t distribution, but raw data don't.
The null hypothesis for SW test is ALWAYS: "the variable comes from a population normally distributed".
The only problem related to sample size below 30 is lack of power.
TL> just a theoretical question...
TL> I'm using the Shapiro-Wilks test to test the normality of a small sample (less than 30).
TL> Which is the right expression for the outcome:
TL> 1) the sample is normal distributed
TL> or
TL> 1) the sample is t distributed
--
Regards,
Dr. Marta Garcνa-Granero,PhD mailto:
[hidden email]
Statistician
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"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)
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