Date: Tue, 1 May 2007 12:45:28 -0500
Reply-To: "Swank, Paul R" <Paul.R.Swank@uth.tmc.edu>
Sender: "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From: "Swank, Paul R" <Paul.R.Swank@uth.tmc.edu>
Subject: Re: shapiro-wilks
In-Reply-To: <962091718.20070501173508@terra.es>
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I am in general compliance here except for the part about accept Ho: One never accepts the null hypothesis. Just because the result is not significant does not mean that the null hypothesis is true. In fact the null hypothesis is probably never true. The real question is whether the differences are small enough not to worry about. So we might say given a p value > .05 (or whatever nominal level is selected) that we have no evidence that leads us to conclude the null is false. In this particular case, we might say that we no evidence that says the distribution is not normal. But it could be a type II error.
Paul R. Swank, Ph.D.
Professor, Developmental Pediatrics
Director of Research,
University of Texas Health Science Center at Houston
-----Original Message-----
From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of Marta García-Granero
Sent: Tuesday, May 01, 2007 10:35 AM
To: SPSSX-L@LISTSERV.UGA.EDU
Subject: Re: shapiro-wilks
Hi Fermin
Monday, April 30, 2007, 6:17:07 PM, You wrote:
OF> I think there is room for confusion here.
OF> Ho: the distribution is non-normal,
OF> Ha: the distribution is normal.
Ouch!
NO, NO, definitely NO. The null hypothesis for a normality test is that the variable IS normal (believe man, I'm a statistics teacher...). Null hypotheses, as I said in my previous mail, say that there are no differences, no effects... In this particular case, it says that the observed distribution is NOT different from the one we would expect had the sample been drawn from a normal population.
If p-value >> alpha then conclude Ha.
Ouch again!!
p-value >> alpha means "accept H0".
If p-value >> It may not be
If p-value >> wise to give more weight to the graph especially if one If p-value >> is unfamiliar with the shapes of the distributions (long If p-value >> tails, short tails).
In big samples, tails are of very little importance (leptokurtosis effect dilutes faster with sample size than skewness, I even read a math demo of that effect time ago). Skewness, on the other hand, is important and is easily spotted with a histogram
OF> Hi Christian
OF> Saturday, April 28, 2007, 4:30:08 AM, You wrote:
CH>> What it the null hypothesis of shapiro wilks test of univariate
CH>> normality. That is if p < .05, does this indicate normality, or
CH>> non- normality?
OF> In general, the null hypotheses for any statistical test is "no
OF> effect", "no differences". This means that for a normality test, the
OF> null hypothesis is "No differences from a normal distribution".
OF> p<.05 means NON-NORMALITY.
OF> Anyway, remember that the p-value is not really informative.
OF> Normality tests have low power if sample size is low (don't use them
OF> for sample sizes below 10-12 cases), and are over sensitive for vey
OF> big samples (if n is bigger than 100 then take a look at the
OF> histogram with a normality curve plotted over it and decide if the
OF> variable looks normal enough).
OF> --
OF> Regards,
OF> Dr. Marta García-Granero,PhD mailto:biostatistics@terra.es
OF> Statistician
OF> ---
OF> "It is unwise to use a statistical procedure whose use one does not
OF> understand. SPSS syntax guide cannot supply this knowledge, and it
OF> is certainly no substitute for the basic understanding of statistics
OF> and statistical thinking that is essential for the wise choice of
OF> methods and the correct interpretation of their results".
OF> (Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)
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--
Regards,
Dr. Marta García-Granero,PhD mailto:biostatistics@terra.es
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)
