I think this is why Marta has put "accept H0" in quotation marks.

-----Original Message----- From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU]On Behalf Of Swank, Paul R Sent: Tuesday, May 01, 2007 10:45 AM To: SPSSX-L@LISTSERV.UGA.EDU Subject: Re: shapiro-wilks

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 Garcma-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 Garcma-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)

OF> NOTICE: This e-mail (and any attachments) may contain PRIVILEGED OR OF> CONFIDENTIAL information and is intended only for the use of the OF> specific individual(s) to whom it is addressed. It may contain OF> information that is privileged and confidential under state and OF> federal law. This information may be used or disclosed only in OF> accordance with law, and you may be subject to penalties under law OF> for improper use or further disclosure of the information in this OF> e-mail and its attachments. If you have received this e-mail in OF> error, please immediately notify the person named above by reply OF> e-mail, and then delete the original e-mail. Thank you.

-- Regards, Dr. Marta Garcma-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)