shapiro-wilks

[chris hansen-4]

What it the null hypothesis of shapiro wilks test of univariate
normality.  That is if p < .05, does this indicate normality, or non-
normality?

Thank you

[Marta García-Granero]

Hi Christian

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 non-
CH> normality?

In general, the null hypotheses for any statistical test is "no
effect", "no differences". This means that for a normality test, the
null hypothesis is "No differences from a normal distribution". p<.05
means NON-NORMALITY.

Anyway, remember that the p-value is not really informative. Normality
tests have low power if sample size is low (don't use them for sample
sizes below 10-12 cases), and are over sensitive for vey big samples
(if n is bigger than 100 then take a look at the histogram with a
normality curve plotted over it and decide if the variable looks
normal enough).



--
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)

[Ornelas, Fermin]

I think there is room for confusion here.

Ho: the distribution is non-normal,
Ha: the distribution is normal.

If p-value > alpha then conclude Ha. It may not be wise to give more weight to the graph especially if one is unfamiliar with the shapes of the distributions (long tails, short tails). Presumably, what one would like to see is a straight line like pattern. But given how difficult sometimes is to achieve normality the test may be more reliable and should validate what is observed in the graph.

Fermin Ornelas, Ph.D.
Management Analyst III, AZ DES
Tel: [phone]
E-mail: [hidden email]


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Marta García-Granero
Sent: Sunday, April 29, 2007 3:19 AM
To: [hidden email]
Subject: Re: shapiro-wilks

Hi Christian

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 non-
CH> normality?

In general, the null hypotheses for any statistical test is "no
effect", "no differences". This means that for a normality test, the
null hypothesis is "No differences from a normal distribution". p<.05
means NON-NORMALITY.

Anyway, remember that the p-value is not really informative. Normality
tests have low power if sample size is low (don't use them for sample
sizes below 10-12 cases), and are over sensitive for vey big samples
(if n is bigger than 100 then take a look at the histogram with a
normality curve plotted over it and decide if the variable looks
normal enough).



--
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)

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

[Martin P. Holt-2]

Fermin Ornelas wrote, in part:

>I think there is room for confusion here.

>Ho: the distribution is non-normal,
>Ha: the distribution is normal.

>If p-value > alpha then conclude Ha.

Now I am confused ! Don't we usually conclude Ha when p-value < alpha ?

Best,

Martin

[Ornelas, Fermin]

I sometimes confuse myself with the way the tests are conducted.
Often for a regular F and t test a low probability value is a good
thing.
Say if you have a p-value= .001 and your alpha is .05 for an F-test it
means that at least 1 of your betas is different from zero (multiple
regression situation). However, when it comes to a normality test it is
set up the other way. That is if your p-value < alpha that is not good.
It means the distribution is not normal. The same thing applies to a
Breusch-Peagan test for constant variance. In the latter, a
non-significant test is a good thing.

Thus, moral of the story when you are about to evaluate a hypothesis
have a good text book in hand.

Fermin Ornelas, Ph.D.
Management Analyst III, AZ DES
Tel: [phone]
E-mail: [hidden email]


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Martin P. Holt
Sent: Tuesday, May 01, 2007 1:11 AM
To: [hidden email]
Subject: Re: shapiro-wilks

Fermin Ornelas wrote, in part:

>I think there is room for confusion here.

>Ho: the distribution is non-normal,
>Ha: the distribution is normal.

>If p-value > alpha then conclude Ha.

Now I am confused ! Don't we usually conclude Ha when p-value < alpha ?

Best,

Martin

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

[Marta García-Granero]

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 non-
CH>> 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". p<.05
OF> means NON-NORMALITY.

OF> Anyway, remember that the p-value is not really informative. Normality
OF> tests have low power if sample size is low (don't use them for sample
OF> sizes below 10-12 cases), and are over sensitive for vey big samples
OF> (if n is bigger than 100 then take a look at the histogram with a
OF> normality curve plotted over it and decide if the variable looks
OF> normal enough).



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

OF> ---
OF> "It is unwise to use a statistical procedure whose use one does
OF> not 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
OF> PRIVILEGED OR CONFIDENTIAL information and is intended only for
OF> the use of the specific individual(s) to whom it is addressed.  It
OF> may contain information that is privileged and confidential under
OF> state and federal law.  This information may be used or disclosed
OF> only in accordance with law, and you may be subject to penalties
OF> under law for improper use or further disclosure of the
OF> information in this e-mail and its attachments. If you have
OF> received this e-mail in error, please immediately notify the
OF> person named above by reply e-mail, and then delete the original
OF> e-mail.  Thank you.



--
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)

[Marta García-Granero]

Hi everybody

Just to end this thread (Fermin Ornelas wrote privately to me a minute
ago), this link has a very succint and excellent explanation on the
topic of the null hypothesis for normality tests and cautions about
their utility. Harvey Motulsky's statistics book is really good
("Intuitive Biostatistics"), I recommend it as a good statistics
refresher, even though is centered onthe use of Prism statistical
package, the concepts can be applied to any other.

http://www.graphpad.com/library/BiostatsSpecial/article_197.htm

Extracted from one of the last paragraphs:

"All three procedures test the same the null hypothesis – that the
data are sampled from a Gaussian distribution. The P value answers
this question: If the null hypothesis were true, what is the chance of
randomly sampling data that deviate as much (or more) from Gaussian as
the data we actually collected?"

This other link is also interesting:

http://www.itl.nist.gov/div898/handbook/prc/section2/prc21.htm

Now, since today I shouldn't be working, I'm going to close my mail
program and play "Luxor 2" for a while.

Marta

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.

If p-value >> alpha then conclude Ha. 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). Presumably, what one would like to
If p-value >> see is a straight line like pattern. But given how
If p-value >> difficult sometimes is to achieve normality the test may
If p-value >> be more reliable and should validate what is observed in
If p-value >> the graph.

OF> Fermin Ornelas, Ph.D.
OF> Management Analyst III, AZ DES
OF> Tel: [phone]
OF> E-mail: [hidden email]


OF> -----Original Message-----
OF> From: SPSSX(r) Discussion [mailto:[hidden email]]
OF> On Behalf Of Marta García-Granero
OF> Sent: Sunday, April 29, 2007 3:19 AM
OF> To: [hidden email]
OF> Subject: Re: shapiro-wilks

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 non-
CH>> 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". p<.05
OF> 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
OF> them for sample sizes below 10-12 cases), and are over sensitive
OF> for vey big samples (if n is bigger than 100 then take a look at
OF> the histogram with a normality curve plotted over it and decide if
OF> the variable looks normal enough).

[Ornelas, Fermin]

Well it is human to make mistakes and it is also human to admit it when that happens especially when one replies too fast.

I had the ho and ha reversed. It should have been:

Ho: distribution is normal
Ha: distribution is non normal

But the rest of the argument should be OK.


Fermin Ornelas, Ph.D.
Management Analyst III, AZ DES
Tel: [phone]
E-mail: [hidden email]


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Marta García-Granero
Sent: Tuesday, May 01, 2007 8:35 AM
To: [hidden email]
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 non-
CH>> 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". p<.05
OF> means NON-NORMALITY.

OF> Anyway, remember that the p-value is not really informative. Normality
OF> tests have low power if sample size is low (don't use them for sample
OF> sizes below 10-12 cases), and are over sensitive for vey big samples
OF> (if n is bigger than 100 then take a look at the histogram with a
OF> normality curve plotted over it and decide if the variable looks
OF> normal enough).



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

OF> ---
OF> "It is unwise to use a statistical procedure whose use one does
OF> not 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
OF> PRIVILEGED OR CONFIDENTIAL information and is intended only for
OF> the use of the specific individual(s) to whom it is addressed.  It
OF> may contain information that is privileged and confidential under
OF> state and federal law.  This information may be used or disclosed
OF> only in accordance with law, and you may be subject to penalties
OF> under law for improper use or further disclosure of the
OF> information in this e-mail and its attachments. If you have
OF> received this e-mail in error, please immediately notify the
OF> person named above by reply e-mail, and then delete the original
OF> e-mail.  Thank you.



--
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]

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:[hidden email]] On Behalf Of Marta García-Granero
Sent: Tuesday, May 01, 2007 10:35 AM
To: [hidden email]
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:[hidden email]
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 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)

[peter link]

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

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Swank, Paul R
Sent: Tuesday, May 01, 2007 10:45 AM
To: [hidden email]
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:[hidden email]] On Behalf Of
Marta Garcma-Granero
Sent: Tuesday, May 01, 2007 10:35 AM
To: [hidden email]
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:[hidden email]
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:[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)

[Art Kendall-2]

In many disciplines the null hypothesis is about [the status quo, the
current, the default, the presumed] proposition, practice, or policy.
In the social and behavioral sciences, it is analogous to the US legal
presumption of innocence.  It is retained (stayed with), rather than
newly accepted.

The proposer of the alternative hypothesis seeks to replace the null
hypothesis, i.e., to have the alternative accepted.  If the evidence is
sufficiently inconsistent with the null hypothesis, the alternative is
asserted. In US criminal proceedings, the accused is found guilty.

A statistically non significant shapiro-wilks test means that the data
has not been proven to be non-normal.

Art Kendall
Social Research Consultants

peter link wrote:

> I think this is why Marta has put "accept H0" in quotation marks.
>
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
> Swank, Paul R
> Sent: Tuesday, May 01, 2007 10:45 AM
> To: [hidden email]
> 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:[hidden email]] On Behalf Of
> Marta Garcma-Granero
> Sent: Tuesday, May 01, 2007 10:35 AM
> To: [hidden email]
> 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:[hidden email]
> 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 Garcma-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)
>
>
>