[R] normality tests [Broadcast]

[Bert Gunter]

False. Box proved ~ca 1952 that standard inferences in the linear regression
model are robust to nonnormality, at least for (nearly) balanced designs.
The **crucial** assumption is independence, which I suspect partially
motivated his time series work on arima modeling. More recently, work on
hierarchical models (e.g. repeated measures/mixed effect models) has also
dealt with lack of independence.


Bert Gunter
Genentech Nonclinical Statistics


-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of wssecn
Sent: Friday, May 25, 2007 2:59 PM
To: r-help
Subject: Re: [R] normality tests [Broadcast]

 The normality of the residuals is important in the inference procedures for
the classical linear regression model, and normality is very important in
correlation analysis (second moment)...

Washington S. Silva

> Thank you all for your replies.... they have been more useful... well
> in my case I have chosen to do some parametric tests (more precisely
> correlation and linear regressions among some variables)... so it
> would be nice if I had an extra bit of support on my decisions... If I
> understood well from all your replies... I shouldn't pay soooo much
> attntion on the normality tests, so it wouldn't matter which one/ones
> I use to report... but rather focus on issues such as the power of the
> test...
> 
> Thanks again.
> 
> On 25/05/07, Lucke, Joseph F <Joseph.F.Lucke at uth.tmc.edu> wrote:
> >  Most standard tests, such as t-tests and ANOVA, are fairly resistant to
> > non-normalilty for significance testing. It's the sample means that have
> > to be normal, not the data.  The CLT kicks in fairly quickly.  Testing
> > for normality prior to choosing a test statistic is generally not a good
> > idea.
> >
> > -----Original Message-----
> > From: r-help-bounces at stat.math.ethz.ch
> > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Liaw, Andy
> > Sent: Friday, May 25, 2007 12:04 PM
> > To: gatemaze at gmail.com; Frank E Harrell Jr
> > Cc: r-help
> > Subject: Re: [R] normality tests [Broadcast]
> >
> > From: gatemaze at gmail.com
> > >
> > > On 25/05/07, Frank E Harrell Jr <f.harrell at vanderbilt.edu> wrote:
> > > > gatemaze at gmail.com wrote:
> > > > > Hi all,
> > > > >
> > > > > apologies for seeking advice on a general stats question. I ve run
> >
> > > > > normality tests using 8 different methods:
> > > > > - Lilliefors
> > > > > - Shapiro-Wilk
> > > > > - Robust Jarque Bera
> > > > > - Jarque Bera
> > > > > - Anderson-Darling
> > > > > - Pearson chi-square
> > > > > - Cramer-von Mises
> > > > > - Shapiro-Francia
> > > > >
> > > > > All show that the null hypothesis that the data come from a normal
> >
> > > > > distro cannot be rejected. Great. However, I don't think
> > > it looks nice
> > > > > to report the values of 8 different tests on a report. One note is
> >
> > > > > that my sample size is really tiny (less than 20
> > > independent cases).
> > > > > Without wanting to start a flame war, are there any
> > > advices of which
> > > > > one/ones would be more appropriate and should be reported
> > > (along with
> > > > > a Q-Q plot). Thank you.
> > > > >
> > > > > Regards,
> > > > >
> > > >
> > > > Wow - I have so many concerns with that approach that it's
> > > hard to know
> > > > where to begin.  But first of all, why care about
> > > normality?  Why not
> > > > use distribution-free methods?
> > > >
> > > > You should examine the power of the tests for n=20.  You'll probably
> >
> > > > find it's not good enough to reach a reliable conclusion.
> > >
> > > And wouldn't it be even worse if I used non-parametric tests?
> >
> > I believe what Frank meant was that it's probably better to use a
> > distribution-free procedure to do the real test of interest (if there is
> > one) instead of testing for normality, and then use a test that assumes
> > normality.
> >
> > I guess the question is, what exactly do you want to do with the outcome
> > of the normality tests?  If those are going to be used as basis for
> > deciding which test(s) to do next, then I concur with Frank's
> > reservation.
> >
> > Generally speaking, I do not find goodness-of-fit for distributions very
> > useful, mostly for the reason that failure to reject the null is no
> > evidence in favor of the null.  It's difficult for me to imagine why
> > "there's insufficient evidence to show that the data did not come from a
> > normal distribution" would be interesting.
> >
> > Andy
> >
> >
> > > >
> > > > Frank
> > > >
> > > >
> > > > --
> > > > Frank E Harrell Jr   Professor and Chair           School
> > > of Medicine
> > > >                       Department of Biostatistics
> > > Vanderbilt University
> > > >
> > >
> > >
> > > --
> > > yianni
> > >
> > > ______________________________________________
> > > R-help at stat.math.ethz.ch mailing list
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide
> > > http://www.R-project.org/posting-guide.html
> > > and provide commented, minimal, self-contained, reproducible code.
> > >
> > >
> > >
> >
> >
> > ------------------------------------------------------------------------
> > ------
> > Notice:  This e-mail message, together with any
> > attachments,...{{dropped}}
> >
> > ______________________________________________
> > R-help at stat.math.ethz.ch mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> > http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> >
> 
> 
> -- 
> yianni
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

______________________________________________
R-help at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.