[R] Normal distribution (Lillie.test())

[Greg Snow]

The t-test is even more standard fare, but I am not familiar with any textbooks that suggest that you use it for categorical data.  I just want people to think about what their question really is and if the test they are tempted to use really answers the right question.

Recommendations change, but they change much slower if nobody pushes for the change.  When I took my first intro stat class the standard procedure for a comparison of 2 means was to first test for equality of variance (sometimes using an alpha=0.2), then do a pooled t-test or an approximate t-test based on the results.  Current intro text books have switched to just suggesting the use of the approximate test (with better approximations now that we have computers to do the ugly formulas) and not bother with a variance test, or maybe use a rule of thumb variance test.  In some cases the pooled test is not even mentioned.

I am not saying to never use a test of normality, but I think many cases of doing normality tests (especially with large sample sizes and on residuals from a regression) are like the drunk looking for his keys under the light post rather than near where he dropped them because the light is better.  Doing a normality test is easy, but often it is answering the wrong question.

My hope is that the textbooks someday will move to suggesting the methodology implemented in the vis.test function (TeachingDemos package, note that the credit for this idea should go much more to the authors listed in the references section than to the function author).  I think that test answers a much more useful question of close enough.  And even the process of getting a significant p-value from that test may give the user confidence to conclude close enough.

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111


> -----Original Message-----
> From: Bert Gunter [mailto:gunter.berton at gene.com]
> Sent: Thursday, February 25, 2010 10:24 AM
> To: Greg Snow; 'Bosken'; r-help at r-project.org
> Subject: RE: [R] Normal distribution (Lillie.test())
> 
> ...
> 
> But,quoting Pogo, "We have met the enemy, and he is us."
> 
> Normality tests are standard fare in a host of statistical texts.
> 
> Bert Gunter
> Genentech Nonclinical Biostatistics
> 
> 
> 
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On
> Behalf Of Greg Snow
> Sent: Thursday, February 25, 2010 9:00 AM
> To: Bosken; r-help at r-project.org
> Subject: Re: [R] Normal distribution (Lillie.test())
> 
> You should probably read fortune(117) and fortune(234) (and possibly
> some of
> the original discussions that lead to the fortunes).  Reading the help
> page
> for the SnowsPenultimateNormalityTest function (TeachingDemos package)
> may
> also help.  If you are happy with the plots, but still feel the need
> for a
> "test" of some sort, then you should investigate using the vis.test
> function
> in the TeachingDemos package.
> 
> Hope this helps,
> 
> --
> Gregory (Greg) L. Snow Ph.D.
> Statistical Data Center
> Intermountain Healthcare
> greg.snow at imail.org
> 801.408.8111
> 
> 
> > -----Original Message-----
> > From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> > project.org] On Behalf Of Bosken
> > Sent: Tuesday, February 23, 2010 4:13 AM
> > To: r-help at r-project.org
> > Subject: Re: [R] Normal distribution (Lillie.test())
> >
> >
> > Hi,
> >
> > Thanks for your reaction;
> >
> > How do you come to the decision that my data not is normal
> distributed?
> >
> > With the 69-95-99.7 test and Q-Q plot seems it ok! But these test are
> > not
> > exact, they only give you an image.
> >
> > Gr. Bosken
> > --
> > View this message in context: http://n4.nabble.com/Normal-
> distribution-
> > Lillie-test-tp1565083p1565762.html
> > Sent from the R help mailing list archive at Nabble.com.
> >
> > ______________________________________________
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