On 23 Apr 2002 03:42:09 -0700, [EMAIL PROTECTED] (Voltolini) wrote:

> Dear friends,
> 
> How to choose between parametric and non parametric tests? 

Once upon a time, I believed that every 'test', every procedure
run and every statistic examined,  should be justified - in some
sense - in advance.  

Well, that is unreasonable.  
Defending all tests in advance is impossible for the beginners, 
time-consuming for experienced statisticians, and  
(for those reasons and more) 
that approach does not give the most robust results.  

What works?  If you have two tests in mind, do them both.  
Usually the results will be exactly the same, so you have
wiped out the reasons for argument.


>                                                  Following any
> texbook we can find the idea of using histograms, curtosis, skewness and...
> tests like Shapiro-Wilk to test normality. In the case of homocedasticity,
> we can use one of the best for this task, the Levene test.

When something comes out different, you have 
a concrete example on hand to be examined.
A good text tells you the basis of a test it recommends.  

As someone taught me years ago, you don't really
understand a test if you can't see what it is sensitive to,
and how it differs from its competitors -- what data will
'reject' with one, and not the other.  

With imagination, and occasionally a little pencil-work,
you should work until you figure the difference between
competing tests that have interested you.   If that is difficult, 
then you especially need to practice until it becomes easier.


> 
> But..... how can we check the test assumptions using other tests with
> assumptions too? Any statistical test is a probability model and any model
> need some assumptions to be accepted! For example, does anyone know what are
> the assumptions of the Shapiro-Wilk and Levene tests? How to test them?

I guess if we could sum up all of statistics in a sentence
or two, it would hardly be worth a graduate degree --
You might want to memorize the assurances that your
statistician gives to you, concerning those tests that
you have to use.  Try to figure out the principles involved, 
and then try to generalize to other tests.

"For example",  your concern with S-W is a concern to me.
I don't like the way to describe it, 'assumptions of the S-W'.

Maybe you are appropriately using the usual test for
normality;  or maybe you are committing the 
so-called type-3  error -- testing the wrong thing, or drawing
the wrong conclusion.  S-W  essentially ranks your scores,
converts those Ranks into expected-z-scores, and correlates 
those numbers with your raw numbers.    Extreme outliers will
make that correlation lower;  'non-normal'  is indicated by
how low that correlation is, compared to chance for 'normal'
data.

Especially   *if*  several variables are skewed differently, that
lower S-W  test would warn  that their p-value can't be trusted. 
So the S-W  can give a warning; but the eventual test may 
still be okay, if the only symptom is one S-W  p-value.

In the same example, it is possible that the test you have
could be okay;  but if you looked closer at the procedure,
the non-normality may eventually lead you to conclude
that  the *model*  you have is wrong, even though the 
p-values are okay (as a test of *something).   That is, 
the test might be  *valid*  as a test, but it could be 
testing differences that don't matter so much to you.  

In a different example:  without a really huge N,
S-W  will show 'non-normal'  with scores that are 
dichotomous or tied on a few scale points.  
In that case, the ANOVA (or whatever)  is safe, 
despite the S-W.

> 
> I am a biologist teaching statistics and trying to teach more than formulas
> for my students, so... please help me with this discussion !

Hope this helps, for a start.

-- 
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
.
.
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