Hi Laurent,

the answer to your question may be more in the field of statistics than in 
the field of R-istics.

It may be tempting to interpret a non-significant result of a statistical 
test as to verify the hypothesis, e.g., as to verify that the distribution 
of the data is Gaussian. Unfortunately, a non-significant test is merely 
non-conclusive (Popper KR, 1979), so one would have to test for 
equivalence, e.g., as TOST (two one-sided tests). To do this with the 
Lilliefors test, however, it may be difficult to come up with a 
justification for a n equivalence limit.

As to whether you can do a Lilliefors test for several groups, that depends 
entirely on your ability to understand what the underlying question would 
be (see Adams D 1979)
    * One could test the hypothesis that the groups are equal with respect 
to their deviation from a Gaussian distribution.
    * One could also test the hypothesis that the residuals across all 
groups follow a Gaussian distribution, comparing the within-group residuals 
with a Gaussian distribution. Note, however, that this implies going one 
step further away from the KS than the Lilliefors in that several group 
means are estimated.
I hope this helps.
Knut

At 10:20 2004-02-06 +0100, you wrote:
>Hi,
>
>I use ks.test or lillie.test to verify a normal distribution. It's performed
>for a group
>My users use SigmaStat software and a One Way ANOVA on several groups
>In the result page there is a probability value to determine if Normality
>test is failed or passed
>So, how can i retrieve this probability value on several groups?
>Is there another function in R to verify normality on several groups?
>
>Thanks
>
>Laurent Houdusse
>Analyste Programmeur

Knut M. Wittkowski, PhD,DSc
------------------------------------------
The Rockefeller University, GCRC
Experimental Design and Biostatistics
1230 York Ave #121B, Box 322, NY,NY 10021
+1(212)327-7175, +1(212)327-8450 (Fax)
kmw@rockefeller.edu
http://www.rucares.org/clinicalresearch/dept/biometry/

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