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
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The Rockefeller University, GCRC
Experimental Design and Biostatistics
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+1(212)327-7175, +1(212)327-8450 (Fax)
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