[R] Lack of independence in anova()

[Spencer Graves]

	  As Duncan Murdoch indicated, the primary issue is not that the 
different tests are (not) statitically independent but that they are 
sensitive to different alternative hypotheses.

	  spencer graves

JRG wrote:

> On 6 Jul 2005 at 12:30, Douglas Bates wrote:
> 
> 
>>On 7/6/05, Douglas Bates <dmbates at gmail.com> wrote:
>>...
>>
>>>Perhaps we could review the sequence of events here.  This exchange
>>>began with your sending me a message claiming that there is a bug in
>>>lm or anova in R because the results of your simulation were what you
>>>expected.  
>>
> 
> At the risk of further roiling the waters ...
> 
> As several have already pointed out, the "usual" F-tests in a balanced ANOVA have independent numerators but a common denominator, 
> and hence the F-statistics cannot be independent.  Is this not the basis of Kimball's Inequality, which states that the effect of 
> the common denominator is that the simultaneous error rate cannot exceed what it would be if the tests *were* in fact independent?
> 
> In other words, you should get a simultaneous error rate for the F-tests that is lower than that under independence of test 
> statistics. Are you?
> 
> ---JRG
> 
> John R. Gleason
> 
> 
> 
> 
>>I meant to write "were not what you expected".  I've got to learn to
>>read the email messages before posting them.
>>
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> 
> 
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