[R] Lack of independence in anova()

Spencer Graves spencer.graves at pdf.com
Wed Jul 6 21:56:13 CEST 2005

	  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
> 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.
>>R-help at stat.math.ethz.ch mailing list
>>PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
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Spencer Graves, PhD
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