[R] Lack of independence in anova()

JRG loesljrg at verizon.net
Wed Jul 6 21:50:07 CEST 2005

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?


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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