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 <[EMAIL PROTECTED]> 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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