Lack of independence in anova() 2005-07-06 - By Duncan Murdoch
On 7/6/2005 1:43 PM, Phillip Good wrote:
> spencer graves asks:
> How is the method of synchronized permutations relevant to a traditional,
> normal theory ANOVA?
>
> One ought now ask as I am doing currently whether traditional, normal
> theory ANOVA is applicable to the analysis of experimental designs. If in
> fact, the results of the various ANOV tests are not independent, then:
> i) shouldn't we be teaching this in courses on the analysis of
> experimental designs? (Can anyone point to an FDA submission or aplied
> statistics publication which conceeds this result?)
> ii) using tests whose results are independent?
I think it's relatively infrequent that we make inferences where
independence matters, so it makes sense to use tests that are marginally
well-behaved. When do you care about the simultaneous behaviour of two
tests?
The nice thing about ANOVA tests is that each one is valid regardless of
the presence or absence of effects in other rows. This doesn't require
independence.
Where you might use independence is to try to construct a combined
p-value looking for a violation of any of several hypotheses, but if
that's the test you're interested in, you should just have pooled the
terms in the numerator.
Duncan Murdoch
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