[R] Lack of independence in anova()

[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