Re: [R] Lack of independence in anova()

From: Duncan Murdoch <murdoch_at_stats.uwo.ca>
Date: Thu 07 Jul 2005 - 10:51:08 EST

(Ted Harding) wrote:
> On 06-Jul-05 Göran Broström wrote:
>

>>On Wed, Jul 06, 2005 at 10:06:45AM -0700, Thomas Lumley wrote:
>>(...)
>>
>>> If X, Y, and Z are independent and Z takes on more than one
>>>value then X/Z and Y/Z can't be independent.
>>
>>Not really true. I  can produce a counterexample on request
>>(admittedly quite trivial though).
>>
>>Göran Broström

>
>
> But true if both X and Y have positive probability of being
> non-zero, n'est-pas?
>
> Tut, tut, Göran!

If X and Y are independent with symmetric distributions about zero, and Z is is supported on +/- A for some non-zero constant A, then X/Z and Y/Z are still independent. There are probably other special cases too.

Duncan Murdoch



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