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

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Thu 07 Jul 2005 - 10:02:06 EST

Hi, Göran: I'll bite:

          (a) I'd like to see your counterexample.

          (b) I'd like to know what is wrong with my the following, apparently defective, proof that they can't be independent: First consider indicator functions of independent events A, B, and C.

          P{(AC)&(BC)} = P{ABC} = PA*PB*PC.           But P(AC)*P(BC) = PA*PB*(PC)^2. Thus, AC and BC can be independent only if PC = 0 or 1, i.e., the indicator of C is constant almost surely.

          Is there a flaw in this? If not, is there some reason this case cannot be extended the product of arbitrary random variables X, Y, and W=1/Z?

	  Thanks,
	  spencer graves

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
>
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Received on Thu Jul 07 10:07:52 2005

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