[R] Lack of independence in anova()

[Spencer Graves]

Hi, Göran:  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

Göran Broström 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).
> 
> Göran Broström
> 
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