[R] Lack of independence in anova()

[Duncan Murdoch]

(Ted Harding) wrote:
> On 06-Jul-05 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
> 
> 
> But true if both X  and Y have positive probability of being
> non-zero, n'est-pas?
> 
> Tut, tut, Göran!

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