Lack of independence in anova() 2005-07-06 - By Duncan Murdoch
(Ted Harding) wrote:
> On 06-Jul-05 G?ran Brostr?m 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?ran Brostr?m
>
>
> But true if both X and Y have positive probability of being
> non-zero, n'est-pas?
>
> Tut, tut, G?ran!
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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