Previous posters have pretty well answered this question, but it may be
helpful to express the situation somewhat differently.

>From the information supplied (or, more pertinently, NOT supplied) we
cannot tell whether the idea of a covariance between P1 and P2 is even
reasonable.  If the nature of the beast is such that P1 and P2, even if
you had adequate data (which you do not:  THAT much is clear!), simply
would not "vary together" in any reasonable sense of the phrase, then
there is no covariance even to be thought of, much less to be estimated.

If there IS such a thing (in the universe of discourse, although not in
your data) as a Cov(P1,P2), you have no information on which to base an
estimate of that covariance;  properly, then, its value is "unknown", or
possibly "indeterminate".

You certainly can NOT assert that  Cov(P1,P2) = 0,  nor (of course) can
you assert that it has any other value;  unless (which I can imagine as
a logical possiblility, but cannot at the moment think of an example)
the nature of P1 and P2 be such that their covariance is zero more or
less by definition.  It would be difficult, I should think, to justify
any such claim.

On 7 Jul 2003, KR wrote:

> If I have two different surveys from which I calculate values of P1
> and P2, would Cov[P1, P2]=0?  The two surveys were performed in
> different years and have different sample sizes.

 -----------------------------------------------------------------------
 Donald F. Burrill                                         [EMAIL PROTECTED]
 56 Sebbins Pond Drive, Bedford, NH 03110                 (603) 626-0816

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