On Fri, 4 May 2001, Alan McLean wrote:
> Can anyone tell me what is the distribution of the ratio of sample
> variances when the ratio of population variances is not 1, but some
> specified other number?
Depends. If the two samples on which the variances are based are
_independent_, s^2(1)/s^2(2) is distributed as (Var(1)/Var(2)) times the
usual F distribution.
(My reference for this is Glass & Stanley (1970), pp 303-306.)
If the sample variances are based on so-called dependent (= correlated)
samples, the problem is, apparently, much more difficult ("beyond the
scope of this textbook", G&S write).
> I want to be able to calculate the probability of getting a sample ratio
> of 1 when the population ratio is, say, 2.
As the above remarks imply, if the samples are independent, that
probability is the same as the probability of getting a sample ratio of
0.5 when the population variances are equal (population ratio = 1).
(Since the distribution is continuous, the probability that the sample
ratio _equals_ 1 -- or 0.5 -- is zero; but presumably your interest
would actually be in, e.g., the probability that the sample ratio lies
in the interval from 0 to 1 (or its complement, the interval from 1 to
infinity); or in some other interval with 1 at one end.)
Actually doing the calculation would require either F tables rather more
extensive than the usual abbreviated versions that have only six to ten
cumulative relative frequencies, or software like Minitab that can
calculate probabilities for the standard F distribution.
(Take your sample ratio, divide it by the hypothesized population ratio,
and ask Minitab to evaluate the quotient as an F value.)
-- Don.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-472-3742
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
