Re: A question
well, i don't have the answer but, a quick simulation (when the ratio of variances is about 2) is as follows maybe this helps in some strange way === MTB > rand 1 c1-c25; SUBC> norm 100 5. MTB > rand 1 c26-c50; SUBC> norm 100 7.07. MTB > rstdev c1-c25, c51 MTB > rstdev c26-c50, c52 MTB > let c51=c51**2 MTB > let c52=c52**2 MTB > let c53=c52/c51 MTB > dotp c53 <<< sampling distribution of ratios of variances Dotplot: C53 Each dot represents up to 95 points . ::. .:::. :. .::. : .::.. .::.. ... .. . +-+-+-+-+-+---C53 0.0 2.5 5.0 7.5 10.0 12.5 MTB > desc c53 Descriptive Statistics: C53 Variable N Mean Median TrMean StDevSE Mean C53 1 2.1625 1.9902 2.0945 0.9360 0.0094 Variable MinimumMaximum Q1 Q3 C53 0.446211.6670 1.5075 2.6281 MTB > At 12:47 PM 5/4/01 +1000, Alan McLean wrote: >Hi to all. > >Can anyone tell me what is the distribution of the ratio of sample >variances when the ratio of population vriances is not 1, but some >specified other number? > >I want to be able to calculate the probability of getting a sample ratio >of 1 when the population ratio is, say, 2. > >Many thanks in advance. >Alan > > >-- >Alan McLean ([EMAIL PROTECTED]) >Department of Econometrics and Business Statistics >Monash University, Caulfield Campus, Melbourne >Tel: +61 03 9903 2102Fax: +61 03 9903 2007 > > >= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >= _ dennis roberts, educational psychology, penn state university 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: A question
Alan McLean wrote: > > Hi to all. > > Can anyone tell me what is the distribution of the ratio of sample > variances when the ratio of population vriances is not 1, but some > specified other number? *If* the population distributions are normal (and this is not a robust assumption - in other words, if it's moderately wrong you are *not* safe from error) it's just a scaled F distribution. If X has variance a^2, Y had variance b^2, then (b^2/a^2) s^2_X/s^2_Y = s^2_(X/a)/s^2_(Y/b) ~ F . -Robert Dawson = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: A question
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
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