Date:         Wed, 12 Oct 2005 22:09:51 -0700
Reply-To:     David L Cassell <davidlcassell@MSN.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         David L Cassell <davidlcassell@MSN.COM>
Subject:      Re: Difference in two F tests
In-Reply-To:  <200510121905.j9CIqw53014566@malibu.cc.uga.edu>
Content-Type: text/plain; format=flowed

flom@NDRI.ORG wrote:
>Suppose you have two linear regressions with the same DV and the same
>data.  One has 4 IV's, one has 6 IV's.  You get an F test for each
>model.  How is the difference in these F's distributed?
>
>(as readers will know, I am aware of the problems with various methods
>of selecting variables.....but this question came up, and I didn't know
>the answer, even in the abstract......I also wasnt sure where to look it
>up.

This is a trick question.  There is no answer.

Even assuming that the 4 IVs and nested within the 6 IVs, the difference
in the F tests is still meaningless.  And, if the sets of regressors are not
nested,
then it makes no sense at all: imagine regressing 4 really highly
significant
regressors for your first case and getting a huge F, then regressing 6
versions
of white noise for your second case and getting an F near 1.  What is even
the point of looking at the difference?

If the 4 IVs are nested inside the 6 IVs, then you can look at the
difference
between the sums of squares, and treat that as testable against the SSE.
You can get an F test that way.  If things are not simple linear regression,
then you ought to be looking at the difference between the values of -2logL
instead, and getting a chi-squared test.

HTH,
David
--
David L. Cassell
mathematical statistician
Design Pathways
3115 NW Norwood Pl.
Corvallis OR 97330

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