I would agree with Naomi but would add that the continent effect should
also be included as a blocking factor, an additive effect. I would probably
treat continent as fixed in this case. Flies are nested within population so why
not analyse the means of the 20 flies? After all, interest is primarily in the
latitudinal effect.
Tel: 61-2- 9895 7628
Fax: 61-2- 9895
7867
>>> Naomi Altman <naomi@stat.psu.edu> 03/28/03
09:26am >>>
As far as I can see, you have a mixed effects model with
random effects
population (and fly) and fixed effect latitude. You
could test the
interaction (which is a mixed effect, usually modeled as
random) by a LRT
or, since the design is balanced, by an F-test using the
MSE from the model.
--Naomi Altman
At 05:09 PM 3/27/2003 -0500,
George W. Gilchrist wrote:
>I have a statistical question that hours of
discussion with various folks
>(and editors...) have not settled in my
mind, so I ask your scholarly
>opinions.
>
>I have measured
wing lengths of 20 flies from 10 different populations along
>a
latitudinal gradient on two different continents. I want to do
a
>regression of wing length on latitude. The question is, should I
regress the
>mean wing length of each population on latitude (giving 16
degrees of
>freedom) or should I regress each individual's wing length on
latitude (396
>df)? The residuals are normally distributed and
homoscedastic across
>latitudes.
>
>The null hypothesis is
that there is no clear gradient in size across
>latitudes. Both of these
models reject the null. The question comes when we
>compare the slopes
between continents. While it looks visually like there is
>a large
difference in the slopes, the means model cannot reject the
null
>hypothesis that they are parallel. Of course, the model with the 396
df does
>reject the null.
>
>Thank you for any advice you can
offer!
>
>Cheers,
George
>
>==================================================================
>George
W.
Gilchrist
Email #1: gwgilc@wm.edu
>Department of Biology, Box
8795 Email #2:
kitesci@cox.net
>College of William &
Mary
Phone: (757) 221-7751
>Williamsburg, VA
23187-8795
Fax: (757) 221-6483
>
http://gwgilc.people.wm.edu/>
>
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Naomi S.
Altman
814-865-3791 (voice)
Associate Professor
Dept. of
Statistics
814-863-7114 (fax)
Penn State
University
814-865-1348 (Statistics)
University Park, PA
16802-2111
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