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/
|