Hello Bruce,
 
Thanks for your response.  By “second shell fits” I mean that the best values for the first shell were fitted then fixed and then the fitting R-range was moved to the second shell.  Similarly to how Matt Newville describes here:
 
http://millenia.cars.aps.anl.gov/pipermail/ifeffit/2009-April/008779.html
 
He describes this as an acceptable approach, although, others in the thread disagree.
 
Essentially, my question is why do the F-test and the RCS results not agree with each other?  The F-test indicates model 2 may not be a statistical improvement over model 1 while the RCS values show that model 2 is definitely an improvement over model 1.  If I consider a reduction in the RCS value of >2x as significant, then I would pick model 2.
 
However, can I apply this logic when fitting the second shell with the best parameters for the first shell fixed and the R-ranges over the second shell?
 
Thank you again,
Matt S