Six groups of oysters (3 male group and 3 female groups) were selected 
from a clean site and six groups of oysters (3 male groups and 3 
female groups) were selected from a polluted site in a tidal creek. 
(Oyster size is a reasonable proxy for gender).  

Six oysters from each group were sacrificed and morphological
measurements were made--the response was an average morphological
measurement from each group of a half-dozen oysters.  Afterwards,
the six groups of oysters from the clean site were transferred
to the polluted site and the six groups of oysters from
the polluted site were transfered to the clean site.  After six 
weeks, six more oysters from each group were sacrificed and 
the measurements were repeated.

Can you identify the design? Is there any serious confounding
in the experiment?  Can both gender and treatment (clean/polluted) 
effects be tested? How would you test them? Run the SAS code
provided on the webpage and explain the results.

This is a crossover design. Treatment is completely confounded with
site--it would have been nice if several oyster banks (clean and
polluted) had been sampled.  As mentioned in class, a crossover design
of this form can be thought of as a series of latin squares.  In this
particular instance, the grouping of pairs of cages into squares is
arbitrary so we would want to make sure we didn't test for a "square"
effect as we've seen in other analyses with replicated squares.  The
test for treatment would be orthogonal to tests for period and cage.
Gender is confounded with a cage contrast (though probably not an
important cage contrast) and the test for Gender in GLM fails. Students
in my most recent classes thought it would be difficult to obtain 
additional polluted sites that were similar in characteristics to 
the initial polluted site.  They also felt the designation of groups 
as male and female was too artificial since sexing of oysters is not
exact. Recently, students wondered whether the effects were really
symmetric since oysters were only at the second site for 6 weeks.
Some students suggested handling joint testing of group and gender 
by nesting group in gender.