A researcher wants to study the effect of different treatment regimens
on muscle growth in fetal rat heart muscle cells.  The 
treatments included a control as well as combinations of growth 
inhibitors and enhancers at different stages of development.  Each 
treatment was assigned to a randomly selected petri dish containing a 
sheet of muscle cells harvested from genetically similar mice.  

10 7-day old cells were harvested from each dish and measured for 
size. The treatments were then applied and after 3 days,  
10 additional 10-day old cells were harvested from each petri dish
and the cells were measured for size.  A measure of relative growth 
was recorded for each dish.

Record your answers to the following questions. Discuss the answers with
your group and submit your work.

What is the treatment? What is the experimental unit? 
Are there any problems with the experimental setup?  How would you
have designed the experiment?

Comments:  Most students recognize that petri dishes and treatment
regimen had been confounded.  If we ignore treatment, the experiment
looks alot like a random effects experiment with petri dish as the
random effect and multiple measurements taken on each level of the
random effect.  If petri dish is ignored, a fixed-effects model
essentially must ignore the correlation between observations from
the same dish.  Students have emphasized experimental protocol in their
discussions of the new experiment (discussion of controls, randomization,
 blocking on lab technician, controlling variation of the source
material) In the end, it was felt that a nested
design would be appropriate, with multiple petri dishes assigned
to each treatment.  Treatment effect would be tested against the
nested term for petri dishes.  There was some discussion as to whether 
a RCBD (with petri dish as block) was feasible.