[R-sig-eco] which factor to nest?

[tavery]

Hi all,
Maybe an expert of this particular design could provide insights into a 
interesting question (or possibly just a derailed view). Possibly 
outside of the R world, but has to be sorted out before R code can be 
generated - which should be trivial...

- 7 beekeepers each with several hives
- some hives treated with antiG, others left as controls
- unbalanced design (not an equal number of treated or control sites 
among or within beekeepers)
- measured parasite numbers (average per hive)
Q: want to know if antiG reduces parasite load

The initial reaction (from a student) was to consider Beekeeper as a 
random factor (although it could be considered fixed), and nest 
Treatment (antiG or control) within Beekeeper. This design is intuitive 
as Beekeepers are 'groups' and hives are 'subgroups' to which treatments 
are applied. Upon some investigation, it appears that the model could be 
flipped i.e. consider Treatment as a fixed factor and nest Beekeeper 
within Treatment. In this latter case, each Beekeeper would be 
represented in each Treatment and a crossed design results i.e. not 
nested at all. Various texts appear to 'arbitrarily' designate factors 
in similar models (see Zar on drug/drugstore example).

a) What design is correct?
b) What am I missing in way of determining groups and the ultimate design?

thanks in advance,
trevor
biology department
acadia