There seems to be a difference of opinion on whether it is better to take a
few samples from many hives or many from a few.  The goal needs to be
kept in mind.  Do you want an indication of the average level of infestation
across your whole operation?  Take a few from several hives (as Allen has
done).  Do you want to know the specific rate of infection in a few hives?
Take several samples from those few.  It does not matter whether you have
100,000 bees in your apiary or ten billion.  If the infection rate can be
assumed to be relatively even across all your hives (as, I think Allen
presumes his might be) then taking more from one hive does not give you
more information than taking a few from many hives.  If he finds one infected
bee in one of his samples of five, he cannot say that that hive has a higher
rate of infection than the others with any confidence at all.  If he samples
250 from a few hives and finds one infected bee in one hive then he can
say that that hive has a higher rate of infection.  But I don't think that that is
his goal.

Peter wrote "You took 175 bees per apiary, that is 175 per let's say 400,000 bees. Very low levels of infestation simply would not show up at this sampling rate."

Note, please, that that there are 400,000 bees is totally irrelevant.  Taking 175 samples from 30,000 bees is no better or worse than taking 175 from 400,000 or from a billion and a half if the infection rate is the same.    Statistical confidence is related to the number of samples taken, not the number of individuals in the population.

Martin Damus

Martin Damus