  Group testing is an active area of current research and has important
applications in medicine, biotechnology, genetics, and product testing. There
have been recent advances in design and estimation, but the simple Dorfman
procedure introduced by R. Dorfman in 1943 is widely used in practice. In many
practical situations the exact value of the probability p of being affected is
unknown. We present both minimax and Bayesian solutions for the group size
problem when p is unknown. For unbounded p we show that the minimax solution
for group size is 8, while using a Bayesian strategy with Jeffreys prior
results in a group size of 13. We also present solutions when p is bounded from
above. For the practitioner we propose strong justification for using a group
size of between eight to thirteen when a constraint on p is not incorporated
and provide useable code for computing the minimax group size under a
constrained p.
