  We consider Markov chain Monte Carlo methods for calculating conditional p
values of statistical models for count data arising in Box-Behnken designs. The
statistical model we consider is a discrete version of the first-order model in
the response surface methodology. For our models, the Markov basis, a key
notion to construct a connected Markov chain on a given sample space, is
characterized as generators of the toric ideals for the centrally symmetric
configurations of root system D_n. We show the structure of the Groebner bases
for these cases. A numerical example for an imaginary data set is given.
