Full Factorial Designs and Distracted Fractions

Design of Experiments is a branch of Statistics, which has a long tradition in the use of algebraic methods. In general all this methods where developed in the case of binary experiments, with level coding either 0, 1 and -1, 1 and refer to computations in Z_2 The classical theory fully exploits the characteristics of the binary case, in particular the fact that the additive structure on the first coding is isomorphic to the multiplicative structure on the second. Recently some connections were discovered between classical problems in statistics and the methods of Computational Commutative Algebra. In the present paper we consider two problems: a sort of inverse to the identifiability problem studied in Pistone-Wynn and the problem of constructing fractions with the projectivity property introduced in the case of binary designs by Box and Hunter