A comparison between the Gröbner bases approach and hidden projection properties in factorial designs

Screening designs are useful for situations where a large number of factors (q)(q) are examined but only few (k)(k) of these are expected to be important. Plackett–Burman designs have traditionally been studied for this purpose. Since these designs are only main effects plans and since the number of runs are greater than the number of active factors (main effects), there are plenty of degrees of freedom unused for identifying and estimating interactions of factors. Computational Algebraic Geometry can be used to solve identifiability problems in design of experiments in Statistics. The theory of Gröbner bases allows one to identify the whole set of estimable effects (main or interactions) of the factors of the design. On the other hand, the hidden projection property approach, that deals with the same identification problem, provides a measure of how efficient the identification of effects is. The advantages and disadvantages of both methods are discussed with application to a certain two level (fractional) factorial designs that arise from Plackett–Burman designs.