Variations from the Guadalupe designs

Abstract

Guadalupe is a central composite design proposed for fertilizer experiments; it consists of 2^{h - g} + 6 h + c treatments, with 6h axial points, equally spaced, e central and 2^{h - g} factorial points, with their projections on the axes interval extremes; these points were moved from the extremes 0 and 6 to the points 1 and 5 or 2 and 4 to give a more satisfactory equilibrium to the fertilizer doses. The check plot of the original Guadalupe is included, in the variations, as an extra treatment. Orthogonalization of the Guadalupe and its variations was made through a linear second degree regression model; the relative position of the axial and factorial points is invariant for the studied cases. By the Box and Wilson criterium the pure quadratic components of the Guadalupe variations present greater efficiency than the original, and the interaction components, smaller efficiency. There is a greater equilibrium between the efficiency of the pure quadratic and interaction coefficients when the factorial paints are at 1 and 5 levels or the design is orthogonal. The proposed Guadalupe variations permit a dynamic analysis by the elimination of external points; according to the remaining points, they may be analysed as a central composite or as an axial design.