Central composite design with two stars

Abstract

This paper deals with the type of design known as “Central Composite, with Two Stars", a symmetric type, composed of a factorial (or fractional factorial) at the level ±W, two stars at levels ± α and ± ɣ α for each factor (at zero level of the remaining factors) and central points, presenting, normally, five or seven levels for each factor. In Agriculture, differently from technological experiments, principally in fertilizer research, due to soil and climatic variability, the experiments should be performed with all treatments allocated at the same time. In experiments with NPK, the responses obtained may be higher and enlarged in the good years smaller in the unfavourable years. These designs fit better these situations, because if the year was good, the complete design takes care of the situation; if the year was bad and the surface response presents a "plateau area", the elimination of the external star allows the determination of "unbiased estimate" of the coefficients of the model on the crescent part of the response surface. This article presents six Tables, Three of them present the orthogonal designs randonized for factors varying from two to seven; the last three tables present designs that are not only orthogonal, but divisible in blocks.