The variance function of the difference and the difference of the variance functions between two estimated responses for a fourth order rotatable design in two dimensions

Abstract

In this paper the variance function of the difference and the difference of the variance functions between two estimated responses for a fourth order design at any two points in the factor space is developed. In particular, the variance function is considered in two dimensions when the design used is rotatable. The variance function in this situation is a function of the distances of the points from the origin of the design and the angle subtending .the points at the origin. Variance functions of these two approaches are discussed in detail and compared when the two points are equidistant from the origin of the design. The criterion for the choice of an optimal design is given