The Behaviour of the Variance Function of the Difference between Two Estimated Responses

Abstract

In this paper the variance function of the difference between the estimated responses at any two points in the factor space is developed. In particular, the variance function is considered 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 for first-order and second-order rotatable designs are discussed in detail when the two points are equidistant from the origin of the design. Examples of the variance function for a rotatable and a non-rotatable design in two dimensions are given.