On some aspects of general balance in designed experiments

Abstract

The paper is about some properties of designed experiments satisfying general balance. Some types of block designs and row-column designs are taken into account. It is assumed that observations follow a randomized model extended on technical errors. In particular, the useful method of checking the property of general balance is proposed. Moreover, the decomposition of treatment space, in which respect the design is generally balanced, is given. This decomposition is based on the eigenvectors of matrices (C-matrices) usually used in examination of the design properties. The relationship between the notions of general balance and efficiency balance is also considered. Finally, the problem of preserving the general balance by a design constructing method, called merging treatments method, is examined.