Variance Balanced Block Designs with Unequal Block Sizes

Abstract

This article gives a general method of construction of variance balanced block designs with unequal block sizes under a heteroscedastic model in which it is assumed that the intra block variances are proportional to non-negative real power of block sizes. It has been shown that all variance-balanced designs can be obtained from a pairwise balanced design. In fact, under the usual homoscedastic model, all the methods of construction of variance balanced designs, hitherto known in the literature, follow from this general method. Some methods of construction of pairwise balanced block designs have also been given.