The analysis of mixed and random effects models for equireplicate variance-balanced block designs

Equirephcate variance-balanced block designs possess many desirable properties and include several important subclasses of designs, such as balanced incomplete block designs. However, while attention has been paid to the derivation of properties and the construction of these designs, methods of analyzing experiments using these designs have not been developed completely. Thus, we consider models appropriate to these designs, construct test statistics for basic hypotheses and derive the distributions for these statistics. Four additive models that include all of the possible combinations of fixed and random effects are examined. The analyses are generalizations of the analyses for balanced incomplete block designs, and include the intra-block, intra-treatment and inter-block analyses, Estimators of fixed treatment effects and their distributions also are given.