Designs for the simultaneous estimation of functions of variance components from two-way crossed classifications

The paper deals with the estimation of the parameters of a variance component model for two-way crossed classifications with replication. Estimates are needed for row, column and interaction components of variance, and also for the ratios of these variances to the error component of variance. A balanced design with k(k≥ 2) observations for all subclasses may sometimes be considered extravagant for the purpose. Alternative designs in which duplicates are taken from a selection of subclasses and a single observation is taken from each of the rest, are proposed in the paper. A simple method of analyaing these schemes is suggested, and some numerical results on the efficiency of these designs are presented.