Optimal allocation with fixed power in a completely randomized design with levels of subsampling

In many completely randomized design experiments, levels of subsampling may be performed on each experimental unit. In such cases the expected mean square error E(MSE) for testing among treatment groups is comprised of variance components analogour to those associated with the primary sampling unit is nested sampling Marcuse (1949) gives a procedure to minimize the cost of obtaining the samples if a desired degree of precision in the E(MSE) is fixed. However, her method gives no consideration to the resulting power of the test for differences among the treatment groups. Our method stipulates that the power, rather than the precision, is fixed at a critical level and the total cost is minimized subject to this constraint.