Optimal Allocation in Multivariate, Two-Stage Sampling Designs

Procedures for determining optimal two-stage sampling designs are well documented when a single variable is measured.Many surveys, however, measure several variables simultaneously, in which case the overall optimal sampling plan is traditionally chosen from among the optima for each variable considered individually.We use a graphical approach to illustrate that the traditional method is not always appropriate and that intersections of variance constraints should be considered as candidates for the overall optimum.