Sampling for Subpopulations in Two-Stage Surveys

Many national household interview surveys aim to produce statistics on small subpopulations, such as specific ethnic groups or the indigenous population of a country. In most countries, there is no reliable frame of the sub-populations of interest, so it is necessary to sample from the general population, which can be very expensive. The most common strategies used in practice for sampling rare subpopulations are the use of a large screening sample, and dis-proportionate sampling by strata. Optimal sample designs have been derived for the case of one-stage sampling, but most household surveys use two or more stages of selection. This paper develops optimal designs for two-stage sampling, where there is auxiliary information on subpopulation membership for each primary sampling unit. Various alternative designs are evaluated using a simulated population derived from the New Zealand Census.