A sampler wants to select a sample of families from a city. An expert can define three kinds of areas according to densities of the survey population. It is roughly estimated that due, to different densities, survey costs per family will be respectively $200, $400 and $600. Large differences may exist when covering a sample of families in a large province or a country they may also occur in a city if screening questionnaires must identify a subclass (e.g. family with members who work abroad) that is very unevenly distributed.

Describe briefly a two-stage sample design. Assume equal sizes for the three strata; also, that the design effect is close to 1, hence the element variance is close to S².