Self-weighting Designs in Stratified Multi-stage Sarnnpling

In particular, a stratified multi-stage srs will be self-weighting with proportional allocation for the first-stage units, and for each of the subsequent stages, a constant sampling fraction for selecting the next-stage units. That is, the first-stage sampling fraction n11t/N111 should be a constant, the second-stage sampling fraction n1112/N1112 a constant, and so on.