ABSTRACT
As for single-stage, so also for multi-stage sampling, sampling with varying probabilities - more specifically with probability proportional to size - would, under favorable conditions, lead to an improvement in the efficiency of estimators if ancillary information is available for such selection. Although pps sampling can be resorted to in all stages of sampling, in general it is restricted to the stages that can be covered in offices; the selection of sample units at other stages, generally the ultimate or the penultimate stages or both which can readily be sampled either systematically or by simple random sampling, is left to the enumerators in the field.
