Sampling with Probabilities Proportional to Size: Adjustment for Changes in the Probabilities

摘要: W E CONSIDER a simplified area sample consisting of one primary sampling unit chosen from each number strata; such selected is to be enumerated completely. The "take" (i.e., the total in whatever being surveyed) can converted an estimate population stratum simply by multiplying units stratum; and this is, for practical purposes, only method estimating if no information about unsampled other than their on hand. If, however, some evidence available relative "sizes" would like incorporate procedure. In application which has now become fairly common, different characteristics are estimated uniform procedure single survey, measure size related all persons several at precedingcensus. Canadian Labor Force sample, that used Monthly Report United States, consists up four successive stages;' theory here considered applicable first stage. stage entire rural territory Canada was divided into 500 areas constituting units, these were assembled strata containing between 5 10 units. There requirement comprising contiguous; but they as similar possible respect type farming, density etc.; nor any attempt made assemble those numbers people contained preceding census. sub-sampling within arranged so multiplication take 100 furnished unbiased total; accomplished, following suggestion Hansen Hurwitz, ratio depended selected, give fixed expected i.e., 0.01 stratum. theorem paper, not affected sub-sampling; we may think matter