Sampling With Varying Probabilities

Abstract

In the preceding chapter, we have discussed simple random sampling in which each unit in the population gets equal chance of being included in the sample. However, when the units vary considerably in size, SRS does not seem to be an appropriate procedure, since it does not take into account the possible importance of the size of the unit. Under such circumstances, selection of units with unequal probabilities may provide more efficient estimators than equal probability sampling. In this scheme, the units are selected with probability proportional to a given measure of size. The size measure is the value of an auxiliary variable (say) x, which is closely associated with the study variable (say) y. This type of sampling is known as varying probability sampling or probability proportional to size (PPS) sampling. For instance, while estimating total number of unemployed youth in a district, the number of households in the village can be used as a size measure when villages are taken as sampling units. Similarly, for estimating total number of tube wells in a certain district, the number of tube wells in a village for a previous period, or net irrigated area for the village, may be taken as size variables.