A note on the effect of auxiliary information on the variance of cluster sampling

Abstract

A model-based synthesis is presented for a number of well-known results concerning the design effect of cluster sampling. This helps to yield a simpler perspective, making the design-based expressions more transparent. In particular, it is shown that the use of auxiliary information removes the extra variance that is due to the variation in the cluster sizes. Moreover, it can reduce the loss of efficiency to the extent it reduces the conditional intracluster correlation given the covariates. The design effect then depends on the remaining conditional intra-cluster correlation and an average cluster size.