Inference for cluster sampling

Summary

Inference for cluster sampling from a specified probability model is developed in this paper. It is assumed that the population cluster means are normally and independently distributed as π _i ~ N ( μ, σ ² _b ) and that the elements within a cluster for given cluster means are normally and independently distributed as ( X _ij | μ _i ) ~ N ( μ _i , σ ² _w ). Inference is developed for infinite clustered populations (with the intraclass correlation value both known and unknown) and for finite clustered populations (with known intraclass correlation).