Hypothesis Testing in Two-Stage Cluster Sampling

Correlated observations often arise in complex sampling schemes such as two-stage cluster sampling. The resulting observations from this sampling scheme usually exhibit certain positive intracluster correlation, as a result of which the standard statistical procedures for testing hypotheses concerning linear combinations of the parameters may lack some of the optimal properties that these possess when the data are uncorrelated. The aim of this paper is to present exact methods for testing these hypotheses by combining within and between cluster information much as in Zhou & Mathew (1993).