A sampling plan that has two (or more) stages of selecting study units is called a two-stage (multistage) cluster sample. A sample of the primary sampling units (the clusters) is selected at the first stage and a sample of the component sampling units is selected from each cluster at the second stage and so on throughout any subsequent stages. In a broader context, if observations on a set of study units are arranged in classes, categories, groups or clusters and some of the cluster means vary significantly, the within cluster observations will tend to be more homogeneous than those from different clusters and in this sense they will tend to be correlated. The intraclass correlation coefficient ρ I quantifies the propensity for observations on units within the same cluster to be more homogeneous than those in different clusters. Early writers referred to the groups of observations as classes, hence the terminology intraclass correlation coefficient, but the evolving widespread use of...
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References and Further Reading
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Johnson, W.D., Koch, G.G. (2011). Intraclass Correlation Coefficient. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_309
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