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Dear Allstaters

Looking for some clarification on the definition of cluster / 
multi-stage sampling.  Discrepancies in texts.

Cluster sampling - random sample of clusters and then everybody in 
cluster is sampled.  (happy with that unless otherwise informed)

Multi-stage : Consider following example.
A random sample of zones within a city is obtained, followed by a random 
sample of households within each zone (two-stage). Assume no further 
naturally occurring clusters in the house.
In multi-stage sampling - would I survey all individuals in each 
household or take a sample of them?  If the latter - is sample random or 
not? 
If random sample - would it be three-stage sampling?  I always assumed 
the number of stages = number of natural clusters sampled embedded 
within other.

Thanks
Philip Sedgwick
St. George', University of London