Many countries use a sample design in their agricultural surveys that is assumed, incorrectly, to be equivalent to stratified simple random sampling without replacement. This article discusses how the variance of a direct expansion based on that design should be estimated.
The variance of direct expansions from a common area sampling design
Kott, P. (1989). The variance of direct expansions from a common area sampling design. Journal of Official Statistics, 5(2), 183-186. http://www.jos.nu/Articles/abstract.asp?article=52183