Cluster sampling

Cluster sampling chooses groups of observational units, such as production days, rather than dispersed individual units. Testing every unit in a selected group is a one-stage cluster sample. Positive within-cluster intraclass correlation reduces the information supplied by a fixed number of sampled units, although collecting clustered observations can be cheaper.

The design effect is a sampling variance under a complex design divided by the corresponding simple-random-sampling variance. For independent equal-size clusters of size $m$ with exchangeable intraclass correlation $\rho$, a common mean-estimation approximation is $1+(m-1)\rho$. It expresses the loss of effective sample size from positive correlation; finite-population and unequal-cluster-size designs require their own calculation.