Cluster sampling examples

Example 1:

Assume that a study with relatively large square sample plots of 50 m x 50 m had been carried out, on which all tree positions were mapped. Because the individual plots were relatively large, there were only resources available to measure \(n=10\) sample plots. The small sample size led to a fairly high value of the estimated error variance.

A colleague of yours suggests: As you have mapped all trees on your 50 m x 50 m plot, you can easily make four plots of 25 m x 25 m out of each original plot. By that, you increase the sample size to the fourfold and, thus, reduce the error variance.

Does this suggestion seem reasonable?

Of course not!! The sampling design and the randomization scheme applied define what the independent observation unit is. In this case, each one of the 50 m x 50 m plots had been selected randomly and constitutes therefore one independent observation. This one single independent observation cannot be subdivided into more independent observations; it is just one. The sub-division may help learning about the spatial distribution of the variable of interest within the clusters and may, therefore, be very instructive for the optimization of the cluster plot design – but it does not help reducing the error variance!